{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Profiling\n",
    "Sometimes computing the likelihood is not as fast as we would like. Theano provides handy profiling tools, which pymc3 provides a wrapper `model.profile` which returns a `ProfileStats` object. Here we'll profile the likelihood and gradient for the stochastic volatility example.\n",
    "\n",
    "First we build the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from pymc3 import *\n",
    "from pymc3.math import exp\n",
    "from pymc3.distributions.timeseries import *\n",
    "\n",
    "n = 400\n",
    "returns = np.genfromtxt(get_data('SP500.csv'))[-n:]\n",
    "with Model() as model:\n",
    "    sigma = Exponential('sigma', 1. / .02, testval=.1)\n",
    "    nu = Exponential('nu', 1. / 10)\n",
    "    s = GaussianRandomWalk('s', sigma ** -2, shape=n)\n",
    "    r = StudentT('r', nu, lam=exp(-2 * s), observed=returns)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then call profile and summarize it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Function profiling\n",
      "==================\n",
      "  Message: /home/jovyan/pymc3/pymc3/model.py:605\n",
      "  Time in 1000 calls to Function.__call__: 1.775136e-01s\n",
      "  Time in Function.fn.__call__: 1.416550e-01s (79.800%)\n",
      "  Time in thunks: 8.041668e-02s (45.302%)\n",
      "  Total compile time: 1.353232e+00s\n",
      "    Number of Apply nodes: 20\n",
      "    Theano Optimizer time: 6.614311e-01s\n",
      "       Theano validate time: 4.212379e-03s\n",
      "    Theano Linker time (includes C, CUDA code generation/compiling): 6.327283e-01s\n",
      "       Import time 3.420997e-02s\n",
      "       Node make_thunk time 6.312668e-01s\n",
      "           Node Elemwise{Composite{(Switch(Identity(GT(i0, i1)), (i2 - (i3 * i0)), i4) + i5 + Switch(Identity(GT(i6, i1)), (i7 - (i8 * i6)), i4) + i9 + i10 + i11)}}[(0, 0)](Elemwise{exp,no_inplace}.0, TensorConstant{0}, TensorConstant{3.9120230674743652}, TensorConstant{50.0}, TensorConstant{-inf}, sigma_log_, Elemwise{exp,no_inplace}.0, TensorConstant{-2.3025850929940455}, TensorConstant{0.1}, nu_log_, Sum{acc_dtype=float64}.0, Sum{acc_dtype=float64}.0) time 5.813510e-01s\n",
      "           Node InplaceDimShuffle{x}(sigma) time 5.518913e-03s\n",
      "           Node Elemwise{Composite{Switch(Identity((GT(Composite{exp((i0 * i1))}(i0, i1), i2) * i3 * GT(inv(sqrt(Composite{exp((i0 * i1))}(i0, i1))), i2))), (((i4 + (i5 * log(((i6 * Composite{exp((i0 * i1))}(i0, i1)) / i7)))) - i8) - (i5 * i9 * log1p(((Composite{exp((i0 * i1))}(i0, i1) * i10) / i7)))), i11)}}(TensorConstant{(1,) of -2.0}, s, TensorConstant{(1,) of 0}, Elemwise{gt,no_inplace}.0, Elemwise{Composite{scalar_gammaln((i0 * i1))}}.0, TensorConstant{(1,) of 0.5}, TensorConstant{(1,) of 0...8309886184}, InplaceDimShuffle{x}.0, Elemwise{Composite{scalar_gammaln((i0 * i1))}}.0, Elemwise{add,no_inplace}.0, TensorConstant{[  4.05769..48400e-06]}, TensorConstant{(1,) of -inf}) time 5.294800e-03s\n",
      "           Node Elemwise{Composite{inv(sqr(i0))}}(InplaceDimShuffle{x}.0) time 4.826069e-03s\n",
      "           Node Elemwise{Composite{log((i0 * i1))}}(TensorConstant{(1,) of 0...9154943092}, Elemwise{Composite{inv(sqr(i0))}}.0) time 4.477978e-03s\n",
      "\n",
      "Time in all call to theano.grad() 0.000000e+00s\n",
      "Time since theano import 10.620s\n",
      "Class\n",
      "---\n",
      "<% time> <sum %> <apply time> <time per call> <type> <#call> <#apply> <Class name>\n",
      "  71.7%    71.7%       0.058s       4.81e-06s     C    12000      12   theano.tensor.elemwise.Elemwise\n",
      "   7.4%    79.1%       0.006s       2.98e-06s     C     2000       2   theano.tensor.elemwise.Sum\n",
      "   7.2%    86.3%       0.006s       2.90e-06s     C     2000       2   theano.tensor.subtensor.Subtensor\n",
      "   7.0%    93.4%       0.006s       2.83e-06s     C     2000       2   theano.tensor.elemwise.DimShuffle\n",
      "   6.6%   100.0%       0.005s       2.66e-06s     C     2000       2   theano.compile.ops.ViewOp\n",
      "   ... (remaining 0 Classes account for   0.00%(0.00s) of the runtime)\n",
      "\n",
      "Ops\n",
      "---\n",
      "<% time> <sum %> <apply time> <time per call> <type> <#call> <#apply> <Op name>\n",
      "  30.5%    30.5%       0.025s       2.45e-05s     C     1000        1   Elemwise{Composite{Switch(Identity((GT(Composite{exp((i0 * i1))}(i0, i1), i2) * i3 * GT(inv(sqrt(Composite{exp((i0 * i1))}(i0, i1))), i2))), (((i4 + (i5 * log(((i6 * Composite{exp((i0 * i1))}(i0, i1)) / i7)))) - i8) - (i5 * i9 * log1p(((Composite{exp((i0 * i1))}(i0, i1) * i10) / i7)))), i11)}}\n",
      "   7.5%    38.0%       0.006s       3.02e-06s     C     2000        2   Elemwise{exp,no_inplace}\n",
      "   7.4%    45.4%       0.006s       2.98e-06s     C     2000        2   Sum{acc_dtype=float64}\n",
      "   7.0%    52.5%       0.006s       2.83e-06s     C     2000        2   InplaceDimShuffle{x}\n",
      "   7.0%    59.4%       0.006s       2.81e-06s     C     2000        2   Elemwise{Composite{scalar_gammaln((i0 * i1))}}\n",
      "   6.6%    66.1%       0.005s       2.66e-06s     C     2000        2   ViewOp\n",
      "   5.1%    71.2%       0.004s       4.14e-06s     C     1000        1   Elemwise{Composite{Switch(i0, (i1 * ((-(i2 * sqr((i3 - i4)))) + i5)), i6)}}\n",
      "   3.9%    75.1%       0.003s       3.16e-06s     C     1000        1   Elemwise{Composite{(Switch(Identity(GT(i0, i1)), (i2 - (i3 * i0)), i4) + i5 + Switch(Identity(GT(i6, i1)), (i7 - (i8 * i6)), i4) + i9 + i10 + i11)}}[(0, 0)]\n",
      "   3.8%    78.9%       0.003s       3.02e-06s     C     1000        1   Subtensor{int64::}\n",
      "   3.6%    82.5%       0.003s       2.93e-06s     C     1000        1   Elemwise{gt,no_inplace}\n",
      "   3.6%    86.2%       0.003s       2.92e-06s     C     1000        1   Elemwise{Composite{log((i0 * i1))}}\n",
      "   3.6%    89.8%       0.003s       2.89e-06s     C     1000        1   Elemwise{Composite{Identity(GT(inv(sqrt(i0)), i1))}}\n",
      "   3.5%    93.2%       0.003s       2.78e-06s     C     1000        1   Subtensor{:int64:}\n",
      "   3.4%    96.7%       0.003s       2.76e-06s     C     1000        1   Elemwise{add,no_inplace}\n",
      "   3.3%   100.0%       0.003s       2.69e-06s     C     1000        1   Elemwise{Composite{inv(sqr(i0))}}\n",
      "   ... (remaining 0 Ops account for   0.00%(0.00s) of the runtime)\n",
      "\n",
      "Apply\n",
      "------\n",
      "<% time> <sum %> <apply time> <time per call> <#call> <id> <Apply name>\n",
      "  30.5%    30.5%       0.025s       2.45e-05s   1000    16   Elemwise{Composite{Switch(Identity((GT(Composite{exp((i0 * i1))}(i0, i1), i2) * i3 * GT(inv(sqrt(Composite{exp((i0 * i1))}(i0, i1))), i2))), (((i4 + (i5 * log(((i6 * Composite{exp((i0 * i1))}(i0, i1)) / i7)))) - i8) - (i5 * i9 * log1p(((Composite{exp((i0 * i1))}(i0, i1) * i10) / i7)))), i11)}}(TensorConstant{(1,) of -2.0}, s, TensorConstant{(1,) of 0}, Elemwise{gt,no_inplace}.0, Elemwise{Composite{scalar_gammaln((i0 * i1))}}.0, TensorConstant{(1,) o\n",
      "   5.1%    35.6%       0.004s       4.14e-06s   1000    15   Elemwise{Composite{Switch(i0, (i1 * ((-(i2 * sqr((i3 - i4)))) + i5)), i6)}}(Elemwise{Composite{Identity(GT(inv(sqrt(i0)), i1))}}.0, TensorConstant{(1,) of 0.5}, Elemwise{Composite{inv(sqr(i0))}}.0, Subtensor{int64::}.0, Subtensor{:int64:}.0, Elemwise{Composite{log((i0 * i1))}}.0, TensorConstant{(1,) of -inf})\n",
      "   3.9%    39.6%       0.003s       3.16e-06s   1000    19   Elemwise{Composite{(Switch(Identity(GT(i0, i1)), (i2 - (i3 * i0)), i4) + i5 + Switch(Identity(GT(i6, i1)), (i7 - (i8 * i6)), i4) + i9 + i10 + i11)}}[(0, 0)](Elemwise{exp,no_inplace}.0, TensorConstant{0}, TensorConstant{3.9120230674743652}, TensorConstant{50.0}, TensorConstant{-inf}, sigma_log_, Elemwise{exp,no_inplace}.0, TensorConstant{-2.3025850929940455}, TensorConstant{0.1}, nu_log_, Sum{acc_dtype=float64}.0, Sum{acc_dtype=float64}.0)\n",
      "   3.9%    43.5%       0.003s       3.14e-06s   1000     0   Elemwise{exp,no_inplace}(sigma_log_)\n",
      "   3.8%    47.2%       0.003s       3.03e-06s   1000    17   Sum{acc_dtype=float64}(Elemwise{Composite{Switch(i0, (i1 * ((-(i2 * sqr((i3 - i4)))) + i5)), i6)}}.0)\n",
      "   3.8%    51.0%       0.003s       3.02e-06s   1000     3   Subtensor{int64::}(s, Constant{1})\n",
      "   3.7%    54.7%       0.003s       2.99e-06s   1000    14   Elemwise{Composite{scalar_gammaln((i0 * i1))}}(TensorConstant{(1,) of 0.5}, Elemwise{add,no_inplace}.0)\n",
      "   3.6%    58.4%       0.003s       2.93e-06s   1000    18   Sum{acc_dtype=float64}(Elemwise{Composite{Switch(Identity((GT(Composite{exp((i0 * i1))}(i0, i1), i2) * i3 * GT(inv(sqrt(Composite{exp((i0 * i1))}(i0, i1))), i2))), (((i4 + (i5 * log(((i6 * Composite{exp((i0 * i1))}(i0, i1)) / i7)))) - i8) - (i5 * i9 * log1p(((Composite{exp((i0 * i1))}(i0, i1) * i10) / i7)))), i11)}}.0)\n",
      "   3.6%    62.0%       0.003s       2.93e-06s   1000    11   Elemwise{gt,no_inplace}(InplaceDimShuffle{x}.0, TensorConstant{(1,) of 0})\n",
      "   3.6%    65.6%       0.003s       2.92e-06s   1000    12   Elemwise{Composite{log((i0 * i1))}}(TensorConstant{(1,) of 0...9154943092}, Elemwise{Composite{inv(sqr(i0))}}.0)\n",
      "   3.6%    69.2%       0.003s       2.91e-06s   1000     1   Elemwise{exp,no_inplace}(nu_log_)\n",
      "   3.6%    72.8%       0.003s       2.89e-06s   1000    13   Elemwise{Composite{Identity(GT(inv(sqrt(i0)), i1))}}(Elemwise{Composite{inv(sqr(i0))}}.0, TensorConstant{(1,) of 0})\n",
      "   3.6%    76.4%       0.003s       2.86e-06s   1000     6   InplaceDimShuffle{x}(sigma)\n",
      "   3.5%    79.9%       0.003s       2.81e-06s   1000     7   InplaceDimShuffle{x}(nu)\n",
      "   3.5%    83.3%       0.003s       2.78e-06s   1000     2   Subtensor{:int64:}(s, Constant{-1})\n",
      "   3.4%    86.8%       0.003s       2.76e-06s   1000     9   Elemwise{add,no_inplace}(TensorConstant{(1,) of 1.0}, InplaceDimShuffle{x}.0)\n",
      "   3.3%    90.1%       0.003s       2.69e-06s   1000     8   Elemwise{Composite{inv(sqr(i0))}}(InplaceDimShuffle{x}.0)\n",
      "   3.3%    93.4%       0.003s       2.68e-06s   1000     5   ViewOp(Elemwise{exp,no_inplace}.0)\n",
      "   3.3%    96.7%       0.003s       2.65e-06s   1000     4   ViewOp(Elemwise{exp,no_inplace}.0)\n",
      "   3.3%   100.0%       0.003s       2.63e-06s   1000    10   Elemwise{Composite{scalar_gammaln((i0 * i1))}}(TensorConstant{(1,) of 0.5}, InplaceDimShuffle{x}.0)\n",
      "   ... (remaining 0 Apply instances account for 0.00%(0.00s) of the runtime)\n",
      "\n",
      "Here are tips to potentially make your code run faster\n",
      "                 (if you think of new ones, suggest them on the mailing list).\n",
      "                 Test them first, as they are not guaranteed to always provide a speedup.\n",
      "  - Try the Theano flag floatX=float32\n",
      "We don't know if amdlibm will accelerate this scalar op. scalar_gammaln\n",
      "We don't know if amdlibm will accelerate this scalar op. scalar_gammaln\n",
      "  - Try installing amdlibm and set the Theano flag lib.amdlibm=True. This speeds up only some Elemwise operation.\n"
     ]
    }
   ],
   "source": [
    "model.profile(model.logpt).summary()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Function profiling\n",
      "==================\n",
      "  Message: /home/jovyan/pymc3/pymc3/model.py:605\n",
      "  Time in 1000 calls to Function.__call__: 3.743136e-01s\n",
      "  Time in Function.fn.__call__: 3.272467e-01s (87.426%)\n",
      "  Time in thunks: 1.778915e-01s (47.525%)\n",
      "  Total compile time: 1.396206e+00s\n",
      "    Number of Apply nodes: 47\n",
      "    Theano Optimizer time: 6.084559e-01s\n",
      "       Theano validate time: 1.443505e-02s\n",
      "    Theano Linker time (includes C, CUDA code generation/compiling): 7.295318e-01s\n",
      "       Import time 8.256626e-02s\n",
      "       Node make_thunk time 7.264183e-01s\n",
      "           Node Elemwise{Composite{Switch(i0, (i1 * (i2 + ((i3 * i4 * i5 * i6) / i7))), i8)}}[(0, 6)](Elemwise{Composite{Identity((GT(i0, i1) * i2 * GT(inv(sqrt(i0)), i1)))}}.0, TensorConstant{(1,) of -2.0}, TensorConstant{(1,) of 0.5}, TensorConstant{(1,) of -0.5}, InplaceDimShuffle{x}.0, TensorConstant{[  4.05769..48400e-06]}, Elemwise{Composite{exp((i0 * i1))}}.0, Elemwise{Add}[(0, 1)].0, TensorConstant{(1,) of 0}) time 5.903370e-01s\n",
      "           Node Join(TensorConstant{0}, Rebroadcast{1}.0, Rebroadcast{1}.0, IncSubtensor{InplaceInc;:int64:}.0) time 1.472402e-02s\n",
      "           Node Elemwise{Composite{Switch(i0, ((i1 * i2 * i3 * i4) / i5), i6)}}(Elemwise{Composite{Identity((GT(i0, i1) * i2 * GT(inv(sqrt(i0)), i1)))}}.0, TensorConstant{(1,) of 0.5}, InplaceDimShuffle{x}.0, Elemwise{Composite{exp((i0 * i1))}}.0, TensorConstant{[  4.05769..48400e-06]}, Elemwise{Add}[(0, 1)].0, TensorConstant{(1,) of 0}) time 1.461983e-02s\n",
      "           Node Elemwise{Composite{Switch(i0, (i1 * i2 * i3), i4)}}(Elemwise{Composite{Identity(GT(inv(sqrt(i0)), i1))}}.0, TensorConstant{(1,) of -1.0}, InplaceDimShuffle{x}.0, Elemwise{sub,no_inplace}.0, TensorConstant{(1,) of 0}) time 7.709503e-03s\n",
      "           Node Elemwise{Composite{(i0 + Switch(Identity(GT(i1, i2)), (i3 * i1), i2) + (((i4 * i5 * psi((i4 * i6))) + (i7 * (i8 / i9)) + (i4 * i10 * psi((i4 * i9))) + (i4 * i11) + (i12 / i9)) * i1))}}[(0, 5)](TensorConstant{1.0}, Elemwise{exp,no_inplace}.0, TensorConstant{0}, TensorConstant{-0.1}, TensorConstant{0.5}, Sum{acc_dtype=float64}.0, Elemwise{add,no_inplace}.0, TensorConstant{3.141592653589793}, Sum{acc_dtype=float64}.0, nu, Sum{acc_dtype=float64}.0, Sum{acc_dtype=float64}.0, Sum{acc_dtype=float64}.0) time 7.651806e-03s\n",
      "\n",
      "Time in all call to theano.grad() 7.784910e-01s\n",
      "Time since theano import 13.326s\n",
      "Class\n",
      "---\n",
      "<% time> <sum %> <apply time> <time per call> <type> <#call> <#apply> <Class name>\n",
      "  54.0%    54.0%       0.096s       4.00e-06s     C    24000      24   theano.tensor.elemwise.Elemwise\n",
      "  12.9%    66.9%       0.023s       3.29e-06s     C     7000       7   theano.tensor.elemwise.Sum\n",
      "   6.4%    73.3%       0.011s       5.70e-06s     C     2000       2   theano.tensor.subtensor.IncSubtensor\n",
      "   4.9%    78.2%       0.009s       2.88e-06s     C     3000       3   theano.tensor.elemwise.DimShuffle\n",
      "   3.8%    81.9%       0.007s       6.69e-06s     C     1000       1   theano.tensor.basic.Join\n",
      "   3.7%    85.6%       0.007s       3.28e-06s     C     2000       2   theano.tensor.subtensor.Subtensor\n",
      "   3.4%    89.0%       0.006s       3.04e-06s     C     2000       2   theano.tensor.basic.Reshape\n",
      "   3.2%    92.3%       0.006s       5.70e-06s     C     1000       1   theano.tensor.basic.Alloc\n",
      "   3.1%    95.4%       0.006s       2.76e-06s     C     2000       2   theano.compile.ops.ViewOp\n",
      "   3.0%    98.3%       0.005s       2.66e-06s     C     2000       2   theano.compile.ops.Rebroadcast\n",
      "   1.7%   100.0%       0.003s       2.95e-06s     C     1000       1   theano.compile.ops.Shape_i\n",
      "   ... (remaining 0 Classes account for   0.00%(0.00s) of the runtime)\n",
      "\n",
      "Ops\n",
      "---\n",
      "<% time> <sum %> <apply time> <time per call> <type> <#call> <#apply> <Op name>\n",
      "  12.9%    12.9%       0.023s       3.29e-06s     C     7000        7   Sum{acc_dtype=float64}\n",
      "   7.6%    20.6%       0.014s       3.40e-06s     C     4000        4   Elemwise{Switch}\n",
      "   4.9%    25.4%       0.009s       2.88e-06s     C     3000        3   InplaceDimShuffle{x}\n",
      "   4.8%    30.2%       0.009s       8.55e-06s     C     1000        1   Elemwise{Composite{Switch(i0, (-log1p((i1 / i2))), i3)}}\n",
      "   4.0%    34.3%       0.007s       7.18e-06s     C     1000        1   IncSubtensor{InplaceInc;int64::}\n",
      "   4.0%    38.2%       0.007s       3.53e-06s     C     2000        2   Elemwise{exp,no_inplace}\n",
      "   3.8%    42.0%       0.007s       6.69e-06s     C     1000        1   Join\n",
      "   3.6%    45.6%       0.006s       6.32e-06s     C     1000        1   Elemwise{Composite{exp((i0 * i1))}}\n",
      "   3.4%    49.0%       0.006s       3.04e-06s     C     2000        2   Reshape{1}\n",
      "   3.2%    52.2%       0.006s       5.70e-06s     C     1000        1   Alloc\n",
      "   3.1%    55.3%       0.006s       2.76e-06s     C     2000        2   ViewOp\n",
      "   3.0%    58.3%       0.005s       2.66e-06s     C     2000        2   Rebroadcast{1}\n",
      "   2.9%    61.2%       0.005s       5.22e-06s     C     1000        1   Elemwise{Composite{Switch(i0, (i1 * (i2 + ((i3 * i4 * i5 * i6) / i7))), i8)}}[(0, 6)]\n",
      "   2.9%    64.1%       0.005s       5.19e-06s     C     1000        1   Elemwise{Composite{Switch(i0, ((i1 * i2 * i3 * i4) / i5), i6)}}\n",
      "   2.9%    67.0%       0.005s       5.14e-06s     C     1000        1   Elemwise{Composite{Identity((GT(i0, i1) * i2 * GT(inv(sqrt(i0)), i1)))}}\n",
      "   2.4%    69.4%       0.004s       4.31e-06s     C     1000        1   Elemwise{Composite{(i0 + Switch(Identity(GT(i1, i2)), (i3 * i1), i2) + (((i4 * i5 * psi((i4 * i6))) + (i7 * (i8 / i9)) + (i4 * i10 * psi((i4 * i9))) + (i4 * i11) + (i12 / i9)) * i1))}}[(0, 5)]\n",
      "   2.4%    71.8%       0.004s       4.23e-06s     C     1000        1   IncSubtensor{InplaceInc;:int64:}\n",
      "   2.2%    74.0%       0.004s       3.96e-06s     C     1000        1   Elemwise{Composite{Switch(i0, (i1 * i2 * i3), i4)}}\n",
      "   2.2%    76.3%       0.004s       3.94e-06s     C     1000        1   Elemwise{sub,no_inplace}\n",
      "   2.2%    78.4%       0.004s       3.83e-06s     C     1000        1   Elemwise{Composite{Switch(i0, (i1 * sqr(i2)), i3)}}\n",
      "   ... (remaining 12 Ops account for  21.59%(0.04s) of the runtime)\n",
      "\n",
      "Apply\n",
      "------\n",
      "<% time> <sum %> <apply time> <time per call> <#call> <id> <Apply name>\n",
      "   4.8%     4.8%       0.009s       8.55e-06s   1000    22   Elemwise{Composite{Switch(i0, (-log1p((i1 / i2))), i3)}}(Elemwise{Composite{Identity((GT(i0, i1) * i2 * GT(inv(sqrt(i0)), i1)))}}.0, Elemwise{mul,no_inplace}.0, InplaceDimShuffle{x}.0, TensorConstant{(1,) of 0})\n",
      "   4.0%     8.8%       0.007s       7.18e-06s   1000    39   IncSubtensor{InplaceInc;int64::}(Elemwise{Composite{Switch(i0, (i1 * (i2 + ((i3 * i4 * i5 * i6) / i7))), i8)}}[(0, 6)].0, Elemwise{Composite{Switch(i0, (i1 * i2 * i3), i4)}}.0, Constant{1})\n",
      "   3.8%    12.6%       0.007s       6.69e-06s   1000    46   Join(TensorConstant{0}, Rebroadcast{1}.0, Rebroadcast{1}.0, IncSubtensor{InplaceInc;:int64:}.0)\n",
      "   3.6%    16.2%       0.006s       6.32e-06s   1000     5   Elemwise{Composite{exp((i0 * i1))}}(TensorConstant{(1,) of -2.0}, s)\n",
      "   3.2%    19.4%       0.006s       5.70e-06s   1000    29   Alloc(Elemwise{switch,no_inplace}.0, Elemwise{Composite{(i0 - Switch(LT(i1, i0), i2, i0))}}[(0, 0)].0)\n",
      "   2.9%    22.3%       0.005s       5.22e-06s   1000    36   Elemwise{Composite{Switch(i0, (i1 * (i2 + ((i3 * i4 * i5 * i6) / i7))), i8)}}[(0, 6)](Elemwise{Composite{Identity((GT(i0, i1) * i2 * GT(inv(sqrt(i0)), i1)))}}.0, TensorConstant{(1,) of -2.0}, TensorConstant{(1,) of 0.5}, TensorConstant{(1,) of -0.5}, InplaceDimShuffle{x}.0, TensorConstant{[  4.05769..48400e-06]}, Elemwise{Composite{exp((i0 * i1))}}.0, Elemwise{Add}[(0, 1)].0, TensorConstant{(1,) of 0})\n",
      "   2.9%    25.2%       0.005s       5.19e-06s   1000    34   Elemwise{Composite{Switch(i0, ((i1 * i2 * i3 * i4) / i5), i6)}}(Elemwise{Composite{Identity((GT(i0, i1) * i2 * GT(inv(sqrt(i0)), i1)))}}.0, TensorConstant{(1,) of 0.5}, InplaceDimShuffle{x}.0, Elemwise{Composite{exp((i0 * i1))}}.0, TensorConstant{[  4.05769..48400e-06]}, Elemwise{Add}[(0, 1)].0, TensorConstant{(1,) of 0})\n",
      "   2.9%    28.1%       0.005s       5.14e-06s   1000    18   Elemwise{Composite{Identity((GT(i0, i1) * i2 * GT(inv(sqrt(i0)), i1)))}}(Elemwise{Composite{exp((i0 * i1))}}.0, TensorConstant{(1,) of 0}, Elemwise{gt,no_inplace}.0)\n",
      "   2.4%    30.5%       0.004s       4.31e-06s   1000    40   Elemwise{Composite{(i0 + Switch(Identity(GT(i1, i2)), (i3 * i1), i2) + (((i4 * i5 * psi((i4 * i6))) + (i7 * (i8 / i9)) + (i4 * i10 * psi((i4 * i9))) + (i4 * i11) + (i12 / i9)) * i1))}}[(0, 5)](TensorConstant{1.0}, Elemwise{exp,no_inplace}.0, TensorConstant{0}, TensorConstant{-0.1}, TensorConstant{0.5}, Sum{acc_dtype=float64}.0, Elemwise{add,no_inplace}.0, TensorConstant{3.141592653589793}, Sum{acc_dtype=float64}.0, nu, Sum{acc_dtype=float64}.0, Sum{\n",
      "   2.4%    32.9%       0.004s       4.23e-06s   1000    42   IncSubtensor{InplaceInc;:int64:}(IncSubtensor{InplaceInc;int64::}.0, Elemwise{Composite{Switch(i0, (i1 * i2), i3)}}[(0, 2)].0, Constant{-1})\n",
      "   2.2%    35.1%       0.004s       3.96e-06s   1000    19   Elemwise{Composite{Switch(i0, (i1 * i2 * i3), i4)}}(Elemwise{Composite{Identity(GT(inv(sqrt(i0)), i1))}}.0, TensorConstant{(1,) of -1.0}, InplaceDimShuffle{x}.0, Elemwise{sub,no_inplace}.0, TensorConstant{(1,) of 0})\n",
      "   2.2%    37.3%       0.004s       3.94e-06s   1000     7   Elemwise{sub,no_inplace}(Subtensor{int64::}.0, Subtensor{:int64:}.0)\n",
      "   2.2%    39.5%       0.004s       3.88e-06s   1000     3   Elemwise{exp,no_inplace}(sigma_log_)\n",
      "   2.2%    41.7%       0.004s       3.83e-06s   1000    20   Elemwise{Composite{Switch(i0, (i1 * sqr(i2)), i3)}}(Elemwise{Composite{Identity(GT(inv(sqrt(i0)), i1))}}.0, TensorConstant{(1,) of 0.5}, Elemwise{sub,no_inplace}.0, TensorConstant{(1,) of 0})\n",
      "   2.1%    43.7%       0.004s       3.66e-06s   1000    10   Elemwise{mul,no_inplace}(Elemwise{Composite{exp((i0 * i1))}}.0, TensorConstant{[  4.05769..48400e-06]})\n",
      "   2.0%    45.8%       0.004s       3.62e-06s   1000    38   Elemwise{Composite{(i0 + Switch(Identity(GT(i1, i2)), (i3 * i1), i2) + (i4 * (((i5 * i6 * Composite{inv(Composite{(sqr(i0) * i0)}(i0))}(i7)) / i8) - (i9 * Composite{inv(Composite{(sqr(i0) * i0)}(i0))}(i7))) * i1))}}[(0, 6)](TensorConstant{1.0}, Elemwise{exp,no_inplace}.0, TensorConstant{0}, TensorConstant{-50.0}, TensorConstant{-2.0}, TensorConstant{0.5}, Sum{acc_dtype=float64}.0, sigma, Elemwise{Composite{inv(sqr(i0))}}.0, Sum{acc_dtype=float64}.0)\n",
      "   2.0%    47.7%       0.003s       3.48e-06s   1000    25   Elemwise{Switch}(Elemwise{Composite{Identity((GT(i0, i1) * i2 * GT(inv(sqrt(i0)), i1)))}}.0, TensorConstant{(1,) of 1.0}, TensorConstant{(1,) of 0.0})\n",
      "   1.9%    49.7%       0.003s       3.45e-06s   1000    24   Elemwise{switch,no_inplace}(Elemwise{Composite{Identity((GT(i0, i1) * i2 * GT(inv(sqrt(i0)), i1)))}}.0, TensorConstant{(1,) of -0..9154943092}, TensorConstant{(1,) of 0})\n",
      "   1.9%    51.6%       0.003s       3.44e-06s   1000     2   Subtensor{int64::}(s, Constant{1})\n",
      "   1.9%    53.5%       0.003s       3.44e-06s   1000    35   Sum{acc_dtype=float64}(Alloc.0)\n",
      "   ... (remaining 27 Apply instances account for 46.46%(0.08s) of the runtime)\n",
      "\n",
      "Here are tips to potentially make your code run faster\n",
      "                 (if you think of new ones, suggest them on the mailing list).\n",
      "                 Test them first, as they are not guaranteed to always provide a speedup.\n",
      "  - Try the Theano flag floatX=float32\n",
      "We don't know if amdlibm will accelerate this scalar op. psi\n",
      "We don't know if amdlibm will accelerate this scalar op. psi\n",
      "  - Try installing amdlibm and set the Theano flag lib.amdlibm=True. This speeds up only some Elemwise operation.\n"
     ]
    }
   ],
   "source": [
    "model.profile(gradient(model.logpt, model.vars)).summary()"
   ]
  }
 ],
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