Normal cdf + copy args in smooth canonicalizer

[dance858]

This PR adds the normal cdf as an atom. It also fixes a subtle error that was raised when we called a smooth full domain atom on a division, like exp(1/x).

[dance858]

@PTNobel

Parth, what do you think about the name "normal_cdf"?

[PTNobel]

MATLAB uses normcdf and SciPy uses norm.cdf and torch uses normal.cdf and JAX uses norm.cdf

Fortran used cdf_normal, R uses ??? pnorm ???

My soft preference is to call it normcdf to match log_normcdf, but as long as we don't use what R does I'm happy.

https://www.mathworks.com/help/stats/normcdf.html
https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html
https://r02pro.github.io/normal-distribution.html

[dance858]

MATLAB uses normcdf and SciPy uses norm.cdf and torch uses normal.cdf and JAX uses norm.cdf

Fortran used cdf_normal, R uses ??? pnorm ???

My soft preference is to call it normcdf to match log_normcdf, but as long as we don't use what R does I'm happy.

https://www.mathworks.com/help/stats/normcdf.html https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html https://r02pro.github.io/normal-distribution.html

Haha great! I'll call it normcdf then.

[github-actions]

Benchmarks that have stayed the same:

   before           after         ratio
 [e6df2dda]       [805a30b0]
     15.2±0ms         16.6±0ms     1.09  simple_QP_benchmarks.ParametrizedQPBenchmark.time_compile_problem
      1.57±0s          1.70±0s     1.08  tv_inpainting.TvInpainting.time_compile_problem
      727±0ms          754±0ms     1.04  simple_QP_benchmarks.LeastSquares.time_compile_problem
      133±0ms          137±0ms     1.03  high_dim_convex_plasticity.ConvexPlasticity.time_compile_problem
      226±0ms          232±0ms     1.03  gini_portfolio.Murray.time_compile_problem
      278±0ms          284±0ms     1.02  slow_pruning_1668_benchmark.SlowPruningBenchmark.time_compile_problem
      4.48±0s          4.58±0s     1.02  svm_l1_regularization.SVMWithL1Regularization.time_compile_problem
      10.1±0s          10.3±0s     1.02  simple_LP_benchmarks.SimpleLPBenchmark.time_compile_problem
      1.05±0s          1.07±0s     1.02  gini_portfolio.Cajas.time_compile_problem
      1.77±0s          1.79±0s     1.01  simple_QP_benchmarks.UnconstrainedQP.time_compile_problem
      875±0ms          885±0ms     1.01  simple_LP_benchmarks.SimpleScalarParametrizedLPBenchmark.time_compile_problem
      713±0ms          716±0ms     1.00  matrix_stuffing.ConeMatrixStuffingBench.time_compile_problem
      285±0ms          286±0ms     1.00  matrix_stuffing.ParamSmallMatrixStuffing.time_compile_problem
      315±0ms          317±0ms     1.00  gini_portfolio.Yitzhaki.time_compile_problem
     42.0±0ms         42.1±0ms     1.00  matrix_stuffing.SmallMatrixStuffing.time_compile_problem
      238±0ms          237±0ms     1.00  simple_QP_benchmarks.SimpleQPBenchmark.time_compile_problem
      2.98±0s          2.98±0s     1.00  quantum_hilbert_matrix.QuantumHilbertMatrix.time_compile_problem
     14.6±0ms         14.5±0ms     1.00  simple_LP_benchmarks.SimpleFullyParametrizedLPBenchmark.time_compile_problem
      20.8±0s          20.6±0s     0.99  sdp_segfault_1132_benchmark.SDPSegfault1132Benchmark.time_compile_problem
      5.16±0s          5.10±0s     0.99  optimal_advertising.OptimalAdvertising.time_compile_problem
      3.98±0s          3.93±0s     0.99  huber_regression.HuberRegression.time_compile_problem
      536±0ms          529±0ms     0.99  semidefinite_programming.SemidefiniteProgramming.time_compile_problem
      12.8±0s          12.4±0s     0.98  finance.CVaRBenchmark.time_compile_problem
      1.02±0s          990±0ms     0.97  finance.FactorCovarianceModel.time_compile_problem
      1.46±0s          1.41±0s     0.96  matrix_stuffing.ParamConeMatrixStuffing.time_compile_problem

[Transurgeon]

can you add a comment about this in the PR title? After that I think its good to merge.

[Transurgeon]

also we should ensure that all full domain atoms have only one argument (since it indexes with 0), but this should be fine.

[dance858]

I think they always have one argument, right?

[PTNobel]

I thought that was part of the contract of being a full domain function and the multiargs had different requirements

[PTNobel]

If we wanted to be safe we could just pass args directly tho!