Average Error: 0.0 → 0.0
Time: 16.2s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\mathsf{fma}\left(y, \log y, x\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\mathsf{fma}\left(y, \log y, x\right) - z}
double f(double x, double y, double z) {
        double r183868 = x;
        double r183869 = y;
        double r183870 = log(r183869);
        double r183871 = r183869 * r183870;
        double r183872 = r183868 + r183871;
        double r183873 = z;
        double r183874 = r183872 - r183873;
        double r183875 = exp(r183874);
        return r183875;
}
↓
double f(double x, double y, double z) {
        double r183876 = y;
        double r183877 = log(r183876);
        double r183878 = x;
        double r183879 = fma(r183876, r183877, r183878);
        double r183880 = z;
        double r183881 = r183879 - r183880;
        double r183882 = exp(r183881);
        return r183882;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[e^{\left(x - z\right) + \log y \cdot y}\]

Derivation

  1. Initial program 0.0

    \[e^{\left(x + y \cdot \log y\right) - z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log y, x\right) - z}}\]

  3. Final simplification0.0

    \[\leadsto e^{\mathsf{fma}\left(y, \log y, x\right) - z}\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))