Average Error: 0.0 → 0.0
Time: 21.8s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\mathsf{fma}\left(\log y, y, x - z\right)}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\mathsf{fma}\left(\log y, y, x - z\right)}
double f(double x, double y, double z) {
        double r13479893 = x;
        double r13479894 = y;
        double r13479895 = log(r13479894);
        double r13479896 = r13479894 * r13479895;
        double r13479897 = r13479893 + r13479896;
        double r13479898 = z;
        double r13479899 = r13479897 - r13479898;
        double r13479900 = exp(r13479899);
        return r13479900;
}
↓
double f(double x, double y, double z) {
        double r13479901 = y;
        double r13479902 = log(r13479901);
        double r13479903 = x;
        double r13479904 = z;
        double r13479905 = r13479903 - r13479904;
        double r13479906 = fma(r13479902, r13479901, r13479905);
        double r13479907 = exp(r13479906);
        return r13479907;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"

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

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