Average Error: 0.0 → 0.0
Time: 27.9s
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 r19547804 = x;
        double r19547805 = y;
        double r19547806 = log(r19547805);
        double r19547807 = r19547805 * r19547806;
        double r19547808 = r19547804 + r19547807;
        double r19547809 = z;
        double r19547810 = r19547808 - r19547809;
        double r19547811 = exp(r19547810);
        return r19547811;
}
↓
double f(double x, double y, double z) {
        double r19547812 = y;
        double r19547813 = log(r19547812);
        double r19547814 = x;
        double r19547815 = z;
        double r19547816 = r19547814 - r19547815;
        double r19547817 = fma(r19547813, r19547812, r19547816);
        double r19547818 = exp(r19547817);
        return r19547818;
}

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 2019172 +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)))