Average Error: 0.0 → 0.0
Time: 27.2s
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 r17474816 = x;
        double r17474817 = y;
        double r17474818 = log(r17474817);
        double r17474819 = r17474817 * r17474818;
        double r17474820 = r17474816 + r17474819;
        double r17474821 = z;
        double r17474822 = r17474820 - r17474821;
        double r17474823 = exp(r17474822);
        return r17474823;
}
↓
double f(double x, double y, double z) {
        double r17474824 = y;
        double r17474825 = log(r17474824);
        double r17474826 = x;
        double r17474827 = z;
        double r17474828 = r17474826 - r17474827;
        double r17474829 = fma(r17474825, r17474824, r17474828);
        double r17474830 = exp(r17474829);
        return r17474830;
}

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)))