Average Error: 0.0 → 0.0
Time: 6.0s
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 r300710 = x;
        double r300711 = y;
        double r300712 = log(r300711);
        double r300713 = r300711 * r300712;
        double r300714 = r300710 + r300713;
        double r300715 = z;
        double r300716 = r300714 - r300715;
        double r300717 = exp(r300716);
        return r300717;
}
↓
double f(double x, double y, double z) {
        double r300718 = y;
        double r300719 = log(r300718);
        double r300720 = x;
        double r300721 = fma(r300718, r300719, r300720);
        double r300722 = z;
        double r300723 = r300721 - r300722;
        double r300724 = exp(r300723);
        return r300724;
}

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 2020045 +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)))