Average Error: 0.0 → 0.0
Time: 17.5s
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 r16215022 = x;
        double r16215023 = y;
        double r16215024 = log(r16215023);
        double r16215025 = r16215023 * r16215024;
        double r16215026 = r16215022 + r16215025;
        double r16215027 = z;
        double r16215028 = r16215026 - r16215027;
        double r16215029 = exp(r16215028);
        return r16215029;
}
↓
double f(double x, double y, double z) {
        double r16215030 = y;
        double r16215031 = log(r16215030);
        double r16215032 = x;
        double r16215033 = z;
        double r16215034 = r16215032 - r16215033;
        double r16215035 = fma(r16215031, r16215030, r16215034);
        double r16215036 = exp(r16215035);
        return r16215036;
}

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 2019158 +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)))