Average Error: 0.0 → 0.0
Time: 11.4s
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 r9817999 = x;
        double r9818000 = y;
        double r9818001 = log(r9818000);
        double r9818002 = r9818000 * r9818001;
        double r9818003 = r9817999 + r9818002;
        double r9818004 = z;
        double r9818005 = r9818003 - r9818004;
        double r9818006 = exp(r9818005);
        return r9818006;
}
↓
double f(double x, double y, double z) {
        double r9818007 = y;
        double r9818008 = log(r9818007);
        double r9818009 = x;
        double r9818010 = z;
        double r9818011 = r9818009 - r9818010;
        double r9818012 = fma(r9818008, r9818007, r9818011);
        double r9818013 = exp(r9818012);
        return r9818013;
}

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 2019170 +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)))