Average Error: 0.0 → 0.0
Time: 25.9s
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 r15221253 = x;
        double r15221254 = y;
        double r15221255 = log(r15221254);
        double r15221256 = r15221254 * r15221255;
        double r15221257 = r15221253 + r15221256;
        double r15221258 = z;
        double r15221259 = r15221257 - r15221258;
        double r15221260 = exp(r15221259);
        return r15221260;
}
↓
double f(double x, double y, double z) {
        double r15221261 = y;
        double r15221262 = log(r15221261);
        double r15221263 = x;
        double r15221264 = z;
        double r15221265 = r15221263 - r15221264;
        double r15221266 = fma(r15221262, r15221261, r15221265);
        double r15221267 = exp(r15221266);
        return r15221267;
}

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 2019165 +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)))