Average Error: 0.0 → 0.0
Time: 10.1s
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 r11632664 = x;
        double r11632665 = y;
        double r11632666 = log(r11632665);
        double r11632667 = r11632665 * r11632666;
        double r11632668 = r11632664 + r11632667;
        double r11632669 = z;
        double r11632670 = r11632668 - r11632669;
        double r11632671 = exp(r11632670);
        return r11632671;
}
↓
double f(double x, double y, double z) {
        double r11632672 = y;
        double r11632673 = log(r11632672);
        double r11632674 = x;
        double r11632675 = z;
        double r11632676 = r11632674 - r11632675;
        double r11632677 = fma(r11632673, r11632672, r11632676);
        double r11632678 = exp(r11632677);
        return r11632678;
}

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 2019169 +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)))