Average Error: 0.0 → 0.0
Time: 10.7s
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 r14153167 = x;
        double r14153168 = y;
        double r14153169 = log(r14153168);
        double r14153170 = r14153168 * r14153169;
        double r14153171 = r14153167 + r14153170;
        double r14153172 = z;
        double r14153173 = r14153171 - r14153172;
        double r14153174 = exp(r14153173);
        return r14153174;
}
↓
double f(double x, double y, double z) {
        double r14153175 = y;
        double r14153176 = log(r14153175);
        double r14153177 = x;
        double r14153178 = z;
        double r14153179 = r14153177 - r14153178;
        double r14153180 = fma(r14153176, r14153175, r14153179);
        double r14153181 = exp(r14153180);
        return r14153181;
}

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 2019162 +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)))