Average Error: 0.0 → 0.0
Time: 16.2s
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 r12265190 = x;
        double r12265191 = y;
        double r12265192 = log(r12265191);
        double r12265193 = r12265191 * r12265192;
        double r12265194 = r12265190 + r12265193;
        double r12265195 = z;
        double r12265196 = r12265194 - r12265195;
        double r12265197 = exp(r12265196);
        return r12265197;
}
↓
double f(double x, double y, double z) {
        double r12265198 = y;
        double r12265199 = log(r12265198);
        double r12265200 = x;
        double r12265201 = z;
        double r12265202 = r12265200 - r12265201;
        double r12265203 = fma(r12265199, r12265198, r12265202);
        double r12265204 = exp(r12265203);
        return r12265204;
}

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 2019168 +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)))