Average Error: 0.0 → 0.0
Time: 10.5s
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 r13719031 = x;
        double r13719032 = y;
        double r13719033 = log(r13719032);
        double r13719034 = r13719032 * r13719033;
        double r13719035 = r13719031 + r13719034;
        double r13719036 = z;
        double r13719037 = r13719035 - r13719036;
        double r13719038 = exp(r13719037);
        return r13719038;
}
↓
double f(double x, double y, double z) {
        double r13719039 = y;
        double r13719040 = log(r13719039);
        double r13719041 = x;
        double r13719042 = z;
        double r13719043 = r13719041 - r13719042;
        double r13719044 = fma(r13719040, r13719039, r13719043);
        double r13719045 = exp(r13719044);
        return r13719045;
}

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)))