Average Error: 0.0 → 0.0
Time: 10.6s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\mathsf{fma}\left(y, \log y, x - z\right)}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\mathsf{fma}\left(y, \log y, x - z\right)}
double f(double x, double y, double z) {
        double r12978944 = x;
        double r12978945 = y;
        double r12978946 = log(r12978945);
        double r12978947 = r12978945 * r12978946;
        double r12978948 = r12978944 + r12978947;
        double r12978949 = z;
        double r12978950 = r12978948 - r12978949;
        double r12978951 = exp(r12978950);
        return r12978951;
}
↓
double f(double x, double y, double z) {
        double r12978952 = y;
        double r12978953 = log(r12978952);
        double r12978954 = x;
        double r12978955 = z;
        double r12978956 = r12978954 - r12978955;
        double r12978957 = fma(r12978952, r12978953, r12978956);
        double r12978958 = exp(r12978957);
        return r12978958;
}

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

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log y, x - z\right)}}\]

  3. Final simplification0.0

    \[\leadsto e^{\mathsf{fma}\left(y, \log y, x - z\right)}\]

Reproduce

herbie shell --seed 2019192 +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)))