Average Error: 0.0 → 0.0
Time: 20.5s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\mathsf{fma}\left(y, \log y, x\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\mathsf{fma}\left(y, \log y, x\right) - z}
double f(double x, double y, double z) {
        double r239525 = x;
        double r239526 = y;
        double r239527 = log(r239526);
        double r239528 = r239526 * r239527;
        double r239529 = r239525 + r239528;
        double r239530 = z;
        double r239531 = r239529 - r239530;
        double r239532 = exp(r239531);
        return r239532;
}
↓
double f(double x, double y, double z) {
        double r239533 = y;
        double r239534 = log(r239533);
        double r239535 = x;
        double r239536 = fma(r239533, r239534, r239535);
        double r239537 = z;
        double r239538 = r239536 - r239537;
        double r239539 = exp(r239538);
        return r239539;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))