Average Error: 0.0 → 0.0
Time: 5.3s
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 r244464 = x;
        double r244465 = y;
        double r244466 = log(r244465);
        double r244467 = r244465 * r244466;
        double r244468 = r244464 + r244467;
        double r244469 = z;
        double r244470 = r244468 - r244469;
        double r244471 = exp(r244470);
        return r244471;
}
↓
double f(double x, double y, double z) {
        double r244472 = y;
        double r244473 = log(r244472);
        double r244474 = x;
        double r244475 = fma(r244472, r244473, r244474);
        double r244476 = z;
        double r244477 = r244475 - r244476;
        double r244478 = exp(r244477);
        return r244478;
}

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 2020045 +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)))