Average Error: 0.0 → 0.0
Time: 39.9s
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 r8429403 = x;
        double r8429404 = y;
        double r8429405 = log(r8429404);
        double r8429406 = r8429404 * r8429405;
        double r8429407 = r8429403 + r8429406;
        double r8429408 = z;
        double r8429409 = r8429407 - r8429408;
        double r8429410 = exp(r8429409);
        return r8429410;
}
↓
double f(double x, double y, double z) {
        double r8429411 = y;
        double r8429412 = log(r8429411);
        double r8429413 = x;
        double r8429414 = z;
        double r8429415 = r8429413 - r8429414;
        double r8429416 = fma(r8429411, r8429412, r8429415);
        double r8429417 = exp(r8429416);
        return r8429417;
}

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 2019200 +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)))