Average Error: 0.0 → 0.0
Time: 21.5s
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 r12442496 = x;
        double r12442497 = y;
        double r12442498 = log(r12442497);
        double r12442499 = r12442497 * r12442498;
        double r12442500 = r12442496 + r12442499;
        double r12442501 = z;
        double r12442502 = r12442500 - r12442501;
        double r12442503 = exp(r12442502);
        return r12442503;
}
↓
double f(double x, double y, double z) {
        double r12442504 = y;
        double r12442505 = log(r12442504);
        double r12442506 = x;
        double r12442507 = z;
        double r12442508 = r12442506 - r12442507;
        double r12442509 = fma(r12442504, r12442505, r12442508);
        double r12442510 = exp(r12442509);
        return r12442510;
}

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 2019172 +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)))