Average Error: 0.0 → 15.7
Time: 5.4s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[{y}^{y} \cdot e^{x - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
{y}^{y} \cdot e^{x - z}
double f(double x, double y, double z) {
        double r218674 = x;
        double r218675 = y;
        double r218676 = log(r218675);
        double r218677 = r218675 * r218676;
        double r218678 = r218674 + r218677;
        double r218679 = z;
        double r218680 = r218678 - r218679;
        double r218681 = exp(r218680);
        return r218681;
}
↓
double f(double x, double y, double z) {
        double r218682 = y;
        double r218683 = pow(r218682, r218682);
        double r218684 = x;
        double r218685 = z;
        double r218686 = r218684 - r218685;
        double r218687 = exp(r218686);
        double r218688 = r218683 * r218687;
        return r218688;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

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Target

Original0.0
Target0.0
Herbie15.7
\[e^{\left(x - z\right) + \log y \cdot y}\]

Derivation

  1. Initial program 0.0

    \[e^{\left(x + y \cdot \log y\right) - z}\]

  2. Final simplification15.7

    \[\leadsto {y}^{y} \cdot e^{x - z}\]

Reproduce

herbie shell --seed 2019308 
(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)))