Average Error: 6.2 → 6.2
Time: 6.0s
Precision: 64
\[\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]
↓
\[\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]
\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}
↓
\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}
double f(double x, double y, double z) {
        double r327711 = 1.0;
        double r327712 = x;
        double r327713 = r327711 / r327712;
        double r327714 = y;
        double r327715 = z;
        double r327716 = r327715 * r327715;
        double r327717 = r327711 + r327716;
        double r327718 = r327714 * r327717;
        double r327719 = r327713 / r327718;
        return r327719;
}
↓
double f(double x, double y, double z) {
        double r327720 = 1.0;
        double r327721 = x;
        double r327722 = r327720 / r327721;
        double r327723 = y;
        double r327724 = z;
        double r327725 = r327724 * r327724;
        double r327726 = r327720 + r327725;
        double r327727 = r327723 * r327726;
        double r327728 = r327722 / r327727;
        return r327728;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.2
Target5.6
Herbie6.2
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(1 + z \cdot z\right) \lt -\infty:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \mathbf{elif}\;y \cdot \left(1 + z \cdot z\right) \lt 8.68074325056725162 \cdot 10^{305}:\\ \;\;\;\;\frac{\frac{1}{x}}{\left(1 + z \cdot z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \end{array}\]

Derivation

  1. Initial program 6.2

    \[\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]

  2. Final simplification6.2

    \[\leadsto \frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z)
  :name "Statistics.Distribution.CauchyLorentz:$cdensity from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< (* y (+ 1 (* z z))) #f) (/ (/ 1 y) (* (+ 1 (* z z)) x)) (if (< (* y (+ 1 (* z z))) 8.680743250567252e+305) (/ (/ 1 x) (* (+ 1 (* z z)) y)) (/ (/ 1 y) (* (+ 1 (* z z)) x))))

  (/ (/ 1 x) (* y (+ 1 (* z z)))))