Average Error: 6.2 → 6.2
Time: 9.6s
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 r272737 = 1.0;
        double r272738 = x;
        double r272739 = r272737 / r272738;
        double r272740 = y;
        double r272741 = z;
        double r272742 = r272741 * r272741;
        double r272743 = r272737 + r272742;
        double r272744 = r272740 * r272743;
        double r272745 = r272739 / r272744;
        return r272745;
}
↓
double f(double x, double y, double z) {
        double r272746 = 1.0;
        double r272747 = x;
        double r272748 = r272746 / r272747;
        double r272749 = y;
        double r272750 = z;
        double r272751 = r272750 * r272750;
        double r272752 = r272746 + r272751;
        double r272753 = r272749 * r272752;
        double r272754 = r272748 / r272753;
        return r272754;
}

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 +o rules:numerics
(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)))))