Average Error: 6.5 → 6.7
Time: 16.1s
Precision: 64
\[\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]
↓
\[\frac{\frac{\frac{1}{x}}{y}}{1 + z \cdot z}\]
\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}
↓
\frac{\frac{\frac{1}{x}}{y}}{1 + z \cdot z}
double f(double x, double y, double z) {
        double r15704818 = 1.0;
        double r15704819 = x;
        double r15704820 = r15704818 / r15704819;
        double r15704821 = y;
        double r15704822 = z;
        double r15704823 = r15704822 * r15704822;
        double r15704824 = r15704818 + r15704823;
        double r15704825 = r15704821 * r15704824;
        double r15704826 = r15704820 / r15704825;
        return r15704826;
}
↓
double f(double x, double y, double z) {
        double r15704827 = 1.0;
        double r15704828 = x;
        double r15704829 = r15704827 / r15704828;
        double r15704830 = y;
        double r15704831 = r15704829 / r15704830;
        double r15704832 = z;
        double r15704833 = r15704832 * r15704832;
        double r15704834 = r15704827 + r15704833;
        double r15704835 = r15704831 / r15704834;
        return r15704835;
}

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

Original6.5
Target5.7
Herbie6.7
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(1 + z \cdot z\right) \lt -\infty:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \mathbf{elif}\;y \cdot \left(1 + z \cdot z\right) \lt 8.680743250567251617010582226806563373013 \cdot 10^{305}:\\ \;\;\;\;\frac{\frac{1}{x}}{\left(1 + z \cdot z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \end{array}\]

Derivation

  1. Initial program 6.5

    \[\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]
  2. Using strategy rm

  3. Applied associate-/r*6.7

    \[\leadsto \color{blue}{\frac{\frac{\frac{1}{x}}{y}}{1 + z \cdot z}}\]

  4. Final simplification6.7

    \[\leadsto \frac{\frac{\frac{1}{x}}{y}}{1 + z \cdot z}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Statistics.Distribution.CauchyLorentz:$cdensity from math-functions-0.1.5.2"

  :herbie-target
  (if (< (* y (+ 1.0 (* z z))) -inf.0) (/ (/ 1.0 y) (* (+ 1.0 (* z z)) x)) (if (< (* y (+ 1.0 (* z z))) 8.680743250567252e+305) (/ (/ 1.0 x) (* (+ 1.0 (* z z)) y)) (/ (/ 1.0 y) (* (+ 1.0 (* z z)) x))))

  (/ (/ 1.0 x) (* y (+ 1.0 (* z z)))))