Average Error: 6.4 → 6.4
Time: 7.5s
Precision: 64
\[\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]
↓
\[\frac{\frac{\frac{1}{y}}{x}}{1 + z \cdot z}\]
\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}
↓
\frac{\frac{\frac{1}{y}}{x}}{1 + z \cdot z}
double f(double x, double y, double z) {
        double r318108 = 1.0;
        double r318109 = x;
        double r318110 = r318108 / r318109;
        double r318111 = y;
        double r318112 = z;
        double r318113 = r318112 * r318112;
        double r318114 = r318108 + r318113;
        double r318115 = r318111 * r318114;
        double r318116 = r318110 / r318115;
        return r318116;
}
↓
double f(double x, double y, double z) {
        double r318117 = 1.0;
        double r318118 = y;
        double r318119 = r318117 / r318118;
        double r318120 = x;
        double r318121 = r318119 / r318120;
        double r318122 = z;
        double r318123 = r318122 * r318122;
        double r318124 = r318117 + r318123;
        double r318125 = r318121 / r318124;
        return r318125;
}

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

Original6.4
Target5.7
Herbie6.4
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(1 + z \cdot z\right) \lt -\infty:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \mathbf{elif}\;y \cdot \left(1 + z \cdot z\right) \lt 8.68074325056725162 \cdot 10^{305}:\\ \;\;\;\;\frac{\frac{1}{x}}{\left(1 + z \cdot z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \end{array}\]

Derivation

  1. Initial program 6.4

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

  3. Applied associate-/r*6.4

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

  4. Simplified6.4

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

  5. Final simplification6.4

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

Reproduce

herbie shell --seed 2020039 
(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)))))