Average Error: 6.4 → 6.5
Time: 11.0s
Precision: 64
\[\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{y}}{\frac{x}{\frac{\sqrt[3]{1}}{1 + z \cdot z}}}\]
\frac{\frac{1}{x}}{y \cdot \left(1 + z \cdot z\right)}
↓
\frac{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{y}}{\frac{x}{\frac{\sqrt[3]{1}}{1 + z \cdot z}}}
double f(double x, double y, double z) {
        double r338046 = 1.0;
        double r338047 = x;
        double r338048 = r338046 / r338047;
        double r338049 = y;
        double r338050 = z;
        double r338051 = r338050 * r338050;
        double r338052 = r338046 + r338051;
        double r338053 = r338049 * r338052;
        double r338054 = r338048 / r338053;
        return r338054;
}
↓
double f(double x, double y, double z) {
        double r338055 = 1.0;
        double r338056 = cbrt(r338055);
        double r338057 = r338056 * r338056;
        double r338058 = y;
        double r338059 = r338057 / r338058;
        double r338060 = x;
        double r338061 = z;
        double r338062 = r338061 * r338061;
        double r338063 = r338055 + r338062;
        double r338064 = r338056 / r338063;
        double r338065 = r338060 / r338064;
        double r338066 = r338059 / r338065;
        return r338066;
}

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
Target5.8
Herbie6.5
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(1 + z \cdot z\right) \lt -\infty:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \mathbf{elif}\;y \cdot \left(1 + z \cdot z\right) \lt 8.68074325056725162 \cdot 10^{305}:\\ \;\;\;\;\frac{\frac{1}{x}}{\left(1 + z \cdot z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{\left(1 + z \cdot z\right) \cdot x}\\ \end{array}\]

Derivation

  1. Initial program 6.4

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

  3. Applied div-inv6.4

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

  4. Applied associate-/l*6.7

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

  5. Simplified6.7

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

  7. Applied associate-/r*6.4

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

  9. Applied add-cube-cbrt6.4

    \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{y \cdot \left(1 + z \cdot z\right)}}{x}\]

  10. Applied times-frac6.3

    \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{y} \cdot \frac{\sqrt[3]{1}}{1 + z \cdot z}}}{x}\]

  11. Applied associate-/l*6.5

    \[\leadsto \color{blue}{\frac{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{y}}{\frac{x}{\frac{\sqrt[3]{1}}{1 + z \cdot z}}}}\]

  12. Final simplification6.5

    \[\leadsto \frac{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{y}}{\frac{x}{\frac{\sqrt[3]{1}}{1 + z \cdot z}}}\]

Reproduce

herbie shell --seed 2020043 
(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)))))