Average Error: 14.8 → 1.1
Time: 38.9s
Precision: 64
\[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{z} \cdot \left(\frac{y}{z + 1} \cdot \frac{\sqrt[3]{x}}{z}\right)\]
\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}
↓
\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{z} \cdot \left(\frac{y}{z + 1} \cdot \frac{\sqrt[3]{x}}{z}\right)
double f(double x, double y, double z) {
        double r15919789 = x;
        double r15919790 = y;
        double r15919791 = r15919789 * r15919790;
        double r15919792 = z;
        double r15919793 = r15919792 * r15919792;
        double r15919794 = 1.0;
        double r15919795 = r15919792 + r15919794;
        double r15919796 = r15919793 * r15919795;
        double r15919797 = r15919791 / r15919796;
        return r15919797;
}
↓
double f(double x, double y, double z) {
        double r15919798 = x;
        double r15919799 = cbrt(r15919798);
        double r15919800 = r15919799 * r15919799;
        double r15919801 = z;
        double r15919802 = r15919800 / r15919801;
        double r15919803 = y;
        double r15919804 = 1.0;
        double r15919805 = r15919801 + r15919804;
        double r15919806 = r15919803 / r15919805;
        double r15919807 = r15919799 / r15919801;
        double r15919808 = r15919806 * r15919807;
        double r15919809 = r15919802 * r15919808;
        return r15919809;
}

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

Original14.8
Target4.2
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt 249.6182814532307077115547144785523414612:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array}\]

Derivation

  1. Initial program 14.8

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

  3. Applied times-frac10.7

    \[\leadsto \color{blue}{\frac{x}{z \cdot z} \cdot \frac{y}{z + 1}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt11.0

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

  6. Applied times-frac6.2

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

  7. Applied associate-*l*1.1

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

  8. Final simplification1.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"

  :herbie-target
  (if (< z 249.6182814532307) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1.0 z)) x) z))

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