Average Error: 14.4 → 1.2
Time: 4.9s
Precision: 64
\[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\]
↓
\[\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{z} \cdot \left(\frac{\sqrt[3]{x}}{z} \cdot \frac{y}{z + 1}\right)\]
\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{\sqrt[3]{x}}{z} \cdot \frac{y}{z + 1}\right)
double f(double x, double y, double z) {
        double r378094 = x;
        double r378095 = y;
        double r378096 = r378094 * r378095;
        double r378097 = z;
        double r378098 = r378097 * r378097;
        double r378099 = 1.0;
        double r378100 = r378097 + r378099;
        double r378101 = r378098 * r378100;
        double r378102 = r378096 / r378101;
        return r378102;
}
↓
double f(double x, double y, double z) {
        double r378103 = x;
        double r378104 = cbrt(r378103);
        double r378105 = r378104 * r378104;
        double r378106 = z;
        double r378107 = r378105 / r378106;
        double r378108 = r378104 / r378106;
        double r378109 = y;
        double r378110 = 1.0;
        double r378111 = r378106 + r378110;
        double r378112 = r378109 / r378111;
        double r378113 = r378108 * r378112;
        double r378114 = r378107 * r378113;
        return r378114;
}

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

Original14.4
Target3.9
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt 249.6182814532307077115547144785523414612:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array}\]

Derivation

  1. Initial program 14.4

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

  3. Applied times-frac11.1

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

  5. Applied add-cube-cbrt11.5

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

  6. Applied times-frac6.4

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

  7. Applied associate-*l*1.2

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

  8. Final simplification1.2

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z 249.6182814532307) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1 z)) x) z))

  (/ (* x y) (* (* z z) (+ z 1))))