Average Error: 15.0 → 5.3
Time: 12.2s
Precision: 64
\[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\]
↓
\[\frac{x}{z \cdot \left(z + 1\right)} \cdot \frac{y}{z}\]
\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}
↓
\frac{x}{z \cdot \left(z + 1\right)} \cdot \frac{y}{z}
double f(double x, double y, double z) {
        double r244235 = x;
        double r244236 = y;
        double r244237 = r244235 * r244236;
        double r244238 = z;
        double r244239 = r244238 * r244238;
        double r244240 = 1.0;
        double r244241 = r244238 + r244240;
        double r244242 = r244239 * r244241;
        double r244243 = r244237 / r244242;
        return r244243;
}
↓
double f(double x, double y, double z) {
        double r244244 = x;
        double r244245 = z;
        double r244246 = 1.0;
        double r244247 = r244245 + r244246;
        double r244248 = r244245 * r244247;
        double r244249 = r244244 / r244248;
        double r244250 = y;
        double r244251 = r244250 / r244245;
        double r244252 = r244249 * r244251;
        return r244252;
}

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

Original15.0
Target4.6
Herbie5.3
\[\begin{array}{l} \mathbf{if}\;z \lt 249.6182814532307077115547144785523414612:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array}\]

Derivation

  1. Initial program 15.0

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

  3. Applied times-frac11.3

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

  5. Applied add-cube-cbrt11.7

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

  6. Applied times-frac6.7

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

  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 simplification5.3

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z 249.618281453230708) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1 z)) x) z))

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