Average Error: 15.1 → 1.2
Time: 2.8s
Precision: binary64
\[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\]
↓
\[\frac{\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{z} \cdot y\right) \cdot \frac{\sqrt[3]{x}}{z}}{z + 1}\]
\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}
↓
\frac{\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{z} \cdot y\right) \cdot \frac{\sqrt[3]{x}}{z}}{z + 1}
(FPCore (x y z) :precision binary64 (/ (* x y) (* (* z z) (+ z 1.0))))
↓
(FPCore (x y z)
 :precision binary64
 (/ (* (* (/ (* (cbrt x) (cbrt x)) z) y) (/ (cbrt x) z)) (+ z 1.0)))
double code(double x, double y, double z) {
	return (x * y) / ((z * z) * (z + 1.0));
}
↓
double code(double x, double y, double z) {
	return ((((cbrt(x) * cbrt(x)) / z) * y) * (cbrt(x) / z)) / (z + 1.0);
}

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

Original15.1
Target4.1
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z < 249.6182814532307:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array}\]

Derivation

  1. Initial program 15.1

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

  3. Applied associate-/r*_binary6413.4

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

  4. Simplified11.4

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

  6. Applied add-cube-cbrt_binary6411.8

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

  7. Applied times-frac_binary646.5

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

  8. Applied associate-*r*_binary641.2

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

  9. Simplified1.2

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

  10. Final simplification1.2

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

Reproduce

herbie shell --seed 2020220 
(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) (+ 1.0 z)) x) z))

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