Average Error: 14.6 → 2.7
Time: 13.3s
Precision: 64
\[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\]
↓
\[\frac{1}{1 + z} \cdot \left(\frac{y}{z} \cdot \frac{x}{z}\right)\]
\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}
↓
\frac{1}{1 + z} \cdot \left(\frac{y}{z} \cdot \frac{x}{z}\right)
double f(double x, double y, double z) {
        double r259005 = x;
        double r259006 = y;
        double r259007 = r259005 * r259006;
        double r259008 = z;
        double r259009 = r259008 * r259008;
        double r259010 = 1.0;
        double r259011 = r259008 + r259010;
        double r259012 = r259009 * r259011;
        double r259013 = r259007 / r259012;
        return r259013;
}
↓
double f(double x, double y, double z) {
        double r259014 = 1.0;
        double r259015 = 1.0;
        double r259016 = z;
        double r259017 = r259015 + r259016;
        double r259018 = r259014 / r259017;
        double r259019 = y;
        double r259020 = r259019 / r259016;
        double r259021 = x;
        double r259022 = r259021 / r259016;
        double r259023 = r259020 * r259022;
        double r259024 = r259018 * r259023;
        return r259024;
}

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

Original14.6
Target4.1
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;z \lt 249.6182814532307077115547144785523414612:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array}\]

Derivation

  1. Initial program 14.6

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

  2. Simplified3.1

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

  4. Applied associate-*r/2.7

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

  5. Simplified2.7

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

  7. Applied div-inv2.7

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

  8. Simplified2.7

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

  9. Final simplification2.7

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

Reproduce

herbie shell --seed 2019196 
(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))))