Average Error: 14.8 → 2.8
Time: 14.3s
Precision: 64
\[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\]
↓
\[\frac{1}{\frac{z}{\frac{x}{z} \cdot \frac{y}{z + 1}}}\]
\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}
↓
\frac{1}{\frac{z}{\frac{x}{z} \cdot \frac{y}{z + 1}}}
double f(double x, double y, double z) {
        double r260613 = x;
        double r260614 = y;
        double r260615 = r260613 * r260614;
        double r260616 = z;
        double r260617 = r260616 * r260616;
        double r260618 = 1.0;
        double r260619 = r260616 + r260618;
        double r260620 = r260617 * r260619;
        double r260621 = r260615 / r260620;
        return r260621;
}
↓
double f(double x, double y, double z) {
        double r260622 = 1.0;
        double r260623 = z;
        double r260624 = x;
        double r260625 = r260624 / r260623;
        double r260626 = y;
        double r260627 = 1.0;
        double r260628 = r260623 + r260627;
        double r260629 = r260626 / r260628;
        double r260630 = r260625 * r260629;
        double r260631 = r260623 / r260630;
        double r260632 = r260622 / r260631;
        return r260632;
}

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
Target3.8
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;z \lt 249.6182814532307077115547144785523414612:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array}\]

Derivation

  1. Initial program 14.8

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

  2. Simplified3.1

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

  4. Applied pow13.1

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

  5. Applied pow13.1

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

  6. Applied pow-prod-down3.1

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

  7. Simplified4.7

    \[\leadsto {\color{blue}{\left(\frac{y \cdot \frac{x}{z \cdot \left(z + 1\right)}}{z}\right)}}^{1}\]
  8. Using strategy rm

  9. Applied pow14.7

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

  10. Applied pow14.7

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

  11. Applied pow-prod-down4.7

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

  12. Simplified3.1

    \[\leadsto {\left(\frac{{\color{blue}{\left(\frac{y \cdot \frac{x}{z}}{1 + z}\right)}}^{1}}{z}\right)}^{1}\]
  13. Using strategy rm

  14. Applied clear-num3.4

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

  15. Simplified2.8

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

  16. Final simplification2.8

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

Reproduce

herbie shell --seed 2019194 
(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))))