Average Error: 5.7 → 0.1
Time: 3.2s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{y}{\frac{z}{y}}\]
x + \frac{y \cdot y}{z}
↓
x + \frac{y}{\frac{z}{y}}
double f(double x, double y, double z) {
        double r786735 = x;
        double r786736 = y;
        double r786737 = r786736 * r786736;
        double r786738 = z;
        double r786739 = r786737 / r786738;
        double r786740 = r786735 + r786739;
        return r786740;
}
↓
double f(double x, double y, double z) {
        double r786741 = x;
        double r786742 = y;
        double r786743 = z;
        double r786744 = r786743 / r786742;
        double r786745 = r786742 / r786744;
        double r786746 = r786741 + r786745;
        return r786746;
}

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

Original5.7
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 5.7

    \[x + \frac{y \cdot y}{z}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

  :herbie-target
  (+ x (* y (/ y z)))

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