Average Error: 6.1 → 0.1
Time: 1.9s
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 r805684 = x;
        double r805685 = y;
        double r805686 = r805685 * r805685;
        double r805687 = z;
        double r805688 = r805686 / r805687;
        double r805689 = r805684 + r805688;
        return r805689;
}
↓
double f(double x, double y, double z) {
        double r805690 = x;
        double r805691 = y;
        double r805692 = z;
        double r805693 = r805692 / r805691;
        double r805694 = r805691 / r805693;
        double r805695 = r805690 + r805694;
        return r805695;
}

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

Original6.1
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.1

    \[x + \frac{y \cdot y}{z}\]
  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 2020081 
(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)))