Average Error: 5.8 → 0.1
Time: 10.3s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{y}{z} \cdot y\]
x + \frac{y \cdot y}{z}
↓
x + \frac{y}{z} \cdot y
double f(double x, double y, double z) {
        double r43121711 = x;
        double r43121712 = y;
        double r43121713 = r43121712 * r43121712;
        double r43121714 = z;
        double r43121715 = r43121713 / r43121714;
        double r43121716 = r43121711 + r43121715;
        return r43121716;
}
↓
double f(double x, double y, double z) {
        double r43121717 = x;
        double r43121718 = y;
        double r43121719 = z;
        double r43121720 = r43121718 / r43121719;
        double r43121721 = r43121720 * r43121718;
        double r43121722 = r43121717 + r43121721;
        return r43121722;
}

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

Original5.8
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 5.8

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

  2. Taylor expanded around 0 5.8

    \[\leadsto x + \color{blue}{\frac{{y}^{2}}{z}}\]

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"

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

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