Average Error: 6.4 → 0.1
Time: 15.5s
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 r618857 = x;
        double r618858 = y;
        double r618859 = r618858 * r618858;
        double r618860 = z;
        double r618861 = r618859 / r618860;
        double r618862 = r618857 + r618861;
        return r618862;
}
↓
double f(double x, double y, double z) {
        double r618863 = x;
        double r618864 = y;
        double r618865 = z;
        double r618866 = r618865 / r618864;
        double r618867 = r618864 / r618866;
        double r618868 = r618863 + r618867;
        return r618868;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original6.4
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.4

    \[x + \frac{y \cdot y}{z}\]
  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 2019303 +o rules:numerics
(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)))