Average Error: 6.1 → 0.1
Time: 7.1s
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 r669865 = x;
        double r669866 = y;
        double r669867 = r669866 * r669866;
        double r669868 = z;
        double r669869 = r669867 / r669868;
        double r669870 = r669865 + r669869;
        return r669870;
}
↓
double f(double x, double y, double z) {
        double r669871 = x;
        double r669872 = y;
        double r669873 = z;
        double r669874 = r669873 / r669872;
        double r669875 = r669872 / r669874;
        double r669876 = r669871 + r669875;
        return r669876;
}

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 2019212 
(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)))