Average Error: 6.4 → 0.1
Time: 5.4s
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 r49959968 = x;
        double r49959969 = y;
        double r49959970 = r49959969 * r49959969;
        double r49959971 = z;
        double r49959972 = r49959970 / r49959971;
        double r49959973 = r49959968 + r49959972;
        return r49959973;
}
↓
double f(double x, double y, double z) {
        double r49959974 = x;
        double r49959975 = y;
        double r49959976 = z;
        double r49959977 = r49959975 / r49959976;
        double r49959978 = r49959977 * r49959975;
        double r49959979 = r49959974 + r49959978;
        return r49959979;
}

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

Original6.4
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 *-un-lft-identity6.4

    \[\leadsto x + \frac{y \cdot y}{\color{blue}{1 \cdot z}}\]

  4. Applied times-frac0.1

    \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{y}{z}}\]

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(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)))