Average Error: 6.5 → 0.1
Time: 7.0s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + y \cdot \frac{y}{z}\]
x + \frac{y \cdot y}{z}
↓
x + y \cdot \frac{y}{z}
double f(double x, double y, double z) {
        double r564043 = x;
        double r564044 = y;
        double r564045 = r564044 * r564044;
        double r564046 = z;
        double r564047 = r564045 / r564046;
        double r564048 = r564043 + r564047;
        return r564048;
}
↓
double f(double x, double y, double z) {
        double r564049 = x;
        double r564050 = y;
        double r564051 = z;
        double r564052 = r564050 / r564051;
        double r564053 = r564050 * r564052;
        double r564054 = r564049 + r564053;
        return r564054;
}

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

Original6.5
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.5

    \[x + \frac{y \cdot y}{z}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity6.5

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

  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

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

Reproduce

herbie shell --seed 2019235 
(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)))