Average Error: 6.2 → 0.1
Time: 7.2s
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 r583233 = x;
        double r583234 = y;
        double r583235 = r583234 * r583234;
        double r583236 = z;
        double r583237 = r583235 / r583236;
        double r583238 = r583233 + r583237;
        return r583238;
}
↓
double f(double x, double y, double z) {
        double r583239 = x;
        double r583240 = y;
        double r583241 = z;
        double r583242 = r583240 / r583241;
        double r583243 = r583240 * r583242;
        double r583244 = r583239 + r583243;
        return r583244;
}

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

Original6.2
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.2

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

  3. Applied *-un-lft-identity6.2

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

  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 2019297 
(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)))