Average Error: 6.0 → 0.1
Time: 15.7s
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 r630175 = x;
        double r630176 = y;
        double r630177 = r630176 * r630176;
        double r630178 = z;
        double r630179 = r630177 / r630178;
        double r630180 = r630175 + r630179;
        return r630180;
}
↓
double f(double x, double y, double z) {
        double r630181 = x;
        double r630182 = y;
        double r630183 = z;
        double r630184 = r630182 / r630183;
        double r630185 = r630182 * r630184;
        double r630186 = r630181 + r630185;
        return r630186;
}

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

Original6.0
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.0

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

  3. Applied *-un-lft-identity6.0

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

  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 2019304 
(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)))