Average Error: 6.1 → 0.1
Time: 2.7s
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 r771800 = x;
        double r771801 = y;
        double r771802 = r771801 * r771801;
        double r771803 = z;
        double r771804 = r771802 / r771803;
        double r771805 = r771800 + r771804;
        return r771805;
}
↓
double f(double x, double y, double z) {
        double r771806 = x;
        double r771807 = y;
        double r771808 = z;
        double r771809 = r771807 / r771808;
        double r771810 = r771807 * r771809;
        double r771811 = r771806 + r771810;
        return r771811;
}

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 *-un-lft-identity6.1

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

  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 1978988140 
(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)))