Average Error: 6.3 → 0.1
Time: 9.1s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{y}{\frac{z}{y}}\]
x + \frac{y \cdot y}{z}
↓
x + \frac{y}{\frac{z}{y}}
double f(double x, double y, double z) {
        double r953819 = x;
        double r953820 = y;
        double r953821 = r953820 * r953820;
        double r953822 = z;
        double r953823 = r953821 / r953822;
        double r953824 = r953819 + r953823;
        return r953824;
}
↓
double f(double x, double y, double z) {
        double r953825 = x;
        double r953826 = y;
        double r953827 = z;
        double r953828 = r953827 / r953826;
        double r953829 = r953826 / r953828;
        double r953830 = r953825 + r953829;
        return r953830;
}

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

Original6.3
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.3

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

  3. Applied associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(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)))