Average Error: 6.1 → 0.1
Time: 7.8s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{y}{z} \cdot y\]
x + \frac{y \cdot y}{z}
↓
x + \frac{y}{z} \cdot y
double f(double x, double y, double z) {
        double r696550 = x;
        double r696551 = y;
        double r696552 = r696551 * r696551;
        double r696553 = z;
        double r696554 = r696552 / r696553;
        double r696555 = r696550 + r696554;
        return r696555;
}
↓
double f(double x, double y, double z) {
        double r696556 = x;
        double r696557 = y;
        double r696558 = z;
        double r696559 = r696557 / r696558;
        double r696560 = r696559 * r696557;
        double r696561 = r696556 + r696560;
        return r696561;
}

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

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"

  :herbie-target
  (+ x (* y (/ y z)))

  (+ x (/ (* y y) z)))