Average Error: 6.3 → 0.1
Time: 3.8s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[\frac{y}{z} \cdot y + x\]
x + \frac{y \cdot y}{z}
↓
\frac{y}{z} \cdot y + x
double f(double x, double y, double z) {
        double r886680 = x;
        double r886681 = y;
        double r886682 = r886681 * r886681;
        double r886683 = z;
        double r886684 = r886682 / r886683;
        double r886685 = r886680 + r886684;
        return r886685;
}
↓
double f(double x, double y, double z) {
        double r886686 = y;
        double r886687 = z;
        double r886688 = r886686 / r886687;
        double r886689 = r886688 * r886686;
        double r886690 = x;
        double r886691 = r886689 + r886690;
        return r886691;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z}, y, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))