Average Error: 5.9 → 0.1
Time: 3.3s
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 r880753 = x;
        double r880754 = y;
        double r880755 = r880754 * r880754;
        double r880756 = z;
        double r880757 = r880755 / r880756;
        double r880758 = r880753 + r880757;
        return r880758;
}
↓
double f(double x, double y, double z) {
        double r880759 = y;
        double r880760 = z;
        double r880761 = r880759 / r880760;
        double r880762 = r880761 * r880759;
        double r880763 = x;
        double r880764 = r880762 + r880763;
        return r880764;
}

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

Original5.9
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 5.9

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

  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 2020047 +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)))