Average Error: 6.5 → 0.1
Time: 2.7s
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 r839601 = x;
        double r839602 = y;
        double r839603 = r839602 * r839602;
        double r839604 = z;
        double r839605 = r839603 / r839604;
        double r839606 = r839601 + r839605;
        return r839606;
}
↓
double f(double x, double y, double z) {
        double r839607 = y;
        double r839608 = z;
        double r839609 = r839607 / r839608;
        double r839610 = r839609 * r839607;
        double r839611 = x;
        double r839612 = r839610 + r839611;
        return r839612;
}

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

Original6.5
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.5

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

  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 2020020 +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)))