Average Error: 6.2 → 0.1
Time: 10.6s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[y \cdot \frac{y}{z} + x\]
x + \frac{y \cdot y}{z}
↓
y \cdot \frac{y}{z} + x
double f(double x, double y, double z) {
        double r581230 = x;
        double r581231 = y;
        double r581232 = r581231 * r581231;
        double r581233 = z;
        double r581234 = r581232 / r581233;
        double r581235 = r581230 + r581234;
        return r581235;
}
↓
double f(double x, double y, double z) {
        double r581236 = y;
        double r581237 = z;
        double r581238 = r581236 / r581237;
        double r581239 = r581236 * r581238;
        double r581240 = x;
        double r581241 = r581239 + r581240;
        return r581241;
}

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

Original6.2
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.2

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

  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. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 +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)))