Average Error: 6.4 → 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 r751246 = x;
        double r751247 = y;
        double r751248 = r751247 * r751247;
        double r751249 = z;
        double r751250 = r751248 / r751249;
        double r751251 = r751246 + r751250;
        return r751251;
}
↓
double f(double x, double y, double z) {
        double r751252 = y;
        double r751253 = z;
        double r751254 = r751252 / r751253;
        double r751255 = r751254 * r751252;
        double r751256 = x;
        double r751257 = r751255 + r751256;
        return r751257;
}

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

Original6.4
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.4

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

  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 2020024 +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)))