Average Error: 6.1 → 0.1
Time: 11.1s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{y}{z} \cdot y\]
x + \frac{y \cdot y}{z}
↓
x + \frac{y}{z} \cdot y
double f(double x, double y, double z) {
        double r40905279 = x;
        double r40905280 = y;
        double r40905281 = r40905280 * r40905280;
        double r40905282 = z;
        double r40905283 = r40905281 / r40905282;
        double r40905284 = r40905279 + r40905283;
        return r40905284;
}
↓
double f(double x, double y, double z) {
        double r40905285 = x;
        double r40905286 = y;
        double r40905287 = z;
        double r40905288 = r40905286 / r40905287;
        double r40905289 = r40905288 * r40905286;
        double r40905290 = r40905285 + r40905289;
        return r40905290;
}

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

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

Derivation

  1. Initial program 6.1

    \[x + \frac{y \cdot y}{z}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity6.1

    \[\leadsto x + \frac{y \cdot y}{\color{blue}{1 \cdot z}}\]

  4. Applied times-frac0.1

    \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{y}{z}}\]

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"

  :herbie-target
  (+ x (* y (/ y z)))

  (+ x (/ (* y y) z)))