Average Error: 6.1 → 0.1
Time: 9.5s
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 r41730536 = x;
        double r41730537 = y;
        double r41730538 = r41730537 * r41730537;
        double r41730539 = z;
        double r41730540 = r41730538 / r41730539;
        double r41730541 = r41730536 + r41730540;
        return r41730541;
}
↓
double f(double x, double y, double z) {
        double r41730542 = x;
        double r41730543 = y;
        double r41730544 = z;
        double r41730545 = r41730543 / r41730544;
        double r41730546 = r41730545 * r41730543;
        double r41730547 = r41730542 + r41730546;
        return r41730547;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 2019174 
(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)))