Average Error: 6.3 → 0.1
Time: 2.1s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{y}{\frac{z}{y}}\]
x + \frac{y \cdot y}{z}
↓
x + \frac{y}{\frac{z}{y}}
double f(double x, double y, double z) {
        double r995122 = x;
        double r995123 = y;
        double r995124 = r995123 * r995123;
        double r995125 = z;
        double r995126 = r995124 / r995125;
        double r995127 = r995122 + r995126;
        return r995127;
}
↓
double f(double x, double y, double z) {
        double r995128 = x;
        double r995129 = y;
        double r995130 = z;
        double r995131 = r995130 / r995129;
        double r995132 = r995129 / r995131;
        double r995133 = r995128 + r995132;
        return r995133;
}

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

Original6.3
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.3

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

  3. Applied associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(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)))