Average Error: 6.1 → 0.1
Time: 2.1s
Precision: 64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{1}{\frac{\frac{z}{y}}{y}}\]
x + \frac{y \cdot y}{z}
↓
x + \frac{1}{\frac{\frac{z}{y}}{y}}
double f(double x, double y, double z) {
        double r798213 = x;
        double r798214 = y;
        double r798215 = r798214 * r798214;
        double r798216 = z;
        double r798217 = r798215 / r798216;
        double r798218 = r798213 + r798217;
        return r798218;
}
↓
double f(double x, double y, double z) {
        double r798219 = x;
        double r798220 = 1.0;
        double r798221 = z;
        double r798222 = y;
        double r798223 = r798221 / r798222;
        double r798224 = r798223 / r798222;
        double r798225 = r798220 / r798224;
        double r798226 = r798219 + r798225;
        return r798226;
}

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 associate-/l*0.1

    \[\leadsto x + \color{blue}{\frac{y}{\frac{z}{y}}}\]
  4. Using strategy rm

  5. Applied clear-num0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020049 
(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)))