Average Error: 6.1 → 0.1
Time: 3.0s
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 r855498 = x;
        double r855499 = y;
        double r855500 = r855499 * r855499;
        double r855501 = z;
        double r855502 = r855500 / r855501;
        double r855503 = r855498 + r855502;
        return r855503;
}
↓
double f(double x, double y, double z) {
        double r855504 = x;
        double r855505 = y;
        double r855506 = z;
        double r855507 = r855506 / r855505;
        double r855508 = r855505 / r855507;
        double r855509 = r855504 + r855508;
        return r855509;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020081 +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)))