Average Error: 6.0 → 0.1
Time: 2.6s
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 r987066 = x;
        double r987067 = y;
        double r987068 = r987067 * r987067;
        double r987069 = z;
        double r987070 = r987068 / r987069;
        double r987071 = r987066 + r987070;
        return r987071;
}
↓
double f(double x, double y, double z) {
        double r987072 = x;
        double r987073 = y;
        double r987074 = z;
        double r987075 = r987074 / r987073;
        double r987076 = r987073 / r987075;
        double r987077 = r987072 + r987076;
        return r987077;
}

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

Original6.0
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.0

    \[x + \frac{y \cdot y}{z}\]
  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 2020083 
(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)))