Average Error: 6.2 → 0.1
Time: 2.3s
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 r764133 = x;
        double r764134 = y;
        double r764135 = r764134 * r764134;
        double r764136 = z;
        double r764137 = r764135 / r764136;
        double r764138 = r764133 + r764137;
        return r764138;
}
↓
double f(double x, double y, double z) {
        double r764139 = x;
        double r764140 = y;
        double r764141 = z;
        double r764142 = r764141 / r764140;
        double r764143 = r764140 / r764142;
        double r764144 = r764139 + r764143;
        return r764144;
}

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

Original6.2
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.2

    \[x + \frac{y \cdot y}{z}\]
  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 2020025 
(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)))