Average Error: 6.5 → 0.1
Time: 2.2s
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 r862502 = x;
        double r862503 = y;
        double r862504 = r862503 * r862503;
        double r862505 = z;
        double r862506 = r862504 / r862505;
        double r862507 = r862502 + r862506;
        return r862507;
}
↓
double f(double x, double y, double z) {
        double r862508 = x;
        double r862509 = y;
        double r862510 = z;
        double r862511 = r862510 / r862509;
        double r862512 = r862509 / r862511;
        double r862513 = r862508 + r862512;
        return r862513;
}

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

Original6.5
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z}\]

Derivation

  1. Initial program 6.5

    \[x + \frac{y \cdot y}{z}\]
  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 2019353 
(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)))