Average Error: 6.1 → 0.1
Time: 1.9s
Precision: binary64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{\frac{y}{z}}{\frac{1}{y}}\]
x + \frac{y \cdot y}{z}
↓
x + \frac{\frac{y}{z}}{\frac{1}{y}}
(FPCore (x y z) :precision binary64 (+ x (/ (* y y) z)))
↓
(FPCore (x y z) :precision binary64 (+ x (/ (/ y z) (/ 1.0 y))))
double code(double x, double y, double z) {
	return x + ((y * y) / z);
}
↓
double code(double x, double y, double z) {
	return x + ((y / z) / (1.0 / y));
}

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*_binary640.1

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

  5. Applied div-inv_binary640.1

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

  6. Applied associate-/r*_binary640.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020224 
(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)))