Average Error: 6.0 → 0.1
Time: 2.3s
Precision: binary64
\[x + \frac{y \cdot y}{z}\]
↓
\[x + \frac{y}{\frac{z}{y}}\]
x + \frac{y \cdot y}{z}
↓
x + \frac{y}{\frac{z}{y}}
(FPCore (x y z) :precision binary64 (+ x (/ (* y y) z)))
↓
(FPCore (x y z) :precision binary64 (+ x (/ y (/ z y))))
double code(double x, double y, double z) {
	return ((double) (x + (((double) (y * y)) / z)));
}
↓
double code(double x, double y, double z) {
	return ((double) (x + (y / (z / 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

Original6.0
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 2020198 
(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)))