Average Error: 15.5 → 0.0
Time: 1.2s
Precision: binary64
\[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} - \frac{0.5}{x}\]
\frac{x - y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} - \frac{0.5}{x}
(FPCore (x y) :precision binary64 (/ (- x y) (* (* x 2.0) y)))
↓
(FPCore (x y) :precision binary64 (- (/ 0.5 y) (/ 0.5 x)))
double code(double x, double y) {
	return (((double) (x - y)) / ((double) (((double) (x * 2.0)) * y)));
}
↓
double code(double x, double y) {
	return ((double) ((0.5 / y) - (0.5 / x)));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.5
Target0.0
Herbie0.0
\[\frac{0.5}{y} - \frac{0.5}{x}\]

Derivation

  1. Initial program 15.5

    \[\frac{x - y}{\left(x \cdot 2\right) \cdot y}\]

  2. Simplified15.4

    \[\leadsto \color{blue}{\frac{x - y}{x \cdot \left(y \cdot 2\right)}}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{1}{y} - 0.5 \cdot \frac{1}{x}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5}{y} - \frac{0.5}{x}}\]

  5. Final simplification0.0

    \[\leadsto \frac{0.5}{y} - \frac{0.5}{x}\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (- (/ 0.5 y) (/ 0.5 x))

  (/ (- x y) (* (* x 2.0) y)))