Average Error: 15.2 → 0.0
Time: 1.9s
Precision: binary64
Cost: 448
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} + \frac{0.5}{x}\]
\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 (x + y) / ((x * 2.0) * y);
}
↓
double code(double x, double y) {
	return (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

Original15.2
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Alternatives

Alternative 1
Error15.8
Cost520
\[\begin{array}{l} \mathbf{if}\;x \leq -200.11380986298124 \lor \neg \left(x \leq 1.206911868784268 \cdot 10^{-44}\right):\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array}\]
Alternative 2
Error32.1
Cost192
\[\frac{0.5}{y}\]
Alternative 3
Error61.9
Cost64
\[-1\]
Alternative 4
Error61.9
Cost64
\[1\]

Error

Derivation

  1. Initial program 15.2

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  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 2021044 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

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

  (/ (+ x y) (* (* x 2.0) y)))