Average Error: 15.5 → 0.0
Time: 3.6s
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

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

Alternatives

Alternative 1
Error16.3
Cost21056
\[\sqrt[3]{\frac{y + x}{y \cdot \left(x \cdot 2\right)}} \cdot \left(\sqrt[3]{\frac{y + x}{y \cdot \left(x \cdot 2\right)}} \cdot \sqrt[3]{\frac{y + x}{y \cdot \left(x \cdot 2\right)}}\right)\]
Alternative 2
Error9.2
Cost20288
\[\frac{\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}}{x \cdot 2} \cdot \frac{\sqrt[3]{y + x}}{y}\]
Alternative 3
Error39.9
Cost14016
\[\sqrt{\frac{y + x}{y \cdot \left(x \cdot 2\right)}} \cdot \sqrt{\frac{y + x}{y \cdot \left(x \cdot 2\right)}}\]
Alternative 4
Error38.4
Cost13632
\[\frac{\sqrt{y + x}}{\frac{y}{\frac{\sqrt{y + x}}{x \cdot 2}}}\]
Alternative 5
Error36.8
Cost13632
\[\frac{\sqrt{y + x}}{x \cdot 2} \cdot \frac{\sqrt{y + x}}{y}\]
Alternative 6
Error44.3
Cost13440
\[\sqrt[3]{\frac{{\left(\frac{y + x}{y \cdot x}\right)}^{3}}{8}}\]
Alternative 7
Error41.7
Cost13376
\[e^{\log \left(\frac{y + x}{y \cdot \left(x \cdot 2\right)}\right)}\]
Alternative 8
Error8.2
Cost704
\[\frac{1}{\frac{x \cdot 2}{\frac{y + x}{y}}}\]
Alternative 9
Error8.0
Cost576
\[\frac{\frac{y + x}{x \cdot 2}}{y}\]
Alternative 10
Error15.5
Cost576
\[\left(y + x\right) \cdot \frac{\frac{0.5}{x}}{y}\]
Alternative 11
Error8.3
Cost576
\[\frac{0.5}{x} \cdot \frac{y + x}{y}\]
Alternative 12
Error15.5
Cost576
\[\frac{y + x}{y \cdot \left(x \cdot 2\right)}\]
Alternative 13
Error31.3
Cost192
\[\frac{0.5}{y}\]
Alternative 14
Error31.8
Cost192
\[\frac{0.5}{x}\]
Alternative 15
Error61.9
Cost64
\[1\]
Alternative 16
Error62.3
Cost64
\[0\]
Alternative 17
Error61.9
Cost64
\[-1\]

Error

Derivation

  1. Initial program 15.5

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

  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 2021042 
(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)))