Average Error: 0.0 → 0.0
Time: 3.2s
Precision: binary64
Cost: 448
\[\frac{x - y}{x + y}\]
↓
\[\frac{x - y}{x + y}\]
\frac{x - y}{x + y}
↓
\frac{x - y}{x + y}
(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
double code(double x, double y) {
	return (x - y) / (x + y);
}
↓
double code(double x, double y) {
	return (x - y) / (x + y);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y}\]

Alternatives

Alternative 1
Error0.1
Cost39872
\[\frac{\sqrt[3]{x - y} \cdot \sqrt[3]{x - y}}{\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}} \cdot \frac{\sqrt[3]{x - y}}{\sqrt[3]{x + y}}\]
Alternative 2
Error0.1
Cost20672
\[\sqrt[3]{\frac{x - y}{x + y}} \cdot \left(\sqrt[3]{\frac{x - y}{x + y}} \cdot \sqrt[3]{\frac{x - y}{x + y}}\right)\]
Alternative 3
Error42.6
Cost14144
\[\frac{x - y}{{x}^{3} + {y}^{3}} \cdot \left(x \cdot x + \left(y \cdot y - x \cdot y\right)\right)\]
Alternative 4
Error42.6
Cost14016
\[\frac{{x}^{3} - {y}^{3}}{\left(x + y\right) \cdot \left(x \cdot x + y \cdot \left(x + y\right)\right)}\]
Alternative 5
Error31.6
Cost13632
\[\frac{1}{\sqrt{x + y}} \cdot \frac{x - y}{\sqrt{x + y}}\]
Alternative 6
Error0.0
Cost13312
\[\sqrt[3]{{\left(\frac{x - y}{x + y}\right)}^{3}}\]
Alternative 7
Error0.0
Cost704
\[\frac{x}{x + y} - \frac{y}{x + y}\]
Alternative 8
Error0.0
Cost576
\[\frac{1}{\frac{x + y}{x - y}}\]
Alternative 9
Error31.4
Cost448
\[1 - 2 \cdot \frac{y}{x}\]
Alternative 10
Error31.6
Cost448
\[-1 + 2 \cdot \frac{x}{y}\]
Alternative 11
Error32.0
Cost64
\[1\]
Alternative 12
Error32.3
Cost64
\[-1\]
Alternative 13
Error62.0
Cost64
\[0\]

Error

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y}\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021042 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

  (/ (- x y) (+ x y)))