Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\log \left(e^{\frac{x}{x + y} - \frac{1}{\frac{x + y}{y}}}\right)\]
\frac{x - y}{x + y}
↓
\log \left(e^{\frac{x}{x + y} - \frac{1}{\frac{x + y}{y}}}\right)
double code(double x, double y) {
	return ((x - y) / (x + y));
}
↓
double code(double x, double y) {
	return log(exp(((x / (x + y)) - (1.0 / ((x + y) / 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
\[\frac{x}{x + y} - \frac{y}{x + y}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.0

    \[\leadsto \frac{x}{x + y} - \color{blue}{\log \left(e^{\frac{y}{x + y}}\right)}\]

  6. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{x}{x + y}}\right)} - \log \left(e^{\frac{y}{x + y}}\right)\]

  7. Applied diff-log0.0

    \[\leadsto \color{blue}{\log \left(\frac{e^{\frac{x}{x + y}}}{e^{\frac{y}{x + y}}}\right)}\]

  8. Simplified0.0

    \[\leadsto \log \color{blue}{\left(e^{\frac{x}{x + y} - \frac{y}{x + y}}\right)}\]
  9. Using strategy rm

  10. Applied clear-num0.0

    \[\leadsto \log \left(e^{\frac{x}{x + y} - \color{blue}{\frac{1}{\frac{x + y}{y}}}}\right)\]

  11. Final simplification0.0

    \[\leadsto \log \left(e^{\frac{x}{x + y} - \frac{1}{\frac{x + y}{y}}}\right)\]

Reproduce

herbie shell --seed 2020075 +o rules:numerics
(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)))