Average Error: 0.0 → 0.0
Time: 3.6s
Precision: binary64
\[\frac{x + y}{x - y}\]
↓
\[\frac{1}{\frac{x - y}{x + y}}\]
\frac{x + y}{x - y}
↓
\frac{1}{\frac{x - y}{x + y}}
(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))
↓
(FPCore (x y) :precision binary64 (/ 1.0 (/ (- x y) (+ x y))))
double code(double x, double y) {
	return (x + y) / (x - y);
}
↓
double code(double x, double y) {
	return 1.0 / ((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
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]

Derivation

  1. Initial program 0.0

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

  3. Applied *-un-lft-identity_binary64_50680.0

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

  4. Applied *-un-lft-identity_binary64_50680.0

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

  5. Applied distribute-lft-out_binary64_51120.0

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

  6. Applied associate-/l*_binary64_51320.0

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

  7. Final simplification0.0

    \[\leadsto \frac{1}{\frac{x - y}{x + y}}\]

Reproduce

herbie shell --seed 2020231 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

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