Average Error: 0.0 → 0.0
Time: 3.9s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{\frac{1}{n - f}}{\frac{1}{n + f}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{\frac{1}{n - f}}{\frac{1}{n + f}}
(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n) :precision binary64 (/ (/ 1.0 (- n f)) (/ 1.0 (+ n f))))
double code(double f, double n) {
	return -(f + n) / (f - n);
}
↓
double code(double f, double n) {
	return (1.0 / (n - f)) / (1.0 / (n + f));
}

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{f + n}{n - f}}\]
  3. Using strategy rm

  4. Applied clear-num_binary640.0

    \[\leadsto \color{blue}{\frac{1}{\frac{n - f}{f + n}}}\]
  5. Using strategy rm

  6. Applied div-inv_binary640.2

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

  7. Applied associate-/r*_binary640.0

    \[\leadsto \color{blue}{\frac{\frac{1}{n - f}}{\frac{1}{f + n}}}\]

  8. Final simplification0.0

    \[\leadsto \frac{\frac{1}{n - f}}{\frac{1}{n + f}}\]

Reproduce

herbie shell --seed 2020262 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))