Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n} \]
↓
\[\frac{1}{\frac{n}{n + f} - \frac{f}{n + f}} \]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{1}{\frac{n}{n + f} - \frac{f}{n + f}}

(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n) :precision binary64 (/ 1.0 (- (/ n (+ n f)) (/ f (+ n f)))))
double code(double f, double n) {
	return -(f + n) / (f - n);
}
↓
double code(double f, double n) {
	return 1.0 / ((n / (n + f)) - (f / (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. Applied clear-num_binary640.0

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

  4. Applied div-sub_binary640.0

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

  5. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2022066 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))