Average Error: 0.0 → 0.0
Time: 1.8min
Precision: binary64
Cost: 448
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{f + n}{n - f}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{f + n}{n - f}
(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n) :precision binary64 (/ (+ f n) (- n f)))
double code(double f, double n) {
	return -(f + n) / (f - n);
}
↓
double code(double f, double n) {
	return (f + n) / (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

Alternatives

Alternative 1
Error16.1
Cost776
\[\begin{array}{l} \mathbf{if}\;n \leq -1.0407031435936754 \cdot 10^{-58} \lor \neg \left(n \leq 2.09220074073275 \cdot 10^{+32}\right):\\ \;\;\;\;1 + \frac{f + f}{n}\\ \mathbf{else}:\\ \;\;\;\;-1 - 2 \cdot \frac{n}{f}\\ \end{array}\]
Alternative 2
Error16.5
Cost1090
\[\begin{array}{l} \mathbf{if}\;n \leq -2.2610510955328207 \cdot 10^{-57}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq 2.09220074073275 \cdot 10^{+32}:\\ \;\;\;\;-1 - 2 \cdot \frac{n}{f}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 3
Error16.8
Cost706
\[\begin{array}{l} \mathbf{if}\;n \leq -1.4025444141795704 \cdot 10^{-59}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq 1.8095093683436817 \cdot 10^{+32}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 4
Error31.8
Cost64
\[-1\]

Error

Time

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 pow1_binary640.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2021040 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))