Average Error: 0.0 → 0.0
Time: 3.7s
Precision: binary64
Cost: 576
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{1}{\frac{n - f}{n + f}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{1}{\frac{n - f}{n + f}}
(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n) :precision binary64 (/ 1.0 (/ (- n f) (+ n f))))
double code(double f, double n) {
	return -(f + n) / (f - n);
}
↓
double code(double f, double n) {
	return 1.0 / ((n - 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

Alternatives

Alternative 1
Error0.0
Cost448
\[\frac{n + f}{n - f}\]
Alternative 2
Error18.0
Cost1229
\[\begin{array}{l} \mathbf{if}\;n \leq -4.442686845312879 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq -4.107632137092257 \cdot 10^{-86} \lor \neg \left(n \leq -4.0647988135274745 \cdot 10^{-153}\right) \land n \leq 1.5476769801282746 \cdot 10^{-17}:\\ \;\;\;\;-1 - \frac{n}{f} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 3
Error18.4
Cost1348
\[\begin{array}{l} \mathbf{if}\;n \leq -1.6685747854616791 \cdot 10^{+84}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq -5.300995057569918 \cdot 10^{-85}:\\ \;\;\;\;-1\\ \mathbf{elif}\;n \leq -4.0647988135274745 \cdot 10^{-153}:\\ \;\;\;\;1\\ \mathbf{elif}\;n \leq 3.013434194537718 \cdot 10^{-17}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 4
Error31.6
Cost64
\[1\]

Error

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. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))