Average Error: 0.0 → 0.0
Time: 1.7min
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
Error16.7
Cost1348
\[\begin{array}{l} \mathbf{if}\;f \leq -6.063673780711014 \cdot 10^{-38}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq -1.290161142027101 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;f \leq -1.4575611998620783 \cdot 10^{-130}:\\ \;\;\;\;-1\\ \mathbf{elif}\;f \leq 1.488042170988726 \cdot 10^{-25}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array}\]
Alternative 2
Error32.9
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied pow1_binary640.0

    \[\leadsto \color{blue}{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{1}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity_binary640.0

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

  6. Applied *-un-lft-identity_binary640.0

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

  7. Applied times-frac_binary640.0

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

  8. Simplified0.0

    \[\leadsto {\left(\color{blue}{1} \cdot \frac{-\left(f + n\right)}{f - n}\right)}^{1}\]
  9. Using strategy rm

  10. Applied pow1_binary640.0

    \[\leadsto {\left(1 \cdot \color{blue}{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{1}}\right)}^{1}\]
  11. Using strategy rm

  12. Applied frac-2neg_binary640.0

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

  13. Simplified0.0

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

  14. Simplified0.0

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

  15. Simplified0.0

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

  16. Final simplification0.0

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

Reproduce

herbie shell --seed 2021045 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))