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

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. Using strategy rm

  3. Applied clear-num_binary640.0

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

  5. Applied div-sub_binary640.0

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

  7. Applied neg-mul-1_binary640.0

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

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

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

  9. Applied times-frac_binary640.0

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

  10. Applied neg-mul-1_binary640.0

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

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

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

  12. Applied times-frac_binary640.0

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

  13. Applied distribute-lft-out--_binary640.0

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

  14. Applied associate-/r*_binary640.0

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

  15. Simplified0.0

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

  16. Final simplification0.0

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

Reproduce

herbie shell --seed 2020292 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))