Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-1}{\frac{\frac{f}{f + n} \cdot \frac{f}{f + n} - \frac{n}{f + n} \cdot \frac{n}{f + n}}{\frac{f}{f + n} + \frac{n}{f + n}}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{-1}{\frac{\frac{f}{f + n} \cdot \frac{f}{f + n} - \frac{n}{f + n} \cdot \frac{n}{f + n}}{\frac{f}{f + n} + \frac{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)) * (f / (f + n))) - ((n / (f + n)) * (n / (f + n)))) / ((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 neg-mul-10.0

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

  4. Applied associate-/l*0.0

    \[\leadsto \color{blue}{\frac{-1}{\frac{f - n}{f + n}}}\]
  5. Using strategy rm

  6. Applied div-sub0.0

    \[\leadsto \frac{-1}{\color{blue}{\frac{f}{f + n} - \frac{n}{f + n}}}\]
  7. Using strategy rm

  8. Applied flip--0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020075 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))