Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-1}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{f - n}{f + n}\right)\right)}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{-1}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{f - n}{f + n}\right)\right)}
double code(double f, double n) {
	return ((double) (((double) -(((double) (f + n)))) / ((double) (f - n))));
}
↓
double code(double f, double n) {
	return ((double) (-1.0 / ((double) log1p(((double) expm1(((double) (((double) (f - n)) / ((double) (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 log1p-expm1-u0.0

    \[\leadsto \frac{-1}{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{f - n}{f + n}\right)\right)}}\]

  7. Final simplification0.0

    \[\leadsto \frac{-1}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{f - n}{f + n}\right)\right)}\]

Reproduce

herbie shell --seed 2020123 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))