Average Error: 0.0 → 0.0
Time: 1.7s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n} \]
↓
\[\mathsf{log1p}\left(e^{\frac{f + n}{n - f}} - 1\right) \]
\frac{-\left(f + n\right)}{f - n}
↓
\mathsf{log1p}\left(e^{\frac{f + n}{n - f}} - 1\right)

(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n) :precision binary64 (log1p (- (exp (/ (+ f n) (- n f))) 1.0)))
double code(double f, double n) {
	return -(f + n) / (f - n);
}
↓
double code(double f, double n) {
	return log1p(exp((f + n) / (n - f)) - 1.0);
}

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. Simplified0.0

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

  3. Applied log1p-expm1-u_binary640.0

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

  4. Applied expm1-udef_binary640.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022068 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))