Average Error: 0.0 → 0.0
Time: 2.2s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n} \]
↓
\[\log \left(e^{\frac{f + n}{n - f}}\right) \]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(e^{\frac{f + n}{n - f}}\right)

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

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 add-cbrt-cube_binary640.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{f + n}{n - f} \cdot \frac{f + n}{n - f}\right) \cdot \frac{f + n}{n - f}}} \]

  4. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{f + n}{n - f}\right)}^{3}}} \]

  5. Applied add-log-exp_binary640.0

    \[\leadsto \color{blue}{\log \left(e^{\sqrt[3]{{\left(\frac{f + n}{n - f}\right)}^{3}}}\right)} \]

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2022055 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))