Average Error: 0.0 → 0.0
Time: 3.6s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{1}{\sqrt[3]{{\left(\frac{n - f}{n + f}\right)}^{3}}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{1}{\sqrt[3]{{\left(\frac{n - f}{n + f}\right)}^{3}}}
(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n) :precision binary64 (/ 1.0 (cbrt (pow (/ (- n f) (+ n f)) 3.0))))
double code(double f, double n) {
	return -(f + n) / (f - n);
}
↓
double code(double f, double n) {
	return 1.0 / cbrt(pow(((n - f) / (n + f)), 3.0));
}

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. Using strategy rm

  4. Applied clear-num_binary640.0

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

  6. Applied add-cbrt-cube_binary640.0

    \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{\left(\frac{n - f}{f + n} \cdot \frac{n - f}{f + n}\right) \cdot \frac{n - f}{f + n}}}}\]

  7. Simplified0.0

    \[\leadsto \frac{1}{\sqrt[3]{\color{blue}{{\left(\frac{n - f}{n + f}\right)}^{3}}}}\]

  8. Final simplification0.0

    \[\leadsto \frac{1}{\sqrt[3]{{\left(\frac{n - f}{n + f}\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020281 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))