Average Error: 0.0 → 0.1
Time: 2.4s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\frac{f + n}{n - f}} \cdot \left(\sqrt[3]{\frac{f + n}{n - f}} \cdot \sqrt[3]{\frac{f + n}{n - f}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\frac{f + n}{n - f}} \cdot \left(\sqrt[3]{\frac{f + n}{n - f}} \cdot \sqrt[3]{\frac{f + n}{n - f}}\right)
(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n)
 :precision binary64
 (*
  (cbrt (/ (+ f n) (- n f)))
  (* (cbrt (/ (+ f n) (- n f))) (cbrt (/ (+ f n) (- n f))))))
double code(double f, double n) {
	return (((double) -(((double) (f + n)))) / ((double) (f - n)));
}
↓
double code(double f, double n) {
	return ((double) (((double) cbrt((((double) (f + n)) / ((double) (n - f))))) * ((double) (((double) cbrt((((double) (f + n)) / ((double) (n - f))))) * ((double) cbrt((((double) (f + n)) / ((double) (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. Using strategy rm

  4. Applied add-cube-cbrt_binary640.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020205 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))