Average Error: 0.0 → 0.0
Time: 2.9s
Precision: binary64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{{\left(\frac{f + n}{n - f}\right)}^{2}} \cdot \sqrt[3]{\frac{f + n}{n - f}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{{\left(\frac{f + n}{n - f}\right)}^{2}} \cdot \sqrt[3]{\frac{f + n}{n - f}}
(FPCore (f n) :precision binary64 (/ (- (+ f n)) (- f n)))
↓
(FPCore (f n)
 :precision binary64
 (* (cbrt (pow (/ (+ f n) (- n f)) 2.0)) (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) pow((((double) (f + n)) / ((double) (n - f))), 2.0)))) * ((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 Error: 0.0 bits

    \[\frac{-\left(f + n\right)}{f - n}\]

  2. SimplifiedError: 0.0 bits

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

  4. Applied add-cbrt-cubeError: 41.6 bits

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

  5. Applied add-cbrt-cubeError: 42.3 bits

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

  6. Applied cbrt-undivError: 42.3 bits

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

  7. SimplifiedError: 0.0 bits

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

  9. Applied add-cube-cbrtError: 0.1 bits

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

  10. Applied unpow-prod-downError: 0.1 bits

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

  11. Applied cbrt-prodError: 0.1 bits

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

  12. SimplifiedError: 0.0 bits

    \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{f + n}{n - f}\right)}^{2}}} \cdot \sqrt[3]{{\left(\sqrt[3]{\frac{f + n}{n - f}}\right)}^{3}}\]

  13. SimplifiedError: 0.0 bits

    \[\leadsto \sqrt[3]{{\left(\frac{f + n}{n - f}\right)}^{2}} \cdot \color{blue}{\sqrt[3]{\frac{f + n}{n - f}}}\]

  14. Final simplificationError: 0.0 bits

    \[\leadsto \sqrt[3]{{\left(\frac{f + n}{n - f}\right)}^{2}} \cdot \sqrt[3]{\frac{f + n}{n - f}}\]

Reproduce

herbie shell --seed 2020203 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))