Average Error: 0.0 → 0.0
Time: 2.3s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right) \cdot \left(\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{1 + x}\right)\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right) \cdot \left(\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{1 + x}\right)\right)}
(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (cbrt
  (*
   (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))
   (*
    (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))
    (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))))))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return cbrt(((1.0 / (x - 1.0)) + (x / (1.0 + x))) * (((1.0 / (x - 1.0)) + (x / (1.0 + x))) * ((1.0 / (x - 1.0)) + (x / (1.0 + x)))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube_binary64_25010.0

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

  4. Final simplification0.0

    \[\leadsto \sqrt[3]{\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right) \cdot \left(\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{1 + x}\right)\right)}\]

Reproduce

herbie shell --seed 2021013 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))