Average Error: 0.0 → 0.0
Time: 4.7s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{1}{-1 + x}\right)}^{3}} + \frac{x}{1 + x}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{1}{-1 + x}\right)}^{3}} + \frac{x}{1 + x}
(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (+ (cbrt (pow (/ 1.0 (+ -1.0 x)) 3.0)) (/ x (+ 1.0 x))))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return cbrt(pow((1.0 / (-1.0 + x)), 3.0)) + (x / (1.0 + x));
}

Error

Bits error versus x

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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_48880.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2021007 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))