Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(x + -1\right)}^{-3}} + \frac{x}{x + 1}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(x + -1\right)}^{-3}} + \frac{x}{x + 1}
(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (+ (cbrt (pow (+ x -1.0) -3.0)) (/ x (+ x 1.0))))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return cbrt(pow((x + -1.0), -3.0)) + (x / (x + 1.0));
}

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_52290.0

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

  4. Simplified0.0

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

  6. Applied inv-pow_binary64_52780.0

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

  7. Applied pow-pow_binary64_52650.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020354 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))