Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{1}{{\left({\left(-1 + x\right)}^{2}\right)}^{0.3333333333333333}}}{\sqrt[3]{-1 + x}} + \frac{x}{1 + x}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\frac{1}{{\left({\left(-1 + x\right)}^{2}\right)}^{0.3333333333333333}}}{\sqrt[3]{-1 + x}} + \frac{x}{1 + x}
(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (+
  (/ (/ 1.0 (pow (pow (+ -1.0 x) 2.0) 0.3333333333333333)) (cbrt (+ -1.0 x)))
  (/ x (+ 1.0 x))))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return ((1.0 / pow(pow((-1.0 + x), 2.0), 0.3333333333333333)) / cbrt(-1.0 + x)) + (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-cube-cbrt_binary64_21590.0

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

  4. Applied associate-/r*_binary64_20680.0

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

  5. Simplified0.0

    \[\leadsto \frac{\color{blue}{\frac{1}{\sqrt[3]{-1 + x} \cdot \sqrt[3]{-1 + x}}}}{\sqrt[3]{x - 1}} + \frac{x}{x + 1}\]
  6. Using strategy rm

  7. Applied pow1/3_binary64_220648.1

    \[\leadsto \frac{\frac{1}{\sqrt[3]{-1 + x} \cdot \color{blue}{{\left(-1 + x\right)}^{0.3333333333333333}}}}{\sqrt[3]{x - 1}} + \frac{x}{x + 1}\]

  8. Applied pow1/3_binary64_220648.1

    \[\leadsto \frac{\frac{1}{\color{blue}{{\left(-1 + x\right)}^{0.3333333333333333}} \cdot {\left(-1 + x\right)}^{0.3333333333333333}}}{\sqrt[3]{x - 1}} + \frac{x}{x + 1}\]

  9. Applied pow-prod-down_binary64_21950.0

    \[\leadsto \frac{\frac{1}{\color{blue}{{\left(\left(-1 + x\right) \cdot \left(-1 + x\right)\right)}^{0.3333333333333333}}}}{\sqrt[3]{x - 1}} + \frac{x}{x + 1}\]

  10. Simplified0.0

    \[\leadsto \frac{\frac{1}{{\color{blue}{\left({\left(\sqrt[3]{-1 + x}\right)}^{6}\right)}}^{0.3333333333333333}}}{\sqrt[3]{x - 1}} + \frac{x}{x + 1}\]
  11. Using strategy rm

  12. Applied pow1/3_binary64_220648.1

    \[\leadsto \frac{\frac{1}{{\left({\color{blue}{\left({\left(-1 + x\right)}^{0.3333333333333333}\right)}}^{6}\right)}^{0.3333333333333333}}}{\sqrt[3]{x - 1}} + \frac{x}{x + 1}\]

  13. Applied pow-pow_binary64_21960.0

    \[\leadsto \frac{\frac{1}{{\color{blue}{\left({\left(-1 + x\right)}^{\left(0.3333333333333333 \cdot 6\right)}\right)}}^{0.3333333333333333}}}{\sqrt[3]{x - 1}} + \frac{x}{x + 1}\]

  14. Simplified0.0

    \[\leadsto \frac{\frac{1}{{\left({\left(-1 + x\right)}^{\color{blue}{2}}\right)}^{0.3333333333333333}}}{\sqrt[3]{x - 1}} + \frac{x}{x + 1}\]

  15. Final simplification0.0

    \[\leadsto \frac{\frac{1}{{\left({\left(-1 + x\right)}^{2}\right)}^{0.3333333333333333}}}{\sqrt[3]{-1 + x}} + \frac{x}{1 + x}\]

Reproduce

herbie shell --seed 2020346 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))