Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{-1 + x} \cdot \sqrt[3]{-1 + x}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{-1 + x}} + \frac{x}{1 + x}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{-1 + x} \cdot \sqrt[3]{-1 + x}} \cdot \frac{\sqrt[3]{1}}{\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
 (+
  (*
   (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ -1.0 x)) (cbrt (+ -1.0 x))))
   (/ (cbrt 1.0) (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 (((cbrt(1.0) * cbrt(1.0)) / (cbrt(-1.0 + x) * cbrt(-1.0 + x))) * (cbrt(1.0) / 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_18180.0

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

  4. Applied add-cube-cbrt_binary64_18180.0

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

  5. Applied times-frac_binary64_17890.0

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

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

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