Average Error: 14.5 → 0.1
Time: 2.7s
Precision: binary64
\[\frac{1}{x + 1} - \frac{1}{x - 1} \]
↓
\[\frac{\frac{2}{1 + x}}{1 - x} \]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{2}{1 + x}}{1 - x}

(FPCore (x) :precision binary64 (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))
↓
(FPCore (x) :precision binary64 (/ (/ 2.0 (+ 1.0 x)) (- 1.0 x)))
double code(double x) {
	return (1.0 / (x + 1.0)) - (1.0 / (x - 1.0));
}
↓
double code(double x) {
	return (2.0 / (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 14.5

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

  3. Applied frac-sub_binary6414.0

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

  4. Applied frac-2neg_binary6414.0

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

  5. Simplified14.0

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

  6. Simplified14.0

    \[\leadsto \frac{\left(1 - x\right) + \left(x + 1\right)}{\color{blue}{\left(1 - x\right) \cdot \left(x + 1\right)}} \]
  7. Using strategy rm

  8. Applied add-cube-cbrt_binary6414.8

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

  9. Applied times-frac_binary6414.8

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

  10. Applied associate-*l/_binary6414.8

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

  11. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{2}{1 + x}}}{1 - x} \]

  12. Final simplification0.1

    \[\leadsto \frac{\frac{2}{1 + x}}{1 - x} \]

Reproduce

herbie shell --seed 2021211 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))