Average Error: 29.2 → 29.3
Time: 7.6s
Precision: binary64
\[\frac{x}{x + 1} - \frac{x + 1}{x - 1}\]
↓
\[x \cdot \frac{1}{1 + x} - \frac{1 + x}{x - 1}\]
\frac{x}{x + 1} - \frac{x + 1}{x - 1}
↓
x \cdot \frac{1}{1 + x} - \frac{1 + x}{x - 1}
(FPCore (x) :precision binary64 (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (- (* x (/ 1.0 (+ 1.0 x))) (/ (+ 1.0 x) (- x 1.0))))
double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}
↓
double code(double x) {
	return (x * (1.0 / (1.0 + x))) - ((1.0 + x) / (x - 1.0));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.2

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

  3. Applied flip-+_binary6429.8

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

  4. Applied associate-/r/_binary6429.8

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

  5. Simplified29.8

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

  7. Applied difference-of-sqr--1_binary6429.8

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

  8. Applied *-un-lft-identity_binary6429.8

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

  9. Applied times-frac_binary6429.3

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

  10. Applied associate-*l*_binary6429.3

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

  11. Simplified29.3

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

  12. Final simplification29.3

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

Reproduce

herbie shell --seed 2020268 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))