Average Error: 14.5 → 0.1
Time: 2.5s
Precision: binary64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{1}{1 + x} \cdot -2}{x + -1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{1}{1 + x} \cdot -2}{x + -1}
(FPCore (x) :precision binary64 (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))
↓
(FPCore (x) :precision binary64 (/ (* (/ 1.0 (+ 1.0 x)) -2.0) (+ x -1.0)))
double code(double x) {
	return (1.0 / (x + 1.0)) - (1.0 / (x - 1.0));
}
↓
double code(double x) {
	return ((1.0 / (1.0 + x)) * -2.0) / (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 14.5

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

  3. Applied frac-sub_binary6413.9

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

  4. Simplified0.4

    \[\leadsto \frac{\color{blue}{-2}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]

  5. Simplified0.4

    \[\leadsto \frac{-2}{\color{blue}{x \cdot x + -1}}\]
  6. Using strategy rm

  7. Applied difference-of-sqr--1_binary640.4

    \[\leadsto \frac{-2}{\color{blue}{\left(x + 1\right) \cdot \left(x - 1\right)}}\]

  8. Applied *-un-lft-identity_binary640.4

    \[\leadsto \frac{\color{blue}{1 \cdot -2}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]

  9. Applied times-frac_binary640.1

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

  10. Simplified0.1

    \[\leadsto \frac{1}{x + 1} \cdot \color{blue}{\frac{-2}{x + -1}}\]
  11. Using strategy rm

  12. Applied associate-*r/_binary640.1

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

  13. Final simplification0.1

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

Alternatives

Reproduce

herbie shell --seed 2021113 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))