Average Error: 14.7 → 0.1
Time: 3.8s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[1 \cdot \frac{\frac{-2}{x - 1}}{x + 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
1 \cdot \frac{\frac{-2}{x - 1}}{x + 1}
double code(double x) {
	return ((double) (((double) (1.0 / ((double) (x + 1.0)))) - ((double) (1.0 / ((double) (x - 1.0))))));
}
↓
double code(double x) {
	return ((double) (1.0 * ((double) (((double) (((double) -(2.0)) / ((double) (x - 1.0)))) / ((double) (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 14.7

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

  3. Applied frac-sub14.0

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

  4. Simplified14.0

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

  5. Simplified14.0

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

  7. Applied difference-of-squares14.0

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

  8. Applied times-frac14.0

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

  9. Taylor expanded around 0 0.1

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

  11. Applied div-inv0.1

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

  12. Applied associate-*l*0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020122 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))