Average Error: 14.5 → 0.1
Time: 4.3m
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{x + -1}}{x + 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{x + -1}}{x + 1}
double f(double x) {
        double r18991327 = 1.0;
        double r18991328 = x;
        double r18991329 = r18991328 + r18991327;
        double r18991330 = r18991327 / r18991329;
        double r18991331 = r18991328 - r18991327;
        double r18991332 = r18991327 / r18991331;
        double r18991333 = r18991330 - r18991332;
        return r18991333;
}
↓
double f(double x) {
        double r18991334 = -2.0;
        double r18991335 = x;
        double r18991336 = -1.0;
        double r18991337 = r18991335 + r18991336;
        double r18991338 = r18991334 / r18991337;
        double r18991339 = 1.0;
        double r18991340 = r18991335 + r18991339;
        double r18991341 = r18991338 / r18991340;
        return r18991341;
}

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-sub13.9

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

  4. Simplified0.4

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

  5. Simplified0.4

    \[\leadsto \frac{-2}{\color{blue}{(x \cdot \left(x + -1\right) + \left(x + -1\right))_*}}\]
  6. Using strategy rm

  7. Applied fma-udef0.4

    \[\leadsto \frac{-2}{\color{blue}{x \cdot \left(x + -1\right) + \left(x + -1\right)}}\]
  8. Using strategy rm

  9. Applied *-un-lft-identity0.4

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

  10. Applied distribute-rgt-out0.4

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

  11. Applied associate-/r*0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))