Average Error: 14.6 → 0.1
Time: 13.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{x - 1}}{1 + x}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{x - 1}}{1 + x}
double f(double x) {
        double r81524 = 1.0;
        double r81525 = x;
        double r81526 = r81525 + r81524;
        double r81527 = r81524 / r81526;
        double r81528 = r81525 - r81524;
        double r81529 = r81524 / r81528;
        double r81530 = r81527 - r81529;
        return r81530;
}
↓
double f(double x) {
        double r81531 = 2.0;
        double r81532 = -r81531;
        double r81533 = x;
        double r81534 = 1.0;
        double r81535 = r81533 - r81534;
        double r81536 = r81532 / r81535;
        double r81537 = r81534 + r81533;
        double r81538 = r81536 / r81537;
        return r81538;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

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

  3. Applied frac-sub14.1

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

  4. Simplified14.1

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

  5. Simplified14.1

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

  6. Taylor expanded around 0 0.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))