Average Error: 14.3 → 0.1
Time: 12.2s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{1}{x + 1} \cdot \frac{-2}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{1}{x + 1} \cdot \frac{-2}{x - 1}
double f(double x) {
        double r6958389 = 1.0;
        double r6958390 = x;
        double r6958391 = r6958390 + r6958389;
        double r6958392 = r6958389 / r6958391;
        double r6958393 = r6958390 - r6958389;
        double r6958394 = r6958389 / r6958393;
        double r6958395 = r6958392 - r6958394;
        return r6958395;
}
↓
double f(double x) {
        double r6958396 = 1.0;
        double r6958397 = x;
        double r6958398 = r6958397 + r6958396;
        double r6958399 = r6958396 / r6958398;
        double r6958400 = -2.0;
        double r6958401 = r6958397 - r6958396;
        double r6958402 = r6958400 / r6958401;
        double r6958403 = r6958399 * r6958402;
        return r6958403;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 14.3

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

  3. Applied frac-sub13.7

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

  4. Simplified13.7

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

  5. Taylor expanded around 0 0.4

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

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

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

  8. Applied times-frac0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))