Average Error: 14.4 → 0.1
Time: 14.2s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{1 + x}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{1 + x}}{x - 1}
double f(double x) {
        double r5961449 = 1.0;
        double r5961450 = x;
        double r5961451 = r5961450 + r5961449;
        double r5961452 = r5961449 / r5961451;
        double r5961453 = r5961450 - r5961449;
        double r5961454 = r5961449 / r5961453;
        double r5961455 = r5961452 - r5961454;
        return r5961455;
}
↓
double f(double x) {
        double r5961456 = 2.0;
        double r5961457 = -r5961456;
        double r5961458 = 1.0;
        double r5961459 = x;
        double r5961460 = r5961458 + r5961459;
        double r5961461 = r5961457 / r5961460;
        double r5961462 = r5961459 - r5961458;
        double r5961463 = r5961461 / r5961462;
        return r5961463;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

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

  3. Applied frac-sub13.8

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

  4. Taylor expanded around 0 0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))