Average Error: 14.4 → 0.1
Time: 12.2s
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 r5990435 = 1.0;
        double r5990436 = x;
        double r5990437 = r5990436 + r5990435;
        double r5990438 = r5990435 / r5990437;
        double r5990439 = r5990436 - r5990435;
        double r5990440 = r5990435 / r5990439;
        double r5990441 = r5990438 - r5990440;
        return r5990441;
}
↓
double f(double x) {
        double r5990442 = 2.0;
        double r5990443 = -r5990442;
        double r5990444 = 1.0;
        double r5990445 = x;
        double r5990446 = r5990444 + r5990445;
        double r5990447 = r5990443 / r5990446;
        double r5990448 = r5990445 - r5990444;
        double r5990449 = r5990447 / r5990448;
        return r5990449;
}

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))))