Average Error: 14.5 → 0.1
Time: 1.2m
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 r23058621 = 1.0;
        double r23058622 = x;
        double r23058623 = r23058622 + r23058621;
        double r23058624 = r23058621 / r23058623;
        double r23058625 = r23058622 - r23058621;
        double r23058626 = r23058621 / r23058625;
        double r23058627 = r23058624 - r23058626;
        return r23058627;
}
↓
double f(double x) {
        double r23058628 = -2.0;
        double r23058629 = x;
        double r23058630 = 1.0;
        double r23058631 = r23058629 + r23058630;
        double r23058632 = r23058628 / r23058631;
        double r23058633 = r23058629 - r23058630;
        double r23058634 = r23058632 / r23058633;
        return r23058634;
}

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-sub14.0

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

  4. Simplified0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019125 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))