Average Error: 14.2 → 0.4
Time: 14.6s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{-2}{\left(1 + x\right) \cdot \left(x - 1\right)}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{-2}{\left(1 + x\right) \cdot \left(x - 1\right)}
double f(double x) {
        double r4426575 = 1.0;
        double r4426576 = x;
        double r4426577 = r4426576 + r4426575;
        double r4426578 = r4426575 / r4426577;
        double r4426579 = r4426576 - r4426575;
        double r4426580 = r4426575 / r4426579;
        double r4426581 = r4426578 - r4426580;
        return r4426581;
}
↓
double f(double x) {
        double r4426582 = 2.0;
        double r4426583 = -r4426582;
        double r4426584 = 1.0;
        double r4426585 = x;
        double r4426586 = r4426584 + r4426585;
        double r4426587 = r4426585 - r4426584;
        double r4426588 = r4426586 * r4426587;
        double r4426589 = r4426583 / r4426588;
        return r4426589;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.2

    \[\frac{1}{x + 1} - \frac{1}{x - 1}\]
  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. Taylor expanded around 0 0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))