Average Error: 14.3 → 0.4
Time: 29.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{-2}{-1 + x \cdot x}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{-2}{-1 + x \cdot x}
double f(double x) {
        double r5372480 = 1.0;
        double r5372481 = x;
        double r5372482 = r5372481 + r5372480;
        double r5372483 = r5372480 / r5372482;
        double r5372484 = r5372481 - r5372480;
        double r5372485 = r5372480 / r5372484;
        double r5372486 = r5372483 - r5372485;
        return r5372486;
}
↓
double f(double x) {
        double r5372487 = -2.0;
        double r5372488 = -1.0;
        double r5372489 = x;
        double r5372490 = r5372489 * r5372489;
        double r5372491 = r5372488 + r5372490;
        double r5372492 = r5372487 / r5372491;
        return r5372492;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

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

  5. Simplified13.7

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

  6. Taylor expanded around 0 0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019149 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))