Average Error: 14.3 → 0.1
Time: 12.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{1}{x + 1} \cdot \frac{-2}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{1}{x + 1} \cdot \frac{-2}{x - 1}
double f(double x) {
        double r6810048 = 1.0;
        double r6810049 = x;
        double r6810050 = r6810049 + r6810048;
        double r6810051 = r6810048 / r6810050;
        double r6810052 = r6810049 - r6810048;
        double r6810053 = r6810048 / r6810052;
        double r6810054 = r6810051 - r6810053;
        return r6810054;
}
↓
double f(double x) {
        double r6810055 = 1.0;
        double r6810056 = x;
        double r6810057 = r6810056 + r6810055;
        double r6810058 = r6810055 / r6810057;
        double r6810059 = -2.0;
        double r6810060 = r6810056 - r6810055;
        double r6810061 = r6810059 / r6810060;
        double r6810062 = r6810058 * r6810061;
        return r6810062;
}

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

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

  5. Taylor expanded around 0 0.4

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

  7. Applied *-un-lft-identity0.4

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

  8. Applied times-frac0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))