Average Error: 13.6 → 0.1
Time: 27.0s
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 r5089225 = 1.0;
        double r5089226 = x;
        double r5089227 = r5089226 + r5089225;
        double r5089228 = r5089225 / r5089227;
        double r5089229 = r5089226 - r5089225;
        double r5089230 = r5089225 / r5089229;
        double r5089231 = r5089228 - r5089230;
        return r5089231;
}
↓
double f(double x) {
        double r5089232 = -2.0;
        double r5089233 = x;
        double r5089234 = 1.0;
        double r5089235 = r5089233 + r5089234;
        double r5089236 = r5089232 / r5089235;
        double r5089237 = r5089233 - r5089234;
        double r5089238 = r5089236 / r5089237;
        return r5089238;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.6

    \[\frac{1}{x + 1} - \frac{1}{x - 1}\]
  2. Using strategy rm

  3. Applied frac-sub13.0

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

  4. Simplified13.0

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

  5. Simplified13.0

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

  6. Taylor expanded around 0 0.5

    \[\leadsto \frac{\color{blue}{-2}}{x \cdot x + -1}\]
  7. Using strategy rm

  8. Applied difference-of-sqr--10.5

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

  9. Applied associate-/r*0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019142 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))