Average Error: 14.8 → 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 r3650334 = 1.0;
        double r3650335 = x;
        double r3650336 = r3650335 + r3650334;
        double r3650337 = r3650334 / r3650336;
        double r3650338 = r3650335 - r3650334;
        double r3650339 = r3650334 / r3650338;
        double r3650340 = r3650337 - r3650339;
        return r3650340;
}
↓
double f(double x) {
        double r3650341 = 2.0;
        double r3650342 = -r3650341;
        double r3650343 = x;
        double r3650344 = 1.0;
        double r3650345 = r3650343 + r3650344;
        double r3650346 = r3650342 / r3650345;
        double r3650347 = r3650343 - r3650344;
        double r3650348 = r3650346 / r3650347;
        return r3650348;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

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

  3. Applied frac-sub14.1

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

  4. Taylor expanded around 0 0.4

    \[\leadsto \frac{\color{blue}{-2}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
  5. 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 2019200 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))