Average Error: 14.6 → 0.1
Time: 17.6s
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 r4151068 = 1.0;
        double r4151069 = x;
        double r4151070 = r4151069 + r4151068;
        double r4151071 = r4151068 / r4151070;
        double r4151072 = r4151069 - r4151068;
        double r4151073 = r4151068 / r4151072;
        double r4151074 = r4151071 - r4151073;
        return r4151074;
}
↓
double f(double x) {
        double r4151075 = -2.0;
        double r4151076 = x;
        double r4151077 = 1.0;
        double r4151078 = r4151076 + r4151077;
        double r4151079 = r4151075 / r4151078;
        double r4151080 = r4151076 - r4151077;
        double r4151081 = r4151079 / r4151080;
        return r4151081;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

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

  3. Applied frac-sub14.0

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

  4. Taylor expanded around -inf 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 2019135 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))