Average Error: 14.4 → 0.1
Time: 15.8s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{1 + x}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{1 + x}}{x - 1}
double f(double x) {
        double r5434168 = 1.0;
        double r5434169 = x;
        double r5434170 = r5434169 + r5434168;
        double r5434171 = r5434168 / r5434170;
        double r5434172 = r5434169 - r5434168;
        double r5434173 = r5434168 / r5434172;
        double r5434174 = r5434171 - r5434173;
        return r5434174;
}
↓
double f(double x) {
        double r5434175 = 2.0;
        double r5434176 = -r5434175;
        double r5434177 = 1.0;
        double r5434178 = x;
        double r5434179 = r5434177 + r5434178;
        double r5434180 = r5434176 / r5434179;
        double r5434181 = r5434178 - r5434177;
        double r5434182 = r5434180 / r5434181;
        return r5434182;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

    \[\frac{1}{x + 1} - \frac{1}{x - 1}\]
  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. 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

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))