Average Error: 14.8 → 0.1
Time: 21.0s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{-\frac{2 \cdot 1}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{-\frac{2 \cdot 1}{x + 1}}{x - 1}
double f(double x) {
        double r5416193 = 1.0;
        double r5416194 = x;
        double r5416195 = r5416194 + r5416193;
        double r5416196 = r5416193 / r5416195;
        double r5416197 = r5416194 - r5416193;
        double r5416198 = r5416193 / r5416197;
        double r5416199 = r5416196 - r5416198;
        return r5416199;
}
↓
double f(double x) {
        double r5416200 = 2.0;
        double r5416201 = 1.0;
        double r5416202 = r5416200 * r5416201;
        double r5416203 = x;
        double r5416204 = r5416203 + r5416201;
        double r5416205 = r5416202 / r5416204;
        double r5416206 = -r5416205;
        double r5416207 = r5416203 - r5416201;
        double r5416208 = r5416206 / r5416207;
        return r5416208;
}

Error

Bits error versus x

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Results

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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. Simplified14.1

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

  5. Taylor expanded around 0 0.4

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

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))