Average Error: 14.4 → 0.1
Time: 11.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{-\frac{1 \cdot 2}{1 + x}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{-\frac{1 \cdot 2}{1 + x}}{x - 1}
double f(double x) {
        double r7229178 = 1.0;
        double r7229179 = x;
        double r7229180 = r7229179 + r7229178;
        double r7229181 = r7229178 / r7229180;
        double r7229182 = r7229179 - r7229178;
        double r7229183 = r7229178 / r7229182;
        double r7229184 = r7229181 - r7229183;
        return r7229184;
}
↓
double f(double x) {
        double r7229185 = 1.0;
        double r7229186 = 2.0;
        double r7229187 = r7229185 * r7229186;
        double r7229188 = x;
        double r7229189 = r7229185 + r7229188;
        double r7229190 = r7229187 / r7229189;
        double r7229191 = -r7229190;
        double r7229192 = r7229188 - r7229185;
        double r7229193 = r7229191 / r7229192;
        return r7229193;
}

Error

Bits error versus x

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Results

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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. Simplified13.7

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

  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

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

Reproduce

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