Average Error: 14.2 → 0.1
Time: 38.4s
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 r5292180 = 1.0;
        double r5292181 = x;
        double r5292182 = r5292181 + r5292180;
        double r5292183 = r5292180 / r5292182;
        double r5292184 = r5292181 - r5292180;
        double r5292185 = r5292180 / r5292184;
        double r5292186 = r5292183 - r5292185;
        return r5292186;
}
↓
double f(double x) {
        double r5292187 = -2.0;
        double r5292188 = x;
        double r5292189 = 1.0;
        double r5292190 = r5292188 + r5292189;
        double r5292191 = r5292187 / r5292190;
        double r5292192 = r5292188 - r5292189;
        double r5292193 = r5292191 / r5292192;
        return r5292193;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 14.2

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

  3. Applied frac-sub13.6

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

  4. Simplified0.4

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

  5. Simplified0.4

    \[\leadsto \frac{-2}{\color{blue}{x \cdot x - 1}}\]
  6. Using strategy rm

  7. Applied difference-of-sqr-10.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))