Average Error: 14.4 → 0.1
Time: 14.8s
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 r4666244 = 1.0;
        double r4666245 = x;
        double r4666246 = r4666245 + r4666244;
        double r4666247 = r4666244 / r4666246;
        double r4666248 = r4666245 - r4666244;
        double r4666249 = r4666244 / r4666248;
        double r4666250 = r4666247 - r4666249;
        return r4666250;
}
↓
double f(double x) {
        double r4666251 = -2.0;
        double r4666252 = x;
        double r4666253 = 1.0;
        double r4666254 = r4666252 + r4666253;
        double r4666255 = r4666251 / r4666254;
        double r4666256 = r4666252 - r4666253;
        double r4666257 = r4666255 / r4666256;
        return r4666257;
}

Error

Bits error versus x

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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-sub13.8

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

  4. Simplified13.7

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

  5. Simplified13.7

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

  7. Applied difference-of-sqr--113.7

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

  8. Applied associate-/r*13.7

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019141 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))