Average Error: 14.4 → 0.1
Time: 19.5s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{\left(-1\right) - 1}{\frac{x + 1}{1}}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{\left(-1\right) - 1}{\frac{x + 1}{1}}}{x - 1}
double f(double x) {
        double r85510 = 1.0;
        double r85511 = x;
        double r85512 = r85511 + r85510;
        double r85513 = r85510 / r85512;
        double r85514 = r85511 - r85510;
        double r85515 = r85510 / r85514;
        double r85516 = r85513 - r85515;
        return r85516;
}
↓
double f(double x) {
        double r85517 = 1.0;
        double r85518 = -r85517;
        double r85519 = r85518 - r85517;
        double r85520 = x;
        double r85521 = r85520 + r85517;
        double r85522 = r85521 / r85517;
        double r85523 = r85519 / r85522;
        double r85524 = r85520 - r85517;
        double r85525 = r85523 / r85524;
        return r85525;
}

Error

Bits error versus x

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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. Simplified0.3

    \[\leadsto \frac{\color{blue}{\left(\left(\left(-1\right) + 0\right) - 1\right) \cdot 1}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
  5. Using strategy rm

  6. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{\left(\left(\left(-1\right) + 0\right) - 1\right) \cdot 1}{x + 1}}{x - 1}}\]

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))