Average Error: 13.9 → 0.1
Time: 43.3s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{2}{1 + x}}{1 - x}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{2}{1 + x}}{1 - x}
double f(double x) {
        double r4945491 = 1.0;
        double r4945492 = x;
        double r4945493 = r4945492 + r4945491;
        double r4945494 = r4945491 / r4945493;
        double r4945495 = r4945492 - r4945491;
        double r4945496 = r4945491 / r4945495;
        double r4945497 = r4945494 - r4945496;
        return r4945497;
}
↓
double f(double x) {
        double r4945498 = 2.0;
        double r4945499 = 1.0;
        double r4945500 = x;
        double r4945501 = r4945499 + r4945500;
        double r4945502 = r4945498 / r4945501;
        double r4945503 = r4945499 - r4945500;
        double r4945504 = r4945502 / r4945503;
        return r4945504;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.9

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

  3. Applied frac-sub13.3

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

  4. Simplified13.3

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

  5. Simplified13.3

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

  7. Applied frac-2neg13.3

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

  8. Simplified0.4

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

  9. Simplified0.4

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

  11. Applied *-un-lft-identity0.4

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

  12. Applied difference-of-squares0.4

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

  13. Applied associate-/r*0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019146 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))