Average Error: 14.3 → 0.1
Time: 3.2s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[1 \cdot \frac{\frac{-2}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
1 \cdot \frac{\frac{-2}{x + 1}}{x - 1}
double f(double x) {
        double r100022 = 1.0;
        double r100023 = x;
        double r100024 = r100023 + r100022;
        double r100025 = r100022 / r100024;
        double r100026 = r100023 - r100022;
        double r100027 = r100022 / r100026;
        double r100028 = r100025 - r100027;
        return r100028;
}
↓
double f(double x) {
        double r100029 = 1.0;
        double r100030 = 2.0;
        double r100031 = -r100030;
        double r100032 = x;
        double r100033 = r100032 + r100029;
        double r100034 = r100031 / r100033;
        double r100035 = r100032 - r100029;
        double r100036 = r100034 / r100035;
        double r100037 = r100029 * r100036;
        return r100037;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

  3. Applied flip--28.8

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

  4. Applied associate-/r/28.8

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

  5. Applied flip-+14.4

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

  6. Applied associate-/r/14.3

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

  7. Applied distribute-lft-out--13.8

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

  8. Taylor expanded around 0 0.4

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

  10. Applied div-inv0.4

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

  11. Applied associate-*l*0.4

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))