Average Error: 14.6 → 0.1
Time: 10.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{1}{x + 1}}{x - 1} \cdot -2\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{1}{x + 1}}{x - 1} \cdot -2
double f(double x) {
        double r2266076 = 1.0;
        double r2266077 = x;
        double r2266078 = r2266077 + r2266076;
        double r2266079 = r2266076 / r2266078;
        double r2266080 = r2266077 - r2266076;
        double r2266081 = r2266076 / r2266080;
        double r2266082 = r2266079 - r2266081;
        return r2266082;
}
↓
double f(double x) {
        double r2266083 = 1.0;
        double r2266084 = x;
        double r2266085 = r2266084 + r2266083;
        double r2266086 = r2266083 / r2266085;
        double r2266087 = r2266084 - r2266083;
        double r2266088 = r2266086 / r2266087;
        double r2266089 = -2.0;
        double r2266090 = r2266088 * r2266089;
        return r2266090;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 14.6

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

  3. Applied flip--29.4

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

  4. Applied associate-/r/29.4

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

  5. Applied flip-+14.6

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

  6. Applied associate-/r/14.6

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

  7. Applied distribute-lft-out--13.9

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

  8. Taylor expanded around -inf 0.4

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

  10. Applied difference-of-squares0.4

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

  11. Applied associate-/r*0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019152 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))