Average Error: 15.0 → 0.1
Time: 3.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{1 \cdot \left(-2\right)}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{1 \cdot \left(-2\right)}{x + 1}}{x - 1}
double f(double x) {
        double r95075 = 1.0;
        double r95076 = x;
        double r95077 = r95076 + r95075;
        double r95078 = r95075 / r95077;
        double r95079 = r95076 - r95075;
        double r95080 = r95075 / r95079;
        double r95081 = r95078 - r95080;
        return r95081;
}
↓
double f(double x) {
        double r95082 = 1.0;
        double r95083 = 2.0;
        double r95084 = -r95083;
        double r95085 = r95082 * r95084;
        double r95086 = x;
        double r95087 = r95086 + r95082;
        double r95088 = r95085 / r95087;
        double r95089 = r95086 - r95082;
        double r95090 = r95088 / r95089;
        return r95090;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.0

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

  3. Applied frac-sub14.3

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

  4. Simplified14.3

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

  5. Simplified14.3

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

  6. Taylor expanded around 0 0.4

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

  8. Applied difference-of-squares0.4

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

  9. Applied associate-/r*0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019308 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))