Average Error: 14.7 → 0.1
Time: 55.5s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{x + 1}}{x - 1}
double f(double x) {
        double r27024211 = 1.0;
        double r27024212 = x;
        double r27024213 = r27024212 + r27024211;
        double r27024214 = r27024211 / r27024213;
        double r27024215 = r27024212 - r27024211;
        double r27024216 = r27024211 / r27024215;
        double r27024217 = r27024214 - r27024216;
        return r27024217;
}
↓
double f(double x) {
        double r27024218 = -2.0;
        double r27024219 = x;
        double r27024220 = 1.0;
        double r27024221 = r27024219 + r27024220;
        double r27024222 = r27024218 / r27024221;
        double r27024223 = r27024219 - r27024220;
        double r27024224 = r27024222 / r27024223;
        return r27024224;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  3. Applied frac-sub14.1

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

  4. Simplified0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019124 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))