Average Error: 14.5 → 0.1
Time: 18.5s
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 r3760303 = 1.0;
        double r3760304 = x;
        double r3760305 = r3760304 + r3760303;
        double r3760306 = r3760303 / r3760305;
        double r3760307 = r3760304 - r3760303;
        double r3760308 = r3760303 / r3760307;
        double r3760309 = r3760306 - r3760308;
        return r3760309;
}
↓
double f(double x) {
        double r3760310 = -2.0;
        double r3760311 = x;
        double r3760312 = 1.0;
        double r3760313 = r3760311 + r3760312;
        double r3760314 = r3760310 / r3760313;
        double r3760315 = r3760311 - r3760312;
        double r3760316 = r3760314 / r3760315;
        return r3760316;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

  3. Applied frac-sub13.9

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

  4. Simplified12.0

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

  6. Applied associate-/r*12.0

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))