Average Error: 14.5 → 0.1
Time: 1.2m
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 r22921378 = 1.0;
        double r22921379 = x;
        double r22921380 = r22921379 + r22921378;
        double r22921381 = r22921378 / r22921380;
        double r22921382 = r22921379 - r22921378;
        double r22921383 = r22921378 / r22921382;
        double r22921384 = r22921381 - r22921383;
        return r22921384;
}
↓
double f(double x) {
        double r22921385 = -2.0;
        double r22921386 = x;
        double r22921387 = 1.0;
        double r22921388 = r22921386 + r22921387;
        double r22921389 = r22921385 / r22921388;
        double r22921390 = r22921386 - r22921387;
        double r22921391 = r22921389 / r22921390;
        return r22921391;
}

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-sub14.0

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

  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 2019104 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))