Average Error: 29.8 → 0.2
Time: 14.9s
Precision: 64
\[\frac{x}{x + 1} - \frac{x + 1}{x - 1}\]
↓
\[\frac{1}{x + 1} \cdot \frac{-3 \cdot x + -1}{x - 1}\]
\frac{x}{x + 1} - \frac{x + 1}{x - 1}
↓
\frac{1}{x + 1} \cdot \frac{-3 \cdot x + -1}{x - 1}
double f(double x) {
        double r4123361 = x;
        double r4123362 = 1.0;
        double r4123363 = r4123361 + r4123362;
        double r4123364 = r4123361 / r4123363;
        double r4123365 = r4123361 - r4123362;
        double r4123366 = r4123363 / r4123365;
        double r4123367 = r4123364 - r4123366;
        return r4123367;
}
↓
double f(double x) {
        double r4123368 = 1.0;
        double r4123369 = x;
        double r4123370 = r4123369 + r4123368;
        double r4123371 = r4123368 / r4123370;
        double r4123372 = -3.0;
        double r4123373 = r4123372 * r4123369;
        double r4123374 = -1.0;
        double r4123375 = r4123373 + r4123374;
        double r4123376 = r4123369 - r4123368;
        double r4123377 = r4123375 / r4123376;
        double r4123378 = r4123371 * r4123377;
        return r4123378;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.8

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

  3. Applied frac-sub30.7

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

  4. Taylor expanded around 0 14.9

    \[\leadsto \frac{\color{blue}{-\left(3 \cdot x + 1\right)}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]

  5. Simplified14.9

    \[\leadsto \frac{\color{blue}{-1 + -3 \cdot x}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity14.9

    \[\leadsto \frac{\color{blue}{1 \cdot \left(-1 + -3 \cdot x\right)}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]

  8. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{1}{x + 1} \cdot \frac{-1 + -3 \cdot x}{x - 1}}\]

  9. Final simplification0.2

    \[\leadsto \frac{1}{x + 1} \cdot \frac{-3 \cdot x + -1}{x - 1}\]

Reproduce

herbie shell --seed 2019139 
(FPCore (x)
  :name "Asymptote C"
  (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))