Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\frac{1 + x}{x \cdot x + -1}}\right) + \frac{x}{1 + x}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\frac{1 + x}{x \cdot x + -1}}\right) + \frac{x}{1 + x}
double f(double x) {
        double r1406521 = 1.0;
        double r1406522 = x;
        double r1406523 = r1406522 - r1406521;
        double r1406524 = r1406521 / r1406523;
        double r1406525 = r1406522 + r1406521;
        double r1406526 = r1406522 / r1406525;
        double r1406527 = r1406524 + r1406526;
        return r1406527;
}
↓
double f(double x) {
        double r1406528 = 1.0;
        double r1406529 = x;
        double r1406530 = r1406528 + r1406529;
        double r1406531 = r1406529 * r1406529;
        double r1406532 = -1.0;
        double r1406533 = r1406531 + r1406532;
        double r1406534 = r1406530 / r1406533;
        double r1406535 = exp(r1406534);
        double r1406536 = log(r1406535);
        double r1406537 = r1406529 / r1406530;
        double r1406538 = r1406536 + r1406537;
        return r1406538;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied flip--0.0

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

  4. Applied associate-/r/0.0

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

  5. Simplified0.0

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

  7. Applied add-log-exp0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))