Average Error: 0.0 → 0.0
Time: 9.5s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \log \left(e^{\frac{x}{x + 1}}\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \log \left(e^{\frac{x}{x + 1}}\right)
double f(double x) {
        double r3225995 = 1.0;
        double r3225996 = x;
        double r3225997 = r3225996 - r3225995;
        double r3225998 = r3225995 / r3225997;
        double r3225999 = r3225996 + r3225995;
        double r3226000 = r3225996 / r3225999;
        double r3226001 = r3225998 + r3226000;
        return r3226001;
}
↓
double f(double x) {
        double r3226002 = 1.0;
        double r3226003 = x;
        double r3226004 = r3226003 - r3226002;
        double r3226005 = r3226002 / r3226004;
        double r3226006 = r3226003 + r3226002;
        double r3226007 = r3226003 / r3226006;
        double r3226008 = exp(r3226007);
        double r3226009 = log(r3226008);
        double r3226010 = r3226005 + r3226009;
        return r3226010;
}

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 add-log-exp0.0

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

  4. Final simplification0.0

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

Reproduce

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