Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{-1 + x \cdot x} \cdot \left(x + 1\right) + \frac{x}{x + 1}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{-1 + x \cdot x} \cdot \left(x + 1\right) + \frac{x}{x + 1}
double f(double x) {
        double r4009964 = 1.0;
        double r4009965 = x;
        double r4009966 = r4009965 - r4009964;
        double r4009967 = r4009964 / r4009966;
        double r4009968 = r4009965 + r4009964;
        double r4009969 = r4009965 / r4009968;
        double r4009970 = r4009967 + r4009969;
        return r4009970;
}
↓
double f(double x) {
        double r4009971 = 1.0;
        double r4009972 = -1.0;
        double r4009973 = x;
        double r4009974 = r4009973 * r4009973;
        double r4009975 = r4009972 + r4009974;
        double r4009976 = r4009971 / r4009975;
        double r4009977 = r4009973 + r4009971;
        double r4009978 = r4009976 * r4009977;
        double r4009979 = r4009973 / r4009977;
        double r4009980 = r4009978 + r4009979;
        return r4009980;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))