Average Error: 0.0 → 0.0
Time: 11.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\left(x + 1\right) \cdot \frac{1}{\left(x + 1\right) \cdot \left(x - 1\right)} + \frac{1}{\frac{x + 1}{x}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\left(x + 1\right) \cdot \frac{1}{\left(x + 1\right) \cdot \left(x - 1\right)} + \frac{1}{\frac{x + 1}{x}}
double f(double x) {
        double r4349070 = 1.0;
        double r4349071 = x;
        double r4349072 = r4349071 - r4349070;
        double r4349073 = r4349070 / r4349072;
        double r4349074 = r4349071 + r4349070;
        double r4349075 = r4349071 / r4349074;
        double r4349076 = r4349073 + r4349075;
        return r4349076;
}
↓
double f(double x) {
        double r4349077 = x;
        double r4349078 = 1.0;
        double r4349079 = r4349077 + r4349078;
        double r4349080 = r4349077 - r4349078;
        double r4349081 = r4349079 * r4349080;
        double r4349082 = r4349078 / r4349081;
        double r4349083 = r4349079 * r4349082;
        double r4349084 = 1.0;
        double r4349085 = r4349079 / r4349077;
        double r4349086 = r4349084 / r4349085;
        double r4349087 = r4349083 + r4349086;
        return r4349087;
}

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 clear-num0.0

    \[\leadsto \frac{1}{x - 1} + \color{blue}{\frac{1}{\frac{x + 1}{x}}}\]
  4. Using strategy rm

  5. Applied flip--0.0

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

  6. Applied associate-/r/0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))