Average Error: 0.0 → 0.0
Time: 1.2m
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}
double f(double x) {
        double r28861022 = 1.0;
        double r28861023 = x;
        double r28861024 = r28861023 - r28861022;
        double r28861025 = r28861022 / r28861024;
        double r28861026 = r28861023 + r28861022;
        double r28861027 = r28861023 / r28861026;
        double r28861028 = r28861025 + r28861027;
        return r28861028;
}
↓
double f(double x) {
        double r28861029 = 1.0;
        double r28861030 = x;
        double r28861031 = r28861030 - r28861029;
        double r28861032 = r28861029 / r28861031;
        double r28861033 = r28861030 + r28861029;
        double r28861034 = r28861033 / r28861030;
        double r28861035 = r28861029 / r28861034;
        double r28861036 = r28861032 + r28861035;
        return r28861036;
}

Error

Bits error versus x

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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 *-un-lft-identity0.0

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

  4. Applied associate-/l*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019120 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))