Average Error: 0.0 → 0.0
Time: 31.3s
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 r13442213 = 1.0;
        double r13442214 = x;
        double r13442215 = r13442214 - r13442213;
        double r13442216 = r13442213 / r13442215;
        double r13442217 = r13442214 + r13442213;
        double r13442218 = r13442214 / r13442217;
        double r13442219 = r13442216 + r13442218;
        return r13442219;
}
↓
double f(double x) {
        double r13442220 = 1.0;
        double r13442221 = x;
        double r13442222 = r13442221 - r13442220;
        double r13442223 = r13442220 / r13442222;
        double r13442224 = r13442221 + r13442220;
        double r13442225 = r13442224 / r13442221;
        double r13442226 = r13442220 / r13442225;
        double r13442227 = r13442223 + r13442226;
        return r13442227;
}

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 clear-num0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))