Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \frac{x}{x + 1}
double f(double x) {
        double r107408 = 1.0;
        double r107409 = x;
        double r107410 = r107409 - r107408;
        double r107411 = r107408 / r107410;
        double r107412 = r107409 + r107408;
        double r107413 = r107409 / r107412;
        double r107414 = r107411 + r107413;
        return r107414;
}
↓
double f(double x) {
        double r107415 = 1.0;
        double r107416 = x;
        double r107417 = r107416 - r107415;
        double r107418 = r107415 / r107417;
        double r107419 = r107416 + r107415;
        double r107420 = r107416 / r107419;
        double r107421 = r107418 + r107420;
        return r107421;
}

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. Using strategy rm

  6. Applied div-inv0.0

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

  7. Applied associate-*l*0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))