Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}
↓
\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}
double f(double t) {
        double r54613 = 1.0;
        double r54614 = 2.0;
        double r54615 = t;
        double r54616 = r54614 * r54615;
        double r54617 = r54613 + r54615;
        double r54618 = r54616 / r54617;
        double r54619 = r54618 * r54618;
        double r54620 = r54613 + r54619;
        double r54621 = r54614 + r54619;
        double r54622 = r54620 / r54621;
        return r54622;
}
↓
double f(double t) {
        double r54623 = 1.0;
        double r54624 = 2.0;
        double r54625 = t;
        double r54626 = r54624 * r54625;
        double r54627 = r54623 + r54625;
        double r54628 = r54626 / r54627;
        double r54629 = r54628 * r54628;
        double r54630 = r54623 + r54629;
        double r54631 = r54624 + r54629;
        double r54632 = r54630 / r54631;
        return r54632;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

  2. Final simplification0.0

    \[\leadsto \frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (t)
  :name "Kahan p13 Example 1"
  :precision binary64
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))