Average Error: 0.1 → 0.1
Time: 8.8s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]
\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{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}
double f(double t) {
        double r1654727 = 1.0;
        double r1654728 = 2.0;
        double r1654729 = t;
        double r1654730 = r1654728 * r1654729;
        double r1654731 = r1654727 + r1654729;
        double r1654732 = r1654730 / r1654731;
        double r1654733 = r1654732 * r1654732;
        double r1654734 = r1654727 + r1654733;
        double r1654735 = r1654728 + r1654733;
        double r1654736 = r1654734 / r1654735;
        return r1654736;
}
↓
double f(double t) {
        double r1654737 = 1.0;
        double r1654738 = t;
        double r1654739 = 2.0;
        double r1654740 = r1654738 * r1654739;
        double r1654741 = r1654737 + r1654738;
        double r1654742 = r1654740 / r1654741;
        double r1654743 = r1654742 * r1654742;
        double r1654744 = r1654737 + r1654743;
        double r1654745 = r1654739 + r1654743;
        double r1654746 = r1654744 / r1654745;
        return r1654746;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019129 
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))