Average Error: 0.0 → 0.0
Time: 18.5s
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 r3206673 = 1.0;
        double r3206674 = 2.0;
        double r3206675 = t;
        double r3206676 = r3206674 * r3206675;
        double r3206677 = r3206673 + r3206675;
        double r3206678 = r3206676 / r3206677;
        double r3206679 = r3206678 * r3206678;
        double r3206680 = r3206673 + r3206679;
        double r3206681 = r3206674 + r3206679;
        double r3206682 = r3206680 / r3206681;
        return r3206682;
}
↓
double f(double t) {
        double r3206683 = 1.0;
        double r3206684 = t;
        double r3206685 = 2.0;
        double r3206686 = r3206684 * r3206685;
        double r3206687 = r3206683 + r3206684;
        double r3206688 = r3206686 / r3206687;
        double r3206689 = r3206688 * r3206688;
        double r3206690 = r3206683 + r3206689;
        double r3206691 = r3206685 + r3206689;
        double r3206692 = r3206690 / r3206691;
        return r3206692;
}

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

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

Reproduce

herbie shell --seed 2019144 
(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))))))