Average Error: 0.0 → 0.0
Time: 16.9s
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 r1931799 = 1.0;
        double r1931800 = 2.0;
        double r1931801 = t;
        double r1931802 = r1931800 * r1931801;
        double r1931803 = r1931799 + r1931801;
        double r1931804 = r1931802 / r1931803;
        double r1931805 = r1931804 * r1931804;
        double r1931806 = r1931799 + r1931805;
        double r1931807 = r1931800 + r1931805;
        double r1931808 = r1931806 / r1931807;
        return r1931808;
}
↓
double f(double t) {
        double r1931809 = 1.0;
        double r1931810 = t;
        double r1931811 = 2.0;
        double r1931812 = r1931810 * r1931811;
        double r1931813 = r1931809 + r1931810;
        double r1931814 = r1931812 / r1931813;
        double r1931815 = r1931814 * r1931814;
        double r1931816 = r1931809 + r1931815;
        double r1931817 = r1931811 + r1931815;
        double r1931818 = r1931816 / r1931817;
        return r1931818;
}

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 2019143 
(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))))))