Average Error: 0.0 → 0.0
Time: 6.0s
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 r1966770 = 1.0;
        double r1966771 = 2.0;
        double r1966772 = t;
        double r1966773 = r1966771 * r1966772;
        double r1966774 = r1966770 + r1966772;
        double r1966775 = r1966773 / r1966774;
        double r1966776 = r1966775 * r1966775;
        double r1966777 = r1966770 + r1966776;
        double r1966778 = r1966771 + r1966776;
        double r1966779 = r1966777 / r1966778;
        return r1966779;
}
↓
double f(double t) {
        double r1966780 = 1.0;
        double r1966781 = t;
        double r1966782 = 2.0;
        double r1966783 = r1966781 * r1966782;
        double r1966784 = r1966780 + r1966781;
        double r1966785 = r1966783 / r1966784;
        double r1966786 = r1966785 * r1966785;
        double r1966787 = r1966780 + r1966786;
        double r1966788 = r1966782 + r1966786;
        double r1966789 = r1966787 / r1966788;
        return r1966789;
}

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 2019163 
(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))))))