Average Error: 0.0 → 0.0
Time: 7.3s
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 r1915721 = 1.0;
        double r1915722 = 2.0;
        double r1915723 = t;
        double r1915724 = r1915722 * r1915723;
        double r1915725 = r1915721 + r1915723;
        double r1915726 = r1915724 / r1915725;
        double r1915727 = r1915726 * r1915726;
        double r1915728 = r1915721 + r1915727;
        double r1915729 = r1915722 + r1915727;
        double r1915730 = r1915728 / r1915729;
        return r1915730;
}
↓
double f(double t) {
        double r1915731 = 1.0;
        double r1915732 = t;
        double r1915733 = 2.0;
        double r1915734 = r1915732 * r1915733;
        double r1915735 = r1915731 + r1915732;
        double r1915736 = r1915734 / r1915735;
        double r1915737 = r1915736 * r1915736;
        double r1915738 = r1915731 + r1915737;
        double r1915739 = r1915733 + r1915737;
        double r1915740 = r1915738 / r1915739;
        return r1915740;
}

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 +o rules:numerics
(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))))))