Average Error: 0.1 → 0.1
Time: 8.4s
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 r2772720 = 1.0;
        double r2772721 = 2.0;
        double r2772722 = t;
        double r2772723 = r2772721 * r2772722;
        double r2772724 = r2772720 + r2772722;
        double r2772725 = r2772723 / r2772724;
        double r2772726 = r2772725 * r2772725;
        double r2772727 = r2772720 + r2772726;
        double r2772728 = r2772721 + r2772726;
        double r2772729 = r2772727 / r2772728;
        return r2772729;
}
↓
double f(double t) {
        double r2772730 = 1.0;
        double r2772731 = t;
        double r2772732 = 2.0;
        double r2772733 = r2772731 * r2772732;
        double r2772734 = r2772730 + r2772731;
        double r2772735 = r2772733 / r2772734;
        double r2772736 = r2772735 * r2772735;
        double r2772737 = r2772730 + r2772736;
        double r2772738 = r2772732 + r2772736;
        double r2772739 = r2772737 / r2772738;
        return r2772739;
}

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 2019121 
(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))))))