Average Error: 0.0 → 0.0
Time: 11.9s
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 r1607813 = 1.0;
        double r1607814 = 2.0;
        double r1607815 = t;
        double r1607816 = r1607814 * r1607815;
        double r1607817 = r1607813 + r1607815;
        double r1607818 = r1607816 / r1607817;
        double r1607819 = r1607818 * r1607818;
        double r1607820 = r1607813 + r1607819;
        double r1607821 = r1607814 + r1607819;
        double r1607822 = r1607820 / r1607821;
        return r1607822;
}
↓
double f(double t) {
        double r1607823 = 1.0;
        double r1607824 = t;
        double r1607825 = 2.0;
        double r1607826 = r1607824 * r1607825;
        double r1607827 = r1607823 + r1607824;
        double r1607828 = r1607826 / r1607827;
        double r1607829 = r1607828 * r1607828;
        double r1607830 = r1607823 + r1607829;
        double r1607831 = r1607825 + r1607829;
        double r1607832 = r1607830 / r1607831;
        return r1607832;
}

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 2019132 
(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))))))