Average Error: 0.0 → 0.0
Time: 4.7s
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 r2934067 = 1.0;
        double r2934068 = 2.0;
        double r2934069 = t;
        double r2934070 = r2934068 * r2934069;
        double r2934071 = r2934067 + r2934069;
        double r2934072 = r2934070 / r2934071;
        double r2934073 = r2934072 * r2934072;
        double r2934074 = r2934067 + r2934073;
        double r2934075 = r2934068 + r2934073;
        double r2934076 = r2934074 / r2934075;
        return r2934076;
}
↓
double f(double t) {
        double r2934077 = 1.0;
        double r2934078 = t;
        double r2934079 = 2.0;
        double r2934080 = r2934078 * r2934079;
        double r2934081 = r2934077 + r2934078;
        double r2934082 = r2934080 / r2934081;
        double r2934083 = r2934082 * r2934082;
        double r2934084 = r2934077 + r2934083;
        double r2934085 = r2934079 + r2934083;
        double r2934086 = r2934084 / r2934085;
        return r2934086;
}

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 2019174 
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 1.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t)))) (+ 2.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t))))))