Average Error: 0.0 → 0.0
Time: 6.6s
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 r1919140 = 1.0;
        double r1919141 = 2.0;
        double r1919142 = t;
        double r1919143 = r1919141 * r1919142;
        double r1919144 = r1919140 + r1919142;
        double r1919145 = r1919143 / r1919144;
        double r1919146 = r1919145 * r1919145;
        double r1919147 = r1919140 + r1919146;
        double r1919148 = r1919141 + r1919146;
        double r1919149 = r1919147 / r1919148;
        return r1919149;
}
↓
double f(double t) {
        double r1919150 = 1.0;
        double r1919151 = t;
        double r1919152 = 2.0;
        double r1919153 = r1919151 * r1919152;
        double r1919154 = r1919150 + r1919151;
        double r1919155 = r1919153 / r1919154;
        double r1919156 = r1919155 * r1919155;
        double r1919157 = r1919150 + r1919156;
        double r1919158 = r1919152 + r1919156;
        double r1919159 = r1919157 / r1919158;
        return r1919159;
}

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 2019172 
(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))))))