Average Error: 0.0 → 0.0
Time: 6.8s
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 r1827235 = 1.0;
        double r1827236 = 2.0;
        double r1827237 = t;
        double r1827238 = r1827236 * r1827237;
        double r1827239 = r1827235 + r1827237;
        double r1827240 = r1827238 / r1827239;
        double r1827241 = r1827240 * r1827240;
        double r1827242 = r1827235 + r1827241;
        double r1827243 = r1827236 + r1827241;
        double r1827244 = r1827242 / r1827243;
        return r1827244;
}
↓
double f(double t) {
        double r1827245 = 1.0;
        double r1827246 = t;
        double r1827247 = 2.0;
        double r1827248 = r1827246 * r1827247;
        double r1827249 = r1827245 + r1827246;
        double r1827250 = r1827248 / r1827249;
        double r1827251 = r1827250 * r1827250;
        double r1827252 = r1827245 + r1827251;
        double r1827253 = r1827247 + r1827251;
        double r1827254 = r1827252 / r1827253;
        return r1827254;
}

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))))))