Average Error: 0.0 → 0.0
Time: 6.5s
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 r1746029 = 1.0;
        double r1746030 = 2.0;
        double r1746031 = t;
        double r1746032 = r1746030 * r1746031;
        double r1746033 = r1746029 + r1746031;
        double r1746034 = r1746032 / r1746033;
        double r1746035 = r1746034 * r1746034;
        double r1746036 = r1746029 + r1746035;
        double r1746037 = r1746030 + r1746035;
        double r1746038 = r1746036 / r1746037;
        return r1746038;
}
↓
double f(double t) {
        double r1746039 = 1.0;
        double r1746040 = t;
        double r1746041 = 2.0;
        double r1746042 = r1746040 * r1746041;
        double r1746043 = r1746039 + r1746040;
        double r1746044 = r1746042 / r1746043;
        double r1746045 = r1746044 * r1746044;
        double r1746046 = r1746039 + r1746045;
        double r1746047 = r1746041 + r1746045;
        double r1746048 = r1746046 / r1746047;
        return r1746048;
}

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 
(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))))))