Average Error: 0.0 → 0.0
Time: 18.1s
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 r2344079 = 1.0;
        double r2344080 = 2.0;
        double r2344081 = t;
        double r2344082 = r2344080 * r2344081;
        double r2344083 = r2344079 + r2344081;
        double r2344084 = r2344082 / r2344083;
        double r2344085 = r2344084 * r2344084;
        double r2344086 = r2344079 + r2344085;
        double r2344087 = r2344080 + r2344085;
        double r2344088 = r2344086 / r2344087;
        return r2344088;
}
↓
double f(double t) {
        double r2344089 = 1.0;
        double r2344090 = t;
        double r2344091 = 2.0;
        double r2344092 = r2344090 * r2344091;
        double r2344093 = r2344089 + r2344090;
        double r2344094 = r2344092 / r2344093;
        double r2344095 = r2344094 * r2344094;
        double r2344096 = r2344089 + r2344095;
        double r2344097 = r2344091 + r2344095;
        double r2344098 = r2344096 / r2344097;
        return r2344098;
}

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 2019146 
(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))))))