Average Error: 0.1 → 0.1
Time: 8.4s
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 r2933392 = 1.0;
        double r2933393 = 2.0;
        double r2933394 = t;
        double r2933395 = r2933393 * r2933394;
        double r2933396 = r2933392 + r2933394;
        double r2933397 = r2933395 / r2933396;
        double r2933398 = r2933397 * r2933397;
        double r2933399 = r2933392 + r2933398;
        double r2933400 = r2933393 + r2933398;
        double r2933401 = r2933399 / r2933400;
        return r2933401;
}
↓
double f(double t) {
        double r2933402 = 1.0;
        double r2933403 = t;
        double r2933404 = 2.0;
        double r2933405 = r2933403 * r2933404;
        double r2933406 = r2933402 + r2933403;
        double r2933407 = r2933405 / r2933406;
        double r2933408 = r2933407 * r2933407;
        double r2933409 = r2933402 + r2933408;
        double r2933410 = r2933404 + r2933408;
        double r2933411 = r2933409 / r2933410;
        return r2933411;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

  2. Final simplification0.1

    \[\leadsto \frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]

Reproduce

herbie shell --seed 2019104 
(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))))))