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

↓

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

double f(double t) {
        double r6348419 = 1.0;
        double r6348420 = 2.0;
        double r6348421 = t;
        double r6348422 = r6348420 * r6348421;
        double r6348423 = r6348419 + r6348421;
        double r6348424 = r6348422 / r6348423;
        double r6348425 = r6348424 * r6348424;
        double r6348426 = r6348419 + r6348425;
        double r6348427 = r6348420 + r6348425;
        double r6348428 = r6348426 / r6348427;
        return r6348428;
}

↓

double f(double t) {
        double r6348429 = 1.0;
        double r6348430 = t;
        double r6348431 = 2.0;
        double r6348432 = r6348430 * r6348431;
        double r6348433 = r6348429 + r6348430;
        double r6348434 = r6348432 / r6348433;
        double r6348435 = r6348434 * r6348434;
        double r6348436 = r6348429 + r6348435;
        double r6348437 = r6348431 + r6348435;
        double r6348438 = r6348436 / r6348437;
        return r6348438;
}

\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}}

Derivation

Initial program 0.1
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
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 2019101 
(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))))))

Error

Derivation

Reproduce