Average Error: 0.1 → 0.1
Time: 16.6s
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 r1935331 = 1.0;
        double r1935332 = 2.0;
        double r1935333 = t;
        double r1935334 = r1935332 * r1935333;
        double r1935335 = r1935331 + r1935333;
        double r1935336 = r1935334 / r1935335;
        double r1935337 = r1935336 * r1935336;
        double r1935338 = r1935331 + r1935337;
        double r1935339 = r1935332 + r1935337;
        double r1935340 = r1935338 / r1935339;
        return r1935340;
}
↓
double f(double t) {
        double r1935341 = 1.0;
        double r1935342 = t;
        double r1935343 = 2.0;
        double r1935344 = r1935342 * r1935343;
        double r1935345 = r1935341 + r1935342;
        double r1935346 = r1935344 / r1935345;
        double r1935347 = r1935346 * r1935346;
        double r1935348 = r1935341 + r1935347;
        double r1935349 = r1935343 + r1935347;
        double r1935350 = r1935348 / r1935349;
        return r1935350;
}

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 2019152 
(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))))))