Average Error: 0.0 → 0.0
Time: 18.6s
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 r2043347 = 1.0;
        double r2043348 = 2.0;
        double r2043349 = t;
        double r2043350 = r2043348 * r2043349;
        double r2043351 = r2043347 + r2043349;
        double r2043352 = r2043350 / r2043351;
        double r2043353 = r2043352 * r2043352;
        double r2043354 = r2043347 + r2043353;
        double r2043355 = r2043348 + r2043353;
        double r2043356 = r2043354 / r2043355;
        return r2043356;
}
↓
double f(double t) {
        double r2043357 = 1.0;
        double r2043358 = t;
        double r2043359 = 2.0;
        double r2043360 = r2043358 * r2043359;
        double r2043361 = r2043357 + r2043358;
        double r2043362 = r2043360 / r2043361;
        double r2043363 = r2043362 * r2043362;
        double r2043364 = r2043357 + r2043363;
        double r2043365 = r2043359 + r2043363;
        double r2043366 = r2043364 / r2043365;
        return r2043366;
}

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 2019149 
(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))))))