Average Error: 0.0 → 0.0
Time: 8.6s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right)}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]
\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 + \log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right)}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}
double f(double t) {
        double r2400360 = 1.0;
        double r2400361 = 2.0;
        double r2400362 = t;
        double r2400363 = r2400361 * r2400362;
        double r2400364 = r2400360 + r2400362;
        double r2400365 = r2400363 / r2400364;
        double r2400366 = r2400365 * r2400365;
        double r2400367 = r2400360 + r2400366;
        double r2400368 = r2400361 + r2400366;
        double r2400369 = r2400367 / r2400368;
        return r2400369;
}
↓
double f(double t) {
        double r2400370 = 1.0;
        double r2400371 = t;
        double r2400372 = 2.0;
        double r2400373 = r2400371 * r2400372;
        double r2400374 = r2400370 + r2400371;
        double r2400375 = r2400373 / r2400374;
        double r2400376 = r2400375 * r2400375;
        double r2400377 = exp(r2400376);
        double r2400378 = log(r2400377);
        double r2400379 = r2400370 + r2400378;
        double r2400380 = r2400372 + r2400376;
        double r2400381 = r2400379 / r2400380;
        return r2400381;
}

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. Using strategy rm

  3. Applied add-log-exp0.0

    \[\leadsto \frac{1 + \color{blue}{\log \left(e^{\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\right)}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

  4. Final simplification0.0

    \[\leadsto \frac{1 + \log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right)}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]

Reproduce

herbie shell --seed 2019158 
(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))))))