Average Error: 0.0 → 0.0
Time: 24.6s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{t \cdot 2}{t + 1} \cdot \frac{t \cdot 2}{t + 1}}{2 + \log \left(e^{\frac{t \cdot 2}{t + 1} \cdot \frac{t \cdot 2}{t + 1}}\right)}\]
\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}{t + 1} \cdot \frac{t \cdot 2}{t + 1}}{2 + \log \left(e^{\frac{t \cdot 2}{t + 1} \cdot \frac{t \cdot 2}{t + 1}}\right)}
double f(double t) {
        double r2691519 = 1.0;
        double r2691520 = 2.0;
        double r2691521 = t;
        double r2691522 = r2691520 * r2691521;
        double r2691523 = r2691519 + r2691521;
        double r2691524 = r2691522 / r2691523;
        double r2691525 = r2691524 * r2691524;
        double r2691526 = r2691519 + r2691525;
        double r2691527 = r2691520 + r2691525;
        double r2691528 = r2691526 / r2691527;
        return r2691528;
}
↓
double f(double t) {
        double r2691529 = 1.0;
        double r2691530 = t;
        double r2691531 = 2.0;
        double r2691532 = r2691530 * r2691531;
        double r2691533 = r2691530 + r2691529;
        double r2691534 = r2691532 / r2691533;
        double r2691535 = r2691534 * r2691534;
        double r2691536 = r2691529 + r2691535;
        double r2691537 = exp(r2691535);
        double r2691538 = log(r2691537);
        double r2691539 = r2691531 + r2691538;
        double r2691540 = r2691536 / r2691539;
        return r2691540;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 1.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t)))) (+ 2.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t))))))