Average Error: 0.0 → 0.0
Time: 28.5s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{\log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right) + 2}\]
\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}}{\log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right) + 2}
double f(double t) {
        double r2691863 = 1.0;
        double r2691864 = 2.0;
        double r2691865 = t;
        double r2691866 = r2691864 * r2691865;
        double r2691867 = r2691863 + r2691865;
        double r2691868 = r2691866 / r2691867;
        double r2691869 = r2691868 * r2691868;
        double r2691870 = r2691863 + r2691869;
        double r2691871 = r2691864 + r2691869;
        double r2691872 = r2691870 / r2691871;
        return r2691872;
}
↓
double f(double t) {
        double r2691873 = 1.0;
        double r2691874 = t;
        double r2691875 = 2.0;
        double r2691876 = r2691874 * r2691875;
        double r2691877 = r2691873 + r2691874;
        double r2691878 = r2691876 / r2691877;
        double r2691879 = r2691878 * r2691878;
        double r2691880 = r2691873 + r2691879;
        double r2691881 = exp(r2691879);
        double r2691882 = log(r2691881);
        double r2691883 = r2691882 + r2691875;
        double r2691884 = r2691880 / r2691883;
        return r2691884;
}

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

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

Reproduce

herbie shell --seed 2019168 
(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))))))