Average Error: 0.0 → 0.0
Time: 57.5s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right)}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]
\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 r2989928 = 1.0;
        double r2989929 = 2.0;
        double r2989930 = t;
        double r2989931 = r2989929 * r2989930;
        double r2989932 = r2989928 + r2989930;
        double r2989933 = r2989931 / r2989932;
        double r2989934 = r2989933 * r2989933;
        double r2989935 = r2989928 + r2989934;
        double r2989936 = r2989929 + r2989934;
        double r2989937 = r2989935 / r2989936;
        return r2989937;
}
↓
double f(double t) {
        double r2989938 = 1.0;
        double r2989939 = t;
        double r2989940 = 2.0;
        double r2989941 = r2989939 * r2989940;
        double r2989942 = r2989938 + r2989939;
        double r2989943 = r2989941 / r2989942;
        double r2989944 = r2989943 * r2989943;
        double r2989945 = exp(r2989944);
        double r2989946 = log(r2989945);
        double r2989947 = r2989938 + r2989946;
        double r2989948 = r2989940 + r2989944;
        double r2989949 = r2989947 / r2989948;
        return r2989949;
}

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 2019151 
(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))))))