Average Error: 0.0 → 0.0
Time: 6.0s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}\]
1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
1 - \frac{1}{\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}
double f(double t) {
        double r22031 = 1.0;
        double r22032 = 2.0;
        double r22033 = t;
        double r22034 = r22032 / r22033;
        double r22035 = r22031 / r22033;
        double r22036 = r22031 + r22035;
        double r22037 = r22034 / r22036;
        double r22038 = r22032 - r22037;
        double r22039 = r22038 * r22038;
        double r22040 = r22032 + r22039;
        double r22041 = r22031 / r22040;
        double r22042 = r22031 - r22041;
        return r22042;
}
↓
double f(double t) {
        double r22043 = 1.0;
        double r22044 = 2.0;
        double r22045 = t;
        double r22046 = r22043 * r22045;
        double r22047 = r22046 + r22043;
        double r22048 = r22044 / r22047;
        double r22049 = r22044 - r22048;
        double r22050 = r22049 * r22049;
        double r22051 = r22050 + r22044;
        double r22052 = r22043 / r22051;
        double r22053 = r22043 - r22052;
        return r22053;
}

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

    \[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1.0 (/ 1.0 (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))))))