Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right)}\]
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}{2 + \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right) \cdot \left(2 - \frac{2}{1 \cdot \left(t + 1\right)}\right)}
double f(double t) {
        double r27066 = 1.0;
        double r27067 = 2.0;
        double r27068 = t;
        double r27069 = r27067 / r27068;
        double r27070 = r27066 / r27068;
        double r27071 = r27066 + r27070;
        double r27072 = r27069 / r27071;
        double r27073 = r27067 - r27072;
        double r27074 = r27073 * r27073;
        double r27075 = r27067 + r27074;
        double r27076 = r27066 / r27075;
        double r27077 = r27066 - r27076;
        return r27077;
}
↓
double f(double t) {
        double r27078 = 1.0;
        double r27079 = 2.0;
        double r27080 = t;
        double r27081 = 1.0;
        double r27082 = r27080 + r27081;
        double r27083 = r27078 * r27082;
        double r27084 = r27079 / r27083;
        double r27085 = r27079 - r27084;
        double r27086 = r27085 * r27085;
        double r27087 = r27079 + r27086;
        double r27088 = r27078 / r27087;
        double r27089 = r27078 - r27088;
        return r27089;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))