Average Error: 0.0 → 0.0
Time: 7.2s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
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 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}
double f(double t) {
        double r1133203 = 1.0;
        double r1133204 = 2.0;
        double r1133205 = t;
        double r1133206 = r1133204 / r1133205;
        double r1133207 = r1133203 / r1133205;
        double r1133208 = r1133203 + r1133207;
        double r1133209 = r1133206 / r1133208;
        double r1133210 = r1133204 - r1133209;
        double r1133211 = r1133210 * r1133210;
        double r1133212 = r1133204 + r1133211;
        double r1133213 = r1133203 / r1133212;
        double r1133214 = r1133203 - r1133213;
        return r1133214;
}
↓
double f(double t) {
        double r1133215 = 1.0;
        double r1133216 = 2.0;
        double r1133217 = t;
        double r1133218 = r1133215 + r1133217;
        double r1133219 = r1133216 / r1133218;
        double r1133220 = r1133216 - r1133219;
        double r1133221 = r1133220 * r1133220;
        double r1133222 = r1133216 + r1133221;
        double r1133223 = r1133215 / r1133222;
        double r1133224 = r1133215 - r1133223;
        return r1133224;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019133 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))