Average Error: 0.0 → 0.0
Time: 8.5s
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 r1379004 = 1.0;
        double r1379005 = 2.0;
        double r1379006 = t;
        double r1379007 = r1379005 / r1379006;
        double r1379008 = r1379004 / r1379006;
        double r1379009 = r1379004 + r1379008;
        double r1379010 = r1379007 / r1379009;
        double r1379011 = r1379005 - r1379010;
        double r1379012 = r1379011 * r1379011;
        double r1379013 = r1379005 + r1379012;
        double r1379014 = r1379004 / r1379013;
        double r1379015 = r1379004 - r1379014;
        return r1379015;
}
↓
double f(double t) {
        double r1379016 = 1.0;
        double r1379017 = 2.0;
        double r1379018 = t;
        double r1379019 = r1379016 + r1379018;
        double r1379020 = r1379017 / r1379019;
        double r1379021 = r1379017 - r1379020;
        double r1379022 = r1379021 * r1379021;
        double r1379023 = r1379017 + r1379022;
        double r1379024 = r1379016 / r1379023;
        double r1379025 = r1379016 - r1379024;
        return r1379025;
}

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 2019132 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))