Average Error: 0.0 → 0.0
Time: 13.8s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)} \cdot \left(\sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)} \cdot \sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\right) + 2}\]
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}{\sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)} \cdot \left(\sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)} \cdot \sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\right) + 2}
double f(double t) {
        double r1270322 = 1.0;
        double r1270323 = 2.0;
        double r1270324 = t;
        double r1270325 = r1270323 / r1270324;
        double r1270326 = r1270322 / r1270324;
        double r1270327 = r1270322 + r1270326;
        double r1270328 = r1270325 / r1270327;
        double r1270329 = r1270323 - r1270328;
        double r1270330 = r1270329 * r1270329;
        double r1270331 = r1270323 + r1270330;
        double r1270332 = r1270322 / r1270331;
        double r1270333 = r1270322 - r1270332;
        return r1270333;
}
↓
double f(double t) {
        double r1270334 = 1.0;
        double r1270335 = 2.0;
        double r1270336 = t;
        double r1270337 = r1270334 + r1270336;
        double r1270338 = r1270335 / r1270337;
        double r1270339 = r1270335 - r1270338;
        double r1270340 = r1270339 * r1270339;
        double r1270341 = cbrt(r1270340);
        double r1270342 = r1270341 * r1270341;
        double r1270343 = r1270341 * r1270342;
        double r1270344 = r1270343 + r1270335;
        double r1270345 = r1270334 / r1270344;
        double r1270346 = r1270334 - r1270345;
        return r1270346;
}

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. Using strategy rm

  4. Applied add-cube-cbrt0.0

    \[\leadsto 1 - \frac{1}{2 + \color{blue}{\left(\sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)} \cdot \sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\right) \cdot \sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}}}\]

  5. Final simplification0.0

    \[\leadsto 1 - \frac{1}{\sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)} \cdot \left(\sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)} \cdot \sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\right) + 2}\]

Reproduce

herbie shell --seed 2019135 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))