Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \sqrt[3]{{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}^{6}}}\]
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 + \sqrt[3]{{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}^{6}}}
double f(double t) {
        double r39319 = 1.0;
        double r39320 = 2.0;
        double r39321 = t;
        double r39322 = r39320 / r39321;
        double r39323 = r39319 / r39321;
        double r39324 = r39319 + r39323;
        double r39325 = r39322 / r39324;
        double r39326 = r39320 - r39325;
        double r39327 = r39326 * r39326;
        double r39328 = r39320 + r39327;
        double r39329 = r39319 / r39328;
        double r39330 = r39319 - r39329;
        return r39330;
}
↓
double f(double t) {
        double r39331 = 1.0;
        double r39332 = 2.0;
        double r39333 = t;
        double r39334 = r39332 / r39333;
        double r39335 = r39331 / r39333;
        double r39336 = r39331 + r39335;
        double r39337 = r39334 / r39336;
        double r39338 = r39332 - r39337;
        double r39339 = 6.0;
        double r39340 = pow(r39338, r39339);
        double r39341 = cbrt(r39340);
        double r39342 = r39332 + r39341;
        double r39343 = r39331 / r39342;
        double r39344 = r39331 - r39343;
        return r39344;
}

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. Using strategy rm

  3. Applied add-cbrt-cube0.0

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

  4. Applied add-cbrt-cube0.0

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

  5. Applied cbrt-unprod0.0

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

  6. Simplified0.0

    \[\leadsto 1 - \frac{1}{2 + \sqrt[3]{\color{blue}{{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}^{6}}}}\]

  7. Final simplification0.0

    \[\leadsto 1 - \frac{1}{2 + \sqrt[3]{{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}^{6}}}\]

Reproduce

herbie shell --seed 2019354 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))