Average Error: 0.0 → 0.0
Time: 23.9s
Precision: 64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \sqrt[3]{{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}^{3}}}{2 + \sqrt[3]{{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}^{3}} \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \sqrt[3]{{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}^{3}}}{2 + \sqrt[3]{{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}^{3}} \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
double f(double t) {
        double r38291 = 1.0;
        double r38292 = 2.0;
        double r38293 = t;
        double r38294 = r38292 / r38293;
        double r38295 = r38291 / r38293;
        double r38296 = r38291 + r38295;
        double r38297 = r38294 / r38296;
        double r38298 = r38292 - r38297;
        double r38299 = r38298 * r38298;
        double r38300 = r38291 + r38299;
        double r38301 = r38292 + r38299;
        double r38302 = r38300 / r38301;
        return r38302;
}
↓
double f(double t) {
        double r38303 = 1.0;
        double r38304 = 2.0;
        double r38305 = t;
        double r38306 = r38304 / r38305;
        double r38307 = r38303 / r38305;
        double r38308 = r38303 + r38307;
        double r38309 = r38306 / r38308;
        double r38310 = r38304 - r38309;
        double r38311 = 3.0;
        double r38312 = pow(r38310, r38311);
        double r38313 = cbrt(r38312);
        double r38314 = r38310 * r38313;
        double r38315 = r38303 + r38314;
        double r38316 = r38313 * r38310;
        double r38317 = r38304 + r38316;
        double r38318 = r38315 / r38317;
        return r38318;
}

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

    \[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

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

  4. Simplified0.0

    \[\leadsto \frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \sqrt[3]{\color{blue}{{\left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}^{3}}} \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
  5. Using strategy rm

  6. Applied add-cbrt-cube0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (t)
  :name "Kahan p13 Example 2"
  :precision binary64
  (/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))