Average Error: 0.0 → 0.0
Time: 25.5s
Precision: 64
\[1.0 - \frac{1.0}{2.0 + \left(2.0 - \frac{\frac{2.0}{t}}{1.0 + \frac{1.0}{t}}\right) \cdot \left(2.0 - \frac{\frac{2.0}{t}}{1.0 + \frac{1.0}{t}}\right)}\]
↓
\[1.0 - \frac{1.0}{2.0 + \sqrt[3]{\left(\left(\left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right) \cdot \left(\left(\left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right)}}\]
1.0 - \frac{1.0}{2.0 + \left(2.0 - \frac{\frac{2.0}{t}}{1.0 + \frac{1.0}{t}}\right) \cdot \left(2.0 - \frac{\frac{2.0}{t}}{1.0 + \frac{1.0}{t}}\right)}
↓
1.0 - \frac{1.0}{2.0 + \sqrt[3]{\left(\left(\left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right) \cdot \left(\left(\left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right)}}
double f(double t) {
        double r1840496 = 1.0;
        double r1840497 = 2.0;
        double r1840498 = t;
        double r1840499 = r1840497 / r1840498;
        double r1840500 = r1840496 / r1840498;
        double r1840501 = r1840496 + r1840500;
        double r1840502 = r1840499 / r1840501;
        double r1840503 = r1840497 - r1840502;
        double r1840504 = r1840503 * r1840503;
        double r1840505 = r1840497 + r1840504;
        double r1840506 = r1840496 / r1840505;
        double r1840507 = r1840496 - r1840506;
        return r1840507;
}
↓
double f(double t) {
        double r1840508 = 1.0;
        double r1840509 = 2.0;
        double r1840510 = t;
        double r1840511 = r1840508 * r1840510;
        double r1840512 = r1840511 + r1840508;
        double r1840513 = r1840509 / r1840512;
        double r1840514 = r1840509 - r1840513;
        double r1840515 = r1840514 * r1840514;
        double r1840516 = r1840515 * r1840514;
        double r1840517 = r1840516 * r1840516;
        double r1840518 = cbrt(r1840517);
        double r1840519 = r1840509 + r1840518;
        double r1840520 = r1840508 / r1840519;
        double r1840521 = r1840508 - r1840520;
        return r1840521;
}

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

    \[1.0 - \frac{1.0}{2.0 + \left(2.0 - \frac{\frac{2.0}{t}}{1.0 + \frac{1.0}{t}}\right) \cdot \left(2.0 - \frac{\frac{2.0}{t}}{1.0 + \frac{1.0}{t}}\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1.0 - \frac{1.0}{2.0 + \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)}}\]
  3. Using strategy rm

  4. Applied add-cbrt-cube0.0

    \[\leadsto 1.0 - \frac{1.0}{2.0 + \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right) \cdot \color{blue}{\sqrt[3]{\left(\left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)}}}\]

  5. Applied add-cbrt-cube0.0

    \[\leadsto 1.0 - \frac{1.0}{2.0 + \color{blue}{\sqrt[3]{\left(\left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)}} \cdot \sqrt[3]{\left(\left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)}}\]

  6. Applied cbrt-unprod0.0

    \[\leadsto 1.0 - \frac{1.0}{2.0 + \color{blue}{\sqrt[3]{\left(\left(\left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)\right) \cdot \left(\left(\left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 + 1.0 \cdot t}\right)\right)}}}\]

  7. Final simplification0.0

    \[\leadsto 1.0 - \frac{1.0}{2.0 + \sqrt[3]{\left(\left(\left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right) \cdot \left(\left(\left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right) \cdot \left(2.0 - \frac{2.0}{1.0 \cdot t + 1.0}\right)\right)}}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1.0 (/ 1.0 (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))))))