Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \sqrt[3]{\left(\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)} \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)}\]
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 + \sqrt[3]{\left(\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)} \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)}
double f(double t) {
        double r1905789 = 1.0;
        double r1905790 = 2.0;
        double r1905791 = t;
        double r1905792 = r1905790 / r1905791;
        double r1905793 = r1905789 / r1905791;
        double r1905794 = r1905789 + r1905793;
        double r1905795 = r1905792 / r1905794;
        double r1905796 = r1905790 - r1905795;
        double r1905797 = r1905796 * r1905796;
        double r1905798 = r1905790 + r1905797;
        double r1905799 = r1905789 / r1905798;
        double r1905800 = r1905789 - r1905799;
        return r1905800;
}
↓
double f(double t) {
        double r1905801 = 1.0;
        double r1905802 = 2.0;
        double r1905803 = t;
        double r1905804 = r1905801 * r1905803;
        double r1905805 = r1905804 + r1905801;
        double r1905806 = r1905802 / r1905805;
        double r1905807 = r1905802 - r1905806;
        double r1905808 = r1905807 * r1905807;
        double r1905809 = r1905808 * r1905807;
        double r1905810 = cbrt(r1905809);
        double r1905811 = r1905810 * r1905807;
        double r1905812 = r1905802 + r1905811;
        double r1905813 = r1905801 / r1905812;
        double r1905814 = r1905801 - r1905813;
        return r1905814;
}

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

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

  4. Applied add-cbrt-cube0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(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)))))))))