Average Error: 0.0 → 0.0
Time: 9.6s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\sqrt[3]{\left(\left(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)\right) \cdot \left(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)\right)\right) \cdot \left(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)\right)} + 2}\]
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(\left(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)\right) \cdot \left(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)\right)\right) \cdot \left(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)\right)} + 2}
double f(double t) {
        double r1545726 = 1.0;
        double r1545727 = 2.0;
        double r1545728 = t;
        double r1545729 = r1545727 / r1545728;
        double r1545730 = r1545726 / r1545728;
        double r1545731 = r1545726 + r1545730;
        double r1545732 = r1545729 / r1545731;
        double r1545733 = r1545727 - r1545732;
        double r1545734 = r1545733 * r1545733;
        double r1545735 = r1545727 + r1545734;
        double r1545736 = r1545726 / r1545735;
        double r1545737 = r1545726 - r1545736;
        return r1545737;
}
↓
double f(double t) {
        double r1545738 = 1.0;
        double r1545739 = 2.0;
        double r1545740 = t;
        double r1545741 = r1545738 + r1545740;
        double r1545742 = r1545739 / r1545741;
        double r1545743 = r1545739 - r1545742;
        double r1545744 = r1545743 * r1545743;
        double r1545745 = r1545744 * r1545744;
        double r1545746 = r1545745 * r1545744;
        double r1545747 = cbrt(r1545746);
        double r1545748 = r1545747 + r1545739;
        double r1545749 = r1545738 / r1545748;
        double r1545750 = r1545738 - r1545749;
        return r1545750;
}

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-cbrt-cube0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))