Average Error: 0.0 → 0.0
Time: 18.3s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\sqrt[3]{\left(2 - \frac{2}{1 + t}\right) \cdot \left(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)\right)} \cdot \left(2 - \frac{2}{1 + t}\right) + 2}\]
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(2 - \frac{2}{1 + t}\right) \cdot \left(\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)\right)} \cdot \left(2 - \frac{2}{1 + t}\right) + 2}
double f(double t) {
        double r1303640 = 1.0;
        double r1303641 = 2.0;
        double r1303642 = t;
        double r1303643 = r1303641 / r1303642;
        double r1303644 = r1303640 / r1303642;
        double r1303645 = r1303640 + r1303644;
        double r1303646 = r1303643 / r1303645;
        double r1303647 = r1303641 - r1303646;
        double r1303648 = r1303647 * r1303647;
        double r1303649 = r1303641 + r1303648;
        double r1303650 = r1303640 / r1303649;
        double r1303651 = r1303640 - r1303650;
        return r1303651;
}
↓
double f(double t) {
        double r1303652 = 1.0;
        double r1303653 = 2.0;
        double r1303654 = t;
        double r1303655 = r1303652 + r1303654;
        double r1303656 = r1303653 / r1303655;
        double r1303657 = r1303653 - r1303656;
        double r1303658 = r1303657 * r1303657;
        double r1303659 = r1303657 * r1303658;
        double r1303660 = cbrt(r1303659);
        double r1303661 = r1303660 * r1303657;
        double r1303662 = r1303661 + r1303653;
        double r1303663 = r1303652 / r1303662;
        double r1303664 = r1303652 - r1303663;
        return r1303664;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019141 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))