Average Error: 0.0 → 0.0
Time: 3.2s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(\left(\sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}} \cdot \sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}}\right) \cdot \sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
1 - \frac{1}{2 + \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 + \left(\left(\sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}} \cdot \sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}}\right) \cdot \sqrt[3]{2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
double f(double t) {
        double r40570 = 1.0;
        double r40571 = 2.0;
        double r40572 = t;
        double r40573 = r40571 / r40572;
        double r40574 = r40570 / r40572;
        double r40575 = r40570 + r40574;
        double r40576 = r40573 / r40575;
        double r40577 = r40571 - r40576;
        double r40578 = r40577 * r40577;
        double r40579 = r40571 + r40578;
        double r40580 = r40570 / r40579;
        double r40581 = r40570 - r40580;
        return r40581;
}
↓
double f(double t) {
        double r40582 = 1.0;
        double r40583 = 2.0;
        double r40584 = t;
        double r40585 = r40583 / r40584;
        double r40586 = r40582 / r40584;
        double r40587 = r40582 + r40586;
        double r40588 = r40585 / r40587;
        double r40589 = r40583 - r40588;
        double r40590 = cbrt(r40589);
        double r40591 = r40590 * r40590;
        double r40592 = r40591 * r40590;
        double r40593 = r40592 * r40589;
        double r40594 = r40583 + r40593;
        double r40595 = r40582 / r40594;
        double r40596 = r40582 - r40595;
        return r40596;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))