Average Error: 0.0 → 0.0
Time: 9.3s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{t \cdot 1 + 1}\right) \cdot \sqrt[3]{{\left(2 - \frac{2}{t \cdot 1 + 1}\right)}^{3}}}\]
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(2 - \frac{2}{t \cdot 1 + 1}\right) \cdot \sqrt[3]{{\left(2 - \frac{2}{t \cdot 1 + 1}\right)}^{3}}}
double f(double t) {
        double r21991 = 1.0;
        double r21992 = 2.0;
        double r21993 = t;
        double r21994 = r21992 / r21993;
        double r21995 = r21991 / r21993;
        double r21996 = r21991 + r21995;
        double r21997 = r21994 / r21996;
        double r21998 = r21992 - r21997;
        double r21999 = r21998 * r21998;
        double r22000 = r21992 + r21999;
        double r22001 = r21991 / r22000;
        double r22002 = r21991 - r22001;
        return r22002;
}
↓
double f(double t) {
        double r22003 = 1.0;
        double r22004 = 2.0;
        double r22005 = t;
        double r22006 = r22005 * r22003;
        double r22007 = r22006 + r22003;
        double r22008 = r22004 / r22007;
        double r22009 = r22004 - r22008;
        double r22010 = 3.0;
        double r22011 = pow(r22009, r22010);
        double r22012 = cbrt(r22011);
        double r22013 = r22009 * r22012;
        double r22014 = r22004 + r22013;
        double r22015 = r22003 / r22014;
        double r22016 = r22003 - r22015;
        return r22016;
}

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

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

  4. Applied add-cbrt-cube0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019235 
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))