Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(\sqrt[3]{2 - \frac{2}{1 + t}} \cdot \sqrt[3]{2 - \frac{2}{1 + t}}\right) \cdot \left(\left(2 - \frac{2}{1 + t}\right) \cdot \sqrt[3]{2 - \frac{2}{1 + t}}\right) + 2}\]
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}{\left(\sqrt[3]{2 - \frac{2}{1 + t}} \cdot \sqrt[3]{2 - \frac{2}{1 + t}}\right) \cdot \left(\left(2 - \frac{2}{1 + t}\right) \cdot \sqrt[3]{2 - \frac{2}{1 + t}}\right) + 2}
double f(double t) {
        double r716937 = 1.0;
        double r716938 = 2.0;
        double r716939 = t;
        double r716940 = r716938 / r716939;
        double r716941 = r716937 / r716939;
        double r716942 = r716937 + r716941;
        double r716943 = r716940 / r716942;
        double r716944 = r716938 - r716943;
        double r716945 = r716944 * r716944;
        double r716946 = r716938 + r716945;
        double r716947 = r716937 / r716946;
        double r716948 = r716937 - r716947;
        return r716948;
}
↓
double f(double t) {
        double r716949 = 1.0;
        double r716950 = 2.0;
        double r716951 = t;
        double r716952 = r716949 + r716951;
        double r716953 = r716950 / r716952;
        double r716954 = r716950 - r716953;
        double r716955 = cbrt(r716954);
        double r716956 = r716955 * r716955;
        double r716957 = r716954 * r716955;
        double r716958 = r716956 * r716957;
        double r716959 = r716958 + r716950;
        double r716960 = r716949 / r716959;
        double r716961 = r716949 - r716960;
        return r716961;
}

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-cube-cbrt0.0

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

  5. Applied associate-*l*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))