Average Error: 0.0 → 0.0
Time: 12.1s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\sqrt[3]{\left(\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2\right) \cdot \left(\left(\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2\right) \cdot \left(\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2\right)\right)}}\]
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}{\sqrt[3]{\left(\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2\right) \cdot \left(\left(\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2\right) \cdot \left(\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2\right)\right)}}
double f(double t) {
        double r2112168 = 1.0;
        double r2112169 = 2.0;
        double r2112170 = t;
        double r2112171 = r2112169 / r2112170;
        double r2112172 = r2112168 / r2112170;
        double r2112173 = r2112168 + r2112172;
        double r2112174 = r2112171 / r2112173;
        double r2112175 = r2112169 - r2112174;
        double r2112176 = r2112175 * r2112175;
        double r2112177 = r2112169 + r2112176;
        double r2112178 = r2112168 / r2112177;
        double r2112179 = r2112168 - r2112178;
        return r2112179;
}
↓
double f(double t) {
        double r2112180 = 1.0;
        double r2112181 = -2.0;
        double r2112182 = t;
        double r2112183 = r2112180 + r2112182;
        double r2112184 = r2112181 / r2112183;
        double r2112185 = r2112181 - r2112184;
        double r2112186 = r2112185 * r2112185;
        double r2112187 = r2112186 - r2112181;
        double r2112188 = r2112187 * r2112187;
        double r2112189 = r2112187 * r2112188;
        double r2112190 = cbrt(r2112189);
        double r2112191 = r2112180 / r2112190;
        double r2112192 = r2112180 - r2112191;
        return r2112192;
}

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

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

  4. Applied add-cbrt-cube0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))