Average Error: 0.0 → 0.0
Time: 9.0s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \sqrt[3]{\left(\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)} \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)}\]
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 + \sqrt[3]{\left(\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)} \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right)}
double f(double t) {
        double r1731071 = 1.0;
        double r1731072 = 2.0;
        double r1731073 = t;
        double r1731074 = r1731072 / r1731073;
        double r1731075 = r1731071 / r1731073;
        double r1731076 = r1731071 + r1731075;
        double r1731077 = r1731074 / r1731076;
        double r1731078 = r1731072 - r1731077;
        double r1731079 = r1731078 * r1731078;
        double r1731080 = r1731072 + r1731079;
        double r1731081 = r1731071 / r1731080;
        double r1731082 = r1731071 - r1731081;
        return r1731082;
}
↓
double f(double t) {
        double r1731083 = 1.0;
        double r1731084 = 2.0;
        double r1731085 = t;
        double r1731086 = r1731083 * r1731085;
        double r1731087 = r1731086 + r1731083;
        double r1731088 = r1731084 / r1731087;
        double r1731089 = r1731084 - r1731088;
        double r1731090 = r1731089 * r1731089;
        double r1731091 = r1731090 * r1731089;
        double r1731092 = cbrt(r1731091);
        double r1731093 = r1731092 * r1731089;
        double r1731094 = r1731084 + r1731093;
        double r1731095 = r1731083 / r1731094;
        double r1731096 = r1731083 - r1731095;
        return r1731096;
}

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

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

  4. Applied add-cbrt-cube0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1.0 (/ 1.0 (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))))))