Average Error: 0.0 → 0.0
Time: 8.4s
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 r547375 = 1.0;
        double r547376 = 2.0;
        double r547377 = t;
        double r547378 = r547376 / r547377;
        double r547379 = r547375 / r547377;
        double r547380 = r547375 + r547379;
        double r547381 = r547378 / r547380;
        double r547382 = r547376 - r547381;
        double r547383 = r547382 * r547382;
        double r547384 = r547376 + r547383;
        double r547385 = r547375 / r547384;
        double r547386 = r547375 - r547385;
        return r547386;
}
↓
double f(double t) {
        double r547387 = 1.0;
        double r547388 = 2.0;
        double r547389 = t;
        double r547390 = r547387 + r547389;
        double r547391 = r547388 / r547390;
        double r547392 = r547388 - r547391;
        double r547393 = cbrt(r547392);
        double r547394 = r547393 * r547393;
        double r547395 = r547392 * r547393;
        double r547396 = r547394 * r547395;
        double r547397 = r547396 + r547388;
        double r547398 = r547387 / r547397;
        double r547399 = r547387 - r547398;
        return r547399;
}

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)))))))))