Average Error: 0.0 → 0.0
Time: 20.2s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \log \left(e^{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\right)}\]
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}{2 + \log \left(e^{\left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\right)}
double f(double t) {
        double r1351565 = 1.0;
        double r1351566 = 2.0;
        double r1351567 = t;
        double r1351568 = r1351566 / r1351567;
        double r1351569 = r1351565 / r1351567;
        double r1351570 = r1351565 + r1351569;
        double r1351571 = r1351568 / r1351570;
        double r1351572 = r1351566 - r1351571;
        double r1351573 = r1351572 * r1351572;
        double r1351574 = r1351566 + r1351573;
        double r1351575 = r1351565 / r1351574;
        double r1351576 = r1351565 - r1351575;
        return r1351576;
}
↓
double f(double t) {
        double r1351577 = 1.0;
        double r1351578 = 2.0;
        double r1351579 = t;
        double r1351580 = r1351577 + r1351579;
        double r1351581 = r1351578 / r1351580;
        double r1351582 = r1351578 - r1351581;
        double r1351583 = r1351582 * r1351582;
        double r1351584 = exp(r1351583);
        double r1351585 = log(r1351584);
        double r1351586 = r1351578 + r1351585;
        double r1351587 = r1351577 / r1351586;
        double r1351588 = r1351577 - r1351587;
        return r1351588;
}

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-log-exp0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019139 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))