Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\log \left(e^{\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right)}\right) - -2}\]
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}{\log \left(e^{\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right)}\right) - -2}
double f(double t) {
        double r1855410 = 1.0;
        double r1855411 = 2.0;
        double r1855412 = t;
        double r1855413 = r1855411 / r1855412;
        double r1855414 = r1855410 / r1855412;
        double r1855415 = r1855410 + r1855414;
        double r1855416 = r1855413 / r1855415;
        double r1855417 = r1855411 - r1855416;
        double r1855418 = r1855417 * r1855417;
        double r1855419 = r1855411 + r1855418;
        double r1855420 = r1855410 / r1855419;
        double r1855421 = r1855410 - r1855420;
        return r1855421;
}
↓
double f(double t) {
        double r1855422 = 1.0;
        double r1855423 = -2.0;
        double r1855424 = t;
        double r1855425 = r1855422 + r1855424;
        double r1855426 = r1855423 / r1855425;
        double r1855427 = r1855423 - r1855426;
        double r1855428 = r1855427 * r1855427;
        double r1855429 = exp(r1855428);
        double r1855430 = log(r1855429);
        double r1855431 = r1855430 - r1855423;
        double r1855432 = r1855422 / r1855431;
        double r1855433 = r1855422 - r1855432;
        return r1855433;
}

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-log-exp0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))