Average Error: 0.0 → 0.0
Time: 10.2s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{2}{1 + 1 \cdot t}\right) \cdot \left(2 - \frac{2}{1 + 1 \cdot t}\right)}\]
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 + \left(2 - \frac{2}{1 + 1 \cdot t}\right) \cdot \left(2 - \frac{2}{1 + 1 \cdot t}\right)}
double f(double t) {
        double r3510268 = 1.0;
        double r3510269 = 2.0;
        double r3510270 = t;
        double r3510271 = r3510269 / r3510270;
        double r3510272 = r3510268 / r3510270;
        double r3510273 = r3510268 + r3510272;
        double r3510274 = r3510271 / r3510273;
        double r3510275 = r3510269 - r3510274;
        double r3510276 = r3510275 * r3510275;
        double r3510277 = r3510269 + r3510276;
        double r3510278 = r3510268 / r3510277;
        double r3510279 = r3510268 - r3510278;
        return r3510279;
}
↓
double f(double t) {
        double r3510280 = 1.0;
        double r3510281 = 2.0;
        double r3510282 = t;
        double r3510283 = r3510280 * r3510282;
        double r3510284 = r3510280 + r3510283;
        double r3510285 = r3510281 / r3510284;
        double r3510286 = r3510281 - r3510285;
        double r3510287 = r3510286 * r3510286;
        double r3510288 = r3510281 + r3510287;
        double r3510289 = r3510280 / r3510288;
        double r3510290 = r3510280 - r3510289;
        return r3510290;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))))))))