Average Error: 0.0 → 0.0
Time: 21.9s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{4 - \left(\left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right)\right) \cdot \left(\left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right)\right)} \cdot \left(2 - \left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right)\right)\]
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}{4 - \left(\left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right)\right) \cdot \left(\left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right)\right)} \cdot \left(2 - \left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right)\right)
double f(double t) {
        double r2212271 = 1.0;
        double r2212272 = 2.0;
        double r2212273 = t;
        double r2212274 = r2212272 / r2212273;
        double r2212275 = r2212271 / r2212273;
        double r2212276 = r2212271 + r2212275;
        double r2212277 = r2212274 / r2212276;
        double r2212278 = r2212272 - r2212277;
        double r2212279 = r2212278 * r2212278;
        double r2212280 = r2212272 + r2212279;
        double r2212281 = r2212271 / r2212280;
        double r2212282 = r2212271 - r2212281;
        return r2212282;
}
↓
double f(double t) {
        double r2212283 = 1.0;
        double r2212284 = 4.0;
        double r2212285 = 2.0;
        double r2212286 = t;
        double r2212287 = r2212286 + r2212283;
        double r2212288 = r2212285 / r2212287;
        double r2212289 = r2212285 - r2212288;
        double r2212290 = r2212289 * r2212289;
        double r2212291 = r2212290 * r2212290;
        double r2212292 = r2212284 - r2212291;
        double r2212293 = r2212283 / r2212292;
        double r2212294 = r2212285 - r2212290;
        double r2212295 = r2212293 * r2212294;
        double r2212296 = r2212283 - r2212295;
        return r2212296;
}

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 flip-+0.0

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

  5. Applied associate-/r/0.0

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

  6. Final simplification0.0

    \[\leadsto 1 - \frac{1}{4 - \left(\left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right)\right) \cdot \left(\left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right)\right)} \cdot \left(2 - \left(2 - \frac{2}{t + 1}\right) \cdot \left(2 - \frac{2}{t + 1}\right)\right)\]

Reproduce

herbie shell --seed 2019119 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))