Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}\]
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(2 - \frac{2}{1 \cdot t + 1}\right) \cdot \left(2 - \frac{2}{1 \cdot t + 1}\right) + 2}
double f(double t) {
        double r1423211 = 1.0;
        double r1423212 = 2.0;
        double r1423213 = t;
        double r1423214 = r1423212 / r1423213;
        double r1423215 = r1423211 / r1423213;
        double r1423216 = r1423211 + r1423215;
        double r1423217 = r1423214 / r1423216;
        double r1423218 = r1423212 - r1423217;
        double r1423219 = r1423218 * r1423218;
        double r1423220 = r1423212 + r1423219;
        double r1423221 = r1423211 / r1423220;
        double r1423222 = r1423211 - r1423221;
        return r1423222;
}
↓
double f(double t) {
        double r1423223 = 1.0;
        double r1423224 = 2.0;
        double r1423225 = t;
        double r1423226 = r1423223 * r1423225;
        double r1423227 = r1423226 + r1423223;
        double r1423228 = r1423224 / r1423227;
        double r1423229 = r1423224 - r1423228;
        double r1423230 = r1423229 * r1423229;
        double r1423231 = r1423230 + r1423224;
        double r1423232 = r1423223 / r1423231;
        double r1423233 = r1423223 - r1423232;
        return r1423233;
}

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

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

Reproduce

herbie shell --seed 2019172 
(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)))))))))