Average Error: 0.0 → 0.1
Time: 18.3s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 - \left(\frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}\right) \cdot \left(\frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}\right)}{\left(\frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1} + 2\right) \cdot \left(1 - \frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}\right)}\]
\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}
↓
\frac{1 - \left(\frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}\right) \cdot \left(\frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}\right)}{\left(\frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1} + 2\right) \cdot \left(1 - \frac{2 \cdot t}{t + 1} \cdot \frac{2 \cdot t}{t + 1}\right)}
double f(double t) {
        double r1524274 = 1.0;
        double r1524275 = 2.0;
        double r1524276 = t;
        double r1524277 = r1524275 * r1524276;
        double r1524278 = r1524274 + r1524276;
        double r1524279 = r1524277 / r1524278;
        double r1524280 = r1524279 * r1524279;
        double r1524281 = r1524274 + r1524280;
        double r1524282 = r1524275 + r1524280;
        double r1524283 = r1524281 / r1524282;
        return r1524283;
}
↓
double f(double t) {
        double r1524284 = 1.0;
        double r1524285 = 2.0;
        double r1524286 = t;
        double r1524287 = r1524285 * r1524286;
        double r1524288 = r1524286 + r1524284;
        double r1524289 = r1524287 / r1524288;
        double r1524290 = r1524289 * r1524289;
        double r1524291 = r1524290 * r1524290;
        double r1524292 = r1524284 - r1524291;
        double r1524293 = r1524290 + r1524285;
        double r1524294 = r1524284 - r1524290;
        double r1524295 = r1524293 * r1524294;
        double r1524296 = r1524292 / r1524295;
        return r1524296;
}

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

    \[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
  2. Using strategy rm

  3. Applied flip-+0.1

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

  4. Applied associate-/l/0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019135 
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))