Average Error: 0.0 → 0.0
Time: 11.4s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{{1}^{3} + {\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}^{3}}{\left(\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t} - 1\right) + 1 \cdot 1\right) \cdot \left(2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}\]
\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}^{3} + {\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}^{3}}{\left(\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} - 1\right) + 1 \cdot 1\right) \cdot \left(2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}
double f(double t) {
        double r49314 = 1.0;
        double r49315 = 2.0;
        double r49316 = t;
        double r49317 = r49315 * r49316;
        double r49318 = r49314 + r49316;
        double r49319 = r49317 / r49318;
        double r49320 = r49319 * r49319;
        double r49321 = r49314 + r49320;
        double r49322 = r49315 + r49320;
        double r49323 = r49321 / r49322;
        return r49323;
}
↓
double f(double t) {
        double r49324 = 1.0;
        double r49325 = 3.0;
        double r49326 = pow(r49324, r49325);
        double r49327 = 2.0;
        double r49328 = t;
        double r49329 = r49327 * r49328;
        double r49330 = r49324 + r49328;
        double r49331 = r49329 / r49330;
        double r49332 = r49331 * r49331;
        double r49333 = pow(r49332, r49325);
        double r49334 = r49326 + r49333;
        double r49335 = r49332 - r49324;
        double r49336 = r49332 * r49335;
        double r49337 = r49324 * r49324;
        double r49338 = r49336 + r49337;
        double r49339 = r49327 + r49332;
        double r49340 = r49338 * r49339;
        double r49341 = r49334 / r49340;
        return r49341;
}

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 flip3-+0.0

    \[\leadsto \frac{\color{blue}{\frac{{1}^{3} + {\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}^{3}}{1 \cdot 1 + \left(\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) - 1 \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)\right)}}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

  4. Applied associate-/l/0.0

    \[\leadsto \color{blue}{\frac{{1}^{3} + {\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}^{3}}{\left(2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(1 \cdot 1 + \left(\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) - 1 \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)\right)\right)}}\]

  5. Simplified0.0

    \[\leadsto \frac{{1}^{3} + {\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}^{3}}{\color{blue}{\left(\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t} - 1\right) + 1 \cdot 1\right) \cdot \left(2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}}\]

  6. Final simplification0.0

    \[\leadsto \frac{{1}^{3} + {\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}^{3}}{\left(\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t} - 1\right) + 1 \cdot 1\right) \cdot \left(2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (t)
  :name "Kahan p13 Example 1"
  :precision binary64
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))