Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{\frac{4 - \left(\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}\right) \cdot \left(\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}\right)}{2 - \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}}\]
\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 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{\frac{4 - \left(\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}\right) \cdot \left(\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}\right)}{2 - \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}}
double f(double t) {
        double r1949263 = 1.0;
        double r1949264 = 2.0;
        double r1949265 = t;
        double r1949266 = r1949264 * r1949265;
        double r1949267 = r1949263 + r1949265;
        double r1949268 = r1949266 / r1949267;
        double r1949269 = r1949268 * r1949268;
        double r1949270 = r1949263 + r1949269;
        double r1949271 = r1949264 + r1949269;
        double r1949272 = r1949270 / r1949271;
        return r1949272;
}
↓
double f(double t) {
        double r1949273 = 1.0;
        double r1949274 = t;
        double r1949275 = 2.0;
        double r1949276 = r1949274 * r1949275;
        double r1949277 = r1949273 + r1949274;
        double r1949278 = r1949276 / r1949277;
        double r1949279 = r1949278 * r1949278;
        double r1949280 = r1949273 + r1949279;
        double r1949281 = 4.0;
        double r1949282 = r1949279 * r1949279;
        double r1949283 = r1949281 - r1949282;
        double r1949284 = r1949275 - r1949279;
        double r1949285 = r1949283 / r1949284;
        double r1949286 = r1949280 / r1949285;
        return r1949286;
}

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-+0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019139 
(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))))))