Average Error: 46.5 → 0.3
Time: 16.1s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{\frac{8 - \frac{2}{{i}^{2}}}{0.5}}\]
\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}
↓
\frac{1}{\frac{8 - \frac{2}{{i}^{2}}}{0.5}}
double f(double i) {
        double r50216 = i;
        double r50217 = r50216 * r50216;
        double r50218 = r50217 * r50217;
        double r50219 = 2.0;
        double r50220 = r50219 * r50216;
        double r50221 = r50220 * r50220;
        double r50222 = r50218 / r50221;
        double r50223 = 1.0;
        double r50224 = r50221 - r50223;
        double r50225 = r50222 / r50224;
        return r50225;
}
↓
double f(double i) {
        double r50226 = 1.0;
        double r50227 = 8.0;
        double r50228 = 2.0;
        double r50229 = i;
        double r50230 = 2.0;
        double r50231 = pow(r50229, r50230);
        double r50232 = r50228 / r50231;
        double r50233 = r50227 - r50232;
        double r50234 = 0.5;
        double r50235 = r50233 / r50234;
        double r50236 = r50226 / r50235;
        return r50236;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.5

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]

  2. Simplified41.6

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

  3. Taylor expanded around 0 16.1

    \[\leadsto \frac{\color{blue}{0.5 \cdot {i}^{2}}}{\left(\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1\right) \cdot 2}\]
  4. Using strategy rm

  5. Applied clear-num16.4

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1\right) \cdot 2}{0.5 \cdot {i}^{2}}}}\]

  6. Simplified16.5

    \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1\right) \cdot \frac{2}{{i}^{2}}}{0.5}}}\]

  7. Taylor expanded around 0 0.3

    \[\leadsto \frac{1}{\frac{\color{blue}{8 - 2 \cdot \frac{1}{{i}^{2}}}}{0.5}}\]

  8. Simplified0.3

    \[\leadsto \frac{1}{\frac{\color{blue}{8 - \frac{2}{{i}^{2}}}}{0.5}}\]

  9. Final simplification0.3

    \[\leadsto \frac{1}{\frac{8 - \frac{2}{{i}^{2}}}{0.5}}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :precision binary64
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1)))