Average Error: 46.6 → 0.2
Time: 8.2s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(2 \cdot 2\right) \cdot \left(4 \cdot i - \frac{1}{i}\right)}\]
\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{i}{\left(2 \cdot 2\right) \cdot \left(4 \cdot i - \frac{1}{i}\right)}
double f(double i) {
        double r63338 = i;
        double r63339 = r63338 * r63338;
        double r63340 = r63339 * r63339;
        double r63341 = 2.0;
        double r63342 = r63341 * r63338;
        double r63343 = r63342 * r63342;
        double r63344 = r63340 / r63343;
        double r63345 = 1.0;
        double r63346 = r63343 - r63345;
        double r63347 = r63344 / r63346;
        return r63347;
}
↓
double f(double i) {
        double r63348 = i;
        double r63349 = 2.0;
        double r63350 = r63349 * r63349;
        double r63351 = 4.0;
        double r63352 = r63351 * r63348;
        double r63353 = 1.0;
        double r63354 = r63353 / r63348;
        double r63355 = r63352 - r63354;
        double r63356 = r63350 * r63355;
        double r63357 = r63348 / r63356;
        return r63357;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.6

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

  2. Simplified0.2

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

  3. Taylor expanded around 0 0.2

    \[\leadsto \frac{i}{\left(2 \cdot 2\right) \cdot \color{blue}{\left(4 \cdot i - 1 \cdot \frac{1}{i}\right)}}\]

  4. Simplified0.2

    \[\leadsto \frac{i}{\left(2 \cdot 2\right) \cdot \color{blue}{\left(4 \cdot i - \frac{1}{i}\right)}}\]

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(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)))