Average Error: 46.3 → 0.1
Time: 16.2s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}\]
\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{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}
double f(double i) {
        double r49399 = i;
        double r49400 = r49399 * r49399;
        double r49401 = r49400 * r49400;
        double r49402 = 2.0;
        double r49403 = r49402 * r49399;
        double r49404 = r49403 * r49403;
        double r49405 = r49401 / r49404;
        double r49406 = 1.0;
        double r49407 = r49404 - r49406;
        double r49408 = r49405 / r49407;
        return r49408;
}
↓
double f(double i) {
        double r49409 = i;
        double r49410 = 2.0;
        double r49411 = r49410 * r49410;
        double r49412 = r49409 / r49411;
        double r49413 = r49410 * r49409;
        double r49414 = r49410 * r49413;
        double r49415 = 1.0;
        double r49416 = r49415 / r49409;
        double r49417 = r49414 - r49416;
        double r49418 = r49412 / r49417;
        return r49418;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.3

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(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)))