Average Error: 45.5 → 0.3
Time: 18.8s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{i}{\left(i \cdot 4 - \frac{1.0}{i}\right) \cdot 4}\]
\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) - 1.0}
↓
\frac{i}{\left(i \cdot 4 - \frac{1.0}{i}\right) \cdot 4}
double f(double i) {
        double r2942554 = i;
        double r2942555 = r2942554 * r2942554;
        double r2942556 = r2942555 * r2942555;
        double r2942557 = 2.0;
        double r2942558 = r2942557 * r2942554;
        double r2942559 = r2942558 * r2942558;
        double r2942560 = r2942556 / r2942559;
        double r2942561 = 1.0;
        double r2942562 = r2942559 - r2942561;
        double r2942563 = r2942560 / r2942562;
        return r2942563;
}
↓
double f(double i) {
        double r2942564 = i;
        double r2942565 = 4.0;
        double r2942566 = r2942564 * r2942565;
        double r2942567 = 1.0;
        double r2942568 = r2942567 / r2942564;
        double r2942569 = r2942566 - r2942568;
        double r2942570 = r2942569 * r2942565;
        double r2942571 = r2942564 / r2942570;
        return r2942571;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.5

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{i}{4 \cdot \left(4 \cdot i - \frac{1.0}{i}\right)}}\]

  3. Taylor expanded around 0 0.3

    \[\leadsto \frac{i}{4 \cdot \color{blue}{\left(4 \cdot i - 1.0 \cdot \frac{1}{i}\right)}}\]

  4. Simplified0.3

    \[\leadsto \frac{i}{4 \cdot \color{blue}{\left(i \cdot 4 - \frac{1.0}{i}\right)}}\]

  5. Final simplification0.3

    \[\leadsto \frac{i}{\left(i \cdot 4 - \frac{1.0}{i}\right) \cdot 4}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0)))