Average Error: 46.5 → 0.3
Time: 31.4s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}\]
\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(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r2955997 = i;
        double r2955998 = r2955997 * r2955997;
        double r2955999 = r2955998 * r2955998;
        double r2956000 = 2.0;
        double r2956001 = r2956000 * r2955997;
        double r2956002 = r2956001 * r2956001;
        double r2956003 = r2955999 / r2956002;
        double r2956004 = 1.0;
        double r2956005 = r2956002 - r2956004;
        double r2956006 = r2956003 / r2956005;
        return r2956006;
}
↓
double f(double i) {
        double r2956007 = i;
        double r2956008 = 4.0;
        double r2956009 = r2956008 * r2956007;
        double r2956010 = 1.0;
        double r2956011 = r2956010 / r2956007;
        double r2956012 = r2956009 - r2956011;
        double r2956013 = 2.0;
        double r2956014 = r2956013 * r2956013;
        double r2956015 = r2956012 * r2956014;
        double r2956016 = r2956007 / r2956015;
        return r2956016;
}

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. Simplified0.3

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

  3. Taylor expanded around 0 0.3

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

  4. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0)))