Average Error: 47.0 → 0.4
Time: 1.9s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{16 - 4 \cdot \frac{1}{{i}^{2}}}\]
\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}{16 - 4 \cdot \frac{1}{{i}^{2}}}
double f(double i) {
        double r48998 = i;
        double r48999 = r48998 * r48998;
        double r49000 = r48999 * r48999;
        double r49001 = 2.0;
        double r49002 = r49001 * r48998;
        double r49003 = r49002 * r49002;
        double r49004 = r49000 / r49003;
        double r49005 = 1.0;
        double r49006 = r49003 - r49005;
        double r49007 = r49004 / r49006;
        return r49007;
}
↓
double f(double i) {
        double r49008 = 1.0;
        double r49009 = 16.0;
        double r49010 = 4.0;
        double r49011 = i;
        double r49012 = 2.0;
        double r49013 = pow(r49011, r49012);
        double r49014 = r49008 / r49013;
        double r49015 = r49010 * r49014;
        double r49016 = r49009 - r49015;
        double r49017 = r49008 / r49016;
        return r49017;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 47.0

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

  2. Simplified16.2

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

  4. Applied clear-num16.5

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

  5. Taylor expanded around 0 0.4

    \[\leadsto \frac{1}{\color{blue}{16 - 4 \cdot \frac{1}{{i}^{2}}}}\]

  6. Final simplification0.4

    \[\leadsto \frac{1}{16 - 4 \cdot \frac{1}{{i}^{2}}}\]

Reproduce

herbie shell --seed 2020033 
(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)))