Average Error: 46.2 → 0.3
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 code(double i) {
	return ((((i * i) * (i * i)) / ((2.0 * i) * (2.0 * i))) / (((2.0 * i) * (2.0 * i)) - 1.0));
}
↓
double code(double i) {
	return (1.0 / (16.0 - (4.0 * (1.0 / pow(i, 2.0)))));
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.2

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

  2. Simplified16.4

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

  4. Applied clear-num16.8

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

  5. Taylor expanded around 0 0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020100 
(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)))