Average Error: 46.9 → 0.3
Time: 1.8s
Precision: binary64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{16 - 4 \cdot \frac{1}{{i}^{2}}}\]
\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 ((double) (((double) (((double) (((double) (i * i)) * ((double) (i * i)))) / ((double) (((double) (2.0 * i)) * ((double) (2.0 * i)))))) / ((double) (((double) (((double) (2.0 * i)) * ((double) (2.0 * i)))) - 1.0))));
}
↓
double code(double i) {
	return ((double) (1.0 / ((double) (16.0 - ((double) (4.0 * ((double) (1.0 / ((double) 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 46.9

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

  2. Simplified16.3

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

  3. Taylor expanded around 0 16.3

    \[\leadsto \frac{i \cdot i}{\color{blue}{\left(4 \cdot {i}^{2} - 1\right)} \cdot \left(2 \cdot 2\right)}\]
  4. Using strategy rm

  5. Applied clear-num16.6

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

  6. Taylor expanded around 0 0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020163 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :precision binary64
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0)))