Average Error: 46.3 → 0.0
Time: 5.4s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{2 \cdot i + \sqrt{1}} \cdot \frac{\frac{i}{2 \cdot i - \sqrt{1}}}{2 \cdot 2}\]
\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{i}{2 \cdot i + \sqrt{1}} \cdot \frac{\frac{i}{2 \cdot i - \sqrt{1}}}{2 \cdot 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 ((i / ((2.0 * i) + sqrt(1.0))) * ((i / ((2.0 * i) - sqrt(1.0))) / (2.0 * 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 46.3

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

  2. Simplified15.7

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

  4. Applied add-sqr-sqrt15.7

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

  5. Applied difference-of-squares15.7

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

  6. Applied associate-*l*15.7

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

  7. Applied times-frac0.1

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

  8. Simplified0.0

    \[\leadsto \frac{i}{2 \cdot i + \sqrt{1}} \cdot \color{blue}{\frac{\frac{i}{2 \cdot i - \sqrt{1}}}{2 \cdot 2}}\]

  9. Final simplification0.0

    \[\leadsto \frac{i}{2 \cdot i + \sqrt{1}} \cdot \frac{\frac{i}{2 \cdot i - \sqrt{1}}}{2 \cdot 2}\]

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(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)))