Average Error: 46.4 → 0.3
Time: 1.2s
Precision: binary64
\[i > 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{0.25}{4 - \frac{1}{i \cdot i}}\]
\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{0.25}{4 - \frac{1}{i \cdot i}}
(FPCore (i)
 :precision binary64
 (/
  (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i)))
  (- (* (* 2.0 i) (* 2.0 i)) 1.0)))
↓
(FPCore (i) :precision binary64 (/ 0.25 (- 4.0 (/ 1.0 (* i i)))))
double code(double i) {
	return ((((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 (0.25 / ((double) (4.0 - (1.0 / ((double) (i * i))))));
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.4

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

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{0.25}{4 - \frac{1}{i \cdot i}}}\]

  3. Final simplification0.3

    \[\leadsto \frac{0.25}{4 - \frac{1}{i \cdot i}}\]

Reproduce

herbie shell --seed 2020210 
(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)))