Average Error: 46.8 → 0.3
Time: 3.4s
Precision: binary64
\[i > 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[0.25 \cdot \frac{1}{4 + \frac{-1}{i \cdot i}}\]
\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}
↓
0.25 \cdot \frac{1}{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 (/ 1.0 (+ 4.0 (/ -1.0 (* i i))))))
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 0.25 * (1.0 / (4.0 + (-1.0 / (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 46.8

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

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{0.25}{4 + \frac{-1}{i \cdot i}}}\]
  3. Using strategy rm

  4. Applied div-inv_binary64_37850.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020231 
(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)))