Average Error: 46.8 → 0.2
Time: 1.9s
Precision: binary64
\[i > 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2}}{2 \cdot \left(i \cdot \left(2 \cdot 2\right) - \frac{1}{i}\right)}\]
\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{\frac{i}{2}}{2 \cdot \left(i \cdot \left(2 \cdot 2\right) - \frac{1}{i}\right)}
(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
 (/ (/ i 2.0) (* 2.0 (- (* i (* 2.0 2.0)) (/ 1.0 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 ((i / 2.0) / ((double) (2.0 * ((double) (((double) (i * ((double) (2.0 * 2.0)))) - (1.0 / i))))));
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 46.8 bits

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

  2. SimplifiedError: 0.2 bits

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

  4. Applied associate-/r*Error: 0.2 bits

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

  5. Final simplificationError: 0.2 bits

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

Reproduce

herbie shell --seed 2020204 
(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)))