Average Error: 46.9 → 0.4
Time: 1.5s
Precision: binary64
\[i > 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{0.25}{4 - {i}^{-2}}\]
\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{0.25}{4 - {i}^{-2}}
(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 (pow i -2.0))))
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 / (4.0 - 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. Simplified0.3

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

  4. Applied pow1_binary640.3

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

  5. Applied pow1_binary640.3

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

  6. Applied pow-prod-up_binary640.3

    \[\leadsto \frac{0.25}{4 - \frac{1}{\color{blue}{{i}^{\left(1 + 1\right)}}}}\]

  7. Applied pow-flip_binary640.4

    \[\leadsto \frac{0.25}{4 - \color{blue}{{i}^{\left(-\left(1 + 1\right)\right)}}}\]

  8. Simplified0.4

    \[\leadsto \frac{0.25}{4 - {i}^{\color{blue}{-2}}}\]

  9. Final simplification0.4

    \[\leadsto \frac{0.25}{4 - {i}^{-2}}\]

Reproduce

herbie shell --seed 2020220 
(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)))