Average Error: 32.0 → 32.0
Time: 1.3s
Precision: binary64
\[\sqrt{\left(x + \frac{\sqrt{3}}{27}\right) \cdot \left(x - \frac{\sqrt{3}}{27}\right)}\]
↓
\[\sqrt{\left(x + \frac{\sqrt{3}}{27}\right) \cdot \left(x - \frac{\sqrt{3}}{27}\right)}\]
\sqrt{\left(x + \frac{\sqrt{3}}{27}\right) \cdot \left(x - \frac{\sqrt{3}}{27}\right)}
↓
\sqrt{\left(x + \frac{\sqrt{3}}{27}\right) \cdot \left(x - \frac{\sqrt{3}}{27}\right)}
double code(double x) {
	return ((double) sqrt(((double) (((double) (x + ((double) (((double) sqrt(3.0)) / 27.0)))) * ((double) (x - ((double) (((double) sqrt(3.0)) / 27.0))))))));
}
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) (x + ((double) (((double) sqrt(3.0)) / 27.0)))) * ((double) (x - ((double) (((double) sqrt(3.0)) / 27.0))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 32.0

    \[\sqrt{\left(x + \frac{\sqrt{3}}{27}\right) \cdot \left(x - \frac{\sqrt{3}}{27}\right)}\]

  2. Final simplification32.0

    \[\leadsto \sqrt{\left(x + \frac{\sqrt{3}}{27}\right) \cdot \left(x - \frac{\sqrt{3}}{27}\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(sqrt (* (+ x (/ (sqrt 3) 27)) (- x (/ (sqrt 3) 27))))"
  :precision binary64
  (sqrt (* (+ x (/ (sqrt 3.0) 27.0)) (- x (/ (sqrt 3.0) 27.0)))))