Average Error: 18.8 → 18.8
Time: 2.8s
Precision: binary64
\[4 \cdot {\left(\cos \left(\frac{x}{3}\right)\right)}^{3} - 3 \cdot \cos \left(\frac{x}{3}\right)\]
↓
\[4 \cdot {\left(\cos \left(\frac{x}{3}\right)\right)}^{3} - 3 \cdot \cos \left(\frac{x}{3}\right)\]
4 \cdot {\left(\cos \left(\frac{x}{3}\right)\right)}^{3} - 3 \cdot \cos \left(\frac{x}{3}\right)
↓
4 \cdot {\left(\cos \left(\frac{x}{3}\right)\right)}^{3} - 3 \cdot \cos \left(\frac{x}{3}\right)
double code(double x) {
	return ((double) (((double) (4.0 * ((double) pow(((double) cos(((double) (x / 3.0)))), 3.0)))) - ((double) (3.0 * ((double) cos(((double) (x / 3.0))))))));
}
↓
double code(double x) {
	return ((double) (((double) (4.0 * ((double) pow(((double) cos(((double) (x / 3.0)))), 3.0)))) - ((double) (3.0 * ((double) cos(((double) (x / 3.0))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.8

    \[4 \cdot {\left(\cos \left(\frac{x}{3}\right)\right)}^{3} - 3 \cdot \cos \left(\frac{x}{3}\right)\]

  2. Final simplification18.8

    \[\leadsto 4 \cdot {\left(\cos \left(\frac{x}{3}\right)\right)}^{3} - 3 \cdot \cos \left(\frac{x}{3}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (* 4.0 (pow (cos (/ x 3.0)) 3.0)) (* 3.0 (cos (/ x 3.0))))"
  :precision binary64
  (- (* 4.0 (pow (cos (/ x 3.0)) 3.0)) (* 3.0 (cos (/ x 3.0)))))