Average Error: 27.2 → 4.5
Time: 9.8s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double c, double s) {
	return ((double) (((double) cos(((double) (2.0 * x)))) / ((double) (((double) pow(c, 2.0)) * ((double) (((double) (x * ((double) pow(s, 2.0)))) * x))))));
}

↓
double code(double x, double c, double s) {
	double VAR;
	if (((x <= -1.1028652727373659e-195) || (!(x <= 2.0020234743380518e-202) && (x <= 1.1274878712839377e+158)))) {
		VAR = ((double) (((double) (((double) cos(((double) (x * 2.0)))) / ((double) (x * ((double) (x * ((double) pow(((double) (c * s)), ((double) (2.0 * 0.5)))))))))) / ((double) pow(((double) (c * s)), ((double) (2.0 / 2.0))))));
	} else {
		VAR = ((double) (((double) (((double) cos(((double) (x * 2.0)))) / x)) / ((double) (((double) (x * ((double) pow(((double) (c * s)), ((double) (2.0 * 0.5)))))) * ((double) pow(((double) (c * s)), ((double) (2.0 / 2.0))))))));
	}
	return VAR;
}

Error
Bits error versus x
Bits error versus c
Bits error versus s
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 2 regimes
  2. if  x  < -1.1028652727373659e-195 or 2.00202347433805179e-202 <  x  < 1.1274878712839377e158
    1. Initial program 25.0
      \[\]
    2. Simplified25.3
      \[\leadsto \]
    3. Using strategy rm
    4. Applied pow-prod-down10.2
      \[\leadsto \]
    5. Using strategy rm
    6. Applied sqr-pow10.2
      \[\leadsto \]
    7. Applied associate-*r*4.7
      \[\leadsto \]
    8. Simplified4.7
      \[\leadsto \]
    9. Using strategy rm
    10. Applied associate-*r*3.0
      \[\leadsto \]
    11. Using strategy rm
    12. Applied associate-/r*2.9
      \[\leadsto \]
    13. Simplified2.9
      \[\leadsto \]
    if -1.1028652727373659e-195 <  x  < 2.00202347433805179e-202 or 1.1274878712839377e158 <  x 
    1. Initial program 33.6
      \[\]
    2. Simplified33.4
      \[\leadsto \]
    3. Using strategy rm
    4. Applied pow-prod-down23.1
      \[\leadsto \]
    5. Using strategy rm
    6. Applied sqr-pow23.1
      \[\leadsto \]
    7. Applied associate-*r*9.5
      \[\leadsto \]
    8. Simplified9.5
      \[\leadsto \]
    9. Using strategy rm
    10. Applied associate-/r*9.2
      \[\leadsto \]
    11. Simplified9.2
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification4.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))