Average Error: 27.9 → 3.4
Time: 8.1s
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) {
	return ((double) (((double) (((double) cbrt(((double) (((double) cos(((double) (x * 2.0)))) / x)))) * ((double) (((double) cbrt(((double) (((double) cos(((double) (x * 2.0)))) / x)))) / ((double) (x * ((double) pow(((double) (c * s)), ((double) (2.0 / 2.0)))))))))) * ((double) (((double) cbrt(((double) (((double) cos(((double) (x * 2.0)))) / x)))) / ((double) pow(((double) (c * s)), ((double) (2.0 / 2.0))))))));
}

Error
Bits error versus x
Bits error versus c
Bits error versus s
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Your Program's Arguments
Results
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Derivation
  1. Initial program 27.9
    \[\]
  2. Simplified27.6
    \[\leadsto \]
  3. Using strategy rm
  4. Applied pow-prod-down13.2
    \[\leadsto \]
  5. Using strategy rm
  6. Applied sqr-pow13.2
    \[\leadsto \]
  7. Applied associate-*r*6.2
    \[\leadsto \]
  8. Using strategy rm
  9. Applied associate-/r*6.0
    \[\leadsto \]
  10. Simplified6.0
    \[\leadsto \]
  11. Using strategy rm
  12. Applied add-cube-cbrt6.3
    \[\leadsto \]
  13. Applied times-frac3.4
    \[\leadsto \]
  14. Simplified3.4
    \[\leadsto \]
  15. Final simplification3.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))