Average Error: 34.6 → 29.6
Time: 22.6s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double n, double U, double t, double l, double Om, double U_42_) {
	return ((double) sqrt(((double) (((double) (((double) (2.0 * n)) * U)) * ((double) (((double) (t - ((double) (2.0 * ((double) (((double) (l * l)) / Om)))))) - ((double) (((double) (n * ((double) pow(((double) (l / Om)), 2.0)))) * ((double) (U - U_42_))))))))));
}

↓
double code(double n, double U, double t, double l, double Om, double U_42_) {
	double VAR;
	if (((((double) (((double) (((double) (2.0 * n)) * U)) * ((double) (((double) (t - ((double) (2.0 * ((double) (((double) (l * l)) / Om)))))) + ((double) (((double) (n * ((double) pow(((double) (l / Om)), 2.0)))) * ((double) (U_42_ - U)))))))) <= 0.0) || !(((double) (((double) (((double) (2.0 * n)) * U)) * ((double) (((double) (t - ((double) (2.0 * ((double) (((double) (l * l)) / Om)))))) + ((double) (((double) (n * ((double) pow(((double) (l / Om)), 2.0)))) * ((double) (U_42_ - U)))))))) <= 7.268202185933052e+232))) {
		VAR = ((double) sqrt(((double) (2.0 * ((double) (n * ((double) (U * ((double) (t - ((double) (2.0 * ((double) (l * ((double) (l / Om))))))))))))))));
	} else {
		VAR = ((double) sqrt(((double) (((double) (((double) (2.0 * n)) * U)) * ((double) (((double) (t - ((double) (2.0 * ((double) (((double) (l * l)) / Om)))))) + ((double) (((double) (n * ((double) pow(((double) (l / Om)), 2.0)))) * ((double) (U_42_ - U))))))))));
	}
	return VAR;
}

Error
Bits error versus n
Bits error versus U
Bits error versus t
Bits error versus l
Bits error versus Om
Bits error versus U*
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 2 regimes
  2. if  (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))  < 0.0 or 7.26820218593305161e232 <  (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) 
    1. Initial program 57.5
      \[\]
    2. Simplified48.9
      \[\leadsto \]
    3. Taylor expanded around 0 49.0
      \[\leadsto \]
    if 0.0 <  (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))  < 7.26820218593305161e232
    1. Initial program 1.8
      \[\]
  3. Recombined 2 regimes into one program.
  4. Final simplification29.6
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (n U t l Om U*)
  :name "Toniolo and Linder, Equation (13)"
  :precision binary64
  (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))