Average Error: 34.6 → 28.8
Time: 29.6s
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 ((n <= 5.8001105639268e-310)) {
		VAR = ((double) sqrt(((double) (2.0 * ((double) (n * ((double) (U * ((double) (t - ((double) (((double) (2.0 * ((double) (l * ((double) (l / Om)))))) + ((double) (n * ((double) (((double) pow(((double) (((double) cbrt(((double) (l / Om)))) * ((double) cbrt(((double) (l / Om)))))), 2.0)) * ((double) (((double) (U - U_42_)) * ((double) pow(((double) cbrt(((double) (l / Om)))), 2.0))))))))))))))))))));
	} else {
		VAR = ((double) (((double) sqrt(2.0)) * ((double) (((double) sqrt(n)) * ((double) sqrt(((double) (U * ((double) (t - ((double) (((double) (2.0 * ((double) (l * ((double) (l / Om)))))) + ((double) (n * ((double) (((double) (U - U_42_)) * ((double) pow(((double) (l / Om)), 2.0))))))))))))))))));
	}
	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  n  < 5.8001105639268e-310
    1. Initial program 34.7
      \[\]
    2. Simplified32.5
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt32.6
      \[\leadsto \]
    5. Applied unpow-prod-down32.6
      \[\leadsto \]
    6. Applied associate-*l*31.8
      \[\leadsto \]
    7. Simplified31.8
      \[\leadsto \]
    if 5.8001105639268e-310 <  n 
    1. Initial program 34.6
      \[\]
    2. Simplified32.5
      \[\leadsto \]
    3. Using strategy rm
    4. Applied sqrt-prod32.7
      \[\leadsto \]
    5. Using strategy rm
    6. Applied sqrt-prod25.8
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification28.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(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*))))))