Average Error: 13.9 → 8.7
Time: 15.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double w0, double M, double D, double h, double l, double d) {
	return ((double) (w0 * ((double) sqrt(((double) (1.0 - ((double) (((double) pow(((double) (((double) (M * D)) / ((double) (2.0 * d)))), 2.0)) * ((double) (h / l))))))))));
}

↓
double code(double w0, double M, double D, double h, double l, double d) {
	double VAR;
	if ((M <= -9.863874069977466e-221)) {
		VAR = ((double) (w0 * ((double) sqrt(((double) (1.0 - ((double) (((double) (((double) (((double) pow(((double) (((double) cbrt(((double) (D / d)))) * ((double) (((double) (M / 2.0)) * ((double) (((double) cbrt(((double) (D / d)))) * ((double) cbrt(((double) (D / d)))))))))), ((double) (2.0 / 2.0)))) / ((double) cbrt(l)))) * ((double) (h / ((double) cbrt(l)))))) * ((double) (((double) pow(((double) (((double) (M / 2.0)) * ((double) (D / d)))), ((double) (2.0 / 2.0)))) / ((double) cbrt(l))))))))))));
	} else {
		double VAR_1;
		if ((M <= 1.4172298698894145e-163)) {
			VAR_1 = ((double) (w0 * ((double) sqrt(((double) (1.0 - ((double) (((double) (h * ((double) pow(((double) (((double) (M * D)) / ((double) (2.0 * d)))), 2.0)))) / l))))))));
		} else {
			VAR_1 = ((double) (w0 * ((double) sqrt(((double) (1.0 - ((double) (((double) (((double) pow(((double) (((double) (M / 2.0)) * ((double) (D / d)))), ((double) (2.0 / 2.0)))) * ((double) (((double) (((double) cbrt(h)) * ((double) cbrt(h)))) * ((double) (((double) pow(((double) (((double) (M / 2.0)) * ((double) (D / d)))), ((double) (2.0 / 2.0)))) * ((double) cbrt(h)))))))) / l))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus w0
Bits error versus M
Bits error versus D
Bits error versus h
Bits error versus l
Bits error versus d
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 3 regimes
  2. if  M  < -9.8638740699774658e-221
    1. Initial program 14.8
      \[\]
    2. Using strategy rm
    3. Applied associate-*r/11.9
      \[\leadsto \]
    4. Simplified11.4
      \[\leadsto \]
    5. Using strategy rm
    6. Applied sqr-pow11.4
      \[\leadsto \]
    7. Applied associate-*r*9.6
      \[\leadsto \]
    8. Simplified9.6
      \[\leadsto \]
    9. Using strategy rm
    10. Applied add-cube-cbrt9.7
      \[\leadsto \]
    11. Applied times-frac8.6
      \[\leadsto \]
    12. Simplified9.4
      \[\leadsto \]
    13. Simplified9.4
      \[\leadsto \]
    14. Using strategy rm
    15. Applied add-cube-cbrt9.4
      \[\leadsto \]
    16. Applied associate-*r*9.4
      \[\leadsto \]
    if -9.8638740699774658e-221 <  M  < 1.4172298698894145e-163
    1. Initial program 8.1
      \[\]
    2. Using strategy rm
    3. Applied associate-*r/3.1
      \[\leadsto \]
    4. Simplified4.4
      \[\leadsto \]
    5. Using strategy rm
    6. Applied frac-times3.1
      \[\leadsto \]
    if 1.4172298698894145e-163 <  M 
    1. Initial program 17.2
      \[\]
    2. Using strategy rm
    3. Applied associate-*r/14.6
      \[\leadsto \]
    4. Simplified14.2
      \[\leadsto \]
    5. Using strategy rm
    6. Applied sqr-pow14.2
      \[\leadsto \]
    7. Applied associate-*r*11.9
      \[\leadsto \]
    8. Simplified11.9
      \[\leadsto \]
    9. Using strategy rm
    10. Applied add-cube-cbrt11.9
      \[\leadsto \]
    11. Applied associate-*l*11.9
      \[\leadsto \]
    12. Simplified11.9
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification8.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (w0 M D h l d)
  :name "Henrywood and Agarwal, Equation (9a)"
  :precision binary64
  (* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))))