Average Error: 13.8 → 9.3
Time: 12.5s
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) {
	return ((double) (w0 * ((double) sqrt(((double) (1.0 - ((double) (((double) (((double) pow(((double) (M * ((double) (D / ((double) (2.0 * d)))))), ((double) (2.0 / 2.0)))) * ((double) (h * ((double) pow(((double) (M * ((double) (D / ((double) (2.0 * d)))))), ((double) (2.0 / 2.0)))))))) / l))))))));
}

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. Initial program 13.8
    \[\]
  2. Simplified13.9
    \[\leadsto \]
  3. Using strategy rm
  4. Applied associate-*r/10.7
    \[\leadsto \]
  5. Simplified10.7
    \[\leadsto \]
  6. Using strategy rm
  7. Applied sqr-pow10.7
    \[\leadsto \]
  8. Applied associate-*r*9.3
    \[\leadsto \]
  9. Final simplification9.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(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))))))