Average Error: 26.8 → 13.2
Time: 20.7s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double d, double h, double l, double M, double D) {
	return ((double) (((double) (((double) pow(((double) (d / h)), ((double) (1.0 / 2.0)))) * ((double) pow(((double) (d / l)), ((double) (1.0 / 2.0)))))) * ((double) (1.0 - ((double) (((double) (((double) (1.0 / 2.0)) * ((double) pow(((double) (((double) (M * D)) / ((double) (2.0 * d)))), 2.0)))) * ((double) (h / l))))))));
}

↓
double code(double d, double h, double l, double M, double D) {
	return ((double) (((double) (((double) pow(((double) (((double) (((double) cbrt(d)) / ((double) cbrt(h)))) * ((double) (((double) cbrt(d)) / ((double) cbrt(h)))))), ((double) (1.0 / 2.0)))) * ((double) pow(((double) (((double) cbrt(d)) / ((double) cbrt(h)))), ((double) (1.0 / 2.0)))))) * ((double) (((double) (((double) pow(((double) (1.0 / ((double) (((double) cbrt(l)) * ((double) cbrt(l)))))), ((double) (1.0 / 2.0)))) * ((double) pow(((double) (d / ((double) cbrt(l)))), ((double) (1.0 / 2.0)))))) * ((double) (1.0 - ((double) (h * ((double) (((double) (1.0 / 2.0)) * ((double) (((double) (((double) pow(((double) (M * ((double) (D / ((double) (d * 2.0)))))), ((double) (2.0 / 2.0)))) / ((double) (((double) cbrt(l)) * ((double) cbrt(l)))))) * ((double) (((double) pow(((double) (M * ((double) (D / ((double) (d * 2.0)))))), ((double) (2.0 / 2.0)))) / ((double) cbrt(l))))))))))))))));
}

Error
Bits error versus d
Bits error versus h
Bits error versus l
Bits error versus M
Bits error versus D
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 26.8
    \[\]
  2. Simplified26.3
    \[\leadsto \]
  3. Using strategy rm
  4. Applied add-cube-cbrt26.6
    \[\leadsto \]
  5. Applied *-un-lft-identity26.6
    \[\leadsto \]
  6. Applied times-frac26.6
    \[\leadsto \]
  7. Applied unpow-prod-down21.4
    \[\leadsto \]
  8. Using strategy rm
  9. Applied add-cube-cbrt21.6
    \[\leadsto \]
  10. Applied add-cube-cbrt21.6
    \[\leadsto \]
  11. Applied times-frac21.6
    \[\leadsto \]
  12. Applied unpow-prod-down15.5
    \[\leadsto \]
  13. Simplified15.5
    \[\leadsto \]
  14. Using strategy rm
  15. Applied add-cube-cbrt15.6
    \[\leadsto \]
  16. Applied sqr-pow15.6
    \[\leadsto \]
  17. Applied times-frac13.2
    \[\leadsto \]
  18. Final simplification13.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (d h l M D)
  :name "Henrywood and Agarwal, Equation (12)"
  :precision binary64
  (* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))