Average Error: 26.3 → 13.5
Time: 18.9s
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) pow(((double) (M * ((double) (D / ((double) (d * 2.0)))))), ((double) (2.0 / 2.0)))) * ((double) (((double) (((double) pow(M, ((double) (2.0 / 2.0)))) / ((double) (((double) cbrt(l)) * ((double) cbrt(l)))))) * ((double) (((double) pow(((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 26.3
    \[\]
  2. Simplified25.8
    \[\leadsto \]
  3. Using strategy rm
  4. Applied add-cube-cbrt26.1
    \[\leadsto \]
  5. Applied add-cube-cbrt26.2
    \[\leadsto \]
  6. Applied times-frac26.2
    \[\leadsto \]
  7. Applied unpow-prod-down19.9
    \[\leadsto \]
  8. Simplified19.9
    \[\leadsto \]
  9. Using strategy rm
  10. Applied add-cube-cbrt20.0
    \[\leadsto \]
  11. Applied *-un-lft-identity20.0
    \[\leadsto \]
  12. Applied times-frac20.0
    \[\leadsto \]
  13. Applied unpow-prod-down15.0
    \[\leadsto \]
  14. Using strategy rm
  15. Applied *-un-lft-identity15.0
    \[\leadsto \]
  16. Applied sqr-pow15.0
    \[\leadsto \]
  17. Applied times-frac12.7
    \[\leadsto \]
  18. Simplified12.7
    \[\leadsto \]
  19. Simplified12.7
    \[\leadsto \]
  20. Using strategy rm
  21. Applied add-cube-cbrt12.8
    \[\leadsto \]
  22. Applied unpow-prod-down12.8
    \[\leadsto \]
  23. Applied times-frac13.5
    \[\leadsto \]
  24. Final simplification13.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(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)))))