Until recently, I didn't have a working HP-33 calculator; my only specimen was a sadly broken HP-33E, destroyed by massive battery corrosion. This has now changed; I recently acquired an HP-33C that is operating perfectly.

The HP-33 was the low-end scientific programmable member of the "Spice" series of HP calculators. It offered a total of 49 program steps and 8 memory registers. The programming model used absolute addressing and no provision was offered for inserting program steps, making program editing a little less than convenient.

Still, 49 fully merged program steps are quite a lot. For instance, they're sufficient to hold a Gamma function implementation that yields results with 8 digits of accuracy:

Note that this program requires that you fill registers 2-7 with preset values. By the way, if you find this program very similar to that for the HP-25, that's no mistake; the two calculators' capabilities are nearly identical.

M2=√2π
M3=68.82784822
M4=755.9596084
M5=4151.488796
M6=11399.36541
M7=12520.43913

01-    23 0  STO 0
02-    23 1  STO 1
03-    24 2  RCL 2
04- 23 61 0  STO× 0
05-    24 3  RCL 3
06- 23 51 0  STO+ 0
07-    24 1  RCL 1
08- 23 61 0  STO× 0
09-    24 4  RCL 4
10- 23 51 0  STO+ 0
11-    24 1  RCL 1
12- 23 61 0  STO× 0
13-    24 5  RCL 5
14- 23 51 0  STO+ 0
15-    24 1  RCL 1
16- 23 61 0  STO× 0
17-    24 6  RCL 6
18- 23 51 0  STO+ 0
19-    24 7  RCL 7
20-    24 1  RCL 1
21-      71  ÷
22- 23 51 0  STO+ 0
23-       5  5
24-      31  ENTER
25-       1  1
26- 23 51 1  STO+ 1
27-      41  -
28-    24 1  RCL 1
29- 23 71 0  STO÷ 0
30-      21  x-y
31-   15 61  x!=0
32-   13 25  GTO 25
33-    24 1  RCL 1
34-      73  .
35-       5  5
36-      51  +
37-      31  ENTER
38-      32  CHS
39-    15 1  ex
40-      21  x-y
41-      31  ENTER
42-      31  ENTER
43-       5  5
44-      41  -
45-    14 3  yx
46-      61  ×
47-    24 0  RCL 0
48-      61  ×