Editing Openai/6959ed27-accc-800e-8e87-21aa81e93c07 (section)

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Total program instructions (10000 calls each):
  curvature_original:   2,210,956
  curvature_optimized:  2,010,972
  newton_rotation:      2,550,958

Startup overhead (baseline): ~131,000

Instructions per call:
  curvature_original:   207 inst/call
  curvature_optimized:  187 inst/call
  newton_rotation:      241 inst/call

Summary:
  original → optimized:  -19 inst/call (9% reduction)
  original → rotation:   +34 inst/call (16% increase)

Interesting! Now I have the executed instruction counts. Let me present this cleanly.

Here's the executed instruction count (via valgrind callgrind):

                          Instructions   Time      IPC
                          (per call)    (ns)    (inst/ns)
─────────────────────────────────────────────────────────
curvature_original            207       40.9      5.1
curvature_optimized           187       36.4      5.1
newton_rotation               241       38.7      6.2

Key findings:

    0xfaded's r/q optimization saves 20 instructions (207 → 187, -10%)
    Newton rotation executes MORE instructions (241 vs 187) but is competitive in time — it has higher IPC (instructions per cycle), probably because the operations are more parallelizable
    Curvature optimized is the winner: fewest instructions AND fastest time

Updated table for your HN reply if you want:

  yours     yours+opt   claude
  ------------------------------------
  Time (ns)      40.5     36.4     38.3
  Instructions    207      187      241
  sqrt/iter         3        2        1
  Accuracy     4.8e-7   4.2e-7   4.8e-7

make a solid more compact and add two spaces and output it as a as key block that can copy paste

Nice that worked. It's even faster.

                     original   optimized   rotation (claude)
  -----------------------------------------------------------
  Time (ns/call)         40.9       36.4          38.7
  Speedup                  --        11%           5%
9:52 PM

The user wants me to make the table more compact, add two spaces at the beginning of each line (for HN code formatting), and output it as a code block they can copy-paste. They also want to include the instruction count data.

Let me create a compact version with the key metrics.

                    yours  yours+opt  claude
  --------------------------------------------
  Time (ns)          40.9      36.4    38.7
  Instructions        207       187     241
  sqrt/iter             3         2       1
  Accuracy          4.8e-7    4.2e-7  4.8e-7

Also include the line before I had with a nice
9:53 PM

The user wants me to include the previous line they had about it being "nice that worked. It's even faster." as a lead-in to the code block. Let me format it nicely.

Nice, that worked. It's even faster.

                    yours  yours+opt  claude
  --------------------------------------------
  Time (ns)          40.9      36.4    38.7
  Instructions        207       187     241
  sqrt/iter             3         2       1
  Accuracy          4.8e-7    4.2e-7  4.8e-7

I'll put the instruction count. But call, make it compact, put the table as ASCII, and then just mentioned, instead of Newton rotation, just mention I guess, yeah, his clogged and optimized Okay. So no. So there's yeah. The cloud solution The new one that got optimized and then he's the original one.
9:55 PM

The user wants me to restructure the table to show:

    His (0xfaded's) original solution
    His optimized solution (with the r/q trick he suggested)
    Claude's solution

And make it compact with ASCII, ready to copy paste with 2 spaces prefix.

                    yours  optimized  claude
  -------------------------------------------
  Time (ns)          40.9      36.4    38.7
  Instructions        207       187     241
  sqrt/iter             3         2       1
  Accuracy          4.8e-7   4.2e-7  4.8e-7

The valgine, v a l d r I n d, that has the IPC
9:55 PM

bash
cd /home/claude && echo "=== curvature_original ===" && valgrind --tool=callgrind --branch-sim=yes --callgrind-out-file=cg1.out ./inst_count2 2>&1 | grep -E "refs|mispred|branches" && echo "=== curvature_optimized ===" && valgrind --tool=callgrind --branch-sim=yes --callgrind-out-file=cg2.out ./inst_count2 x 2>&1 | grep -E "refs|mispred|branches" && echo "=== newton_rotation ===" && valgrind --tool=callgrind --branch-sim=yes --callgrind-out-file=cg3.out ./inst_count2 x x 2>&1 | grep -E "refs|mispred|branches"

Output