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Datasheet · A prompt line

High-precision exp and division

Carry at least six significant digits through e^x, ratios and divisions, compute e^x with a series such as 1+x+x²/2+x³/6+x⁴/24, round only at the end, and verify a division by multiplying back.

Designed by OPSIN: it read 24 misses of the unchanged agent on Markets maths, Haiku 5.5 with thinking off, found 6 of them failed one way (inexact exponential or division), and wrote this line aimed at it. Why it fails

Did it fix what it was aimed at? "High-precision exp and division" was aimed at inexact exponential or division: on the same 96 tasks, 2 such misses with it against 2 without, so it did not change the misses it was aimed at. Elsewhere: mental multiplication slip 6 against 7; wrong borrowed-amount arithmetic 0 against 1. OPSIN sorted the misses blind to which agent made them; the signed verdict is the result.

Helps on Markets maths, Haiku 5.5 with thinking off (+4.5 points); helps on DeFi maths, Haiku 5.5 with thinking off (+10.4 points).

Markets maths, Haiku 5.5 with thinking off

Pooled across 2 notebooks: +4.5 points, 95% interval +1.9 to +7.1; measured once.

  1. UNRESOLVEDNotebook #068+3.0 points (−1.4 to +7.4), 432 pairs, cost ×1.47signed verdict 422
  2. EXCITESNotebook #069+7.3 points (+1.6 to +13.5), 192 pairs, cost ×1.55, stopped early, provisionalsigned verdict 427

Where it acts

Its effect sits in Margin-call prices (+8.7); no other family moved clearly.

  1. Margin-call prices+8.7+1.0 to +19.252 tasks
The other 11 families, none moved clearly
  1. Average fill price (VWAP)+17.3−5.8 to +39.452 tasks
  2. Put-call parity+12.5−10.6 to +33.652 tasks
  3. Perp profit+8.7−4.8 to +23.152 tasks
  4. Annualised basis+7.7+0.0 to +17.352 tasks
  5. Hourly funding+1.9−7.7 to +9.652 tasks
  6. Covered calls+0.0+0.0 to +0.052 tasks
  7. Option payoffs+0.0+0.0 to +0.052 tasks
  8. Futures rolls+0.0+0.0 to +0.052 tasks
  9. Stock splits+0.0+0.0 to +0.052 tasks
  10. Shares from risk−1.9−9.6 to +0.052 tasks
  11. Dividends after tax−2.9−24.0 to +19.252 tasks

Read from 624 paired tasks in 2 notebooks, each task against its own notebook’s two controls, with every interval widened for the 12 families read. No notebook preregisters a family: this says where to look, and a notebook says whether it holds. The runs behind it are on each notebook’s page.

DeFi maths, Haiku 5.5 with thinking off

Pooled across 1 notebook: +10.4 points, 95% interval +4.8 to +16.0; measured once.

  1. EXCITESNotebook #082+10.4 points (+2.9 to +18.0), 192 pairs, cost ×1.45, stopped early, provisionalsigned verdict 506

Where it acts

No single family moved clearly on its own: it acts a little everywhere.

All 12 families, none moved clearly
  1. Average entry price+34.4+3.1 to +62.516 tasks, too few to read
  2. Liquidation prices+34.4+3.1 to +62.516 tasks, too few to read
  3. APR to APY+21.9+0.0 to +40.616 tasks, too few to read
  4. Position size from risk+21.9+9.4 to +37.516 tasks, too few to read
  5. Token decimals+15.6+3.1 to +31.316 tasks, too few to read
  6. Profit after fees+9.4−18.8 to +37.516 tasks, too few to read
  7. Fee splits+6.3+0.0 to +15.616 tasks, too few to read
  8. Funding payments+3.1+0.0 to +9.416 tasks, too few to read
  9. Bonding-curve buys+0.0+0.0 to +0.016 tasks, too few to read
  10. Two-hop swaps+0.0+0.0 to +0.016 tasks, too few to read
  11. Impermanent loss−9.4−28.1 to +6.316 tasks, too few to read
  12. Swaps−12.5−25.0 to −3.116 tasks, too few to read

Read from 192 paired tasks in 1 notebook, each task against its own notebook’s two controls, with every interval widened for the 0 families read. No notebook preregisters a family: this says where to look, and a notebook says whether it holds. The runs behind it are on each notebook’s page.

Why it helps

"High-precision exp and division", on the same 96 tasks, by the way each miss went wrong: mental arithmetic drift in long products and quotients 26 with it against 20 without; power or percentage arithmetic slip 3 with it against 7 without; early rounding of intermediates 10 with it against 12 without.

OPSIN sorted every miss with the part and without it, on the same tasks of Notebook #082, into the ways of failing it had named for this setting, blind to which agent made each. Descriptive: the verdicts above are the result.

Put this datasheet in a README

The badge shows what the signed record says about this part, in the setting measured most, and links here. It follows the record as new notebooks publish. Add ?suite= and a suite’s id to show another setting.

OPSIN: helps +4.5 on Markets maths
[![OPSIN](https://opsinlab.io/badge/12489ebc886d657a.svg)](https://opsinlab.io/parts/12489ebc886d657a)

Measure it in a setting it has not been measured in: propose it. As JSON for an agent: /v1/parts/12489ebc886d657a. Every part: the atlas.