Results

Correct digits left after 10,000 steps, per scenario and library.

Each scenario repeats one step N times in every library's own representation and compares the result with the same loop in 200-digit arithmetic. Daily compounding: FP127 keeps 34 digits, Solady 14. The per-second accrual a lending market runs: 29 against 8.5.

scenario	FP256	FP127	Quad	Maker	ABDK	Solady	PRBMath	Balancer	Aave	Morpho
Daily compound interest	67	34	29	23	15	14	14	14	—	—
Compound interest in one pow	67	34	30	—	15	14	13	14.5	—	—
Square-root bonding curve	70	40	30	—	21	20	20	18	—	—
exp(ln(x)) round trip	71.5	38	28.5	—	15	14	13	14	—	—
Amortising loan	67	35	29	—	15.5	15.5	15.5	15.5	—	—
Running geometric mean	71	38	33	—	18	17	16	17	—	—
Black-Scholes d1 along a price path	67.5	37	30	—	18	17	16	17	—	—
Cumulative product of small factors	69	34	29	—	15	14	14	14	—	—
Annual compounding at 10% (README claim check)	67	rev	29	rev	rev	rev	rev	rev	—	—
Per-second accrual	62	29	24	18	10	8.5	8	9	—	—
Continuous accrual	71	37	33	—	17.5	17.5	17	17	1	1
An option walking out of the money	65	0.5	27	—	0	0	0	4	—	—
Decay, the share released	59	26	21	—	7	11	6	11	—	—

Median correct digits over each scenario's inputs at N = 10,000, against exact inputs; capped at 100. rev: every input reverted. —: the library has no model for that scenario. FP127Lib equals FP127 and is left out.

9,384 cells checked live on Sepolia at block 11,928,247, 0 mismatches. 2026-10-16, runner 0xfcdf2f18…. Re-run: uv run scripts/ladder/livecap.py

Where to go next

Ladder 13 scenarios, every N from 1 to 10,000, the reference input cell by cell.
Edges 139 single calls at the ends of each library's domain: where results go to zero or revert.
Per op gas and precision for each op, against each library.