Per op

	BL19	BL127	ABDKMathQuad	PRBMath SD59x18	Solady
digits	71	38	34	18	18
add	662	128	734	189	3
mul	530	267	709	485	126
div	800	413	818	509	93
exp ^t	3,278	2,835	5,668	2,816	430
ln ^t	3,106	1,944	16,356	7,083	556
pow ^t	5,964	3,317	23,479	10,065	1,279
sqrt ^t	1,205	469	760	978	393

Inline library, median gas per call, over random inputs that take no shortcut for the ops marked ^t and over the input ladder for the rest; digits are precision at 1. BL19 is cheaper than Quad on add, mul, div, exp, ln and pow, not on sqrt. BL127 is cheaper than PRBMath on add, mul, div, ln, pow and sqrt, not on exp. Solady is cheaper than both on every op here, at 18 digits; its add is the unchecked rawAdd. Sources: bl19/gas.json (BL19, Quad), gas.json (the rest).

Only BL19 and BL127 offer erf, erfc, normCdf and both Lambert W branches (Solady has W₀ alone), each correctly rounded or the nearest word. BL19's per-op detail, with the deployed objects, is on its page.

Gas per op

Every op of BL19 and BL127 against every library we compare, all called inline.

op	BL19	BL127	ABDKMathQuad	PRBMath	Solady	ABDK 64.64	Balancer	Solmate	PRB UD60x18	snekmate	OpenZeppelin	Uniswap
abs	133	140	21	121	18	120					18
add	662	128	734	189	3	162			150
atanh ^t	3,882	2,944
avg	663	114		154	60	31			105	113	318
cbrt ^t	2,734	1,936			619		2,313			1,424
ceil	523	147		201					117
clamp	491	241			49
cmp	248		476
compound ^t	5,858	3,078
cosh ^t	3,692	4,073
dist	819	289			32
div	800	413	818	509	93	221		97	261
divDown	987	476			87			150		323	239	179
divUp	988	479			113			176		386	621	282
eq	176		108
erf ^t	10,624	7,559
erfc ^t	10,654	7,186
exp ^t	3,278	2,835	5,668	2,816	430	3,380	1,040	430	2,720	604
exp10 ^t	3,177	3,081
exp2 ^t	3,096	2,712	5,031	2,671		3,225			2,557
expm1 ^t	2,395	2,996
factorial	719	400			579
floor	522	72		201					28
frac	428	69		125					8
fromBL127	440		539
fromFixed18	554	140
fromUint	413
fromUintDown	487		500
fromUintUp	488
gavg ^t	2,099	1,003		960	449	833			949
hypot ^t	3,556	1,164
inv	747	242	1,253	177	93	202			94
lambertW0 ^t	10,672	8,304			3,045
lambertWm1 ^t	10,759	8,156
lerp ^t	6,515	477			282
ln ^t	3,106	1,944	16,356	7,083	556	7,080	1,091	632	6,474	1,226
log10 ^t	3,101	1,934		8,618			1,895		8,233
log1p ^t	2,587	2,064
log2 ^t	2,885	1,723	15,553	6,724		6,990	1,914		6,402
log2Up	679	209			247					505	513
lt	233		488
max	250	125			23						86
min	251	126			23						86
mul	530	267	709	485	126	171		131	237
mulDown	727	315			86			150		323	239	179
mulUp	728	337			110			176		386	621	282
neg	127	116	9	134		76
normCdf ^t	12,354	6,037
pow ^t	5,964	3,317	23,479	10,065	1,279		2,223	1,355	9,544
powu ^t	6,647	5,252		4,006	2,318	3,133		2,559	3,881
round	474	212
sign	139	75	181	84						78
sinh ^t	3,670	4,109
sqrt ^t	1,205	469	760	978	393	828	2,351	456	824		766
sub	745	140	1,230	187	3	162			150
tanh ^t	3,717	3,975
toBL127	343		292
toFixed18	480	121
toFixed18Down	723	160
toFixed18Up	724	185
toIntDown	466		278
toIntUp	467
toUintDown	405		240
toUintUp	406
zeroFloorSub	829	212			17						92

The function each cell measures

ABDKMathQuad: abs abs(x); add add(a, b); cmp cmp(a, b); div div(a, b); eq eq(a, b); exp exp(x); exp2 pow_2(x); fromBL127 from128x128(x) (truncates; fromBL127 rounds to nearest); fromUintDown fromUInt(x) (truncates the significand); inv div(fromUInt(1), x) (composed); ln ln(x); log2 log_2(x); lt cmp(a, b) < 0 (composed); mul mul(a, b); neg neg(x); pow exp(mul(y, ln(x))) (composed); sign sign(x); sqrt sqrt(x); sub sub(a, b); toBL127 to128x128(x) (truncates; toBL127 rounds to nearest); toIntDown toInt(x) (truncates: floor for x >= 0, the rows kept); toUintDown toUInt(x) (truncates: floor for x >= 0)
PRBMath: abs abs(x); add add(a, b); avg avg(a, b); ceil ceil(x); div div(a, b); exp exp(x); exp2 exp2(x); floor floor(x); frac frac(x); gavg gm(a, b); inv inv(x); ln ln(x); log10 log10(x); log2 log2(x); mul mul(a, b); neg unary(x); pow pow(x, y); powu powu(x, n), n a uint256 (n >= 0); sign sign(x); sqrt sqrt(x); sub sub(a, b)
Solady: abs abs(int256); add rawAdd(int256, int256) (unchecked); avg avg(int256, int256); cbrt cbrtWad(x) (x >= 0); clamp clamp(int256, int256, int256); dist dist(int256, int256); div sDivWad(a, b); divDown divWad(a, b) (a >= 0, b > 0); divUp divWadUp(a, b) (a >= 0, b > 0); exp expWad(x); factorial factorial(uint256) on the integer x (integral x); gavg mulSqrt(a, b) (a, b >= 0); inv sDivWad(1e18, x) (composed); lambertW0 lambertW0Wad(x); lerp lerp(a, b, t, 0, 1e18) (t in [0, 1]: Solady clamps t); ln lnWad(x); log2Up log2Up(uint256) on the integer x (integral x >= 1); max max(int256, int256); min min(int256, int256); mul sMulWad(a, b) (toward zero); mulDown mulWad(a, b) (a, b >= 0); mulUp mulWadUp(a, b) (a, b >= 0); pow powWad(x, y); powu rpow(x, n, 1e18) (x >= 0, n >= 0); sqrt sqrtWad(x) (x >= 0); sub rawSub(int256, int256) (unchecked); zeroFloorSub zeroFloorSub(uint256, uint256) (a, b >= 0)
ABDK 64.64: abs abs(x); add add(a, b); avg avg(a, b); div div(a, b); exp exp(x); exp2 exp_2(x); gavg gavg(a, b); inv inv(x); ln ln(x); log2 log_2(x); mul mul(a, b); neg neg(x); powu pow(x, n), n a uint256 (n >= 0); sqrt sqrt(x); sub sub(a, b)
Balancer: cbrt pow(x, 333333333333333333) (composed; x >= 0); exp exp(x); ln ln(x); log10 log(x, 10e18); log2 log(x, 2e18); pow pow(x, y) (x, y >= 0); sqrt pow(x, 0.5e18) (composed; x >= 0)
Solmate: div wadDiv(a, b) (toward zero); divDown divWadDown(a, b) (a, b >= 0); divUp divWadUp(a, b) (a, b >= 0); exp wadExp(x); ln wadLn(x); mul wadMul(a, b) (toward zero); mulDown mulWadDown(a, b) (a, b >= 0); mulUp mulWadUp(a, b) (a, b >= 0); pow wadPow(x, y); powu rpow(x, n, 1e18) (x >= 0, n >= 0); sqrt sqrt(x * 1e18) (composed: the integer root; x >= 0)
PRB UD60x18: add add(a, b) (a, b >= 0); avg avg(a, b) (a, b >= 0); ceil ceil(x) (x >= 0); div div(a, b) (a, b >= 0); exp exp(x) (x >= 0); exp2 exp2(x) (x >= 0); floor floor(x) (x >= 0); frac frac(x) (x >= 0); gavg gm(a, b) (a, b >= 0); inv inv(x) (x >= 0); ln ln(x) (x >= 0); log10 log10(x) (x >= 0); log2 log2(x) (x >= 0); mul mul(a, b) (a, b >= 0); pow pow(x, y) (x, y >= 0); powu powu(x, n), n a uint256 (x >= 0, n >= 0); sqrt sqrt(x) (x >= 0); sub sub(a, b) (a, b >= 0)
snekmate: avg _int256_average(a, b); cbrt _wad_cbrt(x) (x >= 0); divDown _mul_div(a, 1e18, b, False) (a, b >= 0); divUp _mul_div(a, 1e18, b, True) (a, b >= 0); exp _wad_exp(x); ln _wad_ln(x); log2Up _log2(uint256, True) on the integer x (integral x >= 1); mulDown _mul_div(a, b, 1e18, False) (a, b >= 0); mulUp _mul_div(a, b, 1e18, True) (a, b >= 0); sign _signum(x)
OpenZeppelin: abs SignedMath.abs(int256); avg SignedMath.average(a, b) (toward zero; BL127's avg floors); divDown Math.mulDiv(a, 1e18, b) (a, b >= 0); divUp Math.mulDiv(a, 1e18, b, Rounding.Ceil) (a, b >= 0); log2Up Math.log2(uint256, Rounding.Ceil) on the integer x (integral x >= 1); max SignedMath.max(a, b); min SignedMath.min(a, b); mulDown Math.mulDiv(a, b, 1e18) (a, b >= 0); mulUp Math.mulDiv(a, b, 1e18, Rounding.Ceil) (a, b >= 0); sqrt Math.sqrt(x * 1e18) (composed: the integer root; x >= 0); zeroFloorSub Math.saturatingSub(uint256, uint256) (a, b >= 0)
Uniswap: divDown FullMath.mulDiv(a, 1e18, b) (a, b >= 0); divUp FullMath.mulDivRoundingUp(a, 1e18, b) (a, b >= 0); mulDown FullMath.mulDiv(a, b, 1e18) (a, b >= 0); mulUp FullMath.mulDivRoundingUp(a, b, 1e18) (a, b >= 0)

Median gas per inline call: over random inputs that take no shortcut for the ops marked ^t, else over the op's input ladder. BL19 and ABDKMathQuad are measured on the same values (bl19/gas.json), the others on BL127's inputs (gas.json). Empty: the library does not offer the op; rev: it offers it and reverted on every input. Hover a cell for the function it calls. Calling the deployed contract instead adds the staticcall: about 554 gas on BL127's add (682 against 128); every op's object figure is on the BL127 and BL19 pages.

Precision per op

op	vectors	reverts	min bits	mean bits	worst input
abs	98	1	exact	exact
add	377	23	exact	exact
atanh	534	5	130	131	0x000000000000… 0x0000000000000000000000000000000000000b504f333f9de6484597d89b3754
avg	200	0	129	234	0xffffffffffff… 0xfffffffffffffffff21f494c589c000000000000000000000000000000000000,0xfffffffffffffffffffffffffffffd34d62c1fdb28540383534af43c13a51359
cbrt	98	1	130	164	0x000000000000… 0x00000000000000001bce1abd36207803b5f3bb79b2f817e5a2d5e288b8fe5d96
ceil	97	2	exact	exact
clamp	300	0	exact	exact
compound	141	59	130	208	0x000000000000… 0x0000000000000000000000000000000019999999999999999999999999999999,0x0000000000000000000000000000016d00000000000000000000000000000000
cosh	575	4	129	175	0x000000000000… 0x0000000000000000000000000000000000000000000000010000000000000000
dist	190	10	exact	exact
div	377	23	129	193	0x23fccae3cfdc… 0x23fccae3cfdca92920400cceaf07264105d9fd08f1256e2392022e9d1745ab4a,0x00000000000000000000000000000003243f6a8885a308d313198a2e03707344
divDown	363	37	128	188	0xffffffffffff… 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff,0x7870107c047009ebaad71c7ebbaf317671aaa8a105a47733a492aebe56be3702
divUp	367	33	129	190	0x000000000000… 0x0000000000000000000000000000000180000000000000000000000000000000,0x00000000000000000000000000000000004189374bc6a7ef9db22d0e56041893
erf	584	0	132	186	0x000000000000… 0x000000000000000000000000000000029a7e647802374d98add579a7fcc24210
erfc	584	0	130	132	0x000000000000… 0x000000000000000000000000000000029a7e647802374d98add579a7fcc24210
exp	117	4	130	207	0xffffffffffff… 0xffffffffffffffffffffffffffffffa6947ae147ae147ae147ae147ae147ae14
exp10	80	3	131	217	0xffffffffffff… 0xfffffffffffffffffffffffffffffff141f0353d3320c8f151d83c6c95e647d4
exp2	104	3	130	217	0xffffffffffff… 0xffffffffffffffffffffffffffffff7f00000000000000000000000000000000
expm1	577	2	130	153	0x000000000000… 0x0000000000000000000000000000000000000000000000010000000000000000
factorial	12	6	exact	exact
floor	99	0	exact	exact
frac	99	0	exact	exact
fromFixed18	33	4	131	191	0xffffffffffff… 0xfffffffffffffffffffffffffffffffff5cc03f34ac9aaa4896da2872a07e2d0
gavg	200	0	131	210	0x000000000000… 0x0000000000000000000000000000000000000000000000000000000000000400,0x0000000000000000000000000000000000000000000000000000800000000000
hypot	121	0	131	183	0x000000000000… 0x0000000000000000000000000000000080000000000000000000000000000000,0x00000000000000000000000000000003243f6a8885a308d313198a2e03707344
inv	62	3	exact	exact	0x203165f4c782… 0x203165f4c782db9cffce938726dd1ec020de05fd184a1af4395e2a8402671297
lambertW0	140	3	130	134	0xffffffffffff… 0xffffffffffffffffffffffffffffffffa3d70a3d70a3d70a3d70a3d70a3d70a3
lambertWm1	86	6	130	131	0xffffffffffff… 0xffffffffffffffffffffffffffffffffb30b072074fe3b487073a1b28c4adf68
lerp	289	11	exact	exact
ln	322	4	130	135	0x000000000000… 0x0000000000000000000000000019eeee1991f56daa32cdc95baeb71517c3c017
log10	322	4	130	135	0x000000000000… 0x00000000000000000000000000000000005fa366409a1e0f1037a02f8b4a8778
log1p	561	18	130	132	0x000000000000… 0x0000000000000000000000000000000000000000000000010000000000000000
log2	322	4	130	233	0x000000000000… 0x0000000000000000028dfc4db50a10ff45a3860e8964d6a14a662cfe41b5139e
log2Up	322	4	exact	exact
max	200	0	exact	exact
min	200	0	exact	exact
mul	231	169	132	232	0xffffffffffff… 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe,0x8000000000000000000000000000000000000000000000000000000000000001
mulDown	218	182	131	229	0x000000000000… 0x0000000000000000000000000000000000000000000000000000000000000002,0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
mulUp	225	175	129	226	0xffffffffffff… 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe,0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
neg	98	1	exact	exact
normCdf	584	0	147	228	0x000000000000… 0x00000000000000000000000000000004bba8d97f090a853b60da8e5e13acf310
pow	501	99	130	181	0x000000000000… 0x0000000000000000000000000000017b8003884dd86c89a488fc31f62f8cea98,0xfffffffffffffffffffffffffffffffee80023779f2d390dbf519c550fe6719a
powu	435	165	130	204	0xffffffffffff… 0xfffffffffffffffffffffffffffffffc29a12310624d183ca1d03b091fb77270,0x0000000000000000000000000000004000000000000000000000000000000000
round	97	2	exact	exact
sign	99	0	exact	exact
sinh	575	4	130	149	0x000000000000… 0x0000000000000000000000000000000000016a09e667f3bcc908b2fb1366ea95
sqrt	298	3	129	198	0x000000000000… 0x0000000000000000000000000000000000000000000000000000000000020000
sub	380	20	exact	exact
tanh	579	0	130	216	0x000000000000… 0x00000000000000000000000000000000005a827999fcef32422cbec4d9baa55f
toFixed18	99	0	181	199	0xffffffffffff… 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
toFixed18Down	99	0	181	199	0xffffffffffff… 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
toFixed18Up	99	0	182	201	0x000000000000… 0x0000000000000000000000000000000000000000000000000000000000000001
zeroFloorSub	189	11	exact	exact

Relative correct bits of the 127.128 result, msb(|truth|) − msb(|truth − got|), against the real truth (mpmath at 200 decimal places) over the committed vectors in test/bl127/vectors/, for results of magnitude 1 or more. "exact" is bit-identical with the truth. Every op is also held to its rounding contract: nearest within half an ULP, floor, ceil and trunc within one; maxErrUlp in the data. Reverts counts vectors where the oracle and the Yul both reject the input with the same error. Hover a worst input for the whole word. Source: precision.json.

Integer, rounding and comparison ops: bit-exact. mul and sqrt round down and div toward zero, within one ULP; "exact" in the table means equal to an oracle that rounds the same way. The directed ops round the way their names say, within one ULP.
Every transcendental (exp, ln, pow, powu, compound, cbrt, the hyperbolics, erf, erfc, normCdf, both Lambert W branches) is correctly rounded to nearest: each fast value carries a derived error bound and a rounding test, and a wider stage decides what the test cannot, so the word is within half an ULP (maxErrUlp in the data) at every committed vector and on every random input of the sweep, plain and with every test forced. exp(ln x) returns the same word for 10,000 steps. The pow exception of earlier releases (an exponent near 2⁹⁰) is gone in 3.0.