Accuracy table

Every region of every function: maximum and typical error in ULPs, beside SciPy's on the same points.

Summary (worst region of each function)

Errors in ULPs against mpmath; bold: at least as accurate as SciPy in every region.

function	points	regions	ours max	SciPy max	regions where ours <= SciPy
beta	5006	6	1.00	1.9e+07	6/6
betainc	9811	11	8.99	wrong	11/11
betaincc	9812	11	7.32	wrong	11/11
betainccinv	7180	10	wrong	wrong	10/10
betaincinv	7138	10	6.8e+15	wrong	10/10
binom	3000	3	0.50	1.9e+06	3/3
comb	3661	4	0.50	5.4e+08	4/4
digamma	7852	8	31	2.5e+17	8/8
ellipe	3921	5	0.51	3.30	5/5
ellipk	3897	5	0.52	1.83	5/5
ellipkm1	3006	4	0.53	1.73	4/4
erf	3110	5	0.53	2.00	5/5
erfc	4260	7	1.00	2.1e+13	7/7
erfcinv	4201	6	0.54	wrong	6/6
erfcx	5010	6	0.59	481	6/6
erfinv	3928	5	0.57	1.72	5/5
expit	4010	5	1.00	9.5e+13	5/5
factorial	2181	4	0.50	620	4/4
factorial2	326	1	0.50	4.5e+15	1/1
gamma	8143	10	0.50	3.3e+15	10/10
gammainc	7520	10	2.08	8.9e+15	10/10
gammaincc	7520	10	1.81	1.1e+10	10/10
gammainccinv	6260	8	1.13	wrong	8/8
gammaincinv	5791	8	1.19	wrong	8/8
i0	6013	7	2.51	wrong	7/7
i0e	5013	6	2.04	4.77	6/6
i1	6013	7	3.45	wrong	7/7
i1e	5013	6	2.47	6.34	6/6
iv	7687	9	2.87	wrong	9/9
ive	8687	10	12	wrong	10/10
j0	6013	7	1.86	wrong	7/7
j1	6013	7	1.77	wrong	7/7
jn	8077	10	5.19	wrong	10/10
jn_zeros	690	2	0.50	0.85	2/2
jv	8687	10	7.22	wrong	10/10
k0	5013	6	2.91	wrong	6/6
k0e	4013	5	1.52	wrong	5/5
k1	5013	6	2.49	wrong	5/6
k1e	4013	5	2.44	wrong	5/5
kv	7687	9	3.82	wrong	9/9
kve	8687	10	4.55	wrong	10/10
log1pexp	3010	4	0.50	0.96	4/4
log_expit	4010	5	0.50	1.04	5/5
log_factorial	3307	5	1.00	wrong	5/5
log_ndtr	6010	7	1.00	3.6e+12	7/7
log_softmax4	5005	6	0.69	9.0e+15	6/6
logbeta	5004	6	30	wrong	6/6
loggamma	9907	10	0.86	wrong	10/10
logit	3913	5	0.50	1.74	5/5
logsumexp4	5005	6	0.50	3.20	6/6
ndtr	4060	6	0.60	1.8e+12	6/6
ndtri	4080	6	0.62	2.62	6/6
perm	3633	4	0.50	9.41	4/4
polygamma	4014	5	0.50	wrong	5/5
softmax4	5005	6	1.00	437	6/6
xlog1py	3007	4	0.50	1.26	4/4
xlogy	2009	3	0.50	1.18	3/3
y0	5013	6	1.73	wrong	6/6
y1	5013	6	1.70	wrong	6/6
yn	7577	9	5.43	wrong	9/9
yv	8687	10	3.86	wrong	10/10
zeta	5081	8	0.53	1.9e+12	8/8
zeta_hurwitz	6006	7	0.50	306	7/7

Every region

function	region	points	ours max	ours p99.9	SciPy max	SciPy p99.9
beta	special	6	0.48	0.48	1.28	1.28
beta	a,b in (0,1]	1000	0.50	0.50	6.83	5.76
beta	a,b in (1,100]	1000	0.50	0.50	550	540
beta	a,b in (100,1e5]	1000	1.00	0.49	158117	150051
beta	a small, b large	1000	0.50	0.50	1.9e+07	1.5e+07
beta	a<0 non-integer	1000	0.50	0.50	13979	8447
betainc	special	512	1.14	1.14	wrong	wrong
betainc	a,b<1e-3	1000	0.93	0.83	8.9e+15	8.8e+15
betainc	a<1e-3<=b	1000	0.49	0.47	3.06	1.92
betainc	b<1e-3<=a	1000	2.91	2.34	1.7e+13	7.1e+12
betainc	a,b in [1e-3,1)	1000	1.93	1.65	12	9.54
betainc	a,b in [1,100)	1000	4.84	3.70	447	417
betainc	a,b in [100,1e4), x near mean	1000	8.99	6.93	3487	2603
betainc	a,b in [1e4,1e15], x near mean	300	6.35	6.35	8.8e+11	8.8e+11
betainc	a small, b large	999	5.21	5.21	935	935
betainc	x tiny (I to subnormal)	1000	3.25	0.96	5.7e+10	2.1e+10
betainc	x near 1 (I^c to subnormal)	1000	0.50	0.48	0.69	0.59
betaincc	special	512	0.67	0.67	wrong	wrong
betaincc	a,b<1e-3	1000	1.28	0.98	9.0e+15	9.0e+15
betaincc	a<1e-3<=b	1000	4.80	3.27	5.0e+13	7.4e+12
betaincc	b<1e-3<=a	1000	0.50	0.49	4.59	3.13
betaincc	a,b in [1e-3,1)	1000	3.79	1.93	22	14
betaincc	a,b in [1,100)	1000	3.25	2.49	235	142
betaincc	a,b in [100,1e4), x near mean	1000	6.16	5.99	2997	2442
betaincc	a,b in [1e4,1e15], x near mean	300	6.75	6.75	1.9e+14	1.9e+14
betaincc	a small, b large	1000	7.32	3.33	725	598
betaincc	x tiny (I to subnormal)	1000	0.43	0.12	0.43	0.12
betaincc	x near 1 (I^c to subnormal)	1000	3.04	1.96	1.4e+14	1.3e+13
betainccinv	special	507	0.50	0.50	wrong	wrong
betainccinv	a,b<1e-3	594	wrong	wrong	wrong	wrong
betainccinv	a<1e-3<=b or b<1e-3<=a	629	8.1e+15	8.1e+15	wrong	wrong
betainccinv	a,b in [1e-3,1)	1000	20	12	4.5e+15	4.5e+15
betainccinv	a,b in [1,100)	1000	3.16	2.31	35	29
betainccinv	a,b in [100,3000)	1000	0.86	0.79	17	9.55
betainccinv	a,b in [3000,1e15]	150	0.50	0.50	4.9e+06	4.9e+06
betainccinv	a small, b large	300	2.03	2.03	4.5e+15	4.5e+15
betainccinv	p tiny	1000	0.72	0.53	wrong	wrong
betainccinv	p near 1	1000	1.51	1.48	332	179
betaincinv	special	506	0.43	0.43	wrong	wrong
betaincinv	a,b<1e-3	613	5.3e+09	5.3e+09	wrong	wrong
betaincinv	a<1e-3<=b or b<1e-3<=a	569	6.8e+15	6.8e+15	wrong	wrong
betaincinv	a,b in [1e-3,1)	1000	7.78	6.96	4.5e+15	4.5e+15
betaincinv	a,b in [1,100)	1000	2.81	2.74	33	21
betaincinv	a,b in [100,3000)	1000	0.94	0.77	323	194
betaincinv	a,b in [3000,1e15]	150	0.73	0.73	1.4e+07	1.4e+07
betaincinv	a small, b large	300	1.93	1.93	4.5e+15	4.5e+15
betaincinv	p tiny	1000	2.10	1.91	wrong	wrong
betaincinv	p near 1	1000	0.73	0.70	153	14
binom	k integer <=64, n real	1000	0.50	0.50	1375	1312
binom	n,k > 0 real	1000	0.50	0.50	49612	32816
binom	n>0, k real small	1000	0.50	0.50	1.9e+06	1.3e+06
comb	n<=64	661	0.50	0.50	4.00	4.00
comb	n<=1100	1000	0.50	0.50	12572	12546
comb	huge n, small k	1000	0.50	0.50	5.4e+08	5.0e+08
comb	huge n, large k	1000	0.49	0.48	339196	44193
digamma	special	14	0.21	0.21	0.21	0.21
digamma	tiny	2000	0.50	0.50	1.42	1.21
digamma	(0,10)	1000	0.51	0.51	1.97	1.84
digamma	near positive root	917	0.53	0.53	1.28	1.28
digamma	[10,1e300]	1000	0.50	0.49	0.89	0.61
digamma	(-40,0)	1000	0.66	0.54	996	649
digamma	near negative roots	921	31	31	2.5e+17	2.5e+17
digamma	(-1e15,-40]	1000	0.50	0.50	3192	2176
ellipe	special	7	0.28	0.28	0.73	0.73
ellipe	m<-1	1000	0.51	0.51	3.30	2.88
ellipe	[-1,0.5)	1000	0.51	0.51	2.03	1.92
ellipe	[0.5,1-1e-3)	1000	0.50	0.50	1.00	0.95
ellipe	near 1	914	0.51	0.51	0.97	0.97
ellipk	special	7	0.43	0.43	0.43	0.43
ellipk	m<-1	1000	0.51	0.51	1.59	1.47
ellipk	[-1,0.5)	1000	0.51	0.51	1.83	1.80
ellipk	[0.5,1-1e-3)	1000	0.50	0.50	1.31	1.21
ellipk	near 1	890	0.52	0.52	1.44	1.44
ellipkm1	special	6	0.32	0.32	0.32	0.32
ellipkm1	p tiny	1000	0.48	0.48	1.23	0.97
ellipkm1	(1e-3,1]	1000	0.53	0.51	1.35	1.21
ellipkm1	p>1	1000	0.51	0.51	1.73	1.52
erf	special	10	0	0	0	0
erf	tiny	1000	0.51	0.51	1.35	1.35
erf		x	<=0.5	1000	0.53	0.52
erf	0.5<	x	<6	1000	0.50	0.50
erf		x	>=6	100	0	0
erfc	special	10	0	0	0	0
erfc	[-6,0.5)	1000	0.50	0.50	1.70	1.55
erfc	[0.5,5)	1000	0.61	0.58	15	15
erfc	[5,26.5) tail	1000	0.53	0.52	436	433
erfc	[26.5,27.3] subnormal	200	1.00	1.00	2.1e+13	2.1e+13
erfc	x<-6	50	0	0	0	0
erfc	tiny	1000	0.46	0.44	0.46	0.44
erfcinv	special	8	0.39	0.39	wrong	wrong
erfcinv	subnormal	193	0.49	0.49	wrong	wrong
erfcinv	[1e-300,1e-10)	1000	0.50	0.50	2.49	2.43
erfcinv	[1e-10,0.5)	1000	0.53	0.50	2.66	2.56
erfcinv	[0.5,1.5]	1000	0.52	0.51	3.04	2.76
erfcinv	(1.5,2)	1000	0.54	0.51	4.39	4.15
erfcx	special	10	0	0	0	0
erfcx	[-26.6,-0.5)	1000	0.50	0.50	481	464
erfcx	[-0.5,0.5)	1000	0.54	0.50	6.87	6.19
erfcx	[0.5,8)	1000	0.59	0.52	4.19	4.15
erfcx	[8,1e5)	1000	0.50	0.50	2.23	2.22
erfcx	[1e5,1e300]	1000	0.50	0.50	1.05	0.77
erfinv	special	9	0.08	0.08	0.08	0.08
erfinv	tiny	1000	0.51	0.51	1.50	1.50
erfinv		y	<=0.5	1000	0.54	0.54
erfinv	0.5<	y	<0.999	1000	0.57	0.57
erfinv	near ±1	919	0.50	0.50	1.50	1.50
expit	special	10	0	0	0	0
expit	[-746,-30)	1000	1.00	0.50	9.5e+13	3.8e+13
expit	[-30,30)	1000	0.50	0.50	1.47	1.45
expit	[30,40)	1000	0.50	0.50	1.00	0.99
expit	tiny	1000	0.49	0.48	1.74	1.44
factorial	special	10	0.07	0.07	1.07	1.07
factorial	integers	171	0.50	0.50	2.67	2.67
factorial	(0,1)	1000	0.50	0.50	3.59	3.47
factorial	(1,170.6)	1000	0.50	0.50	620	609
factorial2	n in [-5,320]	326	0.50	0.50	4.5e+15	4.5e+15
gamma	special	16	0.35	0.35	0.65	0.65
gamma	tiny	2000	0.50	0.50	2.01	1.81
gamma	(0,2)	1000	0.50	0.50	3.25	3.21
gamma	[2,33)	1000	0.50	0.50	5.76	4.46
gamma	[33,171.6]	1000	0.50	0.50	3.33	3.28
gamma	integers	171	0.50	0.50	2.67	2.67
gamma	overflow	22	0	0	0	0
gamma	(-33,0)	1000	0.50	0.50	6.29	5.63
gamma	near poles	934	0.50	0.50	4.90	4.90
gamma	(-184,-33]	1000	0.50	0.50	3.3e+15	2.8e+15
gammainc	special	120	0.45	0.45	4.5e+15	4.5e+15
gammainc	a<1e-3	1000	0.49	0.48	252	229
gammainc	a in [1e-3,1)	1000	0.70	0.70	36	29
gammainc	a in [1,30)	1000	2.08	1.63	150	119
gammainc	integer, half-integer a	1000	0.90	0.89	251	164
gammainc	a in [30,1e4), x near a	1000	0.88	0.74	3476	3446
gammainc	a in [1e4,1e15], x near a	300	0.56	0.56	8.9e+15	8.9e+15
gammainc	x tiny (P to subnormal)	1000	0.70	0.66	1.6e+14	3.1e+12
gammainc	x large (Q to subnormal)	1000	0.48	0.48	1.10	0.85
gammainc	x huge	100	0	0	0	0
gammaincc	special	120	1.00	1.00	461	461
gammaincc	a<1e-3	1000	0.87	0.69	315	238
gammaincc	a in [1e-3,1)	1000	1.14	1.07	54	39
gammaincc	a in [1,30)	1000	1.81	1.42	141	106
gammaincc	integer, half-integer a	1000	1.27	1.10	153	137
gammaincc	a in [30,1e4), x near a	1000	1.05	1.02	3875	3533
gammaincc	a in [1e4,1e15], x near a	300	0.54	0.54	4.5e+09	4.5e+09
gammaincc	x tiny (P to subnormal)	1000	0.98	0.92	12	9.59
gammaincc	x large (Q to subnormal)	1000	1.31	1.14	1.1e+10	9.9e+09
gammaincc	x huge	100	0	0	0	0
gammainccinv	special	110	0.53	0.53	wrong	wrong
gammainccinv	a<1e-3	1000	0.54	0.51	941	848
gammainccinv	a in [1e-3,1)	1000	0.76	0.72	7062	4585
gammainccinv	a in [1,100)	1000	1.09	1.09	19	18
gammainccinv	a in [100,1e4)	1000	0.53	0.51	0.86	0.67
gammainccinv	a in [1e4,1e15]	150	0.50	0.50	0.50	0.50
gammainccinv	p tiny	1000	0.50	0.50	12	11
gammainccinv	p near 1	1000	1.13	0.69	1004	792
gammaincinv	special	110	0.53	0.53	wrong	wrong
gammaincinv	a<1e-3	531	0.43	0.43	1312	1312
gammaincinv	a in [1e-3,1)	1000	0.94	0.73	8271	4953
gammaincinv	a in [1,100)	1000	1.19	1.15	13	9.99
gammaincinv	a in [100,1e4)	1000	0.52	0.52	0.78	0.76
gammaincinv	a in [1e4,1e15]	150	0.49	0.49	0.49	0.49
gammaincinv	p tiny	1000	0.69	0.68	495	448
gammaincinv	p near 1	1000	0.55	0.54	20	12
i0	special	13	0.80	0.80	wrong	wrong
i0	small x	1000	0.50	0.48	2.50	2.39
i0	moderate	1000	2.51	2.47	2.89	2.62
i0	large x	1000	1.66	1.61	2.54	2.43
i0	over/underflow edge	1000	1.41	1.24	wrong	wrong
i0	huge x	1000	0	0	0	0
i0	negative x	1000	1.77	1.76	wrong	2.86
i0e	special	13	0.96	0.96	1.05	1.05
i0e	small x	1000	1.47	1.30	3.98	3.55
i0e	moderate	1000	1.98	1.91	2.34	2.13
i0e	large x	1000	0.50	0.50	2.26	2.10
i0e	huge x	1000	0.50	0.50	1.59	1.46
i0e	negative x	1000	2.04	1.73	4.77	4.63
i1	special	13	0.12	0.12	wrong	wrong
i1	small x	1000	0.48	0.45	4.66	4.00
i1	moderate	1000	3.45	3.25	7.65	7.16
i1	large x	1000	1.77	1.75	2.26	2.17
i1	over/underflow edge	1000	1.46	1.05	wrong	wrong
i1	huge x	1000	0	0	0	0
i1	negative x	1000	3.08	2.24	6.46	6.06
i1e	special	13	0.82	0.82	2.20	2.20
i1e	small x	1000	0.96	0.86	3.64	3.23
i1e	moderate	1000	2.36	2.12	6.34	4.50
i1e	large x	1000	0.50	0.50	2.02	1.76
i1e	huge x	1000	0.50	0.50	1.71	1.59
i1e	negative x	1000	2.47	1.93	5.53	5.12
iv	special	187	2.09	2.09	wrong	wrong
iv	small x	1000	0.87	0.82	9.0e+15	9.0e+15
iv	moderate	1000	2.12	1.92	12	9.07
iv	large x	1000	2.87	2.19	14	10
iv	over/underflow edge	1000	1.58	1.28	9997	8820
iv	large order	1000	2.01	1.80	wrong	2655
iv	v ~ x	500	2.02	2.02	1483	1483
iv	negative v	1000	2.76	2.69	17	12
iv	integer v	1000	2.18	2.18	12	10
ive	special	187	4.57	4.57	wrong	wrong
ive	small x	1000	0.92	0.79	1.0e+14	1.5e+13
ive	moderate	1000	2.07	1.94	584	435
ive	large x	1000	1.71	1.52	140	139
ive	over/underflow edge	1000	0.51	0.50	4.39	4.35
ive	huge x	1000	0.50	0.50	wrong	wrong
ive	large order	1000	1.37	1.13	8.5e+15	6.1e+15
ive	v ~ x	500	1.01	1.01	2350	2350
ive	negative v	1000	12	5.72	8152	7476
ive	integer v	1000	1.57	1.51	310	297
j0	special	13	0.49	0.49	wrong	wrong
j0	small x	1000	0.50	0.48	2.50	1.58
j0	moderate	1000	1.07	1.06	304	206
j0	large x	1000	1.58	1.49	549	55
j0	huge x	1000	1.86	1.73	340	151
j0	near zeros	1000	0.50	0.50	3.1e+10	2.6e+10
j0	negative x	1000	1.35	1.18	460	302
j1	special	13	0.83	0.83	wrong	wrong
j1	small x	1000	0.59	0.57	2.00	2.00
j1	moderate	1000	1.22	1.15	1114	872
j1	large x	1000	1.57	1.47	486	140
j1	huge x	1000	1.77	1.67	66	60
j1	near zeros	1000	0.50	0.50	3.7e+10	3.1e+10
j1	negative x	1000	1.52	1.37	147	88
jn	special	77	1.84	1.84	wrong	wrong
jn	small x	1000	0.80	0.50	7.1e+15	5.9e+15
jn	moderate	1000	1.41	1.09	1286	571
jn	large x	1000	1.46	1.42	13342	12318
jn	huge x	1000	1.63	1.63	4.1e+18	2.4e+18
jn	near zeros	1000	5.19	3.41	6.5e+11	4.5e+11
jn	negative x	500	1.28	1.28	1730	1730
jn	large order	1000	1.28	1.13	6.3e+15	8.8e+11
jn	v ~ x	500	0.50	0.50	4478	4478
jn	negative n	1000	1.09	1.08	5613	3773
jn_zeros	n <= 10, k <= 50	550	0.50	0.50	0.75	0.75
jn_zeros	n >= 20, k <= 20	140	0.50	0.50	0.85	0.85
jv	special	187	1.84	1.84	wrong	wrong
jv	small x	1000	0.75	0.67	6.3e+15	5.6e+15
jv	moderate	1000	1.45	1.28	40775	6420
jv	large x	1000	1.73	1.62	19644	16312
jv	huge x	1000	1.68	1.65	5.3e+18	2.1e+18
jv	near zeros	1000	1.63	1.57	7.2e+11	3.9e+11
jv	large order	1000	1.35	1.28	6.8e+13	6.5e+09
jv	v ~ x	500	0.50	0.50	3372	3372
jv	negative v	1000	7.22	3.77	1572	1254
jv	integer v	1000	1.21	1.21	1063	823
k0	special	13	0.35	0.35	wrong	wrong
k0	small x	1000	1.14	1.07	3.70	2.64
k0	moderate	1000	2.91	2.34	5.78	4.32
k0	large x	1000	1.54	1.49	2.69	2.60
k0	over/underflow edge	1000	2.00	1.05	3.00	1.75
k0	huge x	1000	0	0	0	0
k0e	special	13	0.61	0.61	wrong	wrong
k0e	small x	1000	1.47	1.46	3.23	3.23
k0e	moderate	1000	1.52	1.45	5.86	4.47
k0e	large x	1000	0.50	0.50	2.14	2.11
k0e	huge x	1000	0.50	0.50	1.93	1.71
k1	special	13	1.29	1.29	wrong	wrong
k1	small x	1000	1.05	0.96	1.05	1.04
k1	moderate	1000	2.49	2.39	2.96	2.91
k1	large x	1000	1.47	1.45	3.04	2.45
k1	over/underflow edge	1000	1.50	1.50	1.94	1.62
k1	huge x	1000	0	0	0	0
k1e	special	13	1.03	1.03	wrong	wrong
k1e	small x	1000	1.49	1.40	1.49	1.40
k1e	moderate	1000	2.44	2.09	2.95	2.86
k1e	large x	1000	0.50	0.50	2.28	2.27
k1e	huge x	1000	0.50	0.50	1.92	1.91
kv	special	187	0.97	0.97	wrong	wrong
kv	small x	1000	1.78	1.58	wrong	wrong
kv	moderate	1000	2.08	1.97	43	41
kv	large x	1000	1.89	1.87	7.4e+15	6.4e+15
kv	over/underflow edge	1000	1.25	1.12	9.0e+15	8.8e+15
kv	large order	1000	1.65	1.64	wrong	wrong
kv	v ~ x	500	1.73	1.73	2679	2679
kv	negative v	1000	3.82	3.36	64	53
kv	integer v	1000	2.87	2.83	74	74
kve	special	187	0.78	0.78	wrong	wrong
kve	small x	1000	1.48	1.25	wrong	292
kve	moderate	1000	1.76	1.67	86	79
kve	large x	1000	1.48	1.36	119	58
kve	over/underflow edge	1000	0.51	0.51	3.59	3.38
kve	huge x	1000	0.50	0.50	wrong	wrong
kve	large order	1000	1.13	1.01	wrong	wrong
kve	v ~ x	500	0.99	0.99	2418	2418
kve	negative v	1000	4.55	3.40	1147	132
kve	integer v	1000	2.88	2.60	73	70
log1pexp	special	10	0.21	0.21	0.21	0.21
log1pexp	[-746,-30)	1000	0.50	0.50	0.70	0.66
log1pexp	[-30,30)	1000	0.50	0.50	0.96	0.95
log1pexp	[30,1e300]	1000	0.00	0.00	0.00	0.00
log_expit	special	10	0.21	0.21	0.21	0.21
log_expit	[-746,-30)	1000	0.41	0.19	0.41	0.19
log_expit	[-30,30)	1000	0.50	0.50	0.93	0.92
log_expit	[30,40)	1000	0.50	0.50	0.93	0.92
log_expit	tiny	1000	0.47	0.47	1.04	0.81
log_factorial	special	7	1.00	1.00	wrong	wrong
log_factorial	(0,3)	1000	0.52	0.51	1734	251
log_factorial	[3,1e5)	1000	0.50	0.50	2.99	2.44
log_factorial	[1e5,1e300]	1000	0.50	0.50	1.29	1.09
log_factorial	integers	300	0.50	0.50	1.77	1.77
log_ndtr	special	10	0.21	0.21	0.21	0.21
log_ndtr	x<-1e5	1000	0.50	0.50	2.97	2.81
log_ndtr	[-1e5,-40)	1000	0.50	0.50	2.79	2.65
log_ndtr	[-40,-1)	1000	0.52	0.50	2.78	2.75
log_ndtr	[-1,1)	1000	0.61	0.59	4.16	3.33
log_ndtr	[1,10)	1000	0.59	0.54	113	98
log_ndtr	[10,38)	1000	1.00	0.50	3.6e+12	3.2e+12
log_softmax4	special	5	0.21	0.21	0.21	0.21
log_softmax4	moderate	1000	0.50	0.50	962930	342308
log_softmax4	one dominant	1000	0.69	0.62	9.0e+15	9.0e+15
log_softmax4	huge	1000	0.56	0.50	8.8e+15	8.8e+15
log_softmax4	wide spread	1000	0.50	0.50	9.0e+15	9.0e+15
log_softmax4	near cancellation	1000	0.50	0.50	9.0e+15	9.0e+15
logbeta	special	4	0.10	0.10	1.05	1.05
logbeta	a,b in (0,1]	1000	0.49	0.49	0.49	0.49
logbeta	a,b in (1,100]	1000	0.50	0.50	28	26
logbeta	a,b in (100,1e300]	1000	0.50	0.50	wrong	wrong
logbeta	a small, b large	1000	0.50	0.50	1.1e+06	954807
logbeta	near log B = 0	1000	30	20	45161	28658
loggamma	special	15	0.39	0.39	wrong	wrong
loggamma	tiny	2000	0.50	0.48	0.87	0.82
loggamma	near 1 and 2	947	0.64	0.64	1.3e+16	1.3e+16
loggamma	(0,3)	1000	0.86	0.74	496	408
loggamma	[3,13)	1000	0.50	0.50	1.12	1.09
loggamma	[13,1e5)	1000	0.50	0.50	1.32	1.30
loggamma	[1e5,1e305]	1000	0.50	0.50	0.84	0.83
loggamma	(-34,0)	1000	0.62	0.50	127	16
loggamma	near poles	945	0.50	0.50	14	14
loggamma	(-1e5,-34]	1000	0.50	0.50	1.71	1.62
logit	special	7	0.39	0.39	0.39	0.39
logit	near 0	1000	0.49	0.48	0.49	0.48
logit	near 1/2	1000	0.50	0.50	0.96	0.95
logit	(0,1)	1000	0.50	0.50	1.74	1.36
logit	near 1	906	0.50	0.50	0.54	0.54
logsumexp4	special	5	0.39	0.39	0.39	0.39
logsumexp4	moderate	1000	0.50	0.50	3.20	1.80
logsumexp4	one dominant	1000	0.50	0.50	0.50	0.50
logsumexp4	huge	1000	0.50	0.50	0.50	0.50
logsumexp4	wide spread	1000	0.50	0.49	0.50	0.49
logsumexp4	near cancellation	1000	0.50	0.50	1.72	1.65
ndtr	special	10	0	0	0	0
ndtr	[-38.5,-10)	1000	0.50	0.50	1.8e+12	1.8e+12
ndtr	[-10,-1)	1000	0.60	0.53	110	109
ndtr	[-1,1)	1000	0.52	0.52	2.64	2.58
ndtr	[1,8.3)	1000	0.50	0.50	1.04	0.94
ndtr	x>=8.3	50	0	0	0	0
ndtri	special	7	0.33	0.33	0.33	0.33
ndtri	subnormal	193	0.50	0.50	1.38	1.38
ndtri	[1e-300,1e-10)	1000	0.50	0.50	2.28	1.38
ndtri	[1e-10,0.5)	1000	0.53	0.51	2.48	2.42
ndtri	[0.5,1)	1000	0.62	0.55	2.62	2.36
ndtri	near 1	880	0.50	0.50	2.17	2.17
perm	n<=64	661	0.50	0.50	7.67	7.67
perm	n<=200	972	0.50	0.50	9.41	9.41
perm	huge n, small k	1000	0.50	0.50	6.94	6.61
perm	huge n, k>64	1000	0.46	0.39	1.77	1.54
polygamma	special	14	0.35	0.35	wrong	wrong
polygamma	x tiny	1000	0.50	0.50	6.54	2.40
polygamma	x in (0,10)	1000	0.50	0.50	6.04	5.94
polygamma	x in [10,1e10)	1000	0.50	0.50	13	12
polygamma	x<0	1000	0.50	0.50	33	23
softmax4	special	5	0	0	0	0
softmax4	moderate	1000	0.50	0.50	17	16
softmax4	one dominant	1000	0.50	0.50	2.31	1.96
softmax4	huge	1000	0.50	0.50	1.90	1.89
softmax4	wide spread	1000	1.00	0.50	437	436
softmax4	near cancellation	1000	0.50	0.50	2.82	2.70
xlog1py	special	7	0	0	0	0
xlog1py	moderate	1000	0.50	0.50	1.01	1.01
xlog1py	y small	1000	0.50	0.50	0.78	0.74
xlog1py	y near -1	1000	0.50	0.50	1.26	1.22
xlogy	special	9	0	0	0	0
xlogy	moderate	1000	0.50	0.50	0.51	0.50
xlogy	y near 1	1000	0.50	0.50	1.18	1.14
y0	special	13	0.43	0.43	wrong	wrong
y0	small x	1000	0.59	0.56	1.31	1.14
y0	moderate	1000	1.04	1.00	690	550
y0	large x	1000	1.73	1.57	339	92
y0	huge x	1000	1.49	1.46	242	73
y0	near zeros	1000	0.50	0.50	1.8e+12	1.3e+12
y1	special	13	0.75	0.75	wrong	wrong
y1	small x	1000	0.50	0.50	1.64	1.57
y1	moderate	1000	0.95	0.85	6079	1702
y1	large x	1000	1.64	1.55	129518	122550
y1	huge x	1000	1.70	1.60	1.0e+19	2.0e+18
y1	near zeros	1000	0.50	0.50	7.3e+11	5.6e+11
yn	special	77	1.40	1.40	wrong	wrong
yn	small x	1000	1.62	1.51	3.81	3.01
yn	moderate	1000	2.57	2.22	2743	500
yn	large x	1000	1.64	1.51	332065	83737
yn	huge x	1000	1.87	1.51	5.1e+18	2.1e+18
yn	near zeros	1000	5.43	5.22	6.5e+11	6.2e+11
yn	large order	1000	1.35	1.04	38847	11771
yn	v ~ x	500	0.50	0.50	172835	172835
yn	negative n	1000	3.46	2.29	1285	1026
yv	special	187	1.40	1.40	wrong	wrong
yv	small x	1000	2.44	2.39	wrong	408
yv	moderate	1000	1.84	1.75	15788	1568
yv	large x	1000	1.64	1.58	7655	2725
yv	huge x	1000	1.67	1.53	1.2e+19	6.3e+18
yv	near zeros	1000	1.67	1.66	2.8e+12	1.3e+12
yv	large order	1000	1.17	1.06	wrong	250879
yv	v ~ x	500	0.50	0.50	13525	13525
yv	negative v	1000	3.86	3.28	1710	1579
yv	integer v	1000	2.50	2.36	217	78
zeta	special	13	0.33	0.33	3.67	3.67
zeta	near pole	968	0.50	0.50	4.36	4.36
zeta	[-1,2]	1000	0.53	0.50	53	49
zeta	(2,64)	1000	0.50	0.50	1.15	0.69
zeta	[64,1e300]	50	0	0	0	0
zeta	(-260,-1)	1000	0.50	0.50	1166	776
zeta	near trivial zeros	1000	0.52	0.50	1.9e+12	1.4e+12
zeta	s<-260	50	0	0	0	0
zeta_hurwitz	special	10	0.35	0.35	0.86	0.86
zeta_hurwitz	s in (1,50), q in (0,10)	1000	0.50	0.50	3.22	2.90
zeta_hurwitz	s near 1	1000	0.50	0.50	2.57	2.45
zeta_hurwitz	q tiny	1000	0.50	0.49	2.65	2.26
zeta_hurwitz	q large	998	0.49	0.49	9.00	9.00
zeta_hurwitz	s large	998	0.50	0.50	306	306
zeta_hurwitz	q<0, integer s	1000	0.50	0.50	12	5.23

Created on October 11, 2026 by tannevaled

Modified on October 11, 2026 by tannevaled

Accuracy Performance