Quadrature table

Every fixture integral: value, reference, true and estimated error, evaluations and diagnostics, beside SciPy's.

integral	value	SciPy 1.18.1	reference	true error	estimate	neval	neval SciPy	ier	ier SciPy
exp	1.718281828459045	1.718281828459045	1.718281828459045	2.2e-16	1.9e-14	21	21	0	0
sin	2	2	2	0	2.2e-14	21	21	0	0
runge	0.5493603067780065	0.5493603067780065	0.5493603067780063	2.2e-16	2.9e-09	147	147	0	0
log_over_sqrt	-3.999999999999983	-3.999999999999983	-4	1.7e-14	2.3e-13	315	315	0	0
inv_sqrt	1.999999999999999	1.999999999999999	2	6.7e-16	3.8e-15	231	231	0	0
x_pow_m09	9.999999999999792	10	10	2.1e-13	6.8e-13	231	231	0	0
log	-0.9999999999999999	-0.9999999999999999	-1	1.1e-16	1.1e-15	231	231	0	0
exp_cos50	0.0003990933855533729	0.0003990933855533731	0.0003990933855530956	2.8e-16	2.7e-09	1281	1281	0	0
tight_runge	0.5493603067780063	0.5493603067780063	0.5493603067780063	0	6.1e-15	231	231	0	0
gauss_inf	1.772453850905516	1.772453850905516	1.772453850905516	2.2e-16	1.4e-08	270	270	0	0
lorentz_half	1.570796326794897	1.570796326794897	1.570796326794897	0	2.6e-10	45	45	0	0
exp_left	1	1	1	0	5.8e-11	135	135	0	0
x2_exp	2	2	2	0	1e-10	165	165	0	0
lorentz_shift	3.14159265358979	3.14159265358979	3.141592653589793	3.6e-15	2e-10	210	210	0	0
kink_points	0.2777777777777778	0.2777777777777778	0.2777777777777778	0	3.1e-15	42	42	0	0
step_points	1.5	1.5	1.5	0	1.7e-14	42	42	0	0
step_nopoints	1.5	1.5	1.5	0	1.7e-14	63	63	0	0
sqrt_kink_points	0.5163460352255528	0.5163460352255528	0.5163460352255527	1.1e-16	5.7e-16	399	399	0	0
cos_weight	-0.01362867976778223	-0.01362867976778224	-0.01362867976778225	1.4e-17	9.3e-18	25	25	0	0
sin_weight_log1p	-0.02203955142238799	-0.022039551422388	-0.022039551422388	3.5e-18	5.3e-12	25	25	0	0
cos_weight_small	0.13676603011974	0.13676603011974	0.13676603011974	2.8e-17	1.5e-15	15	15	0	0
fourier_cos	0.2000000000000001	0.2000000000000001	0.2	8.3e-17	8.9e-11	175	175	0	0
fourier_sin	0.6467611227365523	0.6467611227365522	0.6467611227791301	4.3e-11	9.5e-09	440	440	0	0
fourier_sinc	0.6247132564795974	0.6247132564795976	0.6247132564277136	5.2e-11	1.4e-08	405	405	0	0
fourier_left	0.2000000000000001	0.2000000000000001	0.2	8.3e-17	8.9e-11	175	175	0	0
fourier_left_sin	-0.4000000000000001	-0.4000000000000002	-0.4	1.1e-16	2.2e-11	175	175	0	0
alg_chebyshev	3.141592653589792	3.141592653589793	3.141592653589793	8.9e-16	9.8e-14	50	50	0	0
alg_cos	1.585814200009902	1.585814200009902	1.585814200009903	4.4e-16	2.8e-14	50	50	0	0
alg_loga	-1	-1	-1	0	9.8e-15	40	40	0	0
alg_logb	-0.8535815370311841	-0.8535815370311841	-0.853581537031184	1.1e-16	1.3e-14	50	50	0	0
alg_log	0.3550659331517736	0.3550659331517736	0.3550659331517735	5.6e-17	7.8e-14	50	50	0	0
alg_log_exp	-13.78374913829299	-13.783749138293	-13.783749138293	1.8e-15	1.1e-12	50	50	0	0
cauchy_one	0.6931471805599452	0.6931471805599452	0.6931471805599453	1.1e-16	0	25	25	0	0
cauchy_exp	2.114501750751457	2.114501750751458	2.114501750751457	4.4e-16	2.5e-13	25	25	0	0
cauchy_far	-0.7201092731341771	-0.7201092731341769	-0.7201092731341771	0	8e-15	15	15	0	0
divergent	41.67684067538801	41.67684067538801	—	—	9.4	2079	2079	1	1
sin_inv	0.5024347471020826	0.5024347471020826	0.5040670619069284	0.0016	0.00062	2079	2079	1	1
limit_small	0.5057893582392152	0.5057893582392152	0.5040670619069284	0.0017	0.036	189	189	1	1
inv_x_lim200	145.6489177593801	145.6489177593801	—	—	9.4	8379	8379	1	1
x_pow_m12	-4.999999999999929	-4.99999999999982	—	—	1.1e-12	231	231	5	5
noise	1.000003732298556	1.000003732298556	—	—	1.3e-05	2079	2079	1	1
tiny_exp	1.718281828459045	1.718281828459045	1.718281828459045	2.2e-16	1.9e-14	21	21	0	0
tiny_sqrt	0.6666666666666669	0.6666666666666669	0.6666666666666666	2.2e-16	7.4e-16	231	231	0	0
tiny_log	-0.9999999999999999	-0.9999999999999999	-1	1.1e-16	1.1e-15	231	231	0	0
inf_div	144.9680899031616	144.9680899031616	—	—	8.2	5985	5985	1	1
inf_osc	-4695026.791622601	-4695026.791622601	—	—	1.1e+07	1485	1485	1	1
inf_slow	20.00000000000093	19.9999999999949	20	9.3e-13	2e-12	165	165	0	0
pts_div	73.92435318734103	73.92435318734103	—	—	12	3822	3822	3	3
pts_log_tiny	-1.610864302054893	-1.610864302054893	-1.610864302054893	0	1.8e-15	714	714	0	0
pts_sqrt_tiny	0.4999858572169353	0.4999858572169353	0.4999858572169352	1.1e-16	8.9e-16	483	483	0	0
pts_lim	0.5031802850706445	0.5031802850706445	—	—	0.0099	378	378	1	1
pts_x_m12	-11.73100280255335	-11.73100280255033	—	—	3.6e-09	462	462	5	5
qawo_long	0.009805126090711332	0.00980512609071133	0.009805126090711326	5.2e-18	5.1e-10	375	375	0	0
qawo_long_sin	0.6463803833309545	0.6463803833309544	0.6463803833309545	0	4.3e-11	265	265	0	0
qawo_log	-0.03103234144971901	-0.03103234144971898	-0.03103234144971872	2.9e-16	1.5e-10	355	355	0	0
qawo_rsqrt	0.08425019863769026	0.08425019863769019	0.08425019863768997	2.9e-16	6.1e-09	485	485	0	0
qawo_rsqrt_negsin	-0.08619771502732282	-0.08619771502732287	-0.08619771502732283	1.4e-17	1.1e-11	455	455	0	0
qawo_lim	0.06016101663301937	0.06016101663301937	—	—	0.011	175	175	1	1
qawo_tiny	0.03917846119800483	0.03917846119800483	0.03917846119800483	0	1.8e-15	565	565	2	2
qawo_maxp1	0.08425019863769026	0.08067260531271685	0.08425019863768997	2.9e-16	6.1e-09	485	485	0	0
qawf_limlst	-0.7094246789053589	-0.7094246789053587	—	—	17	185	185	1	1
qawf_rsqrt	-0.5557343384595684	-0.5557343384595682	-0.5557343384850439	2.5e-11	5.2e-09	460	460	0	0
qawf_shift	-0.6142451976501248	-0.6142451976501236	-0.6142451976679612	1.8e-11	6.9e-09	720	720	0	0
qawf_omega0	1	1	1	0	5.8e-11	135	135	0	0
qawf_omega0_sin	0	0	0	0	0	0	0	0	0
qawf_slow_omega	1.538461538461539	1.538461538461538	1.538461538461539	0	2.2e-12	75	75	0	0
qawc_sqrt	0.5680450674862814	0.5680450674862808	0.56804506749331	7e-12	1.3e-08	455	455	0	0
qawc_peak	0.5895475606650807	0.5895475606650808	—	—	8.5e-09	245	245	0	0
qawc_lim	0.5680432251473866	0.5680432251473859	—	—	0.0026	95	95	1	1
qawc_flip	-0.5680450674862814	-0.5680450674862808	—	—	1.3e-08	455	455	0	0
qawc_tiny	0.5680450674933107	0.5680450674933104	—	—	3.9e-14	3375	3075	2	2
qaws_cos30	0.1958302620088027	0.1958302620088027	0.1958302620088027	0	2.8e-09	170	170	0	0
qaws_lim	0.1958302620088041	0.1958302620088041	—	—	2.5e-06	70	70	1	1
qaws_lim2	0.1958302620080664	0.195830262008067	—	—	0.024	40	40	1	1
qaws_logb	-2.44786563847117	-2.44786563847117	-2.44786563847117	0	6.1e-09	230	230	0	0
qaws_loga	0.2924880583049135	0.2924880583049135	0.2924880583049133	2.2e-16	7.5e-09	230	230	0	0
qaws_tiny	0.1958302620088029	0.1958302620088029	—	—	1.1e-14	640	640	2	2
qaws_rough	0.1765709545600959	0.1765709545600959	—	—	1.8e-15	1520	1520	0	0
x_m2	-1	-1	—	—	9.1e-13	231	231	5	5
log_div	-103.4448927227068	-103.4448927227258	—	—	0.51	5397	5397	5	5
inf_x_m09	-9.999999999999616	-9.999999999988473	—	—	3e-12	165	165	5	5
inf_osc_slow	0.8901818656135411	0.8901818656135653	—	—	0.071	14985	14985	5	5
inf_fresnel	-302925597.2580663	-302925597.2580663	1.2533141373155	3e+08	6.1e+08	11970	11970	1	1
qawo_div	140.9566444393158	32.82568427196404	—	—	8.2	6035	1355	1	3
qawo_x_m0999	995.9960479954726	995.9960479959306	—	—	5.8e-07	365	365	5	5
qawo_noise	0.01635436647391766	0.01635436647391769	—	—	1.2e-14	715	715	2	2
qawo_round	-0.0900700925418273	-0.09007009254182735	—	—	5.3e-14	865	865	2	2
qawo_small_w	0.8119100277625456	0.8119100277625472	0.8119100277625464	7.8e-16	2.6e-12	225	225	0	0
qawo_small_w_log	-0.9460830703671835	-0.9460830703671835	-0.946083070367183	5.6e-16	2.5e-10	165	165	0	0
qawo_mid_w	0.4536139761247249	0.4536139761247264	0.4536139761247248	1.7e-16	1.9e-12	265	265	0	0
qawf_tight	0.009900990099009872	0.009900990099009865	0.009900990099009901	2.9e-17	7.4e-16	475	475	0	0
qawf_tight_lorentz	7.13140429077582e-05	7.131404290778598e-05	7.13140429076575e-05	1e-16	3.1e-14	1300	1300	7	7
qawf_loose	0.009900990099009894	0.009900990099009899	0.009900990099009901	6.9e-18	3.7e-08	125	125	0	0
qawf_linear	-0.3506120042760564	-0.350612004276053	—	—	5.3e-14	200	200	0	0
qawc_tough	-4.848716140289297e-09	-4.848824276002552e-09	0	4.8e-09	3.3e-07	2765	2765	3	3
qawc_rough	-0.7447223989982577	-0.7447223989982577	—	—	7.4e-14	2735	2735	0	0
qaws_alglog_cos	-0.007640485288506693	-0.007640485288506721	-0.007640485288506747	5.4e-17	7.7e-09	190	190	0	0
qaws_inner_sing	1.204489465806763	1.204489465806763	—	—	1.3e-07	1770	1770	3	3
br_x_m12_rel	-4.999999999999895	-5.00000000000002	—	—	6.8e-13	1029	777	5	5
br_x_m12_abs	-5.000000000000111	-5.000000000000004	—	—	2.5e-13	903	777	5	5
br_sqrt_noise	0.6666666525477484	0.6666666525477484	—	—	2.8e-07	1449	1449	2	2
br_round_lim1	2.718281828441325	2.718281828441325	—	—	3.1e-14	21	21	1	1
br_lim1	17.76843489238437	17.76843489238437	—	—	26	21	21	1	1
br_sin_ier2	1.943698234633915e-16	2.221501482512777e-16	0	1.9e-16	4.4e-14	21	21	2	2
br_pts_x_m12_12	-4.999999999999764	-4.99999999999975	—	—	2e-12	441	441	5	5
br_pts_x_m12_50	-5.000000000000055	-4.999999999999851	—	—	4.2e-13	903	777	5	5
br_pts_x_m12_noise	-4.999999999978739	-4.99999999997845	—	—	3.6e-11	777	777	5	5
br_pts_p01_noise	0.9090909052792266	0.9090909052792266	—	—	7.7e-07	1659	1659	2	2
br_pts_p01_loose	0.9090913624963983	0.9090913624963983	0.9090909090909091	4.5e-07	0.00059	231	231	0	0
br_pts_lim3	23.96736070075574	23.96736070075561	—	—	33	63	63	1	1
br_pts_sin_ier2	0	0	0	0	4.4e-14	42	42	2	2
br_qawo_ier2	0.9460830703671831	0.9460830703671831	—	—	1.1e-14	15	15	1	1
br_qawo_lim1	14.60472885813529	14.60472885813528	—	—	21	15	15	1	1
br_qawo_small	67.62829008303247	67.22716365045012	—	—	4	2685	2505	3	3
br_qawo_jup	-5.267049177350159	-5.267049177350098	—	—	4.9e-06	345	345	5	5
br_qawo_div	-5.267049177350162	-5.267049177351477	—	—	6.1e-12	885	1125	5	5
br_qawo_x_m105	-20.24609206773401	-20.24609206769644	—	—	6.8e-12	225	225	5	5
br_qawo_ext	3.359427063369166	3.359426545320674	—	—	17	1335	1335	4	4
br_qawf_limexp	0.2321993899612011	0.2321993899612086	—	—	0.005	1250	1250	4	1
br_qawf_ier7	0.008585663617188122	0.008585663617188119	—	—	0.00097	150	150	7	7
br_qawf_ier7b	0.07330393463133657	0.07330393463133664	—	—	0.098	165	165	7	7
br_qawf_ier4	0.9099718468530684	0.9099718468530681	—	—	0.095	630	615	4	4
br_qawf_drl	0.9099718264959826	0.9099718264959824	—	—	0.59	150	150	1	1
br_qawc_lim1	0.5677678532152158	0.5677678532152159	—	—	0.0077	25	25	1	1

Created on October 11, 2026 by tannevaled

Modified on October 11, 2026 by tannevaled

Verification ODE table