Details

sample62.0ms

Algorithm

intervals

Results

23.0ms	288×	body	80	valid
7.0ms	84×	body	80	nan

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	18
1	36	18
2	80	18
3	172	18
4	405	18
5	1244	18
6	4808	18
done	5000	18

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.1b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

2.6b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.9b	(/ (* M D) (* 2.0 d))
12.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

7.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
7.0ms	(/ (* M D) (* 2.0 d))
12.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series640.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
176.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
7.0ms	(/ (* M D) (* 2.0 d))
254.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify5.9min

Counts

125 → 125

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	18	19
1	32	19
2	73	19
3	173	19
4	467	19
5	1332	19
6	3562	19
done	5000	19
0	17	18
1	30	18
2	70	18
3	162	18
4	424	18
5	1273	18
6	3453	18
done	5000	18
0	17	18
1	32	18
2	66	18
3	151	18
4	388	18
5	1083	18
6	3360	18
done	5001	18
0	16	17
1	30	17
2	63	17
3	140	17
4	355	17
5	1039	17
6	3262	17
done	5000	17
0	17	18
1	32	18
2	61	18
3	147	18
4	398	18
5	1145	18
6	3131	18
done	5001	18
0	16	17
1	30	17
2	58	17
3	140	17
4	364	17
5	1084	17
6	2992	17
done	5000	17
0	16	17
1	32	17
2	57	17
3	127	17
4	326	17
5	943	17
6	2907	17
done	5000	17
0	15	16
1	30	16
2	54	16
3	120	16
4	301	16
5	904	16
6	2803	16
done	5000	16
0	15	16
1	33	16
2	78	16
3	166	16
4	361	16
5	923	16
6	2527	16
7	4732	16
done	5001	16
0	14	15
1	31	15
2	75	15
3	163	15
4	353	15
5	907	15
6	2502	15
7	4675	15
done	5001	15
0	15	16
1	33	16
2	78	16
3	166	16
4	361	16
5	923	16
6	2527	16
7	4732	16
done	5001	16
0	14	15
1	31	15
2	75	15
3	163	15
4	353	15
5	907	15
6	2502	15
7	4675	15
done	5001	15
0	15	16
1	35	16
2	83	16
3	193	16
4	542	16
5	2558	16
done	5000	16
0	14	15
1	33	15
2	80	15
3	186	15
4	523	15
5	2496	15
done	5000	15
0	13	14
1	32	14
2	77	14
3	195	14
4	533	14
5	2245	14
done	5000	14
0	13	14
1	31	14
2	73	14
3	159	14
4	357	14
5	1006	14
6	3752	14
done	5000	14
0	18	41
1	48	33
2	168	19
3	733	17
4	4444	17
done	5000	17
0	16	41
1	44	33
2	135	17
3	462	17
4	2273	15
done	5000	15
0	14	29
1	30	29
2	65	29
3	133	29
4	264	29
5	686	29
6	2319	29
done	5000	29
0	13	14
1	29	14
2	64	14
3	132	14
4	265	14
5	679	14
6	2311	14
done	5000	14
0	14	41
1	40	41
2	139	15
3	556	15
4	2773	15
done	5001	15
0	13	14
1	29	14
2	64	14
3	132	14
4	265	14
5	679	14
6	2311	14
done	5000	14
0	13	14
1	29	14
2	64	14
3	132	14
4	265	14
5	679	14
6	2311	14
done	5000	14
0	14	15
1	28	15
2	58	15
3	113	15
4	187	15
5	378	15
6	1061	15
7	3850	15
done	5000	15
0	14	15
1	28	15
2	58	15
3	113	15
4	187	15
5	378	15
6	1061	15
7	3850	15
done	5000	15
0	15	16
1	31	16
2	66	16
3	136	16
4	270	16
5	683	16
6	2321	16
done	5000	16
0	15	16
1	31	16
2	66	16
3	136	16
4	270	16
5	683	16
6	2321	16
done	5000	16
0	14	15
1	28	15
2	55	15
3	100	15
4	153	15
5	260	15
6	650	15
7	2057	15
done	5000	15
0	14	15
1	28	15
2	55	15
3	100	15
4	153	15
5	260	15
6	650	15
7	2057	15
done	5000	15
0	15	16
1	31	16
2	61	16
3	110	16
4	164	16
5	270	16
6	654	16
7	2062	16
done	5000	16
0	15	16
1	31	16
2	61	16
3	110	16
4	164	16
5	270	16
6	654	16
7	2062	16
done	5000	16
0	15	16
1	28	16
2	61	16
3	117	16
4	202	16
5	415	16
6	1239	16
7	4467	16
done	5000	16
0	15	16
1	28	16
2	61	16
3	117	16
4	202	16
5	415	16
6	1239	16
7	4467	16
done	5000	16
0	16	17
1	31	17
2	69	17
3	140	17
4	283	17
5	728	17
6	2481	17
done	5000	17
0	16	17
1	31	17
2	69	17
3	140	17
4	283	17
5	728	17
6	2481	17
done	5000	17
0	14	19
1	30	19
2	67	19
3	133	19
4	250	19
5	585	19
6	1852	19
done	5000	19
0	13	14
1	27	14
2	57	14
3	110	14
4	188	14
5	375	14
6	1080	14
7	3874	14
done	5000	14
0	16	21
1	38	21
2	105	21
3	254	21
4	700	21
5	2544	21
done	5000	21
0	15	18
1	33	18
2	77	18
3	174	18
4	404	18
5	1192	18
6	4354	18
done	5000	18
0	14	17
1	34	15
2	85	15
3	202	15
4	482	15
5	1664	15
done	5000	15
0	15	18
1	33	18
2	76	18
3	169	18
4	389	18
5	1236	18
6	4979	18
done	5000	18
0	14	15
1	30	15
2	65	15
3	133	15
4	266	15
5	686	15
6	2323	15
done	5000	15
0	13	14
1	31	12
2	68	12
3	138	12
4	284	12
5	833	12
6	3168	12
done	5000	12
0	14	17
1	34	17
2	76	15
3	195	15
4	428	15
5	1055	15
6	3363	15
done	5000	15
0	13	14
1	31	14
2	66	12
3	155	12
4	284	12
5	632	12
6	1745	12
done	5000	12
0	11	13
1	29	11
2	64	9
3	134	9
4	239	9
5	510	9
6	1457	9
done	5000	9
0	10	11
1	26	9
2	59	9
3	117	9
4	190	9
5	337	9
6	798	9
7	2421	9
done	5000	9
0	10	11
1	24	11
2	54	11
3	109	11
4	188	11
5	379	11
6	1081	11
7	3860	11
done	5000	11
0	13	14
1	29	14
2	64	14
3	132	14
4	265	14
5	685	14
6	2313	14
done	5000	14
0	13	14
1	29	14
2	64	14
3	132	14
4	265	14
5	685	14
6	2313	14
done	5000	14
0	9	9
1	16	9
2	30	9
3	73	9
4	193	9
5	604	9
6	2228	9
done	5000	9
0	12	13
1	28	13
2	63	13
3	131	13
4	264	13
5	677	13
6	2317	13
done	5000	13
0	10	11
1	22	11
2	38	11
3	81	11
4	205	11
5	623	11
6	2238	11
done	5000	11
0	13	14
1	29	14
2	58	14
3	107	14
4	161	14
5	269	14
6	653	14
7	2063	14
done	5000	14
0	13	14
1	29	14
2	59	14
3	108	14
4	162	14
5	270	14
6	655	14
7	2074	14
done	5000	14
0	12	13
1	28	13
2	63	13
3	131	13
4	264	13
5	677	13
6	2317	13
done	5000	13
0	14	15
1	29	15
2	67	15
3	138	15
4	280	15
5	724	15
6	2493	15
done	5001	15
0	10	11
1	24	11
2	54	11
3	109	11
4	188	11
5	379	11
6	1081	11
7	3860	11
done	5000	11
0	11	11
1	19	11
2	41	11
3	78	11
4	135	11
5	227	11
6	373	11
7	475	11
8	492	11
done	492	11
0	10	10
1	19	10
2	34	10
3	62	10
4	114	10
5	188	10
6	331	10
7	474	10
8	518	10
done	518	10
0	10	10
1	19	10
2	35	10
3	71	10
4	129	10
5	202	10
6	318	10
7	452	10
8	479	10
9	480	10
done	480	10
0	9	9
1	19	9
2	31	9
3	57	9
4	105	9
5	166	9
6	272	9
7	441	9
8	489	9
9	491	9
done	491	9
0	8	8
1	20	8
2	58	8
3	125	8
4	219	8
5	322	8
6	470	8
7	629	8
8	674	8
9	675	8
done	675	8
0	8	8
1	17	8
2	40	8
3	79	8
4	113	8
5	169	8
6	318	8
7	715	8
8	2398	8
done	5001	8
0	15	23
1	36	23
2	229	15
3	1885	15
done	5000	15
0	13	23
1	38	23
2	251	13
3	2325	13
done	5001	13
0	13	23
1	38	23
2	232	13
3	2103	13
done	5000	13
0	11	23
1	40	23
2	258	11
3	2627	9
done	5001	9
0	9	17
1	18	17
2	39	17
3	66	17
4	77	17
done	77	17
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	9	23
1	25	23
2	128	9
3	1015	9
done	5000	9
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	4	4
1	9	4
2	11	4
done	11	4
0	4	4
1	9	4
2	11	4
done	11	4
0	3	3
done	3	3
0	3	3
done	3	3
0	5	5
1	10	5
2	12	5
done	12	5
0	7	7
1	16	7
2	37	7
3	64	7
4	75	7
done	75	7
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	16	17
1	34	17
2	78	17
3	170	17
4	399	17
5	1226	17
6	4789	17
done	5000	17
0	16	17
1	34	17
2	78	17
3	170	17
4	399	17
5	1226	17
6	4789	17
done	5000	17
0	17	35
1	35	35
2	79	35
3	171	35
4	402	35
5	1235	35
6	4807	35
done	5000	35
0	16	17
1	34	17
2	78	17
3	170	17
4	399	17
5	1226	17
6	4789	17
done	5000	17
0	17	50
1	36	32
2	89	18
3	210	18
4	569	18
5	2153	18
done	5001	18
0	17	34
1	36	17
2	80	17
3	172	17
4	403	17
5	1225	17
6	4792	17
done	5000	17
0	16	17
1	34	17
2	78	17
3	170	17
4	399	17
5	1226	17
6	4789	17
done	5000	17
0	16	17
1	34	17
2	78	17
3	170	17
4	399	17
5	1226	17
6	4789	17
done	5000	17
0	16	17
1	34	17
2	78	17
3	170	17
4	399	17
5	1226	17
6	4789	17
done	5000	17
0	2	2
1	4	1
done	4	1
0	15	16
1	33	16
2	77	16
3	169	16
4	400	16
5	1233	16
6	4796	16
done	5000	16
0	18	20
1	51	20
2	156	20
3	659	20
4	3890	20
done	5001	20
0	19	48
1	51	34
2	155	34
3	428	34
4	1479	34
done	5001	34
0	17	32
1	45	32
2	136	24
3	462	24
4	1968	24
done	5000	24
0	15	16
1	32	16
2	67	16
3	135	16
4	268	16
5	686	16
6	2320	16
done	5001	16
0	3	3
1	6	1
done	6	1
0	16	17
1	34	17
2	78	17
3	170	17
4	399	17
5	1226	17
6	4789	17
done	5000	17
0	16	17
1	34	17
2	78	17
3	170	17
4	399	17
5	1226	17
6	4789	17
done	5000	17
0	17	18
1	36	18
2	80	18
3	172	18
4	405	18
5	1244	18
6	4808	18
done	5000	18
0	19	20
1	38	20
2	82	20
3	176	20
4	405	20
5	1237	20
6	4796	20
done	5000	20
0	18	19
1	40	19
2	85	19
3	177	19
4	412	19
5	1266	19
6	4843	19
done	5000	19
0	18	19
1	39	19
2	88	19
3	188	19
4	440	19
5	1341	19
done	5001	19
0	21	56
1	46	38
2	128	22
3	373	22
4	1331	20
done	5000	20
0	19	39
1	38	39
2	82	39
3	174	39
4	405	39
5	1237	39
6	4800	39
done	5000	39
0	18	19
1	37	19
2	81	19
3	173	19
4	406	19
5	1242	19
6	4804	19
done	5000	19
0	19	56
1	48	56
2	121	20
3	280	20
4	772	20
5	3806	20
done	5000	20
0	18	19
1	37	19
2	81	19
3	173	19
4	406	19
5	1242	19
6	4804	19
done	5000	19
0	18	19
1	37	19
2	81	19
3	173	19
4	406	19
5	1242	19
6	4804	19
done	5000	19
0	19	20
1	38	20
2	82	20
3	176	20
4	405	20
5	1237	20
6	4796	20
done	5000	20
0	19	20
1	38	20
2	82	20
3	176	20
4	405	20
5	1237	20
6	4796	20
done	5000	20
0	19	20
1	38	20
2	82	20
3	176	20
4	405	20
5	1237	20
6	4796	20
done	5000	20
0	19	20
1	38	20
2	82	20
3	176	20
4	405	20
5	1237	20
6	4796	20
done	5000	20
0	19	37
1	40	37
2	86	37
3	178	37
4	411	37
5	1245	37
6	4839	37
done	5000	37
0	19	36
1	39	19
2	83	19
3	175	19
4	407	19
5	1249	19
6	4832	19
done	5000	19
0	18	19
1	37	19
2	81	19
3	173	19
4	406	19
5	1242	19
6	4804	19
done	5000	19
0	4	4
1	7	3
done	7	3
0	18	19
1	37	19
2	81	19
3	173	19
4	406	19
5	1242	19
6	4804	19
done	5000	19
0	3	3
1	6	1
done	6	1
0	18	19
1	37	19
2	81	19
3	175	19
4	406	19
5	1249	19
6	4817	19
done	5000	19
0	18	19
1	37	19
2	81	19
3	175	19
4	406	19
5	1249	19
6	4817	19
done	5000	19
0	17	18
1	36	18
2	80	18
3	172	18
4	405	18
5	1244	18
6	4808	18
done	5000	18
0	20	22
1	54	22
2	159	22
3	655	22
4	3868	22
done	5001	22
0	19	34
1	48	34
2	139	26
3	460	26
4	1973	26
done	5000	26
0	32	42
1	80	39
2	184	33
3	709	27
done	5001	27
0	34	46
1	89	40
2	197	34
3	539	31
4	2017	27
done	5001	27
0	35	46
1	88	43
2	190	37
3	577	31
4	2103	31
done	5001	31
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	2	2
done	2	2
0	2	2
done	2	2
0	2	2
done	2	2
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4

prune350.0ms

Filtered

102 candidates to 125 candidates (-22.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	9	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 9.1b

Counts

126 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.3b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
5.9b	(/ (* M D) (* 2.0 d))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
26×	`prod-exp`
23×	`add-cbrt-cube`
20×	`div-exp`
18×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt` `pow-exp`
9×	`associate-l`
6×	`cbrt-undiv` `unpow-prod-down` `cbrt-unprod`
5×	`pow1` `times-frac` `sqrt-prod`
4×	`associate-/r*` `add-log-exp`
3×	`associate-r` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

5.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
8.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
8.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
7.0ms	(/ (* M D) (* 2.0 d))

series676.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
245.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
251.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
7.0ms	(/ (* M D) (* 2.0 d))

simplify5.2min

Counts

108 → 108

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	11	11
1	19	11
2	41	11
3	78	11
4	135	11
5	227	11
6	373	11
7	475	11
8	492	11
done	492	11
0	10	10
1	19	10
2	34	10
3	62	10
4	114	10
5	188	10
6	331	10
7	474	10
8	518	10
done	518	10
0	10	10
1	19	10
2	35	10
3	71	10
4	129	10
5	202	10
6	318	10
7	452	10
8	479	10
9	480	10
done	480	10
0	9	9
1	19	9
2	31	9
3	57	9
4	105	9
5	166	9
6	272	9
7	441	9
8	489	9
9	491	9
done	491	9
0	8	8
1	20	8
2	58	8
3	125	8
4	219	8
5	322	8
6	470	8
7	629	8
8	674	8
9	675	8
done	675	8
0	8	8
1	17	8
2	40	8
3	79	8
4	113	8
5	169	8
6	318	8
7	715	8
8	2398	8
done	5001	8
0	15	23
1	36	23
2	229	15
3	1885	15
done	5000	15
0	13	23
1	38	23
2	251	13
3	2325	13
done	5001	13
0	13	23
1	38	23
2	232	13
3	2103	13
done	5000	13
0	11	23
1	40	23
2	258	11
3	2627	9
done	5001	9
0	9	17
1	18	17
2	39	17
3	66	17
4	77	17
done	77	17
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	9	23
1	25	23
2	128	9
3	1015	9
done	5000	9
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	4	4
1	9	4
2	11	4
done	11	4
0	4	4
1	9	4
2	11	4
done	11	4
0	3	3
done	3	3
0	3	3
done	3	3
0	5	5
1	10	5
2	12	5
done	12	5
0	7	7
1	16	7
2	37	7
3	64	7
4	75	7
done	75	7
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	18	19
1	32	19
2	73	19
3	170	19
4	435	19
5	1128	19
6	2816	19
done	5000	19
0	17	18
1	32	18
2	66	18
3	148	18
4	364	18
5	919	18
6	2623	18
done	5000	18
0	17	18
1	32	18
2	61	18
3	144	18
4	377	18
5	1001	18
6	2528	18
done	5000	18
0	16	17
1	32	17
2	57	17
3	124	17
4	307	17
5	833	17
6	2355	17
done	5000	17
0	15	16
1	33	16
2	78	16
3	163	16
4	346	16
5	807	16
6	1945	16
7	4486	16
done	5000	16
0	15	16
1	33	16
2	78	16
3	163	16
4	346	16
5	807	16
6	1945	16
7	4486	16
done	5000	16
0	15	16
1	35	16
2	83	16
3	190	16
4	515	16
5	2288	16
done	5000	16
0	14	15
1	33	15
2	73	15
3	177	15
4	450	15
5	1776	15
done	5001	15
0	13	14
1	32	14
2	76	14
3	169	14
4	410	14
5	1329	14
done	5000	14
0	13	14
1	29	14
2	65	14
3	136	14
4	284	14
5	733	14
6	2515	14
done	5000	14
0	18	41
1	48	33
2	186	19
3	935	19
done	5000	19
0	16	41
1	48	41
2	192	17
3	1074	15
done	5000	15
0	14	29
1	30	29
2	66	29
3	135	29
4	274	29
5	697	29
6	2312	29
done	5000	29
0	13	14
1	29	14
2	65	14
3	134	14
4	273	14
5	701	14
6	2321	14
done	5000	14
0	14	41
1	37	41
2	110	15
3	429	15
4	2620	15
done	5001	15
0	13	14
1	29	14
2	65	14
3	134	14
4	273	14
5	701	14
6	2321	14
done	5000	14
0	13	14
1	29	14
2	65	14
3	134	14
4	273	14
5	701	14
6	2321	14
done	5000	14
0	11	12
1	29	12
2	66	12
3	139	12
4	291	12
5	741	12
6	2442	12
done	5000	12
0	2	2
done	2	2
0	12	15
1	27	15
2	59	15
3	122	15
4	240	15
5	619	15
6	2236	15
done	5001	15
0	4	4
done	4	4
0	11	12
1	24	12
2	52	12
3	103	12
4	175	12
5	362	12
6	1049	12
7	3893	12
done	5000	12
0	4	4
done	4	4
0	10	11
1	25	9
2	55	9
3	108	9
4	193	9
5	418	9
6	1348	9
done	5000	9
0	3	3
done	3	3
0	3	3
1	5	3
done	5	3
0	12	13
1	28	13
2	62	13
3	124	13
4	232	13
5	524	13
6	1557	13
done	5000	13
0	14	17
1	35	17
2	83	17
3	185	17
4	462	17
5	1490	17
done	5000	17
0	13	14
1	29	14
2	65	14
3	134	14
4	273	14
5	700	14
6	2319	14
done	5001	14
0	12	13
1	30	11
2	70	11
3	149	11
4	326	11
5	951	11
6	3752	11
done	5000	11
0	3	3
done	3	3
0	15	16
1	25	16
2	59	16
3	134	16
4	289	16
5	558	16
6	999	16
7	1524	16
8	2171	16
9	2431	16
10	2461	16
done	2461	16
0	14	15
1	25	15
2	52	15
3	112	15
4	236	15
5	470	15
6	920	15
7	1443	15
8	2117	15
9	2576	15
10	2610	15
done	2610	15
0	14	15
1	25	15
2	47	15
3	116	15
4	264	15
5	496	15
6	890	15
7	1418	15
8	2030	15
9	2378	15
10	2428	15
done	2428	15
0	13	14
1	25	14
2	43	14
3	96	14
4	213	14
5	426	14
6	804	14
7	1341	14
8	1986	14
9	2503	14
10	2562	14
done	2562	14
0	12	13
1	26	13
2	64	13
3	143	13
4	296	13
5	523	13
6	910	13
7	1409	13
8	1954	13
9	2721	13
10	2954	13
11	2966	13
done	2966	13
0	12	13
1	26	13
2	64	13
3	143	13
4	296	13
5	523	13
6	910	13
7	1409	13
8	1954	13
9	2721	13
10	2954	13
11	2966	13
done	2966	13
0	12	13
1	28	13
2	69	13
3	162	13
4	439	13
5	1608	13
done	5000	13
0	11	12
1	28	12
2	63	12
3	154	12
4	391	12
5	1375	12
done	5001	12
0	11	12
1	27	12
2	64	12
3	135	12
4	270	12
5	666	12
6	2279	12
done	5000	12
0	14	35
1	36	27
2	103	15
3	293	15
4	1001	13
5	4242	13
done	5001	13
0	12	25
1	26	25
2	56	25
3	111	25
4	190	25
5	380	25
6	1068	25
7	3866	25
done	5000	25
0	11	12
1	25	12
2	55	12
3	108	12
4	189	12
5	387	12
6	1080	12
7	3877	12
done	5000	12
0	12	35
1	36	35
2	108	13
3	332	13
4	1071	13
5	4135	13
done	5000	13
0	11	12
1	25	12
2	55	12
3	108	12
4	189	12
5	387	12
6	1080	12
7	3877	12
done	5000	12
0	11	12
1	25	12
2	55	12
3	108	12
4	189	12
5	387	12
6	1080	12
7	3877	12
done	5000	12
0	12	13
1	26	13
2	56	13
3	109	13
4	185	13
5	374	13
6	1066	13
7	3865	13
done	5000	13
0	12	13
1	26	13
2	56	13
3	109	13
4	185	13
5	374	13
6	1066	13
7	3865	13
done	5000	13
0	12	13
1	26	13
2	53	13
3	98	13
4	149	13
5	256	13
6	644	13
7	2070	13
done	5001	13
0	12	13
1	26	13
2	53	13
3	98	13
4	149	13
5	256	13
6	644	13
7	2070	13
done	5001	13
0	13	14
1	26	14
2	59	14
3	115	14
4	199	14
5	412	14
6	1233	14
7	4434	14
done	5000	14
0	13	14
1	26	14
2	59	14
3	115	14
4	199	14
5	412	14
6	1233	14
7	4434	14
done	5000	14
0	12	15
1	28	15
2	65	15
3	131	15
4	250	15
5	580	15
6	1830	15
done	5000	15
0	11	12
1	25	12
2	55	12
3	108	12
4	186	12
5	377	12
6	1077	12
7	3881	12
done	5000	12
0	10	11
1	26	9
2	59	9
3	117	9
4	190	9
5	337	9
6	798	9
7	2421	9
done	5000	9
0	11	12
1	25	12
2	55	12
3	108	12
4	184	12
5	375	12
6	1082	12
7	3875	12
done	5001	12
0	11	12
1	25	12
2	55	12
3	108	12
4	184	12
5	375	12
6	1082	12
7	3875	12
done	5001	12
0	7	7
1	12	7
2	21	7
3	47	7
4	112	7
5	302	7
6	988	7
7	3758	7
done	5000	7
0	10	11
1	24	11
2	54	11
3	109	11
4	188	11
5	379	11
6	1081	11
7	3860	11
done	5000	11
0	8	9
1	18	9
2	29	9
3	55	9
4	121	9
5	312	9
6	1003	9
7	3800	9
done	5000	9
0	11	12
1	25	12
2	51	12
3	96	12
4	147	12
5	254	12
6	630	12
7	2065	12
done	5001	12
0	11	12
1	25	12
2	52	12
3	97	12
4	148	12
5	250	12
6	636	12
7	2061	12
done	5000	12
0	10	11
1	24	11
2	54	11
3	109	11
4	188	11
5	379	11
6	1081	11
7	3860	11
done	5000	11
0	12	13
1	25	13
2	58	13
3	114	13
4	198	13
5	414	13
6	1233	13
7	4437	13
done	5000	13
0	16	17
1	34	17
2	75	17
3	162	17
4	380	17
5	1197	17
6	4736	17
done	5000	17
0	16	17
1	34	17
2	75	17
3	162	17
4	380	17
5	1197	17
6	4736	17
done	5000	17
0	17	35
1	35	35
2	76	35
3	163	35
4	379	35
5	1205	35
6	4742	35
done	5000	35
0	16	17
1	34	17
2	75	17
3	162	17
4	380	17
5	1197	17
6	4736	17
done	5000	17
0	17	50
1	36	32
2	86	18
3	190	18
4	505	18
5	1971	18
done	5001	18
0	17	34
1	36	17
2	77	17
3	164	17
4	382	17
5	1211	17
6	4718	17
done	5000	17
0	16	17
1	34	17
2	75	17
3	162	17
4	380	17
5	1197	17
6	4736	17
done	5000	17
0	16	17
1	34	17
2	75	17
3	162	17
4	380	17
5	1197	17
6	4736	17
done	5000	17
0	16	17
1	34	17
2	75	17
3	162	17
4	380	17
5	1197	17
6	4736	17
done	5000	17
0	2	2
1	4	1
done	4	1
0	15	16
1	33	16
2	74	16
3	161	16
4	379	16
5	1200	16
6	4751	16
done	5000	16
0	17	18
1	34	18
2	70	18
3	137	18
4	273	18
5	696	18
6	2326	18
done	5000	18
0	17	18
1	35	18
2	72	18
3	139	18
4	273	18
5	692	18
6	2307	18
done	5000	18
0	2	2
1	4	1
done	4	1
0	15	16
1	33	16
2	74	16
3	161	16
4	379	16
5	1200	16
6	4751	16
done	5000	16
0	18	20
1	51	20
2	143	20
3	535	20
4	3530	20
done	5000	20
0	19	48
1	48	34
2	125	34
3	377	34
4	1540	34
done	5000	34
0	17	32
1	42	32
2	107	32
3	361	32
4	1768	24
done	5001	24
0	15	16
1	32	16
2	68	16
3	135	16
4	271	16
5	690	16
6	2306	16
done	5000	16
0	3	3
1	6	1
done	6	1
0	16	17
1	34	17
2	75	17
3	162	17
4	380	17
5	1197	17
6	4736	17
done	5000	17
0	16	17
1	34	17
2	75	17
3	162	17
4	380	17
5	1197	17
6	4736	17
done	5000	17
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	32	42
1	80	39
2	184	33
3	709	27
done	5001	27
0	34	46
1	89	40
2	197	34
3	539	31
4	2017	27
done	5001	27
0	35	46
1	88	43
2	190	37
3	577	31
4	2103	31
done	5001	31
0	28	36
1	70	33
2	145	26
3	477	21
4	2369	21
done	5001	21
0	33	46
1	91	40
2	228	34
3	910	31
done	5000	31
0	34	46
1	90	43
2	221	37
3	939	31
done	5001	31
0	2	2
done	2	2
0	2	2
done	2	2
0	2	2
done	2	2

prune280.0ms

Filtered

91 candidates to 108 candidates (-18.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 8.8b

Counts

117 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
5.2b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)
5.3b	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
6.1b	(/ (* 2.0 d) (* M D))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-exp-log`
67×	`div-exp`
64×	`prod-exp`
32×	`pow-exp`
31×	`add-sqr-sqrt`
24×	`times-frac` `associate-l`
23×	`unpow-prod-down` `add-cbrt-cube`
21×	`*-un-lft-identity`
18×	`add-cube-cbrt`
10×	`rec-exp` `1-exp`
6×	`cbrt-undiv` `cbrt-unprod` `div-inv`
5×	`pow1` `sqrt-prod` `unswap-sqr`
4×	`associate-/r*` `add-log-exp`
3×	`associate-r`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/l*` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `*-commutative` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 135

Calls

4 calls:

5.0ms	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
14.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)
15.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
7.0ms	(/ (* 2.0 d) (* M D))

series648.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(sqrt (- 1.0 (/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)))
242.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h)
254.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) 2.0) h) l)
11.0ms	(/ (* 2.0 d) (* M D))

simplify8.5min

Counts

147 → 147

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	11	11
1	19	11
2	41	11
3	78	11
4	135	11
5	227	11
6	373	11
7	475	11
8	492	11
done	492	11
0	10	10
1	19	10
2	34	10
3	62	10
4	114	10
5	188	10
6	331	10
7	474	10
8	518	10
done	518	10
0	10	10
1	19	10
2	35	10
3	71	10
4	129	10
5	202	10
6	318	10
7	452	10
8	479	10
9	480	10
done	480	10
0	9	9
1	19	9
2	31	9
3	57	9
4	105	9
5	166	9
6	272	9
7	441	9
8	489	9
9	491	9
done	491	9
0	8	8
1	20	8
2	58	8
3	125	8
4	219	8
5	322	8
6	470	8
7	629	8
8	674	8
9	675	8
done	675	8
0	8	8
1	17	8
2	40	8
3	79	8
4	113	8
5	169	8
6	318	8
7	715	8
8	2398	8
done	5001	8
0	15	23
1	36	23
2	229	15
3	1885	15
done	5000	15
0	13	23
1	38	23
2	251	13
3	2325	13
done	5001	13
0	13	23
1	38	23
2	232	13
3	2103	13
done	5000	13
0	11	23
1	40	23
2	258	11
3	2627	9
done	5001	9
0	9	17
1	18	17
2	39	17
3	66	17
4	77	17
done	77	17
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	9	23
1	25	23
2	128	9
3	1015	9
done	5000	9
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	4	4
1	9	4
2	11	4
done	11	4
0	4	4
1	9	4
2	11	4
done	11	4
0	3	3
done	3	3
0	3	3
done	3	3
0	5	5
1	10	5
2	12	5
done	12	5
0	7	7
1	16	7
2	37	7
3	64	7
4	75	7
done	75	7
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	19	20
1	35	20
2	74	19
3	180	19
4	557	19
5	1651	19
6	4194	19
done	5000	19
0	18	19
1	35	19
2	67	18
3	155	18
4	461	18
5	1389	18
6	3656	18
done	5000	18
0	18	19
1	35	19
2	65	18
3	154	18
4	478	18
5	1476	18
6	3762	18
done	5000	18
0	17	18
1	35	18
2	61	17
3	131	17
4	391	17
5	1235	17
6	3275	17
done	5000	17
0	16	17
1	36	17
2	85	16
3	183	16
4	446	16
5	1344	16
6	3505	16
done	5000	16
0	20	21
1	38	20
2	107	20
3	321	19
4	1056	19
5	3523	19
done	5001	19
0	19	20
1	38	19
2	96	19
3	280	18
4	898	18
5	3217	18
done	5001	18
0	19	20
1	38	19
2	95	19
3	274	18
4	944	18
5	3070	18
done	5001	18
0	18	19
1	38	18
2	87	18
3	237	17
4	806	17
5	2859	17
done	5000	17
0	17	18
1	37	17
2	96	17
3	233	16
4	714	16
5	2717	16
done	5000	16
0	21	22
1	41	21
2	103	20
3	294	19
4	928	19
5	2639	19
done	5000	19
0	20	21
1	41	20
2	92	19
3	258	18
4	801	18
5	2550	18
done	5000	18
0	20	21
1	41	20
2	91	19
3	254	18
4	837	18
5	2306	18
done	5001	18
0	19	20
1	41	19
2	83	18
3	223	17
4	722	17
5	2252	17
done	5000	17
0	18	19
1	40	18
2	94	17
3	219	17
4	627	16
5	2026	16
done	5001	16
0	17	18
1	40	17
2	103	17
3	278	16
4	806	16
5	2366	16
done	5000	16
0	17	18
1	40	17
2	103	17
3	278	16
4	806	16
5	2366	16
done	5000	16
0	17	18
1	41	18
2	100	17
3	275	16
4	828	16
5	3168	16
done	5000	16
0	16	17
1	39	17
2	95	17
3	247	15
4	715	15
5	2528	15
done	5000	15
0	15	16
1	38	16
2	98	16
3	244	14
4	642	14
5	1847	14
done	5000	14
0	15	16
1	35	16
2	87	16
3	209	14
4	507	14
5	1109	14
6	2845	14
done	5000	14
0	20	47
1	54	37
2	208	21
3	1006	19
done	5001	19
0	18	47
1	54	47
2	214	19
3	1154	15
done	5001	15
0	16	33
1	36	33
2	88	33
3	208	29
4	493	29
5	1063	29
6	2625	29
done	5001	29
0	15	16
1	35	16
2	87	16
3	207	14
4	496	14
5	1076	14
6	2646	14
done	5000	14
0	16	47
1	43	47
2	132	17
3	504	15
4	2846	15
done	5000	15
0	15	16
1	35	16
2	87	16
3	207	14
4	496	14
5	1076	14
6	2646	14
done	5000	14
0	15	16
1	35	16
2	87	16
3	207	14
4	496	14
5	1076	14
6	2646	14
done	5000	14
0	13	14
1	35	14
2	88	14
3	216	12
4	518	12
5	1109	12
6	2749	12
done	5000	12
0	2	2
done	2	2
0	14	17
1	33	17
2	81	17
3	199	15
4	472	15
5	1004	15
6	2576	15
done	5001	15
0	4	4
done	4	4
0	13	14
1	30	14
2	74	14
3	180	12
4	400	12
5	752	12
6	1386	12
7	4126	12
done	5000	12
0	4	4
done	4	4
0	11	13
1	28	11
2	74	11
3	182	9
4	412	9
5	783	9
6	1673	9
done	5001	9
0	3	3
done	3	3
0	3	3
1	5	3
done	5	3
0	14	15
1	34	15
2	84	15
3	201	13
4	458	13
5	902	13
6	1893	13
done	5000	13
0	16	19
1	41	19
2	105	19
3	260	17
4	688	17
5	1890	17
done	5000	17
0	15	16
1	35	16
2	87	16
3	207	14
4	496	14
5	1069	14
6	2630	14
done	5000	14
0	13	15
1	33	13
2	89	13
3	223	11
4	551	11
5	1351	11
6	4156	11
done	5000	11
0	3	3
done	3	3
0	16	17
1	28	17
2	60	16
3	154	16
4	459	16
5	987	16
6	1787	16
7	2425	16
8	3099	16
9	3615	16
10	3635	16
done	3635	16
0	15	16
1	28	16
2	53	15
3	129	15
4	369	15
5	837	15
6	1635	15
7	2245	15
8	2945	15
9	3507	15
10	3528	15
done	3528	15
0	15	16
1	28	16
2	51	15
3	128	15
4	407	15
5	880	15
6	1599	15
7	2304	15
8	3105	15
9	3744	15
10	3788	15
done	3788	15
0	14	15
1	28	15
2	47	14
3	105	14
4	326	14
5	755	14
6	1487	14
7	2318	14
8	3094	14
9	3783	14
10	3845	14
11	3849	14
done	3849	14
0	13	14
1	29	14
2	71	13
3	157	13
4	397	13
5	876	13
6	1658	13
7	2337	13
8	2964	13
9	3538	13
10	3601	13
done	3601	13
0	17	18
1	31	17
2	93	17
3	286	16
4	870	16
5	2228	16
6	4147	16
done	5001	16
0	16	17
1	31	16
2	82	16
3	245	15
4	724	15
5	2067	15
6	4026	15
done	5000	15
0	16	17
1	31	16
2	81	16
3	240	15
4	778	15
5	1942	15
6	3690	15
done	5001	15
0	15	16
1	31	15
2	73	15
3	202	14
4	654	14
5	1835	14
6	3518	14
7	4990	14
done	5000	14
0	14	15
1	30	14
2	82	14
3	206	13
4	622	13
5	1836	13
6	3831	13
done	5000	13
0	18	19
1	34	18
2	89	17
3	261	16
4	771	16
5	1906	16
6	3340	16
7	4554	16
done	5000	16
0	17	18
1	34	17
2	78	16
3	226	15
4	655	15
5	1807	15
6	3282	15
7	4478	15
done	5000	15
0	17	18
1	34	17
2	77	16
3	222	15
4	695	15
5	1627	15
6	3047	15
7	4252	15
done	5000	15
0	16	17
1	34	16
2	69	15
3	191	14
4	591	14
5	1580	14
6	2992	14
7	4359	14
done	5000	14
0	15	16
1	33	15
2	80	14
3	195	14
4	551	13
5	1607	13
6	3112	13
7	4368	13
done	5000	13
0	14	15
1	33	14
2	89	14
3	255	13
4	755	13
5	1783	13
6	3439	13
done	5000	13
0	14	15
1	33	14
2	89	14
3	255	13
4	755	13
5	1783	13
6	3439	13
done	5000	13
0	14	15
1	34	15
2	86	14
3	247	13
4	743	13
5	2517	13
done	5000	13
0	13	14
1	34	14
2	85	14
3	228	12
4	663	12
5	2115	12
done	5000	12
0	13	14
1	33	14
2	86	14
3	210	12
4	489	12
5	1027	12
6	2596	12
done	5000	12
0	16	41
1	42	31
2	125	17
3	361	15
4	1233	13
5	4640	13
done	5000	13
0	14	29
1	32	29
2	78	29
3	186	25
4	411	25
5	767	25
6	1410	25
7	4098	25
done	5000	25
0	13	14
1	31	14
2	77	14
3	185	12
4	415	12
5	769	12
6	1425	12
7	4115	12
done	5000	12
0	14	41
1	42	41
2	130	15
3	404	13
4	1287	13
5	4707	13
done	5000	13
0	13	14
1	31	14
2	77	14
3	185	12
4	415	12
5	769	12
6	1425	12
7	4115	12
done	5000	12
0	13	14
1	31	14
2	77	14
3	185	12
4	415	12
5	769	12
6	1425	12
7	4115	12
done	5000	12
0	14	15
1	32	15
2	78	15
3	186	13
4	409	13
5	745	13
6	1401	13
7	4074	13
done	5000	13
0	14	15
1	32	15
2	78	15
3	186	13
4	409	13
5	745	13
6	1401	13
7	4074	13
done	5000	13
0	15	16
1	31	15
2	61	15
3	114	15
4	187	15
5	375	15
6	1070	15
7	3862	15
done	5000	15
0	15	16
1	31	15
2	61	15
3	114	15
4	187	15
5	375	15
6	1070	15
7	3862	15
done	5000	15
0	14	15
1	30	15
2	60	15
3	113	15
4	186	15
5	375	15
6	1066	15
7	3875	15
done	5001	15
0	14	15
1	30	15
2	60	15
3	113	15
4	186	15
5	375	15
6	1066	15
7	3875	15
done	5001	15
0	14	15
1	32	15
2	75	15
3	175	13
4	377	13
5	658	13
6	989	13
7	2315	13
done	5000	13
0	14	15
1	32	15
2	75	15
3	175	13
4	377	13
5	658	13
6	989	13
7	2315	13
done	5000	13
0	15	16
1	32	16
2	81	16
3	194	14
4	427	14
5	809	14
6	1586	14
7	4869	14
done	5000	14
0	15	16
1	32	16
2	81	16
3	194	14
4	427	14
5	809	14
6	1586	14
7	4869	14
done	5000	14
0	14	17
1	34	17
2	87	17
3	208	15
4	482	15
5	966	15
6	2160	15
done	5000	15
0	13	14
1	31	14
2	77	14
3	185	12
4	413	12
5	771	12
6	1430	12
7	4109	12
done	5000	12
0	11	13
1	29	11
2	78	11
3	191	9
4	410	9
5	726	9
6	1133	9
7	2662	9
done	5001	9
0	13	14
1	31	14
2	77	14
3	185	12
4	411	12
5	770	12
6	1425	12
7	4118	12
done	5001	12
0	13	14
1	31	14
2	77	14
3	185	12
4	411	12
5	770	12
6	1425	12
7	4118	12
done	5001	12
0	14	15
1	30	14
2	60	14
3	113	14
4	186	14
5	373	14
6	1066	14
7	3855	14
done	5001	14
0	14	15
1	30	14
2	60	14
3	113	14
4	186	14
5	373	14
6	1066	14
7	3855	14
done	5001	14
0	10	10
1	19	9
2	31	9
3	60	7
4	125	7
5	318	7
6	1018	7
7	3797	7
done	5000	7
0	13	14
1	31	13
2	77	13
3	185	11
4	409	11
5	763	11
6	1427	11
7	4112	11
done	5000	11
0	11	12
1	23	11
2	43	9
3	83	7
4	179	7
5	396	7
6	1082	7
7	3832	7
done	5000	7
0	14	15
1	30	14
2	60	14
3	113	14
4	186	14
5	373	14
6	1066	14
7	3855	14
done	5001	14
0	14	15
1	30	14
2	60	14
3	113	14
4	186	14
5	373	14
6	1066	14
7	3855	14
done	5001	14
0	10	10
1	19	9
2	31	9
3	60	7
4	125	7
5	318	7
6	1018	7
7	3797	7
done	5000	7
0	13	14
1	31	13
2	77	13
3	185	11
4	409	11
5	763	11
6	1427	11
7	4112	11
done	5000	11
0	11	12
1	23	11
2	43	9
3	83	7
4	179	7
5	396	7
6	1082	7
7	3832	7
done	5000	7
0	13	14
1	29	14
2	59	14
3	112	14
4	187	14
5	372	14
6	1066	14
7	3885	14
done	5000	14
0	13	14
1	29	14
2	59	14
3	112	14
4	187	14
5	372	14
6	1066	14
7	3885	14
done	5000	14
0	9	9
1	18	9
2	30	9
3	59	7
4	124	7
5	318	7
6	1005	7
7	3805	7
done	5000	7
0	12	13
1	30	13
2	76	13
3	184	11
4	411	11
5	774	11
6	1427	11
7	4112	11
done	5000	11
0	10	11
1	22	7
2	44	7
3	94	7
4	177	7
5	378	7
6	1085	7
7	3855	7
done	5000	7
0	12	13
1	30	13
2	76	13
3	184	11
4	411	11
5	774	11
6	1427	11
7	4112	11
done	5000	11
0	12	13
1	30	13
2	76	13
3	184	11
4	411	11
5	774	11
6	1427	11
7	4112	11
done	5000	11
0	7	7
1	13	7
2	22	7
3	48	7
4	115	7
5	304	7
6	995	7
7	3761	7
done	5000	7
0	13	14
1	31	14
2	73	14
3	173	12
4	376	12
5	665	12
6	1005	12
7	2297	12
done	5000	12
0	13	14
1	31	14
2	74	14
3	174	12
4	379	12
5	669	12
6	1012	12
7	2324	12
done	5000	12
0	12	13
1	30	13
2	76	13
3	184	11
4	411	11
5	774	11
6	1427	11
7	4112	11
done	5000	11
0	14	15
1	31	15
2	80	15
3	193	13
4	425	13
5	804	13
6	1596	13
7	4869	13
done	5000	13
0	18	19
1	40	19
2	97	19
3	239	17
4	604	17
5	1605	17
done	5000	17
0	18	19
1	40	19
2	97	19
3	239	17
4	604	17
5	1605	17
done	5000	17
0	19	39
1	41	39
2	98	39
3	240	35
4	607	35
5	1613	35
done	5000	35
0	18	19
1	40	19
2	97	19
3	239	17
4	604	17
5	1605	17
done	5000	17
0	19	56
1	42	36
2	108	20
3	267	18
4	728	18
5	2349	18
done	5000	18
0	19	38
1	42	19
2	99	19
3	241	17
4	607	17
5	1590	17
done	5001	17
0	18	19
1	40	19
2	97	19
3	239	17
4	604	17
5	1605	17
done	5000	17
0	18	19
1	40	19
2	97	19
3	239	17
4	604	17
5	1605	17
done	5000	17
0	18	19
1	40	19
2	97	19
3	239	17
4	604	17
5	1605	17
done	5000	17
0	2	2
1	4	1
done	4	1
0	17	18
1	39	18
2	96	18
3	238	16
4	607	16
5	1603	16
done	5001	16
0	19	20
1	40	20
2	92	20
3	212	18
4	490	18
5	1081	18
6	2655	18
done	5001	18
0	19	20
1	41	20
2	94	20
3	216	18
4	492	18
5	1063	18
6	2626	18
done	5000	18
0	2	2
1	4	1
done	4	1
0	17	18
1	39	18
2	96	18
3	238	16
4	607	16
5	1603	16
done	5001	16
0	20	22
1	57	22
2	165	22
3	610	20
4	3744	20
done	5000	20
0	21	54
1	54	38
2	147	38
3	452	34
4	1763	34
done	5000	34
0	19	36
1	48	36
2	129	36
3	438	32
4	1995	24
done	5001	24
0	17	18
1	38	18
2	90	18
3	212	16
4	498	16
5	1067	16
6	2628	16
done	5001	16
0	3	3
1	6	1
done	6	1
0	18	19
1	40	19
2	97	19
3	239	17
4	604	17
5	1605	17
done	5000	17
0	18	19
1	40	19
2	97	19
3	239	17
4	604	17
5	1605	17
done	5000	17
0	7	7
1	13	7
2	30	7
3	55	7
4	77	7
5	78	7
done	78	7
0	7	7
1	13	7
2	30	7
3	55	7
4	77	7
5	78	7
done	78	7
0	7	7
1	13	7
2	30	7
3	55	7
4	77	7
5	78	7
done	78	7
0	32	42
1	80	39
2	184	33
3	709	27
done	5001	27
0	34	46
1	89	40
2	197	34
3	539	31
4	2017	27
done	5001	27
0	35	46
1	88	43
2	190	37
3	577	31
4	2103	31
done	5001	31
0	28	36
1	70	33
2	145	26
3	477	21
4	2369	21
done	5001	21
0	33	46
1	91	40
2	228	34
3	910	31
done	5000	31
0	34	46
1	90	43
2	221	37
3	939	31
done	5001	31
0	2	2
done	2	2
0	2	2
done	2	2
0	2	2
done	2	2

prune368.0ms

Filtered

127 candidates to 147 candidates (-15.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	147	8	155

Merged error: 8.8b

Counts

155 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

4.9b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.9b	(/ (* M D) (* 2.0 d))
5.9b	(/ (* M D) (* 2.0 d))
12.9b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
33×	`add-cbrt-cube`
30×	`prod-exp`
28×	`add-sqr-sqrt`
23×	`div-exp`
15×	`times-frac`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`pow-exp` `cbrt-unprod`
9×	`cbrt-undiv` `associate-l`
7×	`unpow-prod-down`
6×	`unswap-sqr`
5×	`pow1`
4×	`div-inv` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative` `flip--`

Counts

4 → 110

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
7.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(/ (* M D) (* 2.0 d))
12.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series436.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
7.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(/ (* M D) (* 2.0 d))
247.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify4.5min

Counts

122 → 122

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	20	21
1	36	21
2	80	21
3	229	21
4	693	21
5	1957	21
done	5002	21
0	19	20
1	34	20
2	77	20
3	218	20
4	638	20
5	1895	20
done	5000	20
0	19	20
1	36	20
2	73	20
3	198	20
4	560	20
5	1614	20
done	5000	20
0	18	19
1	34	19
2	70	19
3	187	19
4	516	19
5	1556	19
6	4869	19
done	5000	19
0	19	20
1	36	20
2	68	20
3	191	20
4	594	20
5	1678	20
6	4749	20
done	5000	20
0	18	19
1	34	19
2	65	19
3	184	19
4	549	19
5	1603	19
6	4495	19
done	5000	19
0	18	19
1	36	19
2	64	19
3	162	19
4	475	19
5	1397	19
6	4290	19
done	5001	19
0	17	18
1	34	18
2	61	18
3	155	18
4	442	18
5	1333	18
6	4068	18
done	5001	18
0	17	18
1	37	18
2	85	18
3	198	18
4	551	18
5	1592	18
6	4948	18
done	5000	18
0	16	17
1	35	17
2	82	17
3	195	17
4	531	17
5	1531	17
6	4724	17
done	5000	17
0	17	18
1	37	18
2	85	18
3	198	18
4	551	18
5	1592	18
6	4948	18
done	5000	18
0	16	17
1	35	17
2	82	17
3	195	17
4	531	17
5	1531	17
6	4724	17
done	5000	17
0	17	18
1	36	18
2	89	18
3	211	18
4	614	18
5	2945	18
done	5000	18
0	16	17
1	34	17
2	86	17
3	204	17
4	597	17
5	2883	17
done	5001	17
0	15	16
1	33	16
2	81	16
3	204	16
4	576	16
5	2462	16
done	5001	16
0	15	16
1	32	16
2	77	16
3	166	16
4	374	16
5	1053	16
6	3925	16
done	5000	16
0	20	47
1	49	37
2	174	21
3	748	19
4	4459	19
done	5000	19
0	18	47
1	45	37
2	141	19
3	466	19
4	2292	17
done	5000	17
0	16	33
1	31	33
2	69	33
3	140	33
4	283	33
5	728	33
6	2486	33
done	5000	33
0	15	16
1	30	16
2	68	16
3	139	16
4	280	16
5	724	16
6	2497	16
done	5000	16
0	16	47
1	41	47
2	143	17
3	569	17
4	2764	17
done	5001	17
0	15	16
1	30	16
2	68	16
3	139	16
4	280	16
5	724	16
6	2497	16
done	5000	16
0	15	16
1	30	16
2	68	16
3	139	16
4	280	16
5	724	16
6	2497	16
done	5000	16
0	16	17
1	29	17
2	62	17
3	118	17
4	201	17
5	414	17
6	1226	17
7	4431	17
done	5000	17
0	16	17
1	29	17
2	62	17
3	118	17
4	201	17
5	414	17
6	1226	17
7	4431	17
done	5000	17
0	17	18
1	32	18
2	70	18
3	143	18
4	282	18
5	718	18
6	2475	18
done	5000	18
0	17	18
1	32	18
2	70	18
3	143	18
4	282	18
5	718	18
6	2475	18
done	5000	18
0	16	17
1	29	17
2	59	17
3	107	17
4	168	17
5	302	17
6	813	17
7	2640	17
done	5001	17
0	16	17
1	29	17
2	59	17
3	107	17
4	168	17
5	302	17
6	813	17
7	2640	17
done	5001	17
0	17	18
1	32	18
2	65	18
3	117	18
4	179	18
5	309	18
6	812	18
7	2638	18
done	5000	18
0	17	18
1	32	18
2	65	18
3	117	18
4	179	18
5	309	18
6	812	18
7	2638	18
done	5000	18
0	16	18
1	32	16
2	66	16
3	129	16
4	220	16
5	460	16
6	1399	16
done	5000	16
0	16	18
1	32	16
2	66	16
3	129	16
4	220	16
5	460	16
6	1399	16
done	5000	16
0	17	19
1	35	17
2	74	17
3	152	17
4	300	17
5	764	17
6	2622	17
done	5000	17
0	17	19
1	35	17
2	74	17
3	152	17
4	300	17
5	764	17
6	2622	17
done	5000	17
0	16	21
1	31	21
2	71	21
3	143	21
4	267	21
5	634	21
6	1990	21
done	5000	21
0	15	16
1	28	16
2	61	16
3	117	16
4	202	16
5	415	16
6	1239	16
7	4467	16
done	5000	16
0	18	23
1	39	23
2	109	23
3	261	23
4	716	23
5	2577	23
done	5000	23
0	17	20
1	34	20
2	81	20
3	180	20
4	418	20
5	1248	20
6	4594	20
done	5000	20
0	16	19
1	35	17
2	89	17
3	215	17
4	511	17
5	1702	17
done	5001	17
0	17	20
1	34	20
2	80	20
3	176	20
4	408	20
5	1282	20
done	5000	20
0	16	17
1	31	17
2	69	17
3	140	17
4	283	17
5	728	17
6	2481	17
done	5000	17
0	15	16
1	32	14
2	72	14
3	145	14
4	296	14
5	869	14
6	3343	14
done	5000	14
0	16	19
1	35	19
2	80	17
3	202	17
4	444	17
5	1095	17
6	3538	17
done	5000	17
0	15	16
1	32	16
2	70	14
3	162	14
4	304	14
5	668	14
6	1904	14
done	5000	14
0	13	15
1	30	13
2	68	11
3	143	11
4	254	11
5	552	11
6	1619	11
done	5000	11
0	12	13
1	27	11
2	63	11
3	124	11
4	202	11
5	370	11
6	956	11
7	2986	11
done	5000	11
0	12	13
1	25	13
2	58	13
3	114	13
4	198	13
5	414	13
6	1233	13
7	4437	13
done	5000	13
0	15	16
1	30	16
2	68	16
3	141	16
4	280	16
5	725	16
6	2492	16
done	5000	16
0	15	16
1	30	16
2	68	16
3	141	16
4	280	16
5	725	16
6	2492	16
done	5000	16
0	11	11
1	17	11
2	34	11
3	78	11
4	208	11
5	648	11
6	2409	11
done	5000	11
0	14	15
1	29	15
2	67	15
3	138	15
4	280	15
5	724	15
6	2493	15
done	5001	15
0	12	13
1	23	13
2	42	13
3	86	13
4	215	13
5	654	13
6	2403	13
done	5000	13
0	15	16
1	30	16
2	62	16
3	114	16
4	176	16
5	308	16
6	820	16
7	2666	16
done	5001	16
0	15	16
1	30	16
2	63	16
3	115	16
4	177	16
5	309	16
6	815	16
7	2653	16
done	5000	16
0	14	15
1	29	15
2	67	15
3	138	15
4	280	15
5	724	15
6	2493	15
done	5001	15
0	15	17
1	33	15
2	72	15
3	148	15
4	299	15
5	764	15
6	2635	15
done	5000	15
0	12	13
1	25	13
2	58	13
3	114	13
4	198	13
5	414	13
6	1233	13
7	4437	13
done	5000	13
0	11	11
1	19	11
2	41	11
3	78	11
4	135	11
5	227	11
6	373	11
7	475	11
8	492	11
done	492	11
0	10	10
1	19	10
2	34	10
3	62	10
4	114	10
5	188	10
6	331	10
7	474	10
8	518	10
done	518	10
0	10	10
1	19	10
2	35	10
3	71	10
4	129	10
5	202	10
6	318	10
7	452	10
8	479	10
9	480	10
done	480	10
0	9	9
1	19	9
2	31	9
3	57	9
4	105	9
5	166	9
6	272	9
7	441	9
8	489	9
9	491	9
done	491	9
0	8	8
1	20	8
2	58	8
3	125	8
4	219	8
5	322	8
6	470	8
7	629	8
8	674	8
9	675	8
done	675	8
0	8	8
1	17	8
2	40	8
3	79	8
4	113	8
5	169	8
6	318	8
7	715	8
8	2398	8
done	5001	8
0	15	23
1	36	23
2	229	15
3	1885	15
done	5000	15
0	13	23
1	38	23
2	251	13
3	2325	13
done	5001	13
0	13	23
1	38	23
2	232	13
3	2103	13
done	5000	13
0	11	23
1	40	23
2	258	11
3	2627	9
done	5001	9
0	9	17
1	18	17
2	39	17
3	66	17
4	77	17
done	77	17
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	9	23
1	25	23
2	128	9
3	1015	9
done	5000	9
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	4	4
1	9	4
2	11	4
done	11	4
0	4	4
1	9	4
2	11	4
done	11	4
0	3	3
done	3	3
0	3	3
done	3	3
0	5	5
1	10	5
2	12	5
done	12	5
0	7	7
1	16	7
2	37	7
3	64	7
4	75	7
done	75	7
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	11	11
1	19	11
2	41	11
3	78	11
4	135	11
5	227	11
6	373	11
7	475	11
8	492	11
done	492	11
0	10	10
1	19	10
2	34	10
3	62	10
4	114	10
5	188	10
6	331	10
7	474	10
8	518	10
done	518	10
0	10	10
1	19	10
2	35	10
3	71	10
4	129	10
5	202	10
6	318	10
7	452	10
8	479	10
9	480	10
done	480	10
0	9	9
1	19	9
2	31	9
3	57	9
4	105	9
5	166	9
6	272	9
7	441	9
8	489	9
9	491	9
done	491	9
0	8	8
1	20	8
2	58	8
3	125	8
4	219	8
5	322	8
6	470	8
7	629	8
8	674	8
9	675	8
done	675	8
0	8	8
1	17	8
2	40	8
3	79	8
4	113	8
5	169	8
6	318	8
7	715	8
8	2398	8
done	5001	8
0	15	23
1	36	23
2	229	15
3	1885	15
done	5000	15
0	13	23
1	38	23
2	251	13
3	2325	13
done	5001	13
0	13	23
1	38	23
2	232	13
3	2103	13
done	5000	13
0	11	23
1	40	23
2	258	11
3	2627	9
done	5001	9
0	9	17
1	18	17
2	39	17
3	66	17
4	77	17
done	77	17
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	9	23
1	25	23
2	128	9
3	1015	9
done	5000	9
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	8	8
1	17	8
2	38	8
3	65	8
4	76	8
done	76	8
0	4	4
1	9	4
2	11	4
done	11	4
0	4	4
1	9	4
2	11	4
done	11	4
0	3	3
done	3	3
0	3	3
done	3	3
0	5	5
1	10	5
2	12	5
done	12	5
0	7	7
1	16	7
2	37	7
3	64	7
4	75	7
done	75	7
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	5	5
1	8	5
2	12	5
3	15	5
4	16	5
done	16	5
0	19	31
1	39	31
2	105	21
3	290	21
4	964	21
5	4036	19
done	5000	19
0	19	31
1	39	31
2	105	21
3	290	21
4	964	21
5	4036	19
done	5000	19
0	20	63
1	40	63
2	106	43
3	291	43
4	962	43
5	4054	39
done	5000	39
0	19	31
1	39	31
2	105	21
3	290	21
4	964	21
5	4036	19
done	5000	19
0	20	92
1	41	60
2	116	22
3	328	22
4	1304	22
done	5000	20
0	20	62
1	41	31
2	107	21
3	292	21
4	963	21
5	4038	19
done	5000	19
0	19	31
1	39	31
2	105	21
3	290	21
4	964	21
5	4036	19
done	5000	19
0	19	31
1	39	31
2	105	21
3	290	21
4	964	21
5	4036	19
done	5000	19
0	19	31
1	39	31
2	105	21
3	290	21
4	964	21
5	4036	19
done	5000	19
0	2	2
1	4	1
done	4	1
0	18	30
1	38	30
2	104	20
3	286	20
4	966	20
5	4132	18
done	5000	18
0	21	34
1	56	34
2	186	24
3	948	24
done	5001	24
0	22	90
1	55	62
2	184	42
3	739	42
4	3315	42
done	5000	42
0	20	60
1	49	60
2	164	40
3	738	28
4	4139	26
done	5001	26
0	18	30
1	37	30
2	92	20
3	212	20
4	568	20
5	2005	18
done	5001	18
0	3	3
1	6	1
done	6	1
0	19	31
1	39	31
2	105	21
3	290	21
4	964	21
5	4036	19
done	5000	19
0	19	31
1	39	31
2	105	21
3	290	21
4	964	21
5	4036	19
done	5000	19
0	31	42
1	78	39
2	180	33
3	696	27
done	5000	27
0	33	46
1	88	40
2	196	34
3	536	31
4	2025	27
done	5000	27
0	34	46
1	87	43
2	189	37
3	558	31
4	2066	31
done	5000	31
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	7	7
1	13	7
2	27	7
3	48	7
4	77	7
5	88	7
done	88	7
0	2	2
done	2	2
0	2	2
done	2	2
0	2	2
done	2	2

prune334.0ms

Filtered

105 candidates to 122 candidates (-16.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	122	8	130

Merged error: 8.7b

Counts

130 → 8

regimes2.1s

Accuracy

58% (1.4b remaining)

Error of 9.4b against oracle of 8.1b and baseline of 11.4b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	103
1	51	103
done	51	103

end0.0ms

sample2.0s

Algorithm

intervals

Results

771.0ms	9345×	body	80	valid
255.0ms	3190×	body	80	nan

Details

sample62.0ms

simplify3.9s

prune5.0ms

localize22.0ms

rewrite34.0ms

series640.0ms

simplify5.9min

prune350.0ms

localize16.0ms

rewrite32.0ms

series676.0ms

simplify5.2min

prune280.0ms

localize17.0ms

rewrite49.0ms

series648.0ms

simplify8.5min

prune368.0ms

localize24.0ms

rewrite34.0ms

series436.0ms

simplify4.5min

prune334.0ms

regimes2.1s

bsearch2.0ms

simplify4.0ms

end0.0ms

sample2.0s

Profiling