Details

sample20.0ms

Algorithm

intervals

Results

8.0ms

257×

body

valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	5	6
1	9	6
2	10	6
done	10	6

prune4.0ms

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: 28.1b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

27.0b

(sqrt (* (* 2.0 x) x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1`
3×	`sqrt-pow1` `pow-prod-down`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow1/2` `sqrt-prod` `add-cbrt-cube` `add-log-exp`

Counts

1 → 12

Calls

1 calls:

7.0ms

(sqrt (* (* 2.0 x) x))

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

(sqrt (* (* 2.0 x) x))

simplify2.9s

Counts

15 → 15

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	10	7
2	11	7
done	11	7
0	6	7
1	10	7
2	11	7
done	11	7
0	7	15
1	11	15
2	12	15
done	12	15
0	6	7
1	10	7
2	11	7
done	11	7
0	7	20
1	12	12
2	28	8
3	46	8
4	52	8
5	62	8
6	83	8
7	143	8
8	348	8
9	1266	8
done	5000	8
0	4	4
1	5	4
done	5	4
0	2	2
done	2	2
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	6	7
1	10	7
2	11	7
done	11	7
0	6	7
1	10	7
2	11	7
done	11	7
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
0	6	6
1	11	5
2	23	5
done	23	5

prune52.0ms

Filtered

11 candidates to 15 candidates (-36.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	8	7	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	9	7	16

Merged error: 0.1b

Counts

16 → 7

localize7.0ms

Local error

Found 1 expressions with local error:

27.0b

(pow (* (* 2.0 x) x) 1/2)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1×	`pow-to-exp` `unpow-prod-down` `add-cbrt-cube` `unpow1/2` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

6.0ms

(pow (* (* 2.0 x) x) 1/2)

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

(pow (* (* 2.0 x) x) 1/2)

simplify1.0min

Counts

23 → 23

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	8	10
1	13	10
2	30	9
3	39	9
4	48	7
5	105	7
6	310	7
7	1440	7
done	5000	7
0	8	9
1	13	9
2	24	9
3	37	9
4	46	9
5	55	7
6	112	7
7	317	7
8	1423	7
done	5000	7
0	7	8
1	15	8
2	28	8
3	43	8
4	49	8
5	56	8
6	62	7
7	118	7
8	322	7
9	1426	7
done	5000	7
0	7	8
1	15	8
2	28	8
3	43	8
4	49	8
5	56	8
6	62	7
7	118	7
8	322	7
9	1426	7
done	5000	7
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	8	11
1	16	11
2	24	11
3	48	11
4	105	11
5	265	11
6	886	11
7	3337	11
done	5000	11
0	7	8
1	15	8
2	21	8
3	39	8
4	79	8
5	181	8
6	552	8
7	2174	8
done	5000	8
0	6	7
1	17	5
2	25	5
3	36	5
4	60	5
5	120	5
6	334	5
7	1258	5
done	5000	5
0	5	5
1	12	4
2	18	4
3	28	4
4	50	4
5	111	4
6	322	4
7	1255	4
done	5000	4
0	3	3
1	9	2
2	15	2
3	25	2
4	49	2
5	114	2
6	337	2
7	1273	2
done	5000	2
0	7	8
1	19	7
2	36	7
3	68	7
4	130	7
5	345	7
6	1157	7
done	5001	7
0	7	8
1	17	7
2	26	7
3	41	7
4	78	7
5	193	7
6	657	7
7	3026	7
done	5001	7
0	8	17
1	18	15
2	25	15
3	35	15
4	59	15
5	121	15
6	339	15
7	1277	15
done	5000	15
0	7	8
1	17	7
2	24	7
3	34	7
4	56	7
5	125	7
6	345	7
7	1277	7
done	5000	7
0	8	23
1	22	14
2	46	8
3	123	7
4	358	7
5	1241	7
done	5000	7
0	7	8
1	17	7
2	25	7
3	35	7
4	59	7
5	121	7
6	337	7
7	1267	7
done	5001	7
0	7	8
1	17	7
2	25	7
3	35	7
4	59	7
5	121	7
6	337	7
7	1267	7
done	5001	7
0	8	9
1	17	7
2	24	7
3	34	7
4	56	7
5	122	7
6	340	7
7	1273	7
done	5000	7
0	8	9
1	17	7
2	24	7
3	34	7
4	56	7
5	122	7
6	340	7
7	1273	7
done	5000	7
0	10	10
1	21	10
2	39	10
3	70	7
4	167	4
5	409	4
6	1258	4
7	4596	4
done	5000	4
0	12	12
1	24	11
2	48	11
3	110	9
4	251	6
5	807	4
6	2451	4
done	5000	4
0	12	12
1	21	12
2	42	12
3	102	11
4	255	8
5	782	6
6	2666	4
7	3016	1
8	3054	1
9	3055	1
done	3055	1

prune44.0ms

Filtered

14 candidates to 23 candidates (-64.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	22	1	23
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	23	7	30

Merged error: 0.1b

Counts

30 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (* (* 2.0 x) x)))
0.5b	(* (sqrt (sqrt (* (* 2.0 x) x))) (sqrt (sqrt (* (* 2.0 x) x))))
27.0b	(sqrt (* (* 2.0 x) x))
27.0b	(sqrt (* (* 2.0 x) x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

158×	`pow1`
154×	`sqrt-pow1`
82×	`pow-prod-down`
33×	`sqrt-prod`
26×	`add-sqr-sqrt`
24×	`pow1/2`
21×	`pow-prod-up`
13×	`add-cube-cbrt` `*-un-lft-identity` `pow-sqr`
9×	`swap-sqr`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 130

Calls

4 calls:

5.0ms	(sqrt (sqrt (* (* 2.0 x) x)))
17.0ms	(* (sqrt (sqrt (* (* 2.0 x) x))) (sqrt (sqrt (* (* 2.0 x) x))))
4.0ms	(sqrt (* (* 2.0 x) x))
4.0ms	(sqrt (* (* 2.0 x) x))

series24.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (sqrt (* (* 2.0 x) x)))
4.0ms	(* (sqrt (sqrt (* (* 2.0 x) x))) (sqrt (sqrt (* (* 2.0 x) x))))
4.0ms	(sqrt (* (* 2.0 x) x))
4.0ms	(sqrt (* (* 2.0 x) x))

simplify55.2s

Counts

142 → 142

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	10	7
2	11	7
done	11	7
0	6	7
1	10	7
2	11	7
done	11	7
0	7	15
1	11	15
2	12	15
done	12	15
0	6	7
1	10	7
2	11	7
done	11	7
0	7	20
1	12	12
2	28	8
3	46	8
4	52	8
5	62	8
6	83	8
7	143	8
8	348	8
9	1266	8
done	5000	8
0	4	4
1	5	4
done	5	4
0	2	2
done	2	2
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	6	7
1	10	7
2	11	7
done	11	7
0	6	7
1	10	7
2	11	7
done	11	7
0	6	7
1	10	7
2	11	7
done	11	7
0	6	7
1	10	7
2	11	7
done	11	7
0	7	15
1	11	15
2	12	15
done	12	15
0	6	7
1	10	7
2	11	7
done	11	7
0	7	20
1	12	12
2	28	8
3	46	8
4	52	8
5	62	8
6	83	8
7	143	8
8	348	8
9	1266	8
done	5000	8
0	4	4
1	5	4
done	5	4
0	2	2
done	2	2
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	3	3
1	6	1
done	6	1
0	6	7
1	10	7
2	11	7
done	11	7
0	6	7
1	10	7
2	11	7
done	11	7
0	2	3
1	5	1
2	7	1
done	7	1
0	5	5
1	8	1
done	8	1
0	2	3
1	6	1
done	6	1
0	4	7
1	6	3
2	7	1
done	7	1
0	7	9
1	14	3
done	14	1
0	7	9
1	14	3
done	14	1
0	7	9
1	14	3
done	14	1
0	5	5
1	8	3
done	8	1
0	4	7
1	8	3
2	9	1
done	9	1
0	7	9
1	14	3
done	14	1
0	5	11
1	12	5
2	18	1
done	18	1
0	5	11
1	12	5
2	18	1
done	18	1
0	5	11
1	12	5
2	18	1
done	18	1
0	7	9
1	14	3
done	14	1
0	5	11
1	12	5
2	18	1
done	18	1
0	5	11
1	12	5
2	18	1
done	18	1
0	5	11
1	12	5
2	18	1
done	18	1
0	7	9
1	14	3
done	14	1
0	5	11
1	12	5
2	18	1
done	18	1
0	5	11
1	12	5
2	18	1
done	18	1
0	5	11
1	12	5
2	18	1
done	18	1
0	6	13
1	10	5
2	12	5
done	12	5
0	7	15
1	11	6
2	13	6
done	13	6
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	6	13
1	10	5
2	12	5
done	12	5
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	5	11
1	15	11
2	45	11
3	77	11
4	81	9
5	90	7
6	123	7
7	227	7
8	513	7
9	1509	7
done	5000	7
0	2	3
1	6	1
done	6	1
0	8	17
1	14	10
2	16	10
done	16	10
0	8	16
1	14	7
2	18	7
3	19	7
done	19	7
0	8	16
1	14	7
2	20	7
3	25	7
4	43	7
5	83	7
6	194	7
7	572	7
8	2249	7
done	5000	7
0	9	47
1	20	20
2	31	12
3	77	8
4	155	8
5	238	8
6	481	8
7	1504	8
done	5000	8
0	9	33
1	13	15
2	15	15
done	15	15
0	8	16
1	12	7
2	14	7
done	14	7
0	9	47
1	21	20
2	32	8
3	79	8
4	158	8
5	248	8
6	504	8
7	1576	8
done	5000	8
0	6	13
1	10	5
2	12	5
done	12	5
0	8	16
1	13	7
2	14	7
done	14	7
0	8	16
1	13	7
2	14	7
done	14	7
0	9	35
1	17	35
2	20	19
3	29	10
4	44	10
5	70	10
6	141	10
7	357	10
8	1266	10
done	5000	10
0	8	17
1	12	17
2	13	17
done	13	17
0	9	33
1	14	15
2	16	15
done	16	15
0	8	17
1	12	7
2	14	7
done	14	7
0	6	11
1	7	4
2	8	4
done	8	4
0	4	7
done	4	2
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	3	5
1	5	1
done	5	1
0	7	15
1	11	6
2	13	6
done	13	6
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	2	3
1	4	1
done	4	1
0	7	15
1	11	6
2	13	6
done	13	6
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	8	17
1	12	7
2	14	7
done	14	7
0	3	3
1	5	1
2	7	1
done	7	1
0	3	3
1	6	1
done	6	1
0	4	5
1	9	3
2	11	1
done	11	1
0	4	5
1	10	1
done	10	1
0	5	7
1	14	5
2	22	1
done	22	1
0	5	7
1	14	5
2	22	1
done	22	1
0	5	7
1	14	5
2	22	1
done	22	1
0	5	7
1	14	5
2	22	1
done	22	1
0	5	7
1	14	5
2	22	1
done	22	1
0	5	7
1	14	5
2	22	1
done	22	1
0	5	7
1	14	5
2	22	1
done	22	1
0	5	7
1	14	5
2	22	1
done	22	1
0	5	7
1	14	5
2	22	1
done	22	1
0	9	25
1	16	25
2	19	25
done	19	25
0	10	24
1	16	16
2	17	16
done	17	16
0	9	13
1	14	13
2	15	13
done	15	13
0	8	16
1	13	16
2	14	16
done	14	16
0	9	10
1	16	9
2	17	9
done	17	7
0	8	16
1	13	16
2	14	16
done	14	16
0	8	9
1	15	7
2	19	7
done	19	7
0	8	16
1	13	16
2	14	16
done	14	16
0	9	16
1	14	16
2	15	16
done	15	16
0	9	11
1	14	11
2	15	11
done	15	11
0	8	16
1	13	16
2	14	16
done	14	16
0	7	15
1	11	6
2	13	6
done	13	6
0	8	16
1	13	16
2	14	16
done	14	16
0	7	15
1	11	6
2	13	6
done	13	6
0	7	8
1	11	8
2	12	8
done	12	8
0	7	8
1	11	8
2	12	8
done	12	8
0	8	17
1	12	17
2	13	17
done	13	17
0	7	8
1	11	8
2	12	8
done	12	8
0	8	23
1	13	14
2	17	9
3	22	9
4	28	9
5	38	9
6	59	9
7	120	9
8	329	9
9	1247	9
done	5000	9
0	8	16
1	13	8
2	14	8
done	14	8
0	7	8
1	11	8
2	12	8
done	12	8
0	5	5
1	6	5
done	6	5
0	3	3
done	3	3
0	7	8
1	11	8
2	12	8
done	12	8
0	7	8
1	11	8
2	12	8
done	12	8
0	2	2
1	4	1
done	4	1
0	6	7
1	10	7
2	11	7
done	11	7
0	3	3
1	4	1
done	4	1
0	3	3
1	6	1
done	6	1
0	4	5
1	10	3
2	11	1
done	11	1
0	4	5
1	10	3
2	11	1
done	11	1
0	4	5
1	10	3
2	11	1
done	11	1
0	7	8
1	11	8
2	12	8
done	12	8
0	7	8
1	11	8
2	12	8
done	12	8
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
0	6	6
1	11	5
2	23	5
done	23	5
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
0	6	6
1	11	5
2	23	5
done	23	5
0	4	4
1	5	4
done	5	4
0	4	4
1	5	4
done	5	4
0	6	6
1	11	5
2	23	5
done	23	5
0	21	32
1	64	32
2	230	29
3	841	26
4	4128	24
done	5000	24
0	19	28
1	53	28
2	189	25
3	543	25
4	2399	21
done	5000	21
0	19	28
1	54	28
2	195	25
3	609	25
4	2795	21
done	5000	21

prune159.0ms

Filtered

60 candidates to 142 candidates (-136.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	143	6	149

Merged error: 0.1b

Counts

149 → 6

localize4.0ms

Local error

Found 1 expressions with local error:

0.4b	(* x (sqrt 2.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `add-log-exp`

Counts

1 → 22

Calls

1 calls:

6.0ms

(* x (sqrt 2.0))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(* x (sqrt 2.0))

simplify10.7s

Counts

25 → 25

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	4	4
1	5	4
done	5	4
0	6	6
1	7	6
done	7	6
0	5	5
1	9	5
2	10	5
done	10	5
0	5	5
1	8	5
2	14	5
3	22	5
4	45	5
5	101	5
6	240	5
7	694	5
8	2697	5
done	5001	5
0	8	14
1	15	10
2	38	8
3	70	8
4	98	8
5	144	8
6	264	8
7	653	8
8	2091	8
done	5000	8
0	6	11
1	7	11
done	7	11
0	5	5
1	6	5
done	6	5
0	6	14
1	17	14
2	46	6
3	88	6
4	105	6
5	149	6
6	280	6
7	735	6
8	2739	6
done	5000	6
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	6	6
1	7	6
done	7	6
0	6	9
1	9	9
2	11	9
done	11	9
0	6	8
1	8	5
done	8	5
0	5	5
1	6	5
done	6	5
0	4	4
1	7	3
done	7	3
0	5	5
1	6	5
done	6	5
0	3	3
1	6	1
done	6	1
0	5	5
1	6	5
done	6	5
0	5	5
1	6	5
done	6	5
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
0	4	4
1	5	4
done	5	4

prune32.0ms

Filtered

17 candidates to 25 candidates (-47.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	22	9	31

Merged error: 0.1b

Counts

31 → 9

regimes214.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.7b

bsearch13.0ms

Steps

Iters	Range		Point
8	-7.67443757966827e-305	8.126837495347253e-308	1.9786006080648e-310

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	19	16
2	21	16
done	21	16

end0.0ms

sample374.0ms

Algorithm

intervals

Results

219.0ms

8006×

body

valid

Details

sample20.0ms

simplify31.0ms

prune4.0ms

localize7.0ms

rewrite9.0ms

series13.0ms

simplify2.9s

prune52.0ms

localize7.0ms

rewrite7.0ms

series28.0ms

simplify1.0min

prune44.0ms

localize7.0ms

rewrite39.0ms

series24.0ms

simplify55.2s

prune159.0ms

localize4.0ms

rewrite7.0ms

series5.0ms

simplify10.7s

prune32.0ms

regimes214.0ms

bsearch13.0ms

simplify3.0ms

end0.0ms

sample374.0ms

Profiling