Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

257×

body

valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

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

localize4.0ms

Local error

Found 1 expressions with local error:

27.0b

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

rewrite4.0ms

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:

4.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify2.7s

Counts

15 → 15

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	21	99
1	34	84
2	62	80
3	77	80
4	83	80
5	93	80
6	114	80
7	173	80
8	376	80
9	1299	80
done	5000	80

prune47.0ms

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

localize6.0ms

Local error

Found 1 expressions with local error:

27.0b

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

rewrite6.0ms

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)

series25.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

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

simplify2.2s

Counts

23 → 23

Iterations

Useful iterations: 4 (742.0ms)

Iter	Nodes	Cost
0	53	210
1	118	170
2	242	164
3	642	155
4	2834	125
done	5000	125

prune50.0ms

Filtered

14 candidates to 23 candidates (-64.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	21	9	30

Merged error: 0.1b

Counts

30 → 9

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))

rewrite38.0ms

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)))
16.0ms	(* (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))

series18.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(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))

simplify1.5s

Counts

142 → 142

Iterations

Useful iterations: 3 (580.0ms)

Iter	Nodes	Cost
0	100	1759
1	209	1033
2	648	963
3	2731	899
done	5000	899

prune151.0ms

Filtered

58 candidates to 142 candidates (-144.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	143	8	151

Merged error: 0.1b

Counts

151 → 8

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b	(* x (sqrt 2.0))

rewrite6.0ms

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:

5.0ms

(* x (sqrt 2.0))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(* x (sqrt 2.0))

simplify2.0s

Counts

25 → 25

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	37	158
1	69	141
2	122	133
3	158	133
4	216	133
5	350	133
6	757	133
7	2237	133
done	5000	133

prune27.0ms

Filtered

14 candidates to 25 candidates (-78.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	23	10	33

Merged error: 0.1b

Counts

33 → 10

regimes207.0ms

Accuracy

99.1% (0.3b remaining)

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

bsearch12.0ms

Steps

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

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample333.0ms

Algorithm

intervals

Results

201.0ms

8006×

body

valid

Details

sample13.0ms

simplify4.0ms

prune2.0ms

localize4.0ms

rewrite4.0ms

series4.0ms

simplify2.7s

prune47.0ms

localize6.0ms

rewrite6.0ms

series25.0ms

simplify2.2s

prune50.0ms

localize7.0ms

rewrite38.0ms

series18.0ms

simplify1.5s

prune151.0ms

localize3.0ms

rewrite6.0ms

series4.0ms

simplify2.0s

prune27.0ms

regimes207.0ms

bsearch12.0ms

simplify2.0ms

end0.0ms

sample333.0ms

Profiling