Details

sample14.0ms

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))

simplify765.0ms

Counts

15 → 15

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	21	99
1	34	84
2	62	80
3	80	80
4	88	80
5	100	80
6	124	80
7	187	80
8	397	80
9	1338	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

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)

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

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

simplify912.0ms

Counts

23 → 23

Iterations

Useful iterations: 4 (296.0ms)

Iter	Nodes	Cost
0	53	210
1	120	172
2	266	164
3	691	155
4	3124	125
done	5000	125

prune47.0ms

Filtered

13 candidates to 23 candidates (-76.9%)

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))

rewrite41.0ms

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))))
8.0ms	(sqrt (* (* 2.0 x) x))
4.0ms	(sqrt (* (* 2.0 x) x))

series20.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (sqrt (* (* 2.0 x) x)))
5.0ms	(* (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))

simplify704.0ms

Counts

142 → 142

Iterations

Useful iterations: 3 (217.0ms)

Iter	Nodes	Cost
0	100	1759
1	212	1073
2	693	963
3	2724	899
done	5001	899

prune159.0ms

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))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(* x (sqrt 2.0))

simplify869.0ms

Counts

25 → 25

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	37	158
1	71	143
2	160	133
3	242	133
4	306	133
5	453	133
6	906	133
7	2720	133
done	5001	133

prune32.0ms

Filtered

13 candidates to 25 candidates (-92.3%)

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

regimes437.0ms

Accuracy

99.1% (0.3b remaining)

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

bsearch11.0ms

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

sample352.0ms

Algorithm

intervals

Results

210.0ms

8006×

body

valid

Details

sample14.0ms

simplify4.0ms

prune2.0ms

localize4.0ms

rewrite4.0ms

series4.0ms

simplify765.0ms

prune47.0ms

localize7.0ms

rewrite7.0ms

series27.0ms

simplify912.0ms

prune47.0ms

localize7.0ms

rewrite41.0ms

series20.0ms

simplify704.0ms

prune159.0ms

localize3.0ms

rewrite6.0ms

series5.0ms

simplify869.0ms

prune32.0ms

regimes437.0ms

bsearch11.0ms

simplify2.0ms

end0.0ms

sample352.0ms

Profiling