Details

sample13.0ms

Algorithm

intervals

Results

6.0ms

257×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	4	8
1	8	6
2	12	6
3	13	6
done	13	6

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.1b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

27.0b

(sqrt (* x (+ x x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt (* x (+ x x)))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(sqrt (* x (+ x x)))

simplify1.1s

Counts

16 → 16

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	33	132
1	66	102
2	138	91
3	395	89
4	1946	89
done	5001	89

prune40.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	9	7	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	10	7	17

Merged error: 0.1b

Counts

17 → 7

localize6.0ms

Local error

Found 1 expressions with local error:

27.0b

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 18

Calls

1 calls:

6.0ms

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

series28.0ms

Counts

1 → 3

Calls

1 calls:

28.0ms

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

simplify870.0ms

Counts

21 → 21

Iterations

Useful iterations: 4 (248.0ms)

Iter	Nodes	Cost
0	49	197
1	111	167
2	244	161
3	677	149
4	2300	140
done	5000	140

prune40.0ms

Filtered

11 candidates to 21 candidates (-90.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	20	8	28

Merged error: 0.1b

Counts

28 → 8

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-pow1`
71×	`pow1`
33×	`sqrt-prod`
32×	`sqrt-div`
26×	`add-sqr-sqrt`
25×	`pow-prod-down`
22×	`pow1/2`
20×	`associate-*r/`
14×	`pow-prod-up`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`flip3-+` `swap-sqr` `flip-+`
8×	`pow-sqr`
7×	`associate-r` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
4×	`frac-times` `add-log-exp` `unswap-sqr`
2×	`associate-*l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

6.0ms	(sqrt (sqrt (* x (+ x x))))
19.0ms	(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
5.0ms	(sqrt (* x (+ x x)))
6.0ms	(sqrt (* x (+ x x)))

series18.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (sqrt (* x (+ x x))))
4.0ms	(* (sqrt (sqrt (* x (+ x x)))) (sqrt (sqrt (* x (+ x x)))))
4.0ms	(sqrt (* x (+ x x)))
4.0ms	(sqrt (* x (+ x x)))

simplify1.1s

Counts

136 → 136

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	127	1941
1	254	1202
2	865	1029
3	3629	961
done	5000	949

prune115.0ms

Filtered

73 candidates to 136 candidates (-86.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	137	7	144

Merged error: 0.1b

Counts

144 → 7

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b	(* x (sqrt 2))

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))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(* x (sqrt 2))

simplify1.6s

Counts

25 → 25

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	37	158
1	71	144
2	159	136
3	228	133
4	297	133
5	468	133
6	1016	133
7	3890	133
done	5000	133

prune32.0ms

Filtered

14 candidates to 25 candidates (-78.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	22	10	32

Merged error: 0.1b

Counts

32 → 10

regimes57.0ms

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	18	16
2	20	16
done	20	16

end0.0ms

sample345.0ms

Algorithm

intervals

Results

195.0ms

8006×

body

valid

Details

sample13.0ms

simplify5.0ms

prune10.0ms

localize4.0ms

rewrite5.0ms

series4.0ms

simplify1.1s

prune40.0ms

localize6.0ms

rewrite7.0ms

series28.0ms

simplify870.0ms

prune40.0ms

localize7.0ms

rewrite42.0ms

series18.0ms

simplify1.1s

prune115.0ms

localize3.0ms

rewrite6.0ms

series4.0ms

simplify1.6s

prune32.0ms

regimes57.0ms

bsearch12.0ms

simplify2.0ms

end0.0ms

sample345.0ms

Profiling