Details

analyze9.0ms

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample68.0ms

Algorithm

intervals

Results

53.0ms	256×	body	80	valid
3.0ms	258×	pre	80	true
0.0ms	2×	body	80	invalid

simplify235.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (221.0ms)

Iter	Nodes	Cost
0	5682	55

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 2.5b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
0.5b	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
1.0b	(sqrt.f64 PI.f64)
2.1b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_1807`
45×	`add-sqr-sqrt_binary64_1792`
42×	`times-frac_binary64_1802`
36×	`add-cube-cbrt_binary64_1778`
25×	`sqrt-prod_binary64_1786`
22×	`associate-l_binary64_1867`
18×	`frac-add_binary64_1797`
12×	`distribute-lft-out_binary64_1851`
11×	`add-cbrt-cube_binary64_1779`
9×	`add-exp-log_binary64_1771`
8×	`associate-r_binary64_1866` `exp-prod_binary64_1757`
7×	`frac-times_binary64_1799` `pow1_binary64_1749` `associate-*r/_binary64_1868`
6×	`associate-/r*_binary64_1870` `flip-+_binary64_1832` `flip3-+_binary64_1805`
5×	`add-log-exp_binary64_1772`
3×	`unswap-sqr_binary64_1835` `unpow-prod-down_binary64_1738` `div-inv_binary64_1808` `associate-/l*_binary64_1871`
2×	`cbrt-unprod_binary64_1776` `cbrt-undiv_binary64_1777` `div-exp_binary64_1756` `prod-exp_binary64_1754`
1×	`pow1/2_binary64_1739` `rem-sqrt-square_binary64_1795` `distribute-rgt-in_binary64_1850` `frac-2neg_binary64_1800` `sqr-pow_binary64_1839` `rem-exp-log_binary64_1769` `-commutative_binary64_1875` `associate-l/_binary64_1869` `clear-num_binary64_1810` `distribute-lft-in_binary64_1849` `pow-prod-down_binary64_1730` `sqrt-pow1_binary64_1788` `unpow2_binary64_1746`

Counts

4 → 131

Calls

4 calls:

11.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
74.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
4.0ms	(sqrt.f64 PI.f64)
4.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

series2.4s

Counts

4 → 10

Calls

4 calls:

87.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
2.3s	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.0ms	(sqrt.f64 PI.f64)
63.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	366	1950
1	366	1950
0	366	1950
1	366	1950
0	1	3
1	1	3
0	17549	2469
1	17549	2469
0	17549	2469
1	17549	2469
0	1	3
1	1	3
0	570	2004
1	570	2004
0	570	2004
1	570	2004
0	1	3
1	1	3

simplify110.0ms

Counts

141 → 141

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5302	5892

prune374.0ms

Filtered

100 candidates to 141 candidates (-41.0%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	121	20	141
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	123	20	143

Merged error: 0.8b

Counts

143 → 20

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
0.5b	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.9b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

94×	`times-frac_binary64_1802`
86×	`*-un-lft-identity_binary64_1807`
85×	`add-sqr-sqrt_binary64_1792`
66×	`add-cube-cbrt_binary64_1778`
51×	`sqrt-prod_binary64_1786`
46×	`associate-l_binary64_1867`
44×	`unpow-prod-down_binary64_1738`
18×	`frac-add_binary64_1797`
17×	`add-exp-log_binary64_1771`
16×	`sqr-pow_binary64_1839`
12×	`distribute-lft-out_binary64_1851`
11×	`add-cbrt-cube_binary64_1779`
8×	`pow1_binary64_1749` `associate-r_binary64_1866`
7×	`unswap-sqr_binary64_1835` `frac-times_binary64_1799` `associate-/l_binary64_1871` `associate-r/_binary64_1868`
6×	`div-exp_binary64_1756` `associate-/r*_binary64_1870` `flip-+_binary64_1832` `flip3-+_binary64_1805`
4×	`pow-pow_binary64_1731` `add-log-exp_binary64_1772` `prod-exp_binary64_1754`
3×	`div-inv_binary64_1808` `pow-to-exp_binary64_1728` `pow-unpow_binary64_1736` `pow-exp_binary64_1727` `exp-prod_binary64_1757`
2×	`cbrt-unprod_binary64_1776` `cbrt-undiv_binary64_1777`
1×	`pow1/2_binary64_1739` `rem-sqrt-square_binary64_1795` `distribute-rgt-in_binary64_1850` `frac-2neg_binary64_1800` `-commutative_binary64_1875` `associate-l/_binary64_1869` `clear-num_binary64_1810` `distribute-lft-in_binary64_1849` `pow-prod-down_binary64_1730` `sqrt-pow1_binary64_1788`

Counts

4 → 195

Calls

4 calls:

8.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
81.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)

series2.6s

Counts

4 → 10

Calls

4 calls:

76.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
2.5s	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
59.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	379	1992
1	379	1992
0	379	1992
1	379	1992
0	1	3
1	1	3
0	17865	2511
1	17865	2511
0	17865	2511
1	17865	2511
0	1	3
1	1	3
0	583	2046
1	583	2046
0	583	2046
1	583	2046
0	1	3
1	1	3

simplify146.0ms

Counts

205 → 205

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5429	9305

prune481.0ms

Filtered

139 candidates to 205 candidates (-47.5%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	183	22	205
Fresh	15	4	19
Picked	1	0	1
Done	0	0	0
Total	199	26	225

Merged error: 0.1b

Counts

225 → 26

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow.f64 (exp.f64 (fabs.f64 x)) (*.f64 1/2 (fabs.f64 x)))
0.6b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1792`
17×	`*-un-lft-identity_binary64_1807` `add-cube-cbrt_binary64_1778`
14×	`pow-unpow_binary64_1736`
9×	`times-frac_binary64_1802`
8×	`pow-pow_binary64_1731` `pow1_binary64_1749`
6×	`unpow-prod-down_binary64_1738` `sqrt-prod_binary64_1786` `exp-prod_binary64_1757`
4×	`add-cbrt-cube_binary64_1779` `add-exp-log_binary64_1771` `add-log-exp_binary64_1772`
2×	`pow1/2_binary64_1739` `rem-sqrt-square_binary64_1795` `pow-to-exp_binary64_1728` `sqr-pow_binary64_1839` `pow-exp_binary64_1727` `sqrt-pow1_binary64_1788`
1×	`div-inv_binary64_1808`

Counts

4 → 74

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (*.f64 1/2 (fabs.f64 x)))
6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series139.0ms

Counts

4 → 8

Calls

4 calls:

61.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (*.f64 1/2 (fabs.f64 x)))
78.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	616	2019
1	616	2019
0	616	2019
1	616	2019
0	1	3
1	1	3
0	437	2019
1	437	2019
0	437	2019
1	437	2019
0	1	3
1	1	3

simplify101.0ms

Counts

82 → 82

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4921	1109
1	4921	1109

prune232.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	5	20	25
Picked	0	1	1
Done	0	0	0
Total	84	24	108

Merged error: 0.1b

Counts

108 → 24

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.9b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

1233×	`sqrt-prod_binary64_1786`
1231×	`times-frac_binary64_1802`
684×	`add-sqr-sqrt_binary64_1792`
607×	`associate-l_binary64_1867`
592×	`*-un-lft-identity_binary64_1807`
572×	`add-cube-cbrt_binary64_1778`
255×	`unpow-prod-down_binary64_1738`
91×	`sqr-pow_binary64_1839`
31×	`unswap-sqr_binary64_1835`
19×	`add-exp-log_binary64_1771`
18×	`frac-add_binary64_1797`
13×	`add-cbrt-cube_binary64_1779`
12×	`distribute-lft-out_binary64_1851`
11×	`div-inv_binary64_1808`
9×	`pow1_binary64_1749`
8×	`associate-r_binary64_1866`
7×	`frac-times_binary64_1799` `div-exp_binary64_1756` `associate-*r/_binary64_1868`
6×	`flip-+_binary64_1832` `flip3-+_binary64_1805`
5×	`prod-exp_binary64_1754`
4×	`pow-pow_binary64_1731` `add-log-exp_binary64_1772`
3×	`cbrt-unprod_binary64_1776` `cbrt-undiv_binary64_1777` `pow-unpow_binary64_1736` `exp-prod_binary64_1757`
2×	`pow1/2_binary64_1739` `rem-sqrt-square_binary64_1795` `pow-to-exp_binary64_1728` `pow-exp_binary64_1727` `sqrt-pow1_binary64_1788`
1×	`distribute-rgt-in_binary64_1850` `-commutative_binary64_1875` `associate-l/_binary64_1869` `distribute-lft-in_binary64_1849` `pow-prod-down_binary64_1730`

Counts

4 → 726

Calls

4 calls:

217.0ms	(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series3.1s

Counts

4 → 8

Calls

4 calls:

3.1s	(*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64))) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
66.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	379	1992
1	379	1992
0	379	1992
1	379	1992
0	1	3
1	1	3
0	18218	2556
1	18218	2556
0	18218	2556
1	18218	2556
0	1	3
1	1	3

simplify440.0ms

Counts

734 → 734

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5342	49313

prune1.5s

Filtered

442 candidates to 734 candidates (-66.1%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	726	8	734
Fresh	5	17	22
Picked	0	1	1
Done	1	0	1
Total	732	26	758

Merged error: 0.1b

Counts

758 → 26

regimes249.0ms

Accuracy

0% (1.0b remaining)

Error of 1.3b against oracle of 0.2b and baseline of 1.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	67
1	34	67

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
95.0ms	8116×	pre	80	true
23.0ms	116×	body	80	invalid

Details

analyze9.0ms

sample68.0ms

simplify235.0ms

prune9.0ms

localize23.0ms

rewrite99.0ms

series2.4s

simplify110.0ms

prune374.0ms

localize28.0ms

rewrite110.0ms

series2.6s

simplify146.0ms

prune481.0ms

localize39.0ms

rewrite15.0ms

series139.0ms

simplify101.0ms

prune232.0ms

localize34.0ms

rewrite320.0ms

series3.1s

simplify440.0ms

prune1.5s

regimes249.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample1.9s

Profiling