Details

analyze2.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

sample141.0ms

Algorithm

intervals

Results

47.0ms	256×	body	80	valid
39.0ms	285×	body	80	nan
27.0ms	151×	body	80	invalid

simplify66.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5140	41

prune5.0ms

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: 26.8b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

6.0b	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
11.3b	(sqrt.f64 (/.f64 d l))
11.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
13.2b	(sqrt.f64 (/.f64 d h))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log_binary64`
41×	`prod-exp_binary64`
32×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
21×	`add-cbrt-cube_binary64`
16×	`associate-r_binary64` `div-exp_binary64`
14×	`sqrt-div_binary64`
13×	`pow1_binary64`
10×	`pow-exp_binary64`
9×	`cbrt-unprod_binary64` `frac-times_binary64`
6×	`associate-r/_binary64` `associate-l/_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `flip3--_binary64` `rem-sqrt-square_binary64` `insert-posit16` `flip--_binary64`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`

Counts

4 → 129

Calls

4 calls:

21.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
3.0ms	(sqrt.f64 (/.f64 d l))
13.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
4.0ms	(sqrt.f64 (/.f64 d h))

series1.5s

Counts

4 → 12

Calls

4 calls:

683.0ms	(.f64 (.f64 (sqrt.f64 (/.f64 d h)) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
226.0ms	(sqrt.f64 (/.f64 d l))
367.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
226.0ms	(sqrt.f64 (/.f64 d h))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	312	282
1	312	282
0	19	45
1	19	45
0	312	282
1	312	282
0	19	45
1	19	45
0	168	9
1	168	9
0	657	1060
1	657	1060
0	15	9
1	15	9
0	657	1060
1	657	1060
0	15	9
1	15	9
0	1	3
1	1	3
0	312	282
1	312	282
0	19	45
1	19	45
0	312	282
1	312	282
0	19	45
1	19	45
0	168	9
1	168	9
0	1184	1817
1	1184	1817
0	184	1163
1	184	1163
0	1184	1817
1	1184	1817
0	184	1163
1	184	1163
0	24	3
1	24	3

simplify88.0ms

Counts

141 → 141

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5093	3290

prune223.0ms

Filtered

94 candidates to 141 candidates (-50.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	123	18	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	18	142

Merged error: 12.5b

Counts

142 → 18

localize28.0ms

Local error

Found 4 expressions with local error:

4.7b	(/.f64 (.f64 M D) (.f64 d 2))
6.0b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.3b	(sqrt.f64 (/.f64 d l))
11.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-exp-log_binary64`
48×	`prod-exp_binary64`
37×	`add-cbrt-cube_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64` `div-exp_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`pow1_binary64` `cbrt-unprod_binary64` `associate-r_binary64`
13×	`sqrt-prod_binary64` `sqrt-div_binary64`
12×	`associate-*r/_binary64`
10×	`pow-exp_binary64`
9×	`frac-times_binary64`
7×	`pow-prod-down_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 128

Calls

4 calls:

8.0ms	(/.f64 (.f64 M D) (.f64 d 2))
25.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
4.0ms	(sqrt.f64 (/.f64 d l))
13.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

series1.7s

Counts

4 → 12

Calls

4 calls:

267.0ms	(/.f64 (.f64 M D) (.f64 d 2))
817.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
229.0ms	(sqrt.f64 (/.f64 d l))
361.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	657	1060
1	657	1060
0	15	9
1	15	9
0	657	1060
1	657	1060
0	15	9
1	15	9
0	1	3
1	1	3
0	312	282
1	312	282
0	19	45
1	19	45
0	312	282
1	312	282
0	19	45
1	19	45
0	168	9
1	168	9
0	1468	2262
1	1468	2262
0	185	1740
1	185	1740
0	1468	2262
1	1468	2262
0	185	1740
1	185	1740
0	40	3
1	40	3
0	433	384
1	433	384
0	29	24
1	29	24
0	433	384
1	433	384
0	29	24
1	29	24
0	49	23
1	49	23

simplify62.0ms

Counts

140 → 140

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	705	4532
1	705	4532

prune218.0ms

Filtered

100 candidates to 140 candidates (-40.0%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	132	8	140
Fresh	1	16	17
Picked	1	0	1
Done	0	0	0
Total	134	24	158

Merged error: 11.1b

Counts

158 → 24

localize37.0ms

Local error

Found 4 expressions with local error:

2.6b	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
4.7b	(/.f64 (.f64 M D) (.f64 d 2))
6.0b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
11.7b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
37×	`sqrt-div_binary64`
30×	`associate-*r/_binary64`
29×	`frac-times_binary64`
25×	`pow1_binary64`
23×	`cbrt-unprod_binary64`
20×	`div-exp_binary64`
16×	`associate-r_binary64` `associate-*l/_binary64`
14×	`pow-prod-down_binary64` `add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`times-frac_binary64`
10×	`pow-exp_binary64`
8×	`flip3--_binary64` `flip--_binary64`
6×	`cbrt-undiv_binary64`
5×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `associate-l_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 138

Calls

4 calls:

9.0ms	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
7.0ms	(/.f64 (.f64 M D) (.f64 d 2))
43.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
13.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

series2.1s

Counts

4 → 12

Calls

4 calls:

461.0ms	(sqrt.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l))))
270.0ms	(/.f64 (.f64 M D) (.f64 d 2))
959.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
365.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	657	1060
1	657	1060
0	15	9
1	15	9
0	657	1060
1	657	1060
0	15	9
1	15	9
0	1	3
1	1	3
0	1739	2568
1	1739	2568
0	189	1785
1	189	1785
0	1739	2568
1	1739	2568
0	189	1785
1	189	1785
0	40	3
1	40	3
0	433	384
1	433	384
0	29	24
1	29	24
0	433	384
1	433	384
0	29	24
1	29	24
0	49	23
1	49	23
0	419	1821
1	419	1821
0	5121	1626
0	419	1821
1	419	1821
0	5121	1626
0	4971	27
1	4971	27

simplify83.0ms

Counts

150 → 150

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	881	7614
1	881	7614

prune258.0ms

Filtered

107 candidates to 150 candidates (-40.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	23	23
Picked	1	0	1
Done	0	0	0
Total	148	26	174

Merged error: 9.6b

Counts

174 → 26

localize34.0ms

Local error

Found 4 expressions with local error:

4.7b	(/.f64 (.f64 M D) (.f64 d 2))
6.0b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
6.1b	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
11.3b	(sqrt.f64 (/.f64 d l))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

214×	`add-exp-log_binary64`
136×	`prod-exp_binary64`
53×	`add-cbrt-cube_binary64`
37×	`div-exp_binary64`
36×	`cbrt-unprod_binary64`
29×	`times-frac_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
23×	`pow1_binary64`
20×	`pow-exp_binary64`
13×	`sqrt-prod_binary64` `sqrt-div_binary64`
12×	`pow-prod-down_binary64` `associate-*r/_binary64`
9×	`cbrt-undiv_binary64` `frac-times_binary64` `cbrt-prod_binary64`
6×	`associate-*l/_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`div-inv_binary64`
2×	`sub-neg_binary64` `associate-l_binary64` `rem-sqrt-square_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 163

Calls

4 calls:

8.0ms	(/.f64 (.f64 M D) (.f64 d 2))
27.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
23.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
4.0ms	(sqrt.f64 (/.f64 d l))

series2.1s

Counts

4 → 12

Calls

4 calls:

269.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.0s	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
542.0ms	(.f64 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
229.0ms	(sqrt.f64 (/.f64 d l))

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	312	282
1	312	282
0	19	45
1	19	45
0	312	282
1	312	282
0	19	45
1	19	45
0	168	9
1	168	9
0	859	1981
1	859	1981
0	162	1750
1	162	1750
0	859	1981
1	859	1981
0	162	1750
1	162	1750
0	4244	3
1	4244	3
0	1688	2406
1	1688	2406
0	217	1905
1	217	1905
0	1688	2406
1	1688	2406
0	217	1905
1	217	1905
0	4498	3
1	4498	3
0	433	384
1	433	384
0	29	24
1	29	24
0	433	384
1	433	384
0	29	24
1	29	24
0	49	23
1	49	23

simplify82.0ms

Counts

175 → 175

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	856	7258
1	856	7258

prune223.0ms

Filtered

114 candidates to 175 candidates (-53.5%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	2	23	25
Picked	1	0	1
Done	0	0	0
Total	173	28	201

Merged error: 9.4b

Counts

201 → 28

regimes488.0ms

Accuracy

19.5% (3.4b remaining)

Error of 14.4b against oracle of 11.0b and baseline of 15.3b

bsearch108.0ms

Steps

Iters	Range		Point
6	3.119565597615213e+93	1.710610778925083e+94	3.160788038203812e+93

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	149	127
1	149	127

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	8358×	body	80	nan
1.4s	8000×	body	80	valid
855.0ms	4848×	body	80	invalid

Details

analyze2.0s

sample141.0ms

simplify66.0ms

prune5.0ms

localize19.0ms

rewrite48.0ms

series1.5s

simplify88.0ms

prune223.0ms

localize28.0ms

rewrite57.0ms

series1.7s

simplify62.0ms

prune218.0ms

localize37.0ms

rewrite82.0ms

series2.1s

simplify83.0ms

prune258.0ms

localize34.0ms

rewrite73.0ms

series2.1s

simplify82.0ms

prune223.0ms

regimes488.0ms

bsearch108.0ms

simplify9.0ms

end0.0ms

sample4.4s

Profiling