Details

analyze263.0ms

Algorithm

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

sample43.0ms

Algorithm

intervals

Results

12.0ms	204×	body	80	valid
6.0ms	22×	body	1280	valid
6.0ms	256×	pre	80	true
3.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	9×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4969	43
1	4969	43

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 26.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.1b	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
2.4b	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
21.8b	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64` `times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
12×	`distribute-lft-out_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/l/_binary64`
8×	`frac-times_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `flip--_binary64`
5×	`associate-r_binary64`
4×	`associate-r/_binary64` `associate-l_binary64` `insert-posit16` `associate-l/_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64`
2×	`sub-neg_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 146

Calls

4 calls:

11.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
27.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
40.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
21.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

series1.5s

Counts

4 → 12

Calls

4 calls:

262.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
359.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
217.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
708.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4318	72
1	4318	72
0	4318	72
1	4318	72
0	1	3
1	1	3
0	5018	3701
0	5018	3701
0	1	3
1	1	3
0	4990	102
1	4990	102
0	4990	102
1	4990	102
0	1	3
1	1	3
0	1061	177
1	1061	177
0	1061	177
1	1061	177
0	1	3
1	1	3

simplify114.0ms

Counts

158 → 158

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5025	5874

prune263.0ms

Filtered

117 candidates to 158 candidates (-35.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	145	13	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	13	159

Merged error: 11.9b

Counts

159 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
2.0b	(/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
2.4b	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 1)

rewrite869.0ms

Algorithm

rewrite-expression-head

Rules

5126×	`times-frac_binary64`
3533×	`*-un-lft-identity_binary64`
2233×	`add-sqr-sqrt_binary64`
1787×	`add-cube-cbrt_binary64`
650×	`distribute-lft-out_binary64`
223×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
183×	`div-inv_binary64`
167×	`associate-/r/_binary64`
113×	`associate-/r*_binary64`
76×	`flip3-+_binary64` `flip-+_binary64`
41×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
28×	`div-exp_binary64`
25×	`associate-/l*_binary64`
19×	`cbrt-undiv_binary64`
6×	`add-log-exp_binary64`
5×	`associate-/l/_binary64`
4×	`pow1_binary64` `insert-posit16`
3×	`1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3--_binary64` `div-sub_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 1738

Calls

4 calls:

14.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
34.0ms	(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
74.0ms	(/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
481.0ms	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 1)

series1.1s

Counts

4 → 12

Calls

4 calls:

357.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
299.0ms	(/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))
246.0ms	(/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
193.0ms	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 1)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	5393	3975
0	5393	3975
0	1	3
1	1	3
0	4893	3880
1	4893	3880
0	4893	3880
1	4893	3880
0	1	3
1	1	3
0	4627	941
1	4627	941
0	4627	941
1	4627	941
0	1	3
1	1	3
0	4547	90
1	4547	90
0	4547	90
1	4547	90
0	1	3
1	1	3

simplify1.1s

Counts

1750 → 1750

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	5447	131823

prune2.6s

Filtered

591 candidates to 1750 candidates (-196.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	1741	9	1750
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	1751	12	1763

Merged error: 11.8b

Counts

1763 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

2.0b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
2.0b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
2.0b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
2.4b	(+.f64 1 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 3))

rewrite580.0ms

Algorithm

rewrite-expression-head

Rules

3228×	`times-frac_binary64`
2676×	`*-un-lft-identity_binary64`
1504×	`add-sqr-sqrt_binary64`
1144×	`add-cube-cbrt_binary64`
586×	`distribute-lft-out_binary64`
267×	`associate-/r*_binary64`
180×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
138×	`associate-/r/_binary64`
78×	`div-inv_binary64`
64×	`flip3-+_binary64` `flip-+_binary64`
31×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`cbrt-undiv_binary64` `div-exp_binary64`
12×	`associate-/l*_binary64`
6×	`associate-/l/_binary64` `add-log-exp_binary64`
4×	`pow1_binary64` `insert-posit16`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 1420

Calls

4 calls:

49.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
45.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
49.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
243.0ms	(+.f64 1 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

316.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
310.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
329.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
202.0ms	(+.f64 1 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 3))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	5090	4002
0	5090	4002
0	1	3
1	1	3
0	4649	1204
1	4649	1204
0	4649	1204
1	4649	1204
0	1	3
1	1	3
0	4649	1204
1	4649	1204
0	4649	1204
1	4649	1204
0	1	3
1	1	3
0	4649	1204
1	4649	1204
0	4649	1204
1	4649	1204
0	1	3
1	1	3

simplify788.0ms

Counts

1432 → 1432

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	5016	97133

prune9.1s

Filtered

717 candidates to 1432 candidates (-99.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	1430	2	1432
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	1432	12	1444

Merged error: 11.8b

Counts

1444 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

2.0b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
2.0b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
2.0b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
2.3b	(+.f64 1 (pow.f64 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 3) 3))

rewrite820.0ms

Algorithm

rewrite-expression-head

Rules

3228×	`times-frac_binary64`
2676×	`*-un-lft-identity_binary64`
1504×	`add-sqr-sqrt_binary64`
1144×	`add-cube-cbrt_binary64`
586×	`distribute-lft-out_binary64`
267×	`associate-/r*_binary64`
180×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
138×	`associate-/r/_binary64`
78×	`div-inv_binary64`
64×	`flip3-+_binary64` `flip-+_binary64`
31×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`cbrt-undiv_binary64` `div-exp_binary64`
12×	`associate-/l*_binary64`
6×	`associate-/l/_binary64` `add-log-exp_binary64`
4×	`pow1_binary64` `insert-posit16`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 1420

Calls

4 calls:

50.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
44.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
49.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
487.0ms	(+.f64 1 (pow.f64 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 3) 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

312.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
318.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
315.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
222.0ms	(+.f64 1 (pow.f64 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))) (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))))) 3) 3))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	5026	4029
0	5026	4029
0	1	3
1	1	3
0	4649	1204
1	4649	1204
0	4649	1204
1	4649	1204
0	1	3
1	1	3
0	4649	1204
1	4649	1204
0	4649	1204
1	4649	1204
0	1	3
1	1	3
0	4649	1204
1	4649	1204
0	4649	1204
1	4649	1204
0	1	3
1	1	3

simplify747.0ms

Counts

1432 → 1432

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5139	97187

prune15.5s

Filtered

717 candidates to 1432 candidates (-99.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	1430	2	1432
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	1431	13	1444

Merged error: 11.8b

Counts

1444 → 13

regimes217.0ms

Accuracy

0% (0.3b remaining)

Error of 11.7b against oracle of 11.4b and baseline of 11.7b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	81	260
1	81	260

end0.0ms

sample1.1s

Algorithm

intervals

Results

384.0ms	6440×	body	80	valid
182.0ms	8000×	pre	80	true
151.0ms	485×	body	1280	valid
136.0ms	564×	body	640	valid
58.0ms	333×	body	320	valid
23.0ms	178×	body	160	valid

Details

analyze263.0ms

sample43.0ms

simplify85.0ms

prune4.0ms

localize13.0ms

rewrite107.0ms

series1.5s

simplify114.0ms

prune263.0ms

localize15.0ms

rewrite869.0ms

series1.1s

simplify1.1s

prune2.6s

localize25.0ms

rewrite580.0ms

series1.2s

simplify788.0ms

prune9.1s

localize30.0ms

rewrite820.0ms

series1.2s

simplify747.0ms

prune15.5s

regimes217.0ms

bsearch0.0ms

simplify9.0ms

end0.0ms

sample1.1s

Profiling