Details

analyze129.0ms

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

sample37.0ms

Algorithm

intervals

Results

11.0ms	199×	body	80	valid
5.0ms	256×	pre	80	true
5.0ms	17×	body	1280	valid
5.0ms	21×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	6×	body	160	valid

simplify82.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4969	43
1	4969	43

prune3.0ms

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: 22.6b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

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))

1.8b

(+.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)

18.5b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`associate-/r/_binary64`
11×	`flip3-+_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/l/_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
5×	`add-log-exp_binary64`
4×	`frac-times_binary64`
3×	`pow1_binary64` `flip3--_binary64` `insert-posit16` `flip--_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

3 → 114

Calls

3 calls:

28.0ms

(/.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))

42.0ms

(+.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)

18.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

series20.8s

Counts

3 → 9

Calls

3 calls:

6.4s

(/.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))

10.5s

(+.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)

3.9s

(/.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	20692	895
1	20692	895
0	20692	895
1	20692	895
0	1	3
1	1	3
0	38363	1556
1	38363	1556
0	38667	1556
1	38667	1556
0	1	3
1	1	3
0	25359	1135
1	25359	1135
0	25359	1135
1	25359	1135
0	1	3
1	1	3

simplify139.0ms

Counts

123 → 123

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5103	5339

prune215.0ms

Filtered

92 candidates to 123 candidates (-33.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	111	12	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	12	124

Merged error: 13.0b

Counts

124 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))
0.1b	(/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2))
0.1b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha)))
1.8b	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2)) 1)

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

1250×	`times-frac_binary64`
1055×	`*-un-lft-identity_binary64`
619×	`add-sqr-sqrt_binary64`
461×	`add-cube-cbrt_binary64`
218×	`distribute-lft-out_binary64`
96×	`associate-/l*_binary64`
79×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
60×	`associate-/r/_binary64`
33×	`div-inv_binary64`
30×	`associate-/r*_binary64`
26×	`flip3--_binary64` `flip--_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`associate-/l/_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `insert-posit16` `flip-+_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 649

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))
52.0ms	(/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2))
20.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha)))
156.0ms	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2)) 1)

series28.6s

Counts

4 → 12

Calls

4 calls:

4.7s	(/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha))
10.5s	(/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2))
8.3s	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha)))
5.1s	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2)) 1)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	49274	2759
1	49274	2759
0	49274	2759
1	49274	2759
0	1	3
1	1	3
0	27014	895
1	27014	895
0	27014	895
1	27014	895
0	1	3
1	1	3
0	30313	1135
1	30313	1135
0	30313	1135
1	30313	1135
0	1	3
1	1	3
0	20156	712
1	20156	712
0	20156	712
1	20156	712
0	1	3
1	1	3

simplify357.0ms

Counts

661 → 661

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5065	38874

prune992.0ms

Filtered

367 candidates to 661 candidates (-80.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	653	8	661
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	660	13	673

Merged error: 13.0b

Counts

673 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
0.1b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha)))
1.8b	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) 1)
1.9b	(log.f64 (exp.f64 (+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) 1)))

rewrite452.0ms

Algorithm

rewrite-expression-head

Rules

1235×	`times-frac_binary64`
1041×	`*-un-lft-identity_binary64`
603×	`add-sqr-sqrt_binary64`
453×	`add-cube-cbrt_binary64`
219×	`distribute-lft-out_binary64`
93×	`associate-/l*_binary64`
75×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
58×	`associate-/r/_binary64`
32×	`div-inv_binary64`
25×	`associate-/r*_binary64` `flip3--_binary64` `flip--_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `log-pow_binary64`
4×	`log-prod_binary64` `insert-posit16` `exp-prod_binary64`
3×	`flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`rem-log-exp_binary64` `exp-sum_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 627

Calls

4 calls:

47.0ms	(/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
21.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha)))
153.0ms	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) 1)
154.0ms	(log.f64 (exp.f64 (+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) 1)))

series30.0s

Counts

4 → 12

Calls

4 calls:

10.5s	(/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))
8.9s	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) (-.f64 beta alpha)))
5.3s	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) 1)
5.4s	(log.f64 (exp.f64 (+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) 1)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	49551	3131
1	49551	3131
0	49551	3131
1	49551	3131
0	1	3
1	1	3
0	49274	2759
1	49274	2759
0	49274	2759
1	49274	2759
0	1	3
1	1	3
0	27014	895
1	27014	895
0	27014	895
1	27014	895
0	1	3
1	1	3
0	29834	1135
1	29834	1135
0	29834	1135
1	29834	1135
0	1	3
1	1	3

simplify359.0ms

Counts

639 → 639

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5192	38647

prune1.2s

Filtered

348 candidates to 639 candidates (-83.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	639	0	639
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	639	13	652

Merged error: 13.0b

Counts

652 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))))
0.3b	(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
0.4b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
6.9b	(+.f64 (.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))) 1)

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

603×	`times-frac_binary64`
484×	`*-un-lft-identity_binary64`
408×	`add-sqr-sqrt_binary64`
260×	`add-cube-cbrt_binary64`
219×	`sqrt-prod_binary64`
153×	`associate-r_binary64`
67×	`distribute-lft-out_binary64`
45×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
38×	`associate-/r/_binary64`
34×	`associate-l_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
25×	`associate-/l*_binary64`
21×	`flip3-+_binary64` `flip-+_binary64`
19×	`div-inv_binary64`
15×	`unswap-sqr_binary64`
14×	`associate-/r*_binary64`
13×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`sqrt-div_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`insert-posit16`
3×	`associate-/l/_binary64`
2×	`div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 489

Calls

4 calls:

141.0ms	(.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))))
16.0ms	(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
30.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
57.0ms	(+.f64 (.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))) 1)

series31.3s

Counts

4 → 12

Calls

4 calls:

9.3s	(.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))))
4.6s	(/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (*.f64 2 i)))))
8.1s	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))
9.3s	(+.f64 (.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (sqrt.f64 (+.f64 2 (+.f64 (+.f64 alpha beta) (.f64 2 i)))))) 1)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	26102	2316
1	26102	2316
0	26102	2316
1	26102	2316
0	1	3
1	1	3
0	27271	1597
1	27271	1597
0	27271	1597
1	27271	1597
0	27	21
1	27	21
0	22531	1093
1	22531	1093
0	22531	1093
1	22531	1093
0	4979	3
1	4979	3
0	27538	2307
1	27538	2307
0	27538	2307
1	27538	2307
0	1	3
1	1	3

simplify229.0ms

Counts

501 → 501

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	1361	29336
1	1361	29336

prune1.1s

Filtered

269 candidates to 501 candidates (-86.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	499	2	501
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	500	14	514

Merged error: 13.0b

Counts

514 → 14

regimes188.0ms

Accuracy

0% (0.3b remaining)

Error of 12.5b against oracle of 12.2b and baseline of 12.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	47
1	34	47

end0.0ms

sample1.1s

Algorithm

intervals

Results

362.0ms	6336×	body	80	valid
170.0ms	8000×	pre	80	true
156.0ms	524×	body	1280	valid
142.0ms	618×	body	640	valid
57.0ms	334×	body	320	valid
21.0ms	188×	body	160	valid

Details

analyze129.0ms

sample37.0ms

simplify82.0ms

prune3.0ms

localize15.0ms

rewrite94.0ms

series20.8s

simplify139.0ms

prune215.0ms

localize13.0ms

rewrite323.0ms

series28.6s

simplify357.0ms

prune992.0ms

localize16.0ms

rewrite452.0ms

series30.0s

simplify359.0ms

prune1.2s

localize15.0ms

rewrite290.0ms

series31.3s

simplify229.0ms

prune1.1s

regimes188.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample1.1s

Profiling