Details

analyze75.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

sample25.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
1.0ms	11×	body	80	invalid
1.0ms	10×	body	80	nan

simplify121.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	1031	21
1	1031	21

prune5.0ms

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: 0.1b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
8×	`associate-*l/_binary64`
7×	`associate-r_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`sqrt-prod_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `insert-posit16` `frac-times_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `associate-r/_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 103

Calls

4 calls:

9.0ms	(*.f64 (-.f64 a 1/3) 9)
18.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
10.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series1.6s

Counts

4 → 12

Calls

4 calls:

253.0ms	(*.f64 (-.f64 a 1/3) 9)
640.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
397.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
338.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	506	562
1	506	562
0	506	562
1	506	562
0	5409	14
0	738	198
1	738	198
0	738	198
1	738	198
0	5172	3
0	1924	477
1	1924	477
0	1924	477
1	1924	477
0	5110	25
0	270	102
1	270	102
0	270	102
1	270	102
0	5174	18

simplify105.0ms

Counts

115 → 115

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5651	1965

prune139.0ms

Filtered

90 candidates to 115 candidates (-27.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	107	8	115
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 0.0b

Counts

117 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
8.7b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64` `associate-*l/_binary64`
8×	`sqrt-prod_binary64`
6×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 115

Calls

4 calls:

9.0ms	(*.f64 (-.f64 a 1/3) 9)
10.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
22.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

series1.5s

Counts

4 → 12

Calls

4 calls:

245.0ms	(*.f64 (-.f64 a 1/3) 9)
407.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
331.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
483.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	1045	432
1	1045	432
0	1045	432
1	1045	432
0	5110	25
0	506	562
1	506	562
0	506	562
1	506	562
0	5409	14
0	738	198
1	738	198
0	738	198
1	738	198
0	5172	3
0	270	102
1	270	102
0	270	102
1	270	102
0	5174	18

simplify154.0ms

Counts

127 → 127

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4921	2019
1	4921	2019

prune136.0ms

Filtered

100 candidates to 127 candidates (-27.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	128	7	135

Merged error: 0b

Counts

135 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 a 1/3)
0.0b	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
0.4b	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
0.5b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

145×	`add-sqr-sqrt_binary64`
115×	`*-un-lft-identity_binary64`
110×	`times-frac_binary64`
70×	`sqrt-prod_binary64`
57×	`add-cube-cbrt_binary64`
46×	`associate-l_binary64`
29×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-r_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-log-exp_binary64`
9×	`pow1_binary64` `unswap-sqr_binary64`
8×	`associate-/r*_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`frac-add_binary64`
5×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-/r/_binary64` `prod-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`associate-r/_binary64` `div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `pow-div_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 206

Calls

4 calls:

4.0ms	(-.f64 a 1/3)
9.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
37.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
16.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

series1.2s

Counts

4 → 12

Calls

4 calls:

183.0ms	(-.f64 a 1/3)
320.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
278.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
426.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	1132	1170
1	1132	1170
0	1132	1170
1	1132	1170
0	5151	17
0	1020	428
1	1020	428
0	1020	428
1	1020	428
0	1	3
1	1	3
0	1168	238
1	1168	238
0	1168	238
1	1168	238
0	1	3
1	1	3
0	237	84
1	237	84
0	237	84
1	237	84
0	5061	15

simplify97.0ms

Counts

218 → 218

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5394	4088

prune220.0ms

Filtered

143 candidates to 218 candidates (-52.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	219	6	225

Merged error: 0b

Counts

225 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.0b	(+.f64 (-.f64 a 1/3) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand (sqrt.f64 9))))
0.4b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand (sqrt.f64 9)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
22×	`associate-r_binary64` `times-frac_binary64`
19×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
13×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
12×	`sqrt-div_binary64`
10×	`frac-add_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-l_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-*l/_binary64`
4×	`insert-posit16`
3×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`cbrt-unprod_binary64` `prod-exp_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 109

Calls

4 calls:

4.0ms	(-.f64 a 1/3)
4.0ms	(-.f64 a 1/3)
9.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand (sqrt.f64 9))))
17.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand (sqrt.f64 9)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(-.f64 a 1/3)
193.0ms	(-.f64 a 1/3)
258.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand (sqrt.f64 9))))
213.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand (sqrt.f64 9)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	713	444
1	713	444
0	713	444
1	713	444
0	1	3
1	1	3
0	861	138
1	861	138
0	861	138
1	861	138
0	1	3
1	1	3
0	237	84
1	237	84
0	237	84
1	237	84
0	5061	15
0	237	84
1	237	84
0	237	84
1	237	84
0	5061	15

simplify132.0ms

Counts

121 → 121

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5011	2135

prune108.0ms

Filtered

91 candidates to 121 candidates (-33.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	122	5	127

Merged error: 0b

Counts

127 → 5

regimes28.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	24
1	24	24

end0.0ms

sample617.0ms

Algorithm

intervals

Results

447.0ms	8000×	body	80	valid
15.0ms	273×	body	80	invalid
14.0ms	276×	body	80	nan

Details

analyze75.0ms

sample25.0ms

simplify121.0ms

prune5.0ms

localize9.0ms

rewrite48.0ms

series1.6s

simplify105.0ms

prune139.0ms

localize9.0ms

rewrite52.0ms

series1.5s

simplify154.0ms

prune136.0ms

localize13.0ms

rewrite80.0ms

series1.2s

simplify97.0ms

prune220.0ms

localize8.0ms

rewrite41.0ms

series853.0ms

simplify132.0ms

prune108.0ms

regimes28.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample617.0ms

Profiling