Details

analyze425.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

sample63.0ms

Algorithm

intervals

Results

27.0ms	107×	body	320	valid
23.0ms	147×	body	160	valid
2.0ms	28×	body	80	nan
0.0ms	2×	body	80	valid

simplify310.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (295.0ms)

Iter	Nodes	Cost
0	4794	48
1	4794	48

prune6.0ms

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: 36.3b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

8.5b	(cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)))
8.8b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
9×	`sqrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16` `sqrt-div_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `flip3--_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`associate-*r/_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`

Counts

4 → 65

Calls

4 calls:

13.0ms	(cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)))
11.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
6.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series1.0s

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)))
123.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
377.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
385.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14
0	246	1731
1	246	1731
0	246	1731
1	246	1731
0	1	3
1	1	3
0	243	1718
1	243	1718
0	243	1718
1	243	1718
0	101	25
1	101	25

simplify98.0ms

Counts

77 → 77

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4988	1536
1	4988	1536

prune158.0ms

Filtered

63 candidates to 77 candidates (-22.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	58	19	77
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	60	19	79

Merged error: 32.1b

Counts

79 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

3.0b	(-.f64 (.f64 g g) (.f64 h h))
8.5b	(cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)))
30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `pow1/3_binary64` `cbrt-prod_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(-.f64 (.f64 g g) (.f64 h h))
11.0ms	(cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
6.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

195.0ms	(-.f64 (.f64 g g) (.f64 h h))
136.0ms	(cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)))
377.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
379.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14
0	243	1718
1	243	1718
0	243	1718
1	243	1718
0	101	25
1	101	25
0	577	257
1	577	257
0	577	257
1	577	257
0	1	3
1	1	3

simplify89.0ms

Counts

70 → 70

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5573	1056

prune126.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	3	15	18
Picked	1	0	1
Done	0	0	0
Total	68	21	89

Merged error: 32.1b

Counts

89 → 21

localize18.0ms

Local error

Found 4 expressions with local error:

3.0b	(-.f64 (.f64 g g) (.f64 h h))
8.5b	(cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)))
30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `pow1/3_binary64` `cbrt-prod_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(-.f64 (.f64 g g) (.f64 h h))
11.0ms	(cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)))
6.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
6.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series1.1s

Counts

4 → 12

Calls

4 calls:

186.0ms	(-.f64 (.f64 g g) (.f64 h h))
132.0ms	(cbrt.f64 (.f64 -1/2 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a)))
374.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
377.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14
0	243	1718
1	243	1718
0	243	1718
1	243	1718
0	101	25
1	101	25
0	577	257
1	577	257
0	577	257
1	577	257
0	1	3
1	1	3

simplify83.0ms

Counts

70 → 70

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5573	1056

prune121.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	70	21	91

Merged error: 32.1b

Counts

91 → 21

localize26.0ms

Local error

Found 4 expressions with local error:

30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
30.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `insert-posit16` `flip--_binary64`

Counts

4 → 68

Calls

4 calls:

6.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
6.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
6.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
6.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series1.5s

Counts

4 → 12

Calls

4 calls:

377.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
376.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
377.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
376.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

Iterations

Useful iterations: 0 (163.0ms)

Iter	Nodes	Cost
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14
0	649	571
1	649	571
0	649	571
1	649	571
0	4858	14
1	4858	14

simplify85.0ms

Counts

80 → 80

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5477	1140

prune112.0ms

Filtered

64 candidates to 80 candidates (-25.0%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	19	20
Picked	0	1	1
Done	0	0	0
Total	79	22	101

Merged error: 32.1b

Counts

101 → 22

regimes322.0ms

Accuracy

80.4% (0.6b remaining)

Error of 32.2b against oracle of 31.7b and baseline of 34.5b

bsearch87.0ms

Steps

Iters	Range		Point
10	6.110555726927762e-174	2.3955688604852036e-157	1.5431160917667745e-162

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	59	81
1	59	81

end0.0ms

sample1.9s

Algorithm

intervals

Results

913.0ms	3822×	body	320	valid
642.0ms	4024×	body	160	valid
97.0ms	1212×	body	80	nan
13.0ms	154×	body	80	valid

Details

analyze425.0ms

sample63.0ms

simplify310.0ms

prune6.0ms

localize16.0ms

rewrite37.0ms

series1.0s

simplify98.0ms

prune158.0ms

localize18.0ms

rewrite29.0ms

series1.1s

simplify89.0ms

prune126.0ms

localize18.0ms

rewrite29.0ms

series1.1s

simplify83.0ms

prune121.0ms

localize26.0ms

rewrite25.0ms

series1.5s

simplify85.0ms

prune112.0ms

regimes322.0ms

bsearch87.0ms

simplify7.0ms

end0.0ms

sample1.9s

Profiling