Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample29.0ms

Algorithm

intervals

Results

9.0ms	256×	pre	80	true
6.0ms	193×	body	80	valid
4.0ms	27×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	6×	body	160	valid

simplify232.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (216.0ms)

Iter	Nodes	Cost
0	4879	19
1	4879	19

prune2.0ms

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: 15.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.4b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
19×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64` `div-sub_binary64` `insert-posit16` `flip-+_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

2 → 67

Calls

2 calls:

12.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
21.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series690.0ms

Counts

2 → 6

Calls

2 calls:

220.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
470.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	403	411
1	403	411
0	9	9
1	9	9
0	403	411
1	403	411
0	9	9
1	9	9
0	5556	42
0	354	393
1	354	393
0	46	57
1	46	57
0	354	393
1	354	393
0	46	57
1	46	57
0	186	88
1	186	88

simplify40.0ms

Counts

73 → 73

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	665	1730
1	665	1730

prune83.0ms

Filtered

53 candidates to 73 candidates (-37.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	62	11	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	11	74

Merged error: 14.3b

Counts

74 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
2.4b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
24×	`distribute-lft-out_binary64` `add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
10×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64`
4×	`pow1_binary64` `diff-log_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64` `insert-posit16`
3×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`associate--r+_binary64` `associate--r-_binary64`

Counts

4 → 116

Calls

4 calls:

36.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
11.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
9.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
16.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series1.2s

Counts

4 → 12

Calls

4 calls:

339.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
214.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
208.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
465.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	360	351
1	360	351
0	10	9
1	10	9
0	360	351
1	360	351
0	10	9
1	10	9
0	5559	42
0	317	333
1	317	333
0	40	42
1	40	42
0	317	333
1	317	333
0	40	42
1	40	42
0	110	58
1	110	58
0	317	333
1	317	333
0	40	42
1	40	42
0	317	333
1	317	333
0	40	42
1	40	42
0	110	58
1	110	58
0	554	681
1	554	681
0	8	9
1	8	9
0	554	681
1	554	681
0	8	9
1	8	9
0	25	39
1	25	39

simplify46.0ms

Counts

128 → 128

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	431	2789
1	431	2789

prune157.0ms

Filtered

97 candidates to 128 candidates (-32.0%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	113	15	128
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	117	22	139

Merged error: 14.2b

Counts

139 → 22

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 beta)
0.6b	(cbrt.f64 beta)
0.6b	(cbrt.f64 beta)
2.4b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
9×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16`
3×	`pow1/3_binary64` `times-frac_binary64`
2×	`difference-of-sqr-1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt.f64 beta)
1.0ms	(cbrt.f64 beta)
1.0ms	(cbrt.f64 beta)
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series1.3s

Counts

4 → 12

Calls

4 calls:

276.0ms	(cbrt.f64 beta)
279.0ms	(cbrt.f64 beta)
280.0ms	(cbrt.f64 beta)
473.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	360	351
1	360	351
0	10	9
1	10	9
0	360	351
1	360	351
0	10	9
1	10	9
0	5559	42
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	4890	50
1	4890	50
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	4890	50
1	4890	50
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	4890	50
1	4890	50

simplify131.0ms

Counts

67 → 67

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	5100	849

prune131.0ms

Filtered

59 candidates to 67 candidates (-13.6%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	4	17	21
Picked	1	0	1
Done	0	0	0
Total	67	22	89

Merged error: 14.2b

Counts

89 → 22

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 beta)
0.6b	(cbrt.f64 beta)
0.6b	(cbrt.f64 beta)
2.4b	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`pow1/3_binary64`
1×	`flip3-+_binary64` `difference-of-sqr--1_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt.f64 beta)
1.0ms	(cbrt.f64 beta)
1.0ms	(cbrt.f64 beta)
23.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

series1.1s

Counts

4 → 12

Calls

4 calls:

277.0ms	(cbrt.f64 beta)
278.0ms	(cbrt.f64 beta)
278.0ms	(cbrt.f64 beta)
270.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	418	849
1	418	849
0	67	48
1	67	48
0	418	849
1	418	849
0	67	48
1	67	48
0	150	21
1	150	21
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	4890	50
1	4890	50
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	4890	50
1	4890	50
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	40	1603
1	40	1603
0	42	1590
1	42	1590
0	4890	50
1	4890	50

simplify89.0ms

Counts

61 → 61

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5218	675

prune120.0ms

Filtered

55 candidates to 61 candidates (-10.9%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	20	21
Picked	0	1	1
Done	0	0	0
Total	61	22	83

Merged error: 14.2b

Counts

83 → 22

regimes110.0ms

Accuracy

0% (0.5b remaining)

Error of 16.1b against oracle of 15.5b and baseline of 16.1b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	73	80
1	73	80

end0.0ms

sample705.0ms

Algorithm

intervals

Results

176.0ms	5822×	body	80	valid
128.0ms	831×	body	1280	valid
124.0ms	8000×	pre	80	true
86.0ms	737×	body	640	valid
36.0ms	412×	body	320	valid
14.0ms	198×	body	160	valid

Details

analyze2.0ms

sample29.0ms

simplify232.0ms

prune2.0ms

localize8.0ms

rewrite37.0ms

series690.0ms

simplify40.0ms

prune83.0ms

localize12.0ms

rewrite78.0ms

series1.2s

simplify46.0ms

prune157.0ms

localize21.0ms

rewrite23.0ms

series1.3s

simplify131.0ms

prune131.0ms

localize20.0ms

rewrite28.0ms

series1.1s

simplify89.0ms

prune120.0ms

regimes110.0ms

bsearch0.0ms

simplify8.0ms

end0.0ms

sample705.0ms

Profiling