Details

analyze2.2s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

sample47.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	107×	body	80	nan
3.0ms	39×	body	80	invalid

simplify73.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5296	27

prune2.0ms

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: 14.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

1.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))
10.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`associate-r_binary64` `div-exp_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`times-frac_binary64`
13×	`associate-l_binary64`
10×	`unswap-sqr_binary64` `pow-exp_binary64`
7×	`pow1_binary64` `cbrt-unprod_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `flip3--_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 120

Calls

4 calls:

9.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
13.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

712.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
762.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
254.0ms	(/.f64 (.f64 M D) (.f64 2 d))
624.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4227	9
1	4227	9
0	4227	9
1	4227	9
0	1	3
1	1	3
0	968	579
1	968	579
0	968	579
1	968	579
0	1	3
1	1	3
0	4237	417
1	4237	417
0	4237	417
1	4237	417
0	66	3
1	66	3
0	4258	9
1	4258	9
0	4258	9
1	4258	9
0	1	3
1	1	3

simplify75.0ms

Counts

132 → 132

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4986	2841
1	4986	2841

prune133.0ms

Filtered

85 candidates to 132 candidates (-55.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	124	8	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	8	133

Merged error: 6.3b

Counts

133 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

3.0b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
4.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
4.7b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
26×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64` `div-exp_binary64`
13×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64` `associate-l_binary64` `pow-exp_binary64`
6×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64` `times-frac_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`associate-r_binary64` `div-inv_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 103

Calls

4 calls:

10.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
9.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
9.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
11.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series1.4s

Counts

4 → 12

Calls

4 calls:

500.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
294.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
359.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
257.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	968	579
1	968	579
0	968	579
1	968	579
0	1	3
1	1	3
0	1229	1093
1	1229	1093
0	1229	1093
1	1229	1093
0	1	3
1	1	3
0	5196	4644
0	5196	4644
0	12	9
1	12	9
0	1611	166
1	1611	166
0	1611	166
1	1611	166
0	1	3
1	1	3

simplify94.0ms

Counts

115 → 115

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5438	2103

prune102.0ms

Filtered

71 candidates to 115 candidates (-62.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Merged error: 6.0b

Counts

123 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

4.0b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))
4.7b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`cbrt-unprod_binary64` `prod-exp_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`*-un-lft-identity_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-prod_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`associate-r_binary64` `times-frac_binary64` `div-inv_binary64`
2×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

11.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
10.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series1.1s

Counts

4 → 12

Calls

4 calls:

301.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
310.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)))
254.0ms	(/.f64 (.f64 M D) (.f64 2 d))
252.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	968	579
1	968	579
0	968	579
1	968	579
0	1	3
1	1	3
0	968	579
1	968	579
0	968	579
1	968	579
0	1	3
1	1	3
0	5232	4283
0	5232	4283
0	12	9
1	12	9
0	1119	854
1	1119	854
0	1119	854
1	1119	854
0	1	3
1	1	3

simplify94.0ms

Counts

105 → 105

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5150	1768

prune97.0ms

Filtered

64 candidates to 105 candidates (-64.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	103	12	115

Merged error: 6.0b

Counts

115 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

3.0b	(/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 (.f64 2 d) D)) 2) h) l)
4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 (.f64 2 d) D)) 2) h) l)))
4.2b	(.f64 (pow.f64 (/.f64 M (/.f64 (.f64 2 d) D)) 2) h)
5.2b	(/.f64 M (/.f64 (*.f64 2 d) D))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac_binary64`
55×	`add-exp-log_binary64`
52×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`
31×	`associate-l_binary64`
28×	`unpow-prod-down_binary64`
22×	`div-exp_binary64`
20×	`add-cbrt-cube_binary64`
15×	`prod-exp_binary64`
10×	`associate-/r*_binary64` `div-inv_binary64`
8×	`pow-exp_binary64`
7×	`cbrt-undiv_binary64`
6×	`sqrt-prod_binary64`
5×	`pow1_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`cbrt-unprod_binary64` `associate-r_binary64`
2×	`pow-to-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 150

Calls

4 calls:

14.0ms	(/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 (.f64 2 d) D)) 2) h) l)
8.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 (.f64 2 d) D)) 2) h) l)))
15.0ms	(.f64 (pow.f64 (/.f64 M (/.f64 (.f64 2 d) D)) 2) h)
8.0ms	(/.f64 M (/.f64 (*.f64 2 d) D))

series2.0s

Counts

4 → 12

Calls

4 calls:

582.0ms	(/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 (.f64 2 d) D)) 2) h) l)
297.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 (.f64 2 d) D)) 2) h) l)))
700.0ms	(.f64 (pow.f64 (/.f64 M (/.f64 (.f64 2 d) D)) 2) h)
392.0ms	(/.f64 M (/.f64 (*.f64 2 d) D))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	2696	72
1	2696	72
0	2696	72
1	2696	72
0	1	3
1	1	3
0	3385	269
1	3385	269
0	3385	269
1	3385	269
0	1	3
1	1	3
0	5314	4035
0	5314	4035
0	12	9
1	12	9
0	2347	59
1	2347	59
0	2347	59
1	2347	59
0	1	3
1	1	3

simplify113.0ms

Counts

162 → 162

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5022	2990

prune160.0ms

Filtered

121 candidates to 162 candidates (-33.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	161	13	174

Merged error: 5.9b

Counts

174 → 13

regimes518.0ms

Accuracy

13.4% (2.0b remaining)

Error of 9.0b against oracle of 7.0b and baseline of 9.3b

bsearch77.0ms

Steps

Iters	Range		Point
10	2.092123146450679e+110	6.862646012494848e+122	1.0141823989288172e+115
7	-8.039836526493177e-53	-8.15352816014629e-55	-7.930935168441951e-53

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	135	77
1	135	77

end0.0ms

sample1.4s

Algorithm

intervals

Results

592.0ms	8000×	body	80	valid
247.0ms	3155×	body	80	nan
110.0ms	1347×	body	80	invalid

Details

analyze2.2s

sample47.0ms

simplify73.0ms

prune2.0ms

localize13.0ms

rewrite41.0ms

series2.4s

simplify75.0ms

prune133.0ms

localize13.0ms

rewrite43.0ms

series1.4s

simplify94.0ms

prune102.0ms

localize13.0ms

rewrite43.0ms

series1.1s

simplify94.0ms

prune97.0ms

localize13.0ms

rewrite53.0ms

series2.0s

simplify113.0ms

prune160.0ms

regimes518.0ms

bsearch77.0ms

simplify9.0ms

end0.0ms

sample1.4s

Profiling