Details

analyze1.7s

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample129.0ms

Algorithm

intervals

Results

53.0ms	51×	body	1280	valid
25.0ms	42×	body	640	valid
18.0ms	130×	body	80	valid
9.0ms	22×	body	320	valid
4.0ms	29×	body	80	invalid
3.0ms	11×	body	160	valid
0.0ms	4×	body	80	nan

simplify275.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	5148	32

prune9.0ms

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: 11.3b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))
6.1b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
15.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 119

Calls

4 calls:

4.0ms	(/.f64 F (sin.f64 B))
4.0ms	(/.f64 x (tan.f64 B))
17.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
205.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series1.2s

Counts

4 → 12

Calls

4 calls:

200.0ms	(/.f64 F (sin.f64 B))
212.0ms	(/.f64 x (tan.f64 B))
517.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
316.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

Iterations

Useful iterations: 0 (153.0ms)

Iter	Nodes	Cost
0	409	606
1	409	606
0	44	66
1	44	66
0	409	606
1	409	606
0	44	66
1	44	66
0	25	48
1	25	48
0	644	1092
1	644	1092
0	60	147
1	60	147
0	644	1092
1	644	1092
0	60	147
1	60	147
0	4689	3
1	4689	3
0	355	330
1	355	330
0	8	9
1	8	9
0	355	330
1	355	330
0	8	9
1	8	9
0	1	3
1	1	3
0	327	294
1	327	294
0	6	9
1	6	9
0	327	294
1	327	294
0	6	9
1	6	9
0	1	3
1	1	3

simplify196.0ms

Counts

131 → 131

Iterations

Useful iterations: 0 (158.0ms)

Iter	Nodes	Cost
0	4932	2447
1	4932	2447

prune179.0ms

Filtered

100 candidates to 131 candidates (-31.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	12	131
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	121	12	133

Merged error: 6.6b

Counts

133 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
15.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 97

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
14.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
14.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series1.3s

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 x (tan.f64 B))
310.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
516.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
306.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

Iterations

Useful iterations: 0 (233.0ms)

Iter	Nodes	Cost
0	409	606
1	409	606
0	45	69
1	45	69
0	409	606
1	409	606
0	45	69
1	45	69
0	25	48
1	25	48
0	506	801
1	506	801
0	39	30
1	39	30
0	506	801
1	506	801
0	39	30
1	39	30
0	4691	3
1	4691	3
0	619	1106
1	619	1106
0	60	39
1	60	39
0	619	1106
1	619	1106
0	60	39
1	60	39
0	28	3
1	28	3
0	355	330
1	355	330
0	8	9
1	8	9
0	355	330
1	355	330
0	8	9
1	8	9
0	1	3
1	1	3

simplify153.0ms

Counts

109 → 109

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4936	2047
1	4936	2047

prune126.0ms

Filtered

76 candidates to 109 candidates (-43.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Merged error: 6.6b

Counts

121 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
15.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

7.0ms	(/.f64 x (tan.f64 B))
18.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
13.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series1.1s

Counts

4 → 12

Calls

4 calls:

210.0ms	(/.f64 x (tan.f64 B))
336.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
298.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
303.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	409	606
1	409	606
0	45	69
1	45	69
0	409	606
1	409	606
0	45	69
1	45	69
0	25	48
1	25	48
0	556	945
1	556	945
0	69	156
1	69	156
0	556	945
1	556	945
0	69	156
1	69	156
0	64	75
1	64	75
0	644	1182
1	644	1182
0	75	45
1	75	45
0	644	1182
1	644	1182
0	75	45
1	75	45
0	54	3
1	54	3
0	355	330
1	355	330
0	8	9
1	8	9
0	355	330
1	355	330
0	8	9
1	8	9
0	1	3
1	1	3

simplify54.0ms

Counts

154 → 154

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	407	4089
1	407	4089

prune204.0ms

Filtered

120 candidates to 154 candidates (-28.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	155	11	166

Merged error: 6.6b

Counts

166 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
0.3b	(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
0.4b	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
15.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

332×	`times-frac_binary64`
199×	`add-sqr-sqrt_binary64`
177×	`*-un-lft-identity_binary64`
173×	`add-cube-cbrt_binary64`
80×	`associate-r_binary64` `unpow-prod-down_binary64`
68×	`add-exp-log_binary64`
37×	`div-exp_binary64`
32×	`associate-/r*_binary64`
28×	`sqr-pow_binary64`
20×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`
10×	`div-inv_binary64`
9×	`unswap-sqr_binary64`
8×	`pow-to-exp_binary64` `pow1_binary64` `1-exp_binary64` `rec-exp_binary64` `pow-exp_binary64`
7×	`cbrt-undiv_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
2×	`associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `inv-pow_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 315

Calls

4 calls:

34.0ms	(.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
17.0ms	(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
13.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series2.0s

Counts

4 → 12

Calls

4 calls:

599.0ms	(.f64 F (/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))))
679.0ms	(/.f64 1 (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
368.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
308.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	409	606
1	409	606
0	45	69
1	45	69
0	409	606
1	409	606
0	45	69
1	45	69
0	25	48
1	25	48
0	619	1101
1	619	1101
0	81	156
1	81	156
0	619	1101
1	619	1101
0	81	156
1	81	156
0	71	57
1	71	57
0	763	1436
1	763	1436
0	59	445
1	59	445
0	763	1436
1	763	1436
0	59	445
1	59	445
0	5900	39
0	824	1527
1	824	1527
0	4809	9
1	4809	9
0	824	1527
1	824	1527
0	4809	9
1	4809	9
0	1	3
1	1	3

simplify113.0ms

Counts

327 → 327

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	662	11655
1	662	11655

prune495.0ms

Filtered

221 candidates to 327 candidates (-48.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	325	2	327
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	325	13	338

Merged error: 6.1b

Counts

338 → 13

regimes104.0ms

Accuracy

0% (0.9b remaining)

Error of 10.2b against oracle of 9.3b and baseline of 10.2b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	35
1	41	35

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1649×	body	1280	valid
834.0ms	1419×	body	640	valid
549.0ms	3956×	body	80	valid
275.0ms	673×	body	320	valid
93.0ms	665×	body	80	invalid
84.0ms	303×	body	160	valid
11.0ms	117×	body	80	nan

Details

analyze1.7s

sample129.0ms

simplify275.0ms

prune9.0ms

localize21.0ms

rewrite237.0ms

series1.2s

simplify196.0ms

prune179.0ms

localize20.0ms

rewrite46.0ms

series1.3s

simplify153.0ms

prune126.0ms

localize20.0ms

rewrite55.0ms

series1.1s

simplify54.0ms

prune204.0ms

localize22.0ms

rewrite103.0ms

series2.0s

simplify113.0ms

prune495.0ms

regimes104.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample3.6s

Profiling