Details

analyze1.8s (14%)

Algorithm

1×

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
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 25 to 23 computations (8% saved)

sample85.0ms (0.7%)

Algorithm

1×

intervals

Results

39.0ms	61×	body	1024	valid
16.0ms	140×	body	128	valid
15.0ms	36×	body	512	valid
5.0ms	19×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify242.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune3.0ms (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: 18.2b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
7.2b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite53.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_786`
20×	`pow1_binary64_809`
18×	`add-cbrt-cube_binary64_784`
15×	`*-un-lft-identity_binary64_751`
12×	`prod-exp_binary64_797` `add-sqr-sqrt_binary64_772`
11×	`add-cube-cbrt_binary64_783`
10×	`associate-r_binary64_693`
9×	`pow-prod-down_binary64_819` `cbrt-unprod_binary64_781`
8×	`sqrt-prod_binary64_766`
7×	`unpow-prod-down_binary64_827`
4×	`pow-exp_binary64_816` `add-log-exp_binary64_787` `sqrt-div_binary64_767`
3×	`times-frac_binary64_757` `pow-unpow_binary64_825` `div-exp_binary64_799`
2×	`distribute-lft-out_binary64_704` `flip3-+_binary64_754` `-commutative_binary64_684` `associate-r/_binary64_695` `associate-l_binary64_694` `flip-+_binary64_725`
1×	`pow-to-exp_binary64_817` `unpow2_binary64_813` `sqr-pow_binary64_723` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `pow-pow_binary64_820` `div-inv_binary64_748` `sqrt-pow1_binary64_768`

Counts

4 → 86

Calls

4 calls:

20.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

series871.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

316.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
268.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
220.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
66.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5201	2385

prune386.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 11.3b

Counts

99 → 9

Compiler

Compiled 3197 to 2576 computations (19.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-prod_binary64_766`
18×	`*-un-lft-identity_binary64_751`
16×	`add-sqr-sqrt_binary64_772`
12×	`sqrt-div_binary64_767`
10×	`add-cube-cbrt_binary64_783` `pow1_binary64_809` `sqrt-pow1_binary64_768`
6×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828`
4×	`distribute-lft-out_binary64_704` `flip3-+_binary64_754` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786` `flip-+_binary64_725`

Counts

4 → 76

Calls

4 calls:

12.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series1.5s (12%)

Counts

4 → 12

Calls

4 calls:

513.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
505.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
261.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
261.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4952	2368
1	4952	2368

prune248.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	87	10	97

Merged error: 11.3b

Counts

97 → 10

Compiler

Compiled 4636 to 3799 computations (18.1% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.4b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.9b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_751`
16×	`sqrt-prod_binary64_766`
12×	`add-sqr-sqrt_binary64_772`
9×	`add-cube-cbrt_binary64_783`
8×	`sqrt-div_binary64_767`
7×	`cbrt-prod_binary64_779` `pow1_binary64_809`
4×	`distribute-lft-out_binary64_704` `flip3-+_binary64_754` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786` `flip-+_binary64_725`
3×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `sqrt-pow1_binary64_768`
2×	`cbrt-div_binary64_780`
1×	`pow1/3_binary64_830`

Counts

4 → 65

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series1.3s (10.1%)

Counts

4 → 12

Calls

4 calls:

499.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
269.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
265.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
261.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5025	2199

prune332.0ms (2.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	77	10	87

Merged error: 11.3b

Counts

87 → 10

Compiler

Compiled 5531 to 4564 computations (17.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.6b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))
15.7b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
15.7b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_751`
14×	`pow1_binary64_809`
13×	`cbrt-prod_binary64_779` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
11×	`add-sqr-sqrt_binary64_772`
9×	`add-cube-cbrt_binary64_783`
7×	`sqrt-prod_binary64_766`
6×	`prod-exp_binary64_797` `pow-prod-down_binary64_819` `cbrt-unprod_binary64_781` `cbrt-div_binary64_780`
4×	`add-log-exp_binary64_787`
3×	`pow1/3_binary64_830` `distribute-lft-out_binary64_704` `flip3-+_binary64_754` `associate-l_binary64_694` `flip-+_binary64_725`
2×	`rem-sqrt-square_binary64_764` `sqrt-div_binary64_767` `sqrt-pow1_binary64_768`
1×	`pow1/2_binary64_828` `-commutative_binary64_684` `associate-r*_binary64_693`

Counts

4 → 70

Calls

4 calls:

10.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
7.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))

series1.8s (14.1%)

Counts

4 → 12

Calls

4 calls:

513.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
506.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
493.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
304.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J -2)))

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4889	2721
1	4889	2721

prune218.0ms (1.7%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	81	11	92

Merged error: 11.2b

Counts

92 → 11

Compiler

Compiled 4104 to 3325 computations (19% saved)

regimes254.0ms (2%)

Compiler: Compiled 2798 to 2484 computations (11.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 24 to 22 computations (8.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	152
1	46	152

end0.0ms (0%)

sample3.2s (24.8%)

Algorithm

1×

intervals

Results

1.3s	2004×	body	1024	valid
539.0ms	4542×	body	128	valid
427.0ms	986×	body	512	valid
126.0ms	466×	body	256	valid
2.0ms	2×	body	2048	valid
1.0ms	2×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 578 to 507 computations (12.3% saved)

Details

analyze1.8s (14%)

sample85.0ms (0.7%)

simplify242.0ms (1.9%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite53.0ms (0.4%)

series871.0ms (6.8%)

simplify58.0ms (0.5%)

prune386.0ms (3%)

localize19.0ms (0.1%)

rewrite52.0ms (0.4%)

series1.5s (12%)

simplify66.0ms (0.5%)

prune248.0ms (1.9%)

localize27.0ms (0.2%)

rewrite52.0ms (0.4%)

series1.3s (10.1%)

simplify63.0ms (0.5%)

prune332.0ms (2.6%)

localize20.0ms (0.2%)

rewrite46.0ms (0.4%)

series1.8s (14.1%)

simplify106.0ms (0.8%)

prune218.0ms (1.7%)

regimes254.0ms (2%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (24.8%)

Profiling