Details

analyze1.9s (14.6%)

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)

sample90.0ms (0.7%)

Algorithm

1×

intervals

Results

38.0ms	58×	body	1024	valid
22.0ms	148×	body	128	valid
13.0ms	32×	body	512	valid
5.0ms	18×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify239.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

prune4.0ms (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: 24.4b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize16.0ms (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)
10.1b	(.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))))
12.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite49.0ms (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:

17.0ms	(.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))))
9.0ms	(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)
6.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

series830.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

305.0ms	(.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))))
257.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
203.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
65.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5201	2385

prune190.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	92	7	99

Merged error: 17.1b

Counts

99 → 7

Compiler

Compiled 3125 to 2512 computations (19.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

10.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
10.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
12.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
12.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite49.0ms (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:

10.0ms	(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)))

series1.7s (13%)

Counts

4 → 12

Calls

4 calls:

484.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
482.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
455.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
253.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4952	2368
1	4952	2368

prune260.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	87	8	95

Merged error: 17.1b

Counts

95 → 8

Compiler

Compiled 4548 to 3722 computations (18.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

10.2b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
12.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
12.7b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
19.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary64_766`
26×	`cbrt-prod_binary64_779`
25×	`*-un-lft-identity_binary64_751`
19×	`add-sqr-sqrt_binary64_772`
15×	`add-cube-cbrt_binary64_783`
12×	`sqrt-div_binary64_767`
10×	`unpow-prod-down_binary64_827` `cube-prod_binary64_776`
8×	`pow1_binary64_809`
6×	`sqrt-pow1_binary64_768`
5×	`distribute-lft-out_binary64_704`
4×	`flip3-+_binary64_754` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786` `flip-+_binary64_725`
2×	`cube-div_binary64_777` `cbrt-div_binary64_780`
1×	`rem-cbrt-cube_binary64_774` `cube-mult_binary64_778` `pow1/3_binary64_830` `sqr-pow_binary64_723` `unpow3_binary64_814`

Counts

4 → 91

Calls

4 calls:

15.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3))
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 (11.6%)

Counts

4 → 12

Calls

4 calls:

493.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
482.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3))
270.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
248.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4984	3137
1	4984	3137

prune324.0ms (2.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	103	8	111

Merged error: 17.1b

Counts

111 → 8

Compiler

Compiled 5536 to 4571 computations (17.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
2.8b	(.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)))
20.6b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
20.6b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite48.0ms (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:

12.0ms	(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:

515.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
503.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
495.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
302.0ms	(.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)))

simplify103.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4889	2721
1	4889	2721

prune227.0ms (1.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	82	8	90

Merged error: 17.1b

Counts

90 → 8

Compiler

Compiled 4104 to 3325 computations (19% saved)

regimes175.0ms (1.4%)

Compiler: Compiled 1796 to 1614 computations (10.1% 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%)

sample3.1s (24%)

Algorithm

1×

intervals

Results

1.3s	2013×	body	1024	valid
559.0ms	4524×	body	128	valid
424.0ms	980×	body	512	valid
134.0ms	480×	body	256	valid
3.0ms	3×	body	2048	valid
1.0ms	2×	body	512	invalid
1.0ms	1×	body	1024	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 411 to 362 computations (11.9% saved)

Details

analyze1.9s (14.6%)

sample90.0ms (0.7%)

simplify239.0ms (1.9%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite49.0ms (0.4%)

series830.0ms (6.4%)

simplify55.0ms (0.4%)

prune190.0ms (1.5%)

localize23.0ms (0.2%)

rewrite49.0ms (0.4%)

series1.7s (13%)

simplify65.0ms (0.5%)

prune260.0ms (2%)

localize22.0ms (0.2%)

rewrite58.0ms (0.4%)

series1.5s (11.6%)

simplify83.0ms (0.6%)

prune324.0ms (2.5%)

localize19.0ms (0.2%)

rewrite48.0ms (0.4%)

series1.8s (14.1%)

simplify103.0ms (0.8%)

prune227.0ms (1.8%)

regimes175.0ms (1.4%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (24%)

Profiling