Details

analyze1.9s (17.9%)

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 (0.9%)

Algorithm

1×

intervals

Results

47.0ms	74×	body	1024	valid
15.0ms	135×	body	128	valid
12.0ms	31×	body	512	valid
4.0ms	15×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify178.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

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

Error

17.7b

Counts

2 → 1

Compiler

Compiled 48 to 44 computations (8.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 U (.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)
7.4b	(.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))))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_798`
22×	`add-cbrt-cube_binary64_796`
16×	`*-un-lft-identity_binary64_760`
15×	`pow1_binary64_821`
13×	`add-sqr-sqrt_binary64_782`
12×	`prod-exp_binary64_809` `add-cube-cbrt_binary64_795`
9×	`cbrt-unprod_binary64_793`
8×	`sqrt-prod_binary64_776`
7×	`associate-r_binary64_700` `unpow-prod-down_binary64_839`
6×	`div-exp_binary64_811` `pow-prod-down_binary64_831` `times-frac_binary64_766`
4×	`add-log-exp_binary64_799` `pow-exp_binary64_828` `sqrt-div_binary64_777`
3×	`cbrt-undiv_binary64_794` `associate-/l*_binary64_705` `pow-unpow_binary64_837`
2×	`distribute-lft-out_binary64_711` `flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734` `associate-*r/_binary64_702`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `unpow2_binary64_825` `sqrt-pow1_binary64_778` `associate-/r_binary64_704` `pow-to-exp_binary64_829` `associate-l_binary64_701` `sqr-pow_binary64_732` `pow1/2_binary64_840` `clear-num_binary64_759` `-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 91

Calls

4 calls:

19.0ms	(.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)))
7.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
6.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))

series499.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(.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))))
142.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
107.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
79.0ms	(/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2))))

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4989	2554
1	4989	2554

prune189.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Error

13.4b

Counts

104 → 7

Compiler

Compiled 3270 to 2604 computations (20.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
7.4b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-prod_binary64_776`
18×	`*-un-lft-identity_binary64_760`
16×	`add-sqr-sqrt_binary64_782`
12×	`sqrt-div_binary64_777`
10×	`sqrt-pow1_binary64_778` `add-cube-cbrt_binary64_795` `pow1_binary64_821`
6×	`rem-sqrt-square_binary64_773` `pow1/2_binary64_840`
4×	`distribute-lft-out_binary64_711` `flip3-+_binary64_763` `add-exp-log_binary64_798` `add-log-exp_binary64_799` `flip-+_binary64_734` `add-cbrt-cube_binary64_796`

Counts

4 → 76

Calls

4 calls:

9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series867.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

289.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
286.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
150.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
142.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5157	2368

prune253.0ms (2.4%)

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

Error

13.4b

Counts

95 → 8

Compiler

Compiled 4569 to 3739 computations (18.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.6b	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_760`
16×	`sqrt-prod_binary64_776`
12×	`add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795`
8×	`sqrt-div_binary64_777`
7×	`cbrt-prod_binary64_791` `pow1_binary64_821`
4×	`distribute-lft-out_binary64_711` `flip3-+_binary64_763` `add-exp-log_binary64_798` `add-log-exp_binary64_799` `flip-+_binary64_734` `add-cbrt-cube_binary64_796`
3×	`rem-sqrt-square_binary64_773` `sqrt-pow1_binary64_778` `pow1/2_binary64_840`
2×	`cbrt-div_binary64_792`
1×	`pow1/3_binary64_842`

Counts

4 → 65

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(cbrt.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)))

series714.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

286.0ms	(cbrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
144.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
142.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
142.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5106	2083

prune317.0ms (3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	77	8	85

Error

13.4b

Counts

85 → 8

Compiler

Compiled 5392 to 4444 computations (17.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.4b	(.f64 (sqrt.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)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.2b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite58.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_760`
16×	`sqrt-prod_binary64_776` `pow1_binary64_821`
13×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
12×	`add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795`
8×	`sqrt-div_binary64_777`
7×	`associate-l_binary64_701`
6×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
4×	`distribute-lft-out_binary64_711` `flip3-+_binary64_763` `add-log-exp_binary64_799` `flip-+_binary64_734`
3×	`rem-sqrt-square_binary64_773` `sqrt-pow1_binary64_778` `pow1/2_binary64_840`
2×	`associate-*l/_binary64_703`
1×	`associate-r_binary64_700` `*-commutative_binary64_691`

Counts

4 → 75

Calls

4 calls:

17.0ms	(.f64 (sqrt.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)))
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)))
8.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

series649.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(.f64 (sqrt.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)))
157.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
153.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
145.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5028	2542

prune470.0ms (4.5%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	85	10	95

Error

13.4b

Counts

95 → 10

Compiler

Compiled 7313 to 5910 computations (19.2% saved)

regimes439.0ms (4.2%)

Accuracy

Total 0.7b remaining (5.2%)

Threshold costs 0.7b (5.2%)

Compiler

Compiled 5864 to 5107 computations (12.9% 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%)

sample3.3s (32%)

Algorithm

1×

intervals

Results

1.2s	2025×	body	1024	valid
517.0ms	4463×	body	128	valid
405.0ms	971×	body	512	valid
140.0ms	536×	body	256	valid
4.0ms	5×	body	2048	valid
1.0ms	6×	body	128	invalid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 967 to 838 computations (13.3% saved)

Details

analyze1.9s (17.9%)

sample90.0ms (0.9%)

simplify178.0ms (1.7%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite51.0ms (0.5%)

series499.0ms (4.8%)

simplify70.0ms (0.7%)

prune189.0ms (1.8%)

localize17.0ms (0.2%)

rewrite48.0ms (0.5%)

series867.0ms (8.3%)

simplify65.0ms (0.6%)

prune253.0ms (2.4%)

localize24.0ms (0.2%)

rewrite49.0ms (0.5%)

series714.0ms (6.9%)

simplify70.0ms (0.7%)

prune317.0ms (3%)

localize23.0ms (0.2%)

rewrite58.0ms (0.6%)

series649.0ms (6.2%)

simplify52.0ms (0.5%)

prune470.0ms (4.5%)

regimes439.0ms (4.2%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (32%)

Profiling