Details

analyze2.1s (19.3%)

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)

sample78.0ms (0.7%)

Algorithm

1×

intervals

Results

36.0ms	64×	body	1024	valid
16.0ms	147×	body	128	valid
10.0ms	26×	body	512	valid
5.0ms	19×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify186.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

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: 18.6b

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)
6.8b	(.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))))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite50.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_798`
20×	`pow1_binary64_821`
18×	`add-cbrt-cube_binary64_796`
15×	`*-un-lft-identity_binary64_760`
12×	`prod-exp_binary64_809` `add-sqr-sqrt_binary64_782`
11×	`add-cube-cbrt_binary64_795`
10×	`associate-r_binary64_700`
9×	`cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
8×	`sqrt-prod_binary64_776`
7×	`unpow-prod-down_binary64_839`
4×	`add-log-exp_binary64_799` `pow-exp_binary64_828` `sqrt-div_binary64_777`
3×	`div-exp_binary64_811` `pow-unpow_binary64_837` `times-frac_binary64_766`
2×	`distribute-lft-out_binary64_711` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-l_binary64_701` `associate-r/_binary64_702` `-commutative_binary64_691`
1×	`rem-sqrt-square_binary64_773` `unpow2_binary64_825` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `pow-to-exp_binary64_829` `sqr-pow_binary64_732` `pow1/2_binary64_840` `pow-pow_binary64_832`

Counts

4 → 86

Calls

4 calls:

16.0ms	(.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)
5.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

series462.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(.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))))
143.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
113.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
36.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5257	2394

prune184.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	8	99

Merged error: 11.5b

Counts

99 → 8

Compiler

Compiled 3188 to 2562 computations (19.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
0.3b	(.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
6.6b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite54.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_798`
20×	`pow1_binary64_821`
18×	`add-cbrt-cube_binary64_796`
16×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
12×	`prod-exp_binary64_809`
11×	`add-cube-cbrt_binary64_795`
9×	`sqrt-prod_binary64_776` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
8×	`associate-r_binary64_700`
7×	`unpow-prod-down_binary64_839`
6×	`sqrt-div_binary64_777` `associate-*r/_binary64_702`
4×	`add-log-exp_binary64_799` `pow-exp_binary64_828` `associate-l_binary64_701`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `div-exp_binary64_811` `pow-unpow_binary64_837` `times-frac_binary64_766`
2×	`unswap-sqr_binary64_728` `distribute-lft-out_binary64_711` `*-commutative_binary64_691`
1×	`rem-sqrt-square_binary64_773` `unpow2_binary64_825` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `pow-to-exp_binary64_829` `sqr-pow_binary64_732` `pow1/2_binary64_840` `pow-pow_binary64_832`

Counts

4 → 90

Calls

4 calls:

14.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
13.0ms	(.f64 (cos.f64 (/.f64 K 2)) (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	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)

series653.0ms (6%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
171.0ms	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))))
146.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
102.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5251	2895

prune191.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	101	9	110

Merged error: 11.5b

Counts

110 → 9

Compiler

Compiled 3400 to 2733 computations (19.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.8b	(.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)))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite61.0ms (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:

16.0ms	(.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)))
11.0ms	(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)))

series637.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(.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)))
148.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
148.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
140.0ms	(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 (24.0ms)

Iter	Nodes	Cost
0	5028	2542

prune441.0ms (4.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	87	9	96

Merged error: 11.5b

Counts

96 → 9

Compiler

Compiled 7516 to 6092 computations (18.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3)
6.6b	(.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3)))
10.6b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
14.4b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`cbrt-prod_binary64_791`
13×	`pow1_binary64_821`
12×	`add-exp-log_binary64_798`
11×	`-un-lft-identity_binary64_760` `associate-r*_binary64_700`
10×	`add-cbrt-cube_binary64_796` `add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795`
8×	`sqrt-div_binary64_777` `associate-*r/_binary64_702`
6×	`cube-div_binary64_789`
4×	`prod-exp_binary64_809` `flip3-+_binary64_763` `sqrt-prod_binary64_776` `add-log-exp_binary64_799` `flip-+_binary64_734` `cbrt-div_binary64_792` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
3×	`cube-mult_binary64_790` `unpow3_binary64_826` `sqr-pow_binary64_732` `cube-prod_binary64_788` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839`
2×	`pow-exp_binary64_828` `rem-cube-cbrt_binary64_783` `pow-pow_binary64_832`
1×	`pow1/3_binary64_842` `rem-cbrt-cube_binary64_784` `rem-sqrt-square_binary64_773` `distribute-lft-out_binary64_711` `sqrt-pow1_binary64_778` `pow-to-exp_binary64_829` `associate-l_binary64_701` `pow1/2_binary64_840` `*-commutative_binary64_691`

Counts

4 → 87

Calls

4 calls:

12.0ms	(pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3)
9.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
9.0ms	(.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3)))
3.0ms	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3))

series1.1s (10.2%)

Counts

4 → 12

Calls

4 calls:

567.0ms	(pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3)
228.0ms	(cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3))
170.0ms	(.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (/.f64 K 2)) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) 3)))
146.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4927	3295
1	4927	3295

prune203.0ms (1.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	96	12	108

Merged error: 11.4b

Counts

108 → 12

Compiler

Compiled 3501 to 2837 computations (19% saved)

regimes520.0ms (4.8%)

Compiler: Compiled 6140 to 5496 computations (10.5% saved)

bsearch3.0ms (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	41	136
1	41	136

end0.0ms (0%)

sample3.5s (32.3%)

Algorithm

1×

intervals

Results

1.1s	1988×	body	1024	valid
510.0ms	4534×	body	128	valid
400.0ms	976×	body	512	valid
147.0ms	499×	body	256	valid
3.0ms	3×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	4×	body	128	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 1125 to 1001 computations (11% saved)

Details

analyze2.1s (19.3%)

sample78.0ms (0.7%)

simplify186.0ms (1.7%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite50.0ms (0.5%)

series462.0ms (4.3%)

simplify65.0ms (0.6%)

prune184.0ms (1.7%)

localize17.0ms (0.2%)

rewrite54.0ms (0.5%)

series653.0ms (6%)

simplify72.0ms (0.7%)

prune191.0ms (1.8%)

localize21.0ms (0.2%)

rewrite61.0ms (0.6%)

series637.0ms (5.9%)

simplify52.0ms (0.5%)

prune441.0ms (4.1%)

localize20.0ms (0.2%)

rewrite44.0ms (0.4%)

series1.1s (10.2%)

simplify107.0ms (1%)

prune203.0ms (1.9%)

regimes520.0ms (4.8%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (32.3%)

Profiling