Details

analyze1.8s (10.1%)

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 (0.4%)

Algorithm

1×

intervals

Results

33.0ms	60×	body	1024	valid
16.0ms	143×	body	128	valid
14.0ms	35×	body	512	valid
5.0ms	18×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify183.0ms (1%)

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

Merged error: 19.1b

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)
7.6b	(.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))))
10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite51.0ms (0.3%)

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)))
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)))

series1.6s (8.8%)

Counts

4 → 54

Calls

4 calls:

648.0ms	(.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))))
464.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
337.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
126.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

Compiler

Compiled 2451 to 2198 computations (10.3% saved)

simplify62.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4957	3747
1	4957	3747

prune271.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	131	9	140
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	131	10	141

Merged error: 8.3b

Counts

141 → 10

Compiler

Compiled 4365 to 3378 computations (22.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
1.8b	(.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)))
16.5b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
16.5b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_760`
14×	`pow1_binary64_821`
13×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `cbrt-prod_binary64_791`
11×	`add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795`
7×	`sqrt-prod_binary64_776`
6×	`prod-exp_binary64_809` `cbrt-div_binary64_792` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
4×	`add-log-exp_binary64_799`
3×	`pow1/3_binary64_842` `distribute-lft-out_binary64_711` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-l_binary64_701`
2×	`rem-sqrt-square_binary64_773` `sqrt-pow1_binary64_778` `sqrt-div_binary64_777`
1×	`associate-r_binary64_700` `pow1/2_binary64_840` `*-commutative_binary64_691`

Counts

4 → 70

Calls

4 calls:

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

series2.8s (15.9%)

Counts

4 → 58

Calls

4 calls:

948.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
688.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
673.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
530.0ms	(.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)))

Compiler

Compiled 5527 to 4845 computations (12.3% saved)

simplify86.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4964	4654
1	4964	4654

prune418.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	127	11	138

Merged error: 8.3b

Counts

138 → 11

Compiler

Compiled 6785 to 5358 computations (21% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(sqrt.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/3))
1.8b	(.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)))
16.5b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
17.3b	(pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/3)

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_760`
14×	`add-exp-log_binary64_798` `pow1_binary64_821`
13×	`add-cbrt-cube_binary64_796`
12×	`add-sqr-sqrt_binary64_782`
10×	`add-cube-cbrt_binary64_795`
9×	`unpow-prod-down_binary64_839`
8×	`sqrt-prod_binary64_776`
6×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
4×	`add-log-exp_binary64_799` `cbrt-prod_binary64_791`
3×	`rem-sqrt-square_binary64_773` `distribute-lft-out_binary64_711` `associate-l_binary64_701` `sqr-pow_binary64_732` `pow-unpow_binary64_837`
2×	`cbrt-div_binary64_792`
1×	`pow1/3_binary64_842` `flip3-+_binary64_763` `sqrt-pow1_binary64_778` `pow-exp_binary64_828` `flip-+_binary64_734` `pow-to-exp_binary64_829` `unpow1/3_binary64_827` `associate-r_binary64_700` `pow1/2_binary64_840` `*-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 74

Calls

4 calls:

9.0ms	(pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/3)
9.0ms	(sqrt.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/3))
8.0ms	(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)))

series2.8s (15.9%)

Counts

4 → 58

Calls

4 calls:

961.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
679.0ms	(pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/3)
669.0ms	(sqrt.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)) 1/3))
538.0ms	(.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)))

Compiler

Compiled 5573 to 4891 computations (12.2% saved)

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4989	4570
1	4989	4570

prune415.0ms (2.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	132	11	143

Merged error: 8.3b

Counts

143 → 11

Compiler

Compiled 6901 to 5465 computations (20.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.6b	(.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)))
10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite59.0ms (0.3%)

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)))
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)))

series2.3s (12.8%)

Counts

4 → 78

Calls

4 calls:

709.0ms	(.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)))
535.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
528.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
524.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

Compiler

Compiled 9020 to 7543 computations (16.4% saved)

simplify110.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4950	4825
1	4950	4825

prune932.0ms (5.2%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	153	11	164

Merged error: 8.3b

Counts

164 → 11

Compiler

Compiled 12773 to 10104 computations (20.9% saved)

regimes447.0ms (2.5%)

Compiler: Compiled 4460 to 3966 computations (11.1% 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	42	126
1	42	126

end0.0ms (0%)

sample3.2s (17.7%)

Algorithm

1×

intervals

Results

1.1s	2026×	body	1024	valid
507.0ms	4472×	body	128	valid
393.0ms	1015×	body	512	valid
121.0ms	484×	body	256	valid
2.0ms	3×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 838 to 741 computations (11.6% saved)

Details

analyze1.8s (10.1%)

sample78.0ms (0.4%)

simplify183.0ms (1%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite51.0ms (0.3%)

series1.6s (8.8%)

simplify62.0ms (0.3%)

prune271.0ms (1.5%)

localize18.0ms (0.1%)

rewrite41.0ms (0.2%)

series2.8s (15.9%)

simplify86.0ms (0.5%)

prune418.0ms (2.3%)

localize24.0ms (0.1%)

rewrite44.0ms (0.2%)

series2.8s (15.9%)

simplify68.0ms (0.4%)

prune415.0ms (2.3%)

localize20.0ms (0.1%)

rewrite59.0ms (0.3%)

series2.3s (12.8%)

simplify110.0ms (0.6%)

prune932.0ms (5.2%)

regimes447.0ms (2.5%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (17.7%)

Profiling