Details

analyze1.8s (14.2%)

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)

sample87.0ms (0.7%)

Algorithm

1×

intervals

Results

41.0ms	64×	body	1024	valid
16.0ms	143×	body	128	valid
14.0ms	34×	body	512	valid
4.0ms	15×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify252.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (82.0ms)

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: 20.4b

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)
8.5b	(.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)))

rewrite54.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_1149`
20×	`pow1_binary64_1172`
18×	`add-cbrt-cube_binary64_1147`
15×	`*-un-lft-identity_binary64_1111`
12×	`prod-exp_binary64_1160` `add-sqr-sqrt_binary64_1133`
11×	`add-cube-cbrt_binary64_1146`
10×	`associate-r_binary64_1051`
9×	`cbrt-unprod_binary64_1144` `pow-prod-down_binary64_1182`
8×	`sqrt-prod_binary64_1127`
7×	`unpow-prod-down_binary64_1190`
4×	`sqrt-div_binary64_1128` `pow-exp_binary64_1179` `add-log-exp_binary64_1150`
3×	`times-frac_binary64_1117` `pow-unpow_binary64_1188` `div-exp_binary64_1162`
2×	`-commutative_binary64_1042` `flip-+_binary64_1085` `flip3-+_binary64_1114` `associate-l_binary64_1052` `distribute-lft-out_binary64_1062` `associate-r/_binary64_1053`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `unpow2_binary64_1176` `pow-pow_binary64_1183` `sqrt-pow1_binary64_1129` `sqr-pow_binary64_1083` `pow-to-exp_binary64_1180`

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

series886.0ms (7%)

Counts

4 → 12

Calls

4 calls:

329.0ms	(.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))))
277.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
207.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
72.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5148	2394

prune424.0ms (3.3%)

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: 15.1b

Counts

99 → 9

Compiler

Compiled 7258 to 6141 computations (15.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
8.5b	(sqrt.f64 (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)))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-prod_binary64_1127`
18×	`*-un-lft-identity_binary64_1111`
16×	`add-sqr-sqrt_binary64_1133`
12×	`sqrt-div_binary64_1128`
10×	`add-cube-cbrt_binary64_1146` `sqrt-pow1_binary64_1129` `pow1_binary64_1172`
6×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124`
4×	`add-cbrt-cube_binary64_1147` `flip-+_binary64_1085` `flip3-+_binary64_1114` `add-log-exp_binary64_1150` `distribute-lft-out_binary64_1062` `add-exp-log_binary64_1149`

Counts

4 → 76

Calls

4 calls:

13.0ms	(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 (11.9%)

Counts

4 → 12

Calls

4 calls:

508.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
488.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
260.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
259.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5153	2368

prune368.0ms (2.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	88	9	97

Merged error: 15.1b

Counts

97 → 9

Compiler

Compiled 6530 to 5471 computations (16.2% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.5b	(sqrt.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (sqrt.f64 (cbrt.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)))
17.4b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
17.4b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1111`
8×	`add-sqr-sqrt_binary64_1133` `cbrt-prod_binary64_1142` `pow1_binary64_1172`
7×	`add-cube-cbrt_binary64_1146`
6×	`sqrt-div_binary64_1128` `cbrt-div_binary64_1143`
5×	`sqrt-prod_binary64_1127`
4×	`add-cbrt-cube_binary64_1147` `flip-+_binary64_1085` `flip3-+_binary64_1114` `add-log-exp_binary64_1150` `add-exp-log_binary64_1149`
3×	`distribute-lft-out_binary64_1062` `sqrt-pow1_binary64_1129`
2×	`pow1/2_binary64_1191` `pow1/3_binary64_1193` `associate-*r/_binary64_1053`
1×	`rem-sqrt-square_binary64_1124` `pow-prod-down_binary64_1182`

Counts

4 → 57

Calls

4 calls:

13.0ms	(sqrt.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (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	(sqrt.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)))

series2.1s (16.2%)

Counts

4 → 12

Calls

4 calls:

791.0ms	(sqrt.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))))
513.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
496.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
254.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4922	2421
1	4922	2421

prune318.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Merged error: 15.1b

Counts

78 → 9

Compiler

Compiled 5364 to 4409 computations (17.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
8.5b	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.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)))

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_1172`
29×	`add-exp-log_binary64_1149`
20×	`add-cbrt-cube_binary64_1147`
19×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `pow-prod-down_binary64_1182`
13×	`*-un-lft-identity_binary64_1111`
10×	`add-sqr-sqrt_binary64_1133`
9×	`add-cube-cbrt_binary64_1146`
8×	`sqrt-prod_binary64_1127`
7×	`associate-r_binary64_1051`
6×	`cbrt-prod_binary64_1142`
4×	`sqrt-div_binary64_1128` `add-log-exp_binary64_1150`
2×	`pow1/3_binary64_1193` `flip-+_binary64_1085` `flip3-+_binary64_1114` `distribute-lft-out_binary64_1062` `associate-*r/_binary64_1053`
1×	`pow1/2_binary64_1191` `-commutative_binary64_1042` `rem-sqrt-square_binary64_1124` `associate-l*_binary64_1052` `sqrt-pow1_binary64_1129`

Counts

4 → 74

Calls

4 calls:

27.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (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)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

series816.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

313.0ms	(.f64 (.f64 (.f64 (.f64 J -2) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
258.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
126.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
118.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4933	2191
1	4933	2191

prune235.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	85	10	95

Merged error: 15.1b

Counts

95 → 10

Compiler

Compiled 3965 to 3284 computations (17.2% saved)

regimes214.0ms (1.7%)

Compiler: Compiled 2192 to 1974 computations (9.9% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (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 (24.5%)

Algorithm

1×

intervals

Results

1.3s	1992×	body	1024	valid
523.0ms	4476×	body	128	valid
427.0ms	1022×	body	512	valid
139.0ms	509×	body	256	valid
1.0ms	1×	body	2048	valid
0.0ms	1×	body	512	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 477 to 422 computations (11.5% saved)

Details

analyze1.8s (14.2%)

sample87.0ms (0.7%)

simplify252.0ms (2%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite54.0ms (0.4%)

series886.0ms (7%)

simplify83.0ms (0.7%)

prune424.0ms (3.3%)

localize19.0ms (0.1%)

rewrite52.0ms (0.4%)

series1.5s (11.9%)

simplify69.0ms (0.5%)

prune368.0ms (2.9%)

localize29.0ms (0.2%)

rewrite51.0ms (0.4%)

series2.1s (16.2%)

simplify87.0ms (0.7%)

prune318.0ms (2.5%)

localize19.0ms (0.2%)

rewrite50.0ms (0.4%)

series816.0ms (6.4%)

simplify77.0ms (0.6%)

prune235.0ms (1.8%)

regimes214.0ms (1.7%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.1s (24.5%)

Profiling