Details

analyze1.9s (14.8%)

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)

sample91.0ms (0.7%)

Algorithm

1×

intervals

Results

46.0ms	67×	body	1024	valid
17.0ms	145×	body	128	valid
13.0ms	31×	body	512	valid
4.0ms	13×	body	256	valid

Compiler

Compiled 49 to 48 computations (2% saved)

simplify244.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4871	37
1	4871	37

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: 15.9b

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)
4.6b	(.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)))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64_1460`
20×	`pow1_binary64_1483`
18×	`add-cbrt-cube_binary64_1458`
15×	`*-un-lft-identity_binary64_1425`
12×	`prod-exp_binary64_1471` `add-sqr-sqrt_binary64_1446`
11×	`add-cube-cbrt_binary64_1457`
10×	`associate-r_binary64_1367`
9×	`cbrt-unprod_binary64_1455` `pow-prod-down_binary64_1493`
8×	`sqrt-prod_binary64_1440`
7×	`unpow-prod-down_binary64_1501`
4×	`sqrt-div_binary64_1441` `pow-exp_binary64_1490` `add-log-exp_binary64_1461`
3×	`times-frac_binary64_1431` `pow-unpow_binary64_1499` `div-exp_binary64_1473`
2×	`associate-l_binary64_1368` `flip3-+_binary64_1428` `associate-r/_binary64_1369` `distribute-lft-out_binary64_1378` `flip-+_binary64_1399` `-commutative_binary64_1358`
1×	`pow-pow_binary64_1494` `pow-to-exp_binary64_1491` `pow1/2_binary64_1502` `unpow2_binary64_1487` `sqrt-pow1_binary64_1442` `div-inv_binary64_1422` `rem-sqrt-square_binary64_1438` `sqr-pow_binary64_1397`

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

series864.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

306.0ms	(.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))))
272.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
218.0ms	(pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)
67.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5201	2385

prune207.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	10	99

Merged error: 11.0b

Counts

99 → 10

Compiler

Compiled 3268 to 2636 computations (19.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
4.5b	(sqrt.f64 (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)))

rewrite53.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`sqrt-prod_binary64_1440`
18×	`*-un-lft-identity_binary64_1425`
16×	`add-sqr-sqrt_binary64_1446`
12×	`sqrt-div_binary64_1441`
10×	`add-cube-cbrt_binary64_1457` `sqrt-pow1_binary64_1442` `pow1_binary64_1483`
6×	`pow1/2_binary64_1502` `rem-sqrt-square_binary64_1438`
4×	`flip3-+_binary64_1428` `distribute-lft-out_binary64_1378` `add-cbrt-cube_binary64_1458` `flip-+_binary64_1399` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`

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)))

series1.5s (11.8%)

Counts

4 → 12

Calls

4 calls:

502.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
494.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2))))
272.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
266.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4952	2368
1	4952	2368

prune275.0ms (2.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	86	12	98

Merged error: 10.9b

Counts

98 → 12

Compiler

Compiled 4785 to 3926 computations (18% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.5b	(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))))))
10.3b	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
14.4b	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
14.4b	(cbrt.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

13×	`*-un-lft-identity_binary64_1425`
8×	`cbrt-prod_binary64_1453` `add-sqr-sqrt_binary64_1446` `pow1_binary64_1483`
7×	`add-cube-cbrt_binary64_1457`
6×	`cbrt-div_binary64_1454` `sqrt-div_binary64_1441`
5×	`sqrt-prod_binary64_1440`
4×	`flip3-+_binary64_1428` `add-cbrt-cube_binary64_1458` `flip-+_binary64_1399` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
3×	`distribute-lft-out_binary64_1378` `sqrt-pow1_binary64_1442`
2×	`pow1/2_binary64_1502` `associate-*r/_binary64_1369` `pow1/3_binary64_1504`
1×	`rem-sqrt-square_binary64_1438` `pow-prod-down_binary64_1493`

Counts

4 → 57

Calls

4 calls:

14.0ms	(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 (16.1%)

Counts

4 → 12

Calls

4 calls:

829.0ms	(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))))))
509.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
499.0ms	(cbrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
262.0ms	(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

69 → 69

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4910	2421
1	4910	2421

prune297.0ms (2.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	69	12	81

Merged error: 10.9b

Counts

81 → 12

Compiler

Compiled 5150 to 4216 computations (18.1% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

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)))
10.3b	(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

16×	`sqrt-prod_binary64_1440` `*-un-lft-identity_binary64_1425`
12×	`add-sqr-sqrt_binary64_1446`
8×	`add-cube-cbrt_binary64_1457` `sqrt-div_binary64_1441` `pow1_binary64_1483`
4×	`flip3-+_binary64_1428` `pow1/2_binary64_1502` `distribute-lft-out_binary64_1378` `add-cbrt-cube_binary64_1458` `sqrt-pow1_binary64_1442` `flip-+_binary64_1399` `rem-sqrt-square_binary64_1438` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`

Counts

4 → 64

Calls

4 calls:

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)))
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)))

series1.0s (8%)

Counts

4 → 12

Calls

4 calls:

276.0ms	(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)))
255.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))
250.0ms	(sqrt.f64 (+.f64 1 (pow.f64 (/.f64 U (.f64 (.f64 2 J) (cos.f64 (/.f64 K 2)))) 2)))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5044	1980

prune412.0ms (3.2%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	76	12	88

Merged error: 10.9b

Counts

88 → 12

Compiler

Compiled 6516 to 5371 computations (17.6% saved)

regimes268.0ms (2.1%)

Compiler: Compiled 3218 to 2838 computations (11.8% 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%)

sample3.2s (24.4%)

Algorithm

1×

intervals

Results

1.3s	2012×	body	1024	valid
517.0ms	4487×	body	128	valid
412.0ms	987×	body	512	valid
134.0ms	510×	body	256	valid
5.0ms	4×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 648 to 566 computations (12.7% saved)

Details

analyze1.9s (14.8%)

sample91.0ms (0.7%)

simplify244.0ms (1.9%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite49.0ms (0.4%)

series864.0ms (6.6%)

simplify60.0ms (0.5%)

prune207.0ms (1.6%)

localize19.0ms (0.1%)

rewrite53.0ms (0.4%)

series1.5s (11.8%)

simplify66.0ms (0.5%)

prune275.0ms (2.1%)

localize28.0ms (0.2%)

rewrite52.0ms (0.4%)

series2.1s (16.1%)

simplify83.0ms (0.6%)

prune297.0ms (2.3%)

localize25.0ms (0.2%)

rewrite52.0ms (0.4%)

series1.0s (8%)

simplify68.0ms (0.5%)

prune412.0ms (3.2%)

regimes268.0ms (2.1%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (24.4%)

Profiling