Details

analyze2.3s (13%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample92.0ms (0.5%)

Algorithm

1×

intervals

Results

20.0ms	194×	body	128	valid
18.0ms	24×	body	1024	valid
11.0ms	107×	body	128	invalid
7.0ms	20×	body	512	valid
6.0ms	11×	body	1024	invalid
5.0ms	14×	body	512	invalid
4.0ms	18×	body	256	valid
2.0ms	8×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify296.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	4986	49
1	4986	49

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 37.5b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite90.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_1370`
102×	`flip--_binary64_1400` `flip3--_binary64_1429`
68×	`frac-times_binary64_1435`
66×	`sqrt-div_binary64_1441`
64×	`frac-add_binary64_1433`
44×	`pow1_binary64_1483`
34×	`associate-*r/_binary64_1369`
17×	`pow-prod-down_binary64_1493`
16×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
8×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455`
6×	`add-sqr-sqrt_binary64_1446`
5×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
4×	`pow-sqr_binary64_1398` `add-log-exp_binary64_1461` `pow-prod-up_binary64_1492`
3×	`sqrt-prod_binary64_1440`
2×	`pow-plus_binary64_1485`
1×	`associate-l_binary64_1368` `flip3-+_binary64_1428` `pow1/2_binary64_1502` `pow2_binary64_1503` `associate-r_binary64_1367` `sqrt-pow1_binary64_1442` `flip-+_binary64_1399` `swap-sqr_binary64_1392` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358`

Counts

4 → 135

Calls

4 calls:

24.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
15.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.6s (9.3%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
298.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5181	10334

prune311.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	7	148

Merged error: 24.2b

Counts

148 → 7

Compiler

Compiled 8786 to 2934 computations (66.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite120.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip--_binary64_1400` `flip3--_binary64_1429`
196×	`frac-times_binary64_1435`
138×	`sqrt-div_binary64_1441`
136×	`frac-add_binary64_1433`
130×	`associate-*l/_binary64_1370`
74×	`associate-*r/_binary64_1369`
73×	`cos-mult_binary64_1576`
12×	`add-sqr-sqrt_binary64_1446` `pow1_binary64_1483`
9×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
6×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
4×	`add-log-exp_binary64_1461`
3×	`associate-l_binary64_1368` `associate-r_binary64_1367` `sqrt-prod_binary64_1440` `swap-sqr_binary64_1392`
1×	`unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `pow-plus_binary64_1485` `flip3-+_binary64_1428` `pow1/2_binary64_1502` `cbrt-unprod_binary64_1455` `pow2_binary64_1503` `sqrt-pow1_binary64_1442` `pow-sqr_binary64_1398` `flip-+_binary64_1399` `sqr-cos-a_binary64_1571` `rem-sqrt-square_binary64_1438` `*-commutative_binary64_1358` `pow-prod-up_binary64_1492` `pow-prod-down_binary64_1493`

Counts

4 → 192

Calls

4 calls:

33.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

series1.4s (8%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
61.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify218.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4942	17322
1	4942	17322

prune473.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	202	9	211

Merged error: 23.7b

Counts

211 → 9

Compiler

Compiled 13642 to 4258 computations (68.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
34.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))

rewrite60.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

20.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
20.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.7s (15.2%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5087	1704

prune140.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	56	9	65

Merged error: 23.7b

Counts

65 → 9

Compiler

Compiled 3551 to 1795 computations (49.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
34.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
34.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))

rewrite81.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

22.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
20.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
20.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series4.0s (22.8%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5087	2306

prune207.0ms (1.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	64	9	73

Merged error: 23.7b

Counts

73 → 9

Compiler

Compiled 5482 to 2672 computations (51.3% saved)

regimes260.0ms (1.5%)

Compiler: Compiled 2046 to 1446 computations (29.3% saved)

bsearch46.0ms (0.3%)

Steps

Iters	Range		Point
5	-1.7714013476336796e+101	-8.066535164560587e+100	-1.406260383903362e+101

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	62
1	56	62

end0.0ms (0%)

sample2.9s (16.3%)

Algorithm

1×

intervals

Results

638.0ms	6053×	body	128	valid
431.0ms	797×	body	1024	valid
276.0ms	729×	body	512	valid
264.0ms	474×	body	1024	invalid
245.0ms	2381×	body	128	invalid
119.0ms	344×	body	512	invalid
112.0ms	417×	body	256	valid
40.0ms	173×	body	256	invalid
4.0ms	4×	body	2048	valid

Compiler

Compiled 384 to 264 computations (31.3% saved)

Details

analyze2.3s (13%)

sample92.0ms (0.5%)

simplify296.0ms (1.7%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite90.0ms (0.5%)

series1.6s (9.3%)

simplify101.0ms (0.6%)

prune311.0ms (1.8%)

localize19.0ms (0.1%)

rewrite120.0ms (0.7%)

series1.4s (8%)

simplify218.0ms (1.2%)

prune473.0ms (2.7%)

localize25.0ms (0.1%)

rewrite60.0ms (0.3%)

series2.7s (15.2%)

simplify67.0ms (0.4%)

prune140.0ms (0.8%)

localize25.0ms (0.1%)

rewrite81.0ms (0.5%)

series4.0s (22.8%)

simplify68.0ms (0.4%)

prune207.0ms (1.2%)

regimes260.0ms (1.5%)

bsearch46.0ms (0.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (16.3%)

Profiling