Details

analyze2.8s (17.3%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample397.0ms (2.5%)

Algorithm

1×

intervals

Results

305.0ms	182×	body	1024	valid
32.0ms	34×	body	512	valid
32.0ms	6×	body	2048	valid
7.0ms	27×	body	128	valid
4.0ms	7×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify261.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	367	39
1	367	39

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: 13.2b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.5b	(cos.f64 (-.f64 lambda1 lambda2))
3.6b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1477` `pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
9×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
6×	`associate-r_binary64_1395` `cancel-sign-sub-inv_binary64_1421`
4×	`prod-exp_binary64_1504` `cos-sum_binary64_1589` `add-log-exp_binary64_1494` `sin-sum_binary64_1588` `cbrt-unprod_binary64_1488` `associate-l_binary64_1396` `pow-prod-down_binary64_1526`
3×	`cos-diff_binary64_1592`
2×	`sin-cos-mult_binary64_1611` `*-commutative_binary64_1386` `sub-neg_binary64_1448`
1×	`distribute-rgt-in_binary64_1405` `sin-diff_binary64_1591` `distribute-lft-in_binary64_1404` `associate-*l/_binary64_1398` `unswap-sqr_binary64_1423`

Counts

4 → 64

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series389.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
115.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
35.0ms	(sin.f64 (-.f64 lambda1 lambda2))
31.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4859	1102
1	4859	1102

prune370.0ms (2.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	12	77

Merged error: 6.1b

Counts

77 → 12

Compiler

Compiled 7154 to 3720 computations (48% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
0.2b	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1477`
13×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
10×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
9×	`associate-r_binary64_1395`
7×	`associate-l_binary64_1396`
5×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526`
4×	`cos-sum_binary64_1589` `add-log-exp_binary64_1494`
3×	`cos-diff_binary64_1592` `-commutative_binary64_1386` `cancel-sign-sub-inv_binary64_1421` `associate-l/_binary64_1398`
2×	`sin-cos-mult_binary64_1611` `unswap-sqr_binary64_1423`
1×	`distribute-rgt-in_binary64_1405` `flip--_binary64_1430` `distribute-lft-in_binary64_1404` `sub-neg_binary64_1448` `flip3--_binary64_1459`

Counts

4 → 72

Calls

4 calls:

9.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series558.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
206.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
72.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify49.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5127	1472

prune231.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Merged error: 0.1b

Counts

96 → 10

Compiler

Compiled 5515 to 1916 computations (65.3% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.2b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
18×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488` `pow-prod-down_binary64_1526`
12×	`add-sqr-sqrt_binary64_1477`
8×	`associate-r_binary64_1395` `add-cube-cbrt_binary64_1490` `associate-l_binary64_1396` `*-un-lft-identity_binary64_1455`
4×	`sin-cos-mult_binary64_1611` `add-log-exp_binary64_1494` `-commutative_binary64_1386` `associate-l/_binary64_1398`
3×	`sin-mult_binary64_1610`
2×	`associate-*r/_binary64_1397` `cos-mult_binary64_1609` `frac-times_binary64_1465` `unswap-sqr_binary64_1423`
1×	`flip--_binary64_1430` `flip3--_binary64_1459`

Counts

4 → 89

Calls

4 calls:

10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
10.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
10.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series769.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
239.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
209.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
70.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5153	1911

prune553.0ms (3.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Merged error: 0.0b

Counts

111 → 9

Compiler

Compiled 13037 to 5229 computations (59.9% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1486`
23×	`add-sqr-sqrt_binary64_1477`
15×	`add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
11×	`pow1_binary64_1516`
9×	`pow1/3_binary64_1537`
6×	`associate-r_binary64_1395` `swap-sqr_binary64_1422` `associate-l_binary64_1396` `add-exp-log_binary64_1493`
4×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `unswap-sqr_binary64_1423`
2×	`pow-prod-up_binary64_1525` `pow-prod-down_binary64_1526` `pow-sqr_binary64_1428`
1×	`prod-exp_binary64_1504` `pow-plus_binary64_1518` `*-commutative_binary64_1386` `pow2_binary64_1536` `cbrt-unprod_binary64_1488`

Counts

4 → 73

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
2.0ms	(cbrt.f64 (sin.f64 lambda1))
2.0ms	(cbrt.f64 (sin.f64 lambda1))
2.0ms	(cbrt.f64 (sin.f64 lambda1))

series535.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
130.0ms	(cbrt.f64 (sin.f64 lambda1))
125.0ms	(cbrt.f64 (sin.f64 lambda1))
120.0ms	(cbrt.f64 (sin.f64 lambda1))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4872	797
1	4872	797

prune173.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	85	9	94

Merged error: 0.0b

Counts

94 → 9

Compiler

Compiled 5738 to 1161 computations (79.8% saved)

regimes187.0ms (1.2%)

Compiler: Compiled 2304 to 1270 computations (44.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	170	89
1	170	89

end0.0ms (0%)

sample8.2s (51.5%)

Algorithm

1×

intervals

Results

6.0s	5412×	body	1024	valid
789.0ms	1237×	body	512	valid
497.0ms	189×	body	2048	valid
139.0ms	801×	body	128	valid
137.0ms	361×	body	256	valid

Compiler

Compiled 518 to 282 computations (45.6% saved)

Details

analyze2.8s (17.3%)

sample397.0ms (2.5%)

simplify261.0ms (1.6%)

prune4.0ms (0%)

localize25.0ms (0.2%)

rewrite35.0ms (0.2%)

series389.0ms (2.4%)

simplify71.0ms (0.4%)

prune370.0ms (2.3%)

localize36.0ms (0.2%)

rewrite37.0ms (0.2%)

series558.0ms (3.5%)

simplify49.0ms (0.3%)

prune231.0ms (1.4%)

localize40.0ms (0.2%)

rewrite50.0ms (0.3%)

series769.0ms (4.8%)

simplify70.0ms (0.4%)

prune553.0ms (3.5%)

localize39.0ms (0.2%)

rewrite25.0ms (0.2%)

series535.0ms (3.4%)

simplify81.0ms (0.5%)

prune173.0ms (1.1%)

regimes187.0ms (1.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.2s (51.5%)

Profiling