Details

analyze2.8s (18.8%)

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)

sample257.0ms (1.7%)

Algorithm

1×

intervals

Results

195.0ms	173×	body	1024	valid
30.0ms	50×	body	512	valid
10.0ms	4×	body	2048	valid
4.0ms	10×	body	256	valid
3.0ms	19×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify181.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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: 15.3b

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 phi1) (cos.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.4b	(cos.f64 (-.f64 lambda1 lambda2))
5.4b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64_1483` `pow1_binary64_1508` `add-sqr-sqrt_binary64_1469` `add-exp-log_binary64_1485`
9×	`add-cube-cbrt_binary64_1482` `*-un-lft-identity_binary64_1447`
6×	`associate-r_binary64_1387` `cancel-sign-sub-inv_binary64_1413`
4×	`prod-exp_binary64_1496` `cbrt-unprod_binary64_1480` `associate-l_binary64_1388` `cos-sum_binary64_1581` `pow-prod-down_binary64_1518` `sin-sum_binary64_1580` `add-log-exp_binary64_1486`
3×	`cos-diff_binary64_1584`
2×	`sub-neg_binary64_1440` `sin-cos-mult_binary64_1603` `*-commutative_binary64_1378`
1×	`distribute-rgt-in_binary64_1397` `unswap-sqr_binary64_1415` `distribute-lft-in_binary64_1396` `sin-diff_binary64_1583` `associate-*l/_binary64_1390`

Counts

4 → 64

Calls

4 calls:

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

series342.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

207.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
68.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
37.0ms	(sin.f64 (-.f64 lambda1 lambda2))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4876	1051
1	4876	1051

prune109.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	11	77

Merged error: 8.1b

Counts

77 → 11

Compiler

Compiled 2516 to 544 computations (78.4% saved)

localize34.0ms (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 phi1) (cos.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1469`
13×	`add-cbrt-cube_binary64_1483` `pow1_binary64_1508` `add-exp-log_binary64_1485`
10×	`add-cube-cbrt_binary64_1482` `*-un-lft-identity_binary64_1447`
9×	`associate-r_binary64_1387`
7×	`associate-l_binary64_1388`
5×	`prod-exp_binary64_1496` `cbrt-unprod_binary64_1480` `pow-prod-down_binary64_1518`
4×	`cos-sum_binary64_1581` `add-log-exp_binary64_1486`
3×	`-commutative_binary64_1378` `cancel-sign-sub-inv_binary64_1413` `cos-diff_binary64_1584` `associate-l/_binary64_1390`
2×	`sin-cos-mult_binary64_1603` `unswap-sqr_binary64_1415`
1×	`flip--_binary64_1422` `sub-neg_binary64_1440` `distribute-rgt-in_binary64_1397` `flip3--_binary64_1451` `distribute-lft-in_binary64_1396`

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

series583.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

264.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
217.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
70.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
31.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5082	1472

prune129.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.1b

Counts

95 → 11

Compiler

Compiled 3562 to 621 computations (82.6% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (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)))

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_1483` `pow1_binary64_1508` `add-exp-log_binary64_1485`
18×	`prod-exp_binary64_1496` `cbrt-unprod_binary64_1480` `pow-prod-down_binary64_1518`
12×	`add-sqr-sqrt_binary64_1469`
8×	`associate-r_binary64_1387` `associate-l_binary64_1388` `add-cube-cbrt_binary64_1482` `*-un-lft-identity_binary64_1447`
5×	`sin-cos-mult_binary64_1603`
4×	`*-commutative_binary64_1378` `add-log-exp_binary64_1486`
3×	`sin-mult_binary64_1602`
2×	`unswap-sqr_binary64_1415` `frac-times_binary64_1457` `associate-r/_binary64_1389` `cos-mult_binary64_1601` `associate-l/_binary64_1390`

Counts

4 → 88

Calls

4 calls:

10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
10.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

series581.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

232.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
212.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
72.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
65.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4960	1556
1	4960	1556

prune170.0ms (1.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	97	14	111

Merged error: 0.0b

Counts

111 → 14

Compiler

Compiled 5434 to 873 computations (83.9% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
3.5b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64_1508`
20×	`add-cbrt-cube_binary64_1483` `add-exp-log_binary64_1485`
13×	`add-sqr-sqrt_binary64_1469`
10×	`prod-exp_binary64_1496` `cbrt-unprod_binary64_1480` `pow-prod-down_binary64_1518`
9×	`add-cube-cbrt_binary64_1482` `*-un-lft-identity_binary64_1447`
7×	`associate-r_binary64_1387` `associate-l_binary64_1388`
5×	`add-log-exp_binary64_1486`
3×	`log-prod_binary64_1533` `log-pow_binary64_1536` `sin-cos-mult_binary64_1603` `*-commutative_binary64_1378`
2×	`unswap-sqr_binary64_1415` `cos-mult_binary64_1601`
1×	`exp-prod_binary64_1499` `sin-mult_binary64_1602` `exp-to-pow_binary64_1509` `frac-times_binary64_1457` `associate-r/_binary64_1389` `rem-log-exp_binary64_1488` `associate-l/_binary64_1390`

Counts

4 → 77

Calls

4 calls:

9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series531.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
155.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
71.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
64.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5019	1196

prune117.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	90	13	103

Merged error: 0.0b

Counts

103 → 13

Compiler

Compiled 4399 to 510 computations (88.4% saved)

regimes243.0ms (1.6%)

Compiler: Compiled 3237 to 1812 computations (44% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	156	77
1	156	77

end0.0ms (0%)

sample8.4s (55.8%)

Algorithm

1×

intervals

Results

5.9s	5369×	body	1024	valid
816.0ms	1279×	body	512	valid
513.0ms	185×	body	2048	valid
150.0ms	405×	body	256	valid
134.0ms	762×	body	128	valid

Compiler

Compiled 695 to 389 computations (44% saved)

Details

analyze2.8s (18.8%)

sample257.0ms (1.7%)

simplify181.0ms (1.2%)

prune4.0ms (0%)

localize25.0ms (0.2%)

rewrite30.0ms (0.2%)

series342.0ms (2.3%)

simplify88.0ms (0.6%)

prune109.0ms (0.7%)

localize34.0ms (0.2%)

rewrite36.0ms (0.2%)

series583.0ms (3.9%)

simplify45.0ms (0.3%)

prune129.0ms (0.9%)

localize35.0ms (0.2%)

rewrite46.0ms (0.3%)

series581.0ms (3.9%)

simplify77.0ms (0.5%)

prune170.0ms (1.1%)

localize39.0ms (0.3%)

rewrite34.0ms (0.2%)

series531.0ms (3.5%)

simplify65.0ms (0.4%)

prune117.0ms (0.8%)

regimes243.0ms (1.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.4s (55.8%)

Profiling