Details

analyze1.9s (19.8%)

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample138.0ms (1.4%)

Algorithm

1×

intervals

Results

93.0ms	141×	body	1024	valid
19.0ms	51×	body	512	valid
5.0ms	21×	body	256	valid
5.0ms	4×	body	2048	valid
5.0ms	39×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify118.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	271	32
1	271	32

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: 0.7b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.7b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.5b	(sin.f64 (-.f64 lambda1 lambda2))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `add-cube-cbrt_binary64_113` `cancel-sign-sub-inv_binary64_44` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `sin-sum_binary64_211` `add-exp-log_binary64_116` `cos-sum_binary64_212` `pow1_binary64_139`
3×	`cos-diff_binary64_215`
2×	`associate-+r+_binary64_10` `sub-neg_binary64_71`
1×	`+-commutative_binary64_8` `distribute-lft-in_binary64_27` `flip-+_binary64_52` `sin-diff_binary64_214` `distribute-rgt-in_binary64_28` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 44

Calls

4 calls:

9.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series186.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
43.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
17.0ms	(cos.f64 (-.f64 lambda1 lambda2))
16.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5235	1058

prune92.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	43	13	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	13	57

Merged error: 0.5b

Counts

57 → 13

Compiler

Compiled 1908 to 475 computations (75.1% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.7b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
3.5b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `pow1_binary64_139`
4×	`sin-sum_binary64_211`
3×	`associate-l_binary64_19` `associate-r_binary64_18` `cancel-sign-sub-inv_binary64_44`
2×	`associate-+r+_binary64_10`
1×	`+-commutative_binary64_8` `distribute-lft-in_binary64_27` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `sin-diff_binary64_214` `distribute-rgt-in_binary64_28` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `sin-mult_binary64_233` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 51

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series358.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
55.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
40.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
20.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4989	1442
1	4989	1442

prune87.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	64	12	76

Merged error: 0.1b

Counts

76 → 12

Compiler

Compiled 2528 to 530 computations (79% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.7b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_100`
8×	`add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117` `associate-r_binary64_18`
2×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-+r+_binary64_10` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46`
1×	`+-commutative_binary64_8` `distribute-lft-in_binary64_27` `flip-+_binary64_52` `distribute-rgt-in_binary64_28` `sin-cos-mult_binary64_234` `sin-mult_binary64_233` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 58

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series403.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

260.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
66.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
40.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
38.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4952	1640
1	4952	1640

prune98.0ms (1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	70	12	82

Merged error: 0.1b

Counts

82 → 12

Compiler

Compiled 3216 to 568 computations (82.3% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.5b	(sin.f64 (-.f64 lambda1 lambda2))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cos-sum_binary64_212` `cancel-sign-sub-inv_binary64_44`
8×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `sin-sum_binary64_211` `add-exp-log_binary64_116` `sub-neg_binary64_71` `pow1_binary64_139`
3×	`cos-diff_binary64_215`
1×	`sin-diff_binary64_214`

Counts

4 → 48

Calls

4 calls:

7.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series60.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(sin.f64 (-.f64 lambda1 lambda2))
14.0ms	(cos.f64 (-.f64 lambda1 lambda2))
14.0ms	(cos.f64 (-.f64 lambda1 lambda2))
14.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify125.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4803	720
1	4803	720

prune95.0ms (1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	60	12	72

Merged error: 0.1b

Counts

72 → 12

Compiler

Compiled 3240 to 665 computations (79.5% saved)

regimes407.0ms (4.2%)

Compiler: Compiled 5474 to 3153 computations (42.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	56
1	57	56

end0.0ms (0%)

sample5.1s (53%)

Algorithm

1×

intervals

Results

3.0s	4503×	body	1024	valid
660.0ms	1689×	body	512	valid
174.0ms	696×	body	256	valid
163.0ms	118×	body	2048	valid
118.0ms	994×	body	128	valid

Compiler

Compiled 829 to 479 computations (42.2% saved)

Details

analyze1.9s (19.8%)

sample138.0ms (1.4%)

simplify118.0ms (1.2%)

prune3.0ms (0%)

localize16.0ms (0.2%)

rewrite24.0ms (0.2%)

series186.0ms (1.9%)

simplify74.0ms (0.8%)

prune92.0ms (1%)

localize27.0ms (0.3%)

rewrite20.0ms (0.2%)

series358.0ms (3.7%)

simplify85.0ms (0.9%)

prune87.0ms (0.9%)

localize24.0ms (0.2%)

rewrite24.0ms (0.2%)

series403.0ms (4.2%)

simplify101.0ms (1%)

prune98.0ms (1%)

localize27.0ms (0.3%)

rewrite28.0ms (0.3%)

series60.0ms (0.6%)

simplify125.0ms (1.3%)

prune95.0ms (1%)

regimes407.0ms (4.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.1s (53%)

Profiling