Details

analyze1.9s (20.1%)

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)

sample137.0ms (1.5%)

Algorithm

1×

intervals

Results

91.0ms	145×	body	1024	valid
17.0ms	46×	body	512	valid
8.0ms	33×	body	256	valid
5.0ms	3×	body	2048	valid
3.0ms	29×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify113.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	271	32
1	271	32

prune7.0ms (0.1%)

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: 1.1b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize17.0ms (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)))))
0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0b	(cos.f64 (-.f64 lambda1 lambda2))
4.1b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `cancel-sign-sub-inv_binary64_385`
4×	`cos-sum_binary64_553` `sin-sum_binary64_552` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`cos-diff_binary64_556`
2×	`associate-+r+_binary64_351` `sub-neg_binary64_412`
1×	`flip3-+_binary64_422` `sin-diff_binary64_555` `distribute-rgt-in_binary64_369` `sum-log_binary64_510` `distribute-lft-in_binary64_368` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 44

Calls

4 calls:

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

series194.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
44.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5235	1058

prune89.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	44	12	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	12	57

Merged error: 0.9b

Counts

57 → 12

Compiler

Compiled 1885 to 461 computations (75.5% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(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) (cos.f64 (-.f64 lambda1 lambda2)))))
0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_441`
7×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
4×	`cos-sum_binary64_553`
3×	`associate-r_binary64_359` `associate-l_binary64_360` `cancel-sign-sub-inv_binary64_385` `cos-diff_binary64_556`
2×	`associate-+r+_binary64_351`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `sin-cos-mult_binary64_575` `sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sum-log_binary64_510` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 51

Calls

4 calls:

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

series216.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
50.0ms	(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) (cos.f64 (-.f64 lambda1 lambda2)))))
38.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4818	1256
1	4818	1256

prune88.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	64	11	75

Merged error: 0.1b

Counts

75 → 11

Compiler

Compiled 2492 to 515 computations (79.3% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_441` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
9×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359`
7×	`associate-l_binary64_360`
6×	`add-log-exp_binary64_458`
5×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`*-commutative_binary64_350`
2×	`unswap-sqr_binary64_387` `sin-mult_binary64_574`
1×	`flip3-+_binary64_422` `associate-*l/_binary64_362` `sin-cos-mult_binary64_575` `sum-log_binary64_510` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 68

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))

series278.0ms (3%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
78.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
39.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
39.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4968	1145
1	4968	1145

prune110.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	80	11	91

Merged error: 0.1b

Counts

91 → 11

Compiler

Compiled 3688 to 606 computations (83.6% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.0b	(cos.f64 (-.f64 lambda1 lambda2))
4.0b	(cos.f64 (-.f64 lambda1 lambda2))
4.0b	(cos.f64 (-.f64 lambda1 lambda2))
4.1b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cos-sum_binary64_553` `cancel-sign-sub-inv_binary64_385`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`sub-neg_binary64_412` `add-log-exp_binary64_458` `sin-sum_binary64_552` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`cos-diff_binary64_556`
1×	`sin-diff_binary64_555`

Counts

4 → 48

Calls

4 calls:

5.0ms	(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))

series65.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(sin.f64 (-.f64 lambda1 lambda2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify132.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4803	720
1	4803	720

prune97.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	60	11	71

Merged error: 0.1b

Counts

71 → 11

Compiler

Compiled 3240 to 665 computations (79.5% saved)

regimes393.0ms (4.2%)

Compiler: Compiled 5649 to 3174 computations (43.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	61
1	59	61

end0.0ms (0%)

sample5.1s (54.7%)

Algorithm

1×

intervals

Results

2.8s	4506×	body	1024	valid
678.0ms	1756×	body	512	valid
404.0ms	711×	body	256	valid
142.0ms	103×	body	2048	valid
121.0ms	924×	body	128	valid

Compiler

Compiled 857 to 483 computations (43.6% saved)

Details

analyze1.9s (20.1%)

sample137.0ms (1.5%)

simplify113.0ms (1.2%)

prune7.0ms (0.1%)

localize17.0ms (0.2%)

rewrite19.0ms (0.2%)

series194.0ms (2.1%)

simplify73.0ms (0.8%)

prune89.0ms (0.9%)

localize24.0ms (0.3%)

rewrite21.0ms (0.2%)

series216.0ms (2.3%)

simplify100.0ms (1.1%)

prune88.0ms (0.9%)

localize26.0ms (0.3%)

rewrite30.0ms (0.3%)

series278.0ms (3%)

simplify77.0ms (0.8%)

prune110.0ms (1.2%)

localize29.0ms (0.3%)

rewrite28.0ms (0.3%)

series65.0ms (0.7%)

simplify132.0ms (1.4%)

prune97.0ms (1%)

regimes393.0ms (4.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.1s (54.7%)

Profiling