Details

analyze1.9s (16.7%)

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)

sample164.0ms (1.4%)

Algorithm

1×

intervals

Results

118.0ms	150×	body	1024	valid
22.0ms	55×	body	512	valid
4.0ms	18×	body	256	valid
4.0ms	31×	body	128	valid
4.0ms	2×	body	2048	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify187.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	211	32
1	211	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)

localize21.0ms (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))))
3.9b	(sin.f64 (-.f64 lambda1 lambda2))
3.9b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms (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	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (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)))))

series370.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
74.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
32.0ms	(sin.f64 (-.f64 lambda1 lambda2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4992	1058
1	4992	1058

prune94.0ms (0.8%)

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: 0.4b

Counts

57 → 13

Compiler

Compiled 1888 to 476 computations (74.8% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
3.9b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_441`
12×	`sin-sum_binary64_552`
11×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`cancel-sign-sub-inv_binary64_385`
8×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
6×	`add-log-exp_binary64_458` `associate-r_binary64_359` `associate-l_binary64_360`
4×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
3×	`sub-neg_binary64_412`
2×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350`
1×	`flip3-+_binary64_422` `sin-diff_binary64_555` `sin-mult_binary64_574` `sum-log_binary64_510` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 68

Calls

4 calls:

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

series479.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

247.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
125.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
72.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
35.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4900	1267
1	4900	1267

prune115.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	80	13	93

Merged error: 0.1b

Counts

93 → 13

Compiler

Compiled 3304 to 601 computations (81.8% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_441`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
6×	`add-log-exp_binary64_458` `associate-r_binary64_359` `associate-l_binary64_360`
2×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `distribute-lft-in_binary64_368` `-commutative_binary64_350` `cancel-sign-sub-inv_binary64_385`
1×	`flip3-+_binary64_422` `sin-mult_binary64_574` `sum-log_binary64_510` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `+-commutative_binary64_349`

Counts

4 → 61

Calls

4 calls:

10.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))

series678.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

275.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
226.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
105.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))
72.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4988	1901
1	4988	1901

prune110.0ms (1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	73	13	86

Merged error: 0.1b

Counts

86 → 13

Compiler

Compiled 3632 to 584 computations (83.9% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.9b	(sin.f64 (-.f64 lambda1 lambda2))
3.9b	(cos.f64 (-.f64 lambda1 lambda2))
3.9b	(cos.f64 (-.f64 lambda1 lambda2))
3.9b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite30.0ms (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:

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

series108.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(sin.f64 (-.f64 lambda1 lambda2))
27.0ms	(cos.f64 (-.f64 lambda1 lambda2))
26.0ms	(cos.f64 (-.f64 lambda1 lambda2))
25.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify170.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (157.0ms)

Iter	Nodes	Cost
0	4684	720
1	4684	720

prune96.0ms (0.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	60	13	73

Merged error: 0.1b

Counts

73 → 13

Compiler

Compiled 3240 to 665 computations (79.5% saved)

regimes591.0ms (5.1%)

Compiler: Compiled 7945 to 4854 computations (38.9% 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%)

sample5.9s (51.7%)

Algorithm

1×

intervals

Results

3.4s	4449×	body	1024	valid
747.0ms	1746×	body	512	valid
216.0ms	117×	body	2048	valid
202.0ms	751×	body	256	valid
120.0ms	937×	body	128	valid

Compiler

Compiled 1185 to 723 computations (39% saved)

Details

analyze1.9s (16.7%)

sample164.0ms (1.4%)

simplify187.0ms (1.6%)

prune3.0ms (0%)

localize21.0ms (0.2%)

rewrite20.0ms (0.2%)

series370.0ms (3.2%)

simplify86.0ms (0.7%)

prune94.0ms (0.8%)

localize32.0ms (0.3%)

rewrite32.0ms (0.3%)

series479.0ms (4.2%)

simplify96.0ms (0.8%)

prune115.0ms (1%)

localize30.0ms (0.3%)

rewrite29.0ms (0.3%)

series678.0ms (5.9%)

simplify70.0ms (0.6%)

prune110.0ms (1%)

localize31.0ms (0.3%)

rewrite30.0ms (0.3%)

series108.0ms (0.9%)

simplify170.0ms (1.5%)

prune96.0ms (0.8%)

regimes591.0ms (5.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (51.7%)

Profiling