Details

analyze3.0s (19.1%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 20 to 18 computations (10% saved)

sample219.0ms (1.4%)

Algorithm

1×

intervals

Results

154.0ms	177×	body	1024	valid
28.0ms	54×	body	512	valid
15.0ms	7×	body	2048	valid
3.0ms	10×	body	256	valid
1.0ms	8×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify111.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	96	31
1	96	31

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: 15.6b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.3b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
6×	`associate-l_binary64_19` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `cos-sum_binary64_212`
3×	`cancel-sign-sub-inv_binary64_44`
2×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46`
1×	`acos-asin_binary64_259` `sin-mult_binary64_233` `cos-diff_binary64_215` `sub-neg_binary64_71`

Counts

4 → 57

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

series221.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
38.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
37.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
17.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4809	1492
1	4809	1492

prune104.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 3.8b

Counts

70 → 12

Compiler

Compiled 2131 to 511 computations (76% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.3b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_100`
10×	`add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
9×	`associate-l_binary64_19` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117`
3×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46`
2×	`sin-mult_binary64_233`
1×	`acos-asin_binary64_259`

Counts

4 → 64

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series327.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
58.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
39.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
37.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5083	1948

prune113.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	75	13	88

Merged error: 3.7b

Counts

88 → 13

Compiler

Compiled 2998 to 640 computations (78.7% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 lambda2))
0.6b	(cbrt.f64 (sin.f64 lambda2))
0.6b	(cbrt.f64 (sin.f64 lambda2))
1.3b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_109`
7×	`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` `add-exp-log_binary64_116` `pow1_binary64_139`
3×	`pow1/3_binary64_160`
1×	`acos-asin_binary64_259`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt.f64 (sin.f64 lambda2))
1.0ms	(cbrt.f64 (sin.f64 lambda2))
1.0ms	(cbrt.f64 (sin.f64 lambda2))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))))))

series281.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(cbrt.f64 (sin.f64 lambda2))
75.0ms	(cbrt.f64 (sin.f64 lambda2))
74.0ms	(cbrt.f64 (sin.f64 lambda2))
56.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))))))

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4938	882
1	4938	882

prune85.0ms (0.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	53	13	66

Merged error: 3.7b

Counts

66 → 13

Compiler

Compiled 2528 to 677 computations (73.2% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
0.6b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
1.1b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_100`
13×	`*-un-lft-identity_binary64_78`
9×	`associate-l_binary64_19` `add-cube-cbrt_binary64_113`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
6×	`add-log-exp_binary64_117` `associate-r_binary64_18`
4×	`difference-of-squares_binary64_47`
3×	`cancel-sign-sub-inv_binary64_44`
2×	`-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `times-frac_binary64_84` `flip--_binary64_53` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `asin-acos_binary64_258`
1×	`diff-log_binary64_170` `associate--r-_binary64_17` `sin-mult_binary64_233` `sub-neg_binary64_71`

Counts

4 → 68

Calls

4 calls:

10.0ms	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
8.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series486.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

302.0ms	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
98.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
50.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
37.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5029	3373

prune109.0ms (0.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	69	11	80
Fresh	4	7	11
Picked	1	0	1
Done	1	0	1
Total	75	18	93

Merged error: 3.4b

Counts

93 → 18

Compiler

Compiled 3282 to 618 computations (81.2% saved)

regimes1.5s (9.8%)

Compiler: Compiled 23408 to 14062 computations (39.9% saved)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	206	57
1	206	57

end0.0ms (0%)

sample8.5s (54.4%)

Algorithm

1×

intervals

Results

4.9s	5527×	body	1024	valid
779.0ms	1432×	body	512	valid
606.0ms	281×	body	2048	valid
167.0ms	471×	body	256	valid
50.0ms	289×	body	128	valid
2.0ms	2×	body	1024	invalid
1.0ms	2×	body	256	invalid

Compiler

Compiled 2238 to 1348 computations (39.8% saved)

Details

analyze3.0s (19.1%)

sample219.0ms (1.4%)

simplify111.0ms (0.7%)

prune3.0ms (0%)

localize20.0ms (0.1%)

rewrite19.0ms (0.1%)

series221.0ms (1.4%)

simplify80.0ms (0.5%)

prune104.0ms (0.7%)

localize27.0ms (0.2%)

rewrite24.0ms (0.1%)

series327.0ms (2.1%)

simplify79.0ms (0.5%)

prune113.0ms (0.7%)

localize34.0ms (0.2%)

rewrite10.0ms (0.1%)

series281.0ms (1.8%)

simplify103.0ms (0.7%)

prune85.0ms (0.5%)

localize30.0ms (0.2%)

rewrite32.0ms (0.2%)

series486.0ms (3.1%)

simplify98.0ms (0.6%)

prune109.0ms (0.7%)

regimes1.5s (9.8%)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample8.5s (54.4%)

Profiling