Details

analyze1.9s (18.2%)

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)

sample135.0ms (1.3%)

Algorithm

1×

intervals

Results

88.0ms	134×	body	1024	valid
20.0ms	52×	body	512	valid
7.0ms	27×	body	256	valid
5.0ms	41×	body	128	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify118.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

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

Error

1.4b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.2b	(cos.f64 (-.f64 lambda1 lambda2))
4.3b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_100` `sin-sum_binary64_211` `cancel-sign-sub-inv_binary64_44`
10×	`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`
5×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28`
4×	`cos-sum_binary64_212` `sub-neg_binary64_71`
3×	`associate-l_binary64_19` `associate-r_binary64_18` `cos-diff_binary64_215`
2×	`associate-+r+_binary64_10`
1×	`+-commutative_binary64_8` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `sin-diff_binary64_214` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 63

Calls

4 calls:

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

series205.0ms (2%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
62.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
18.0ms	(sin.f64 (-.f64 lambda1 lambda2))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify134.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	4859	1221
1	4859	1221

prune110.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	63	12	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	12	76

Error

1.1b

Counts

76 → 12

Compiler

Compiled 2335 to 513 computations (78% saved)

localize23.0ms (0.2%)

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 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))
4.3b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

8.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
7.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))

series252.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))
60.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
43.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
18.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify118.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4830	1267
1	4830	1267

prune107.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Error

0.1b

Counts

92 → 12

Compiler

Compiled 3241 to 567 computations (82.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

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 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (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 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))

rewrite22.0ms (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` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `sin-cos-mult_binary64_234` `sin-mult_binary64_233` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 56

Calls

4 calls:

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

series279.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))
71.0ms	(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 lambda2) (cos.f64 lambda1)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))
39.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
38.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4809	1434
1	4809	1434

prune115.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	67	13	80

Error

0.1b

Counts

80 → 13

Compiler

Compiled 3462 to 634 computations (81.7% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
4×	`log-prod_binary64_164` `log-pow_binary64_167`
3×	`associate-l_binary64_19` `associate-r_binary64_18` `exp-prod_binary64_130`
1×	`+-commutative_binary64_8` `*-commutative_binary64_9` `exp-sum_binary64_124` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `rem-log-exp_binary64_119` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `sin-mult_binary64_233` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 53

Calls

4 calls:

6.0ms	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2))))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))

series456.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))))
128.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))
68.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2))))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))
39.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4945	1620
1	4945	1620

prune78.0ms (0.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	64	14	78

Error

0.1b

Counts

78 → 14

Compiler

Compiled 2908 to 337 computations (88.4% saved)

regimes619.0ms (5.9%)

Accuracy

Total 0.2b remaining (70%)

Threshold costs 0.2b (70%)

Compiler

Compiled 9121 to 5183 computations (43.2% 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%)

sample5.5s (52.1%)

Algorithm

1×

intervals

Results

3.0s	4465×	body	1024	valid
670.0ms	1709×	body	512	valid
186.0ms	752×	body	256	valid
166.0ms	123×	body	2048	valid
114.0ms	951×	body	128	valid

Compiler

Compiled 1350 to 769 computations (43% saved)

Details

analyze1.9s (18.2%)

sample135.0ms (1.3%)

simplify118.0ms (1.1%)

prune3.0ms (0%)

localize20.0ms (0.2%)

rewrite29.0ms (0.3%)

series205.0ms (2%)

simplify134.0ms (1.3%)

prune110.0ms (1.1%)

localize23.0ms (0.2%)

rewrite31.0ms (0.3%)

series252.0ms (2.4%)

simplify118.0ms (1.1%)

prune107.0ms (1%)

localize26.0ms (0.2%)

rewrite22.0ms (0.2%)

series279.0ms (2.7%)

simplify94.0ms (0.9%)

prune115.0ms (1.1%)

localize31.0ms (0.3%)

rewrite23.0ms (0.2%)

series456.0ms (4.4%)

simplify83.0ms (0.8%)

prune78.0ms (0.7%)

regimes619.0ms (5.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.5s (52.1%)

Profiling