Details

analyze2.0s (16.4%)

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)

sample186.0ms (1.5%)

Algorithm

1×

intervals

Results

105.0ms	107×	body	1280	valid
47.0ms	72×	body	640	valid
11.0ms	29×	body	320	valid
6.0ms	20×	body	160	valid
4.0ms	28×	body	80	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify52.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	272	32
1	272	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: 0.5b

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)))
0.4b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.6b	(sin.f64 (-.f64 lambda1 lambda2))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`sub-neg_binary64` `insert-posit16`
3×	`associate-r_binary64` `sin-sum_binary64` `associate-l_binary64` `cos-diff_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sin-diff_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 55

Calls

4 calls:

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

series403.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
124.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
33.0ms	(sin.f64 (-.f64 lambda1 lambda2))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify149.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	5005	992

prune103.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	56	11	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	11	68

Merged error: 0.4b

Counts

68 → 11

Compiler

Compiled 2040 to 510 computations (75% saved)

localize28.0ms (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) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
3.6b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`insert-posit16`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`associate-+r+_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sin-diff_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 52

Calls

4 calls:

7.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
6.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 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) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series624.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

417.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
92.0ms	(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))))))
77.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
38.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify222.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (197.0ms)

Iter	Nodes	Cost
0	4953	1479
1	4953	1479

prune95.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	65	10	75

Merged error: 0.0b

Counts

75 → 10

Compiler

Compiled 2511 to 533 computations (78.8% saved)

localize29.0ms (0.2%)

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

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
4×	`insert-posit16`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-+r+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `sin-mult_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 65

Calls

4 calls:

12.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
6.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 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) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series861.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

418.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
259.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
108.0ms	(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))))))
75.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify124.0ms (1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5037	2171

prune109.0ms (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	77	10	87

Merged error: 0.0b

Counts

87 → 10

Compiler

Compiled 3542 to 554 computations (84.4% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.6b	(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))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `sub-neg_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `insert-posit16`
3×	`cos-diff_binary64` `cos-sum_binary64`
1×	`sin-diff_binary64` `sin-sum_binary64`

Counts

4 → 40

Calls

4 calls:

6.0ms	(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))

series118.0ms (1%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(cos.f64 (-.f64 lambda1 lambda2))
31.0ms	(sin.f64 (-.f64 lambda1 lambda2))
28.0ms	(cos.f64 (-.f64 lambda1 lambda2))
28.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify282.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (261.0ms)

Iter	Nodes	Cost
0	4763	536
1	4763	536

prune89.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	52	10	62

Merged error: 0.0b

Counts

62 → 10

Compiler

Compiled 2760 to 613 computations (77.8% saved)

regimes187.0ms (1.6%)

Compiler: Compiled 2458 to 1246 computations (49.3% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	57	56
1	57	56

end0.0ms (0%)

sample6.2s (51.8%)

Algorithm

1×

intervals

Results

3.6s	3557×	body	1280	valid
1.4s	2410×	body	640	valid
368.0ms	925×	body	320	valid
110.0ms	406×	body	160	valid
91.0ms	702×	body	80	valid

Compiler

Compiled 462 to 239 computations (48.3% saved)

Details

analyze2.0s (16.4%)

sample186.0ms (1.5%)

simplify52.0ms (0.4%)

prune3.0ms (0%)

localize20.0ms (0.2%)

rewrite30.0ms (0.3%)

series403.0ms (3.4%)

simplify149.0ms (1.2%)

prune103.0ms (0.9%)

localize28.0ms (0.2%)

rewrite20.0ms (0.2%)

series624.0ms (5.2%)

simplify222.0ms (1.8%)

prune95.0ms (0.8%)

localize29.0ms (0.2%)

rewrite26.0ms (0.2%)

series861.0ms (7.2%)

simplify124.0ms (1%)

prune109.0ms (0.9%)

localize30.0ms (0.3%)

rewrite24.0ms (0.2%)

series118.0ms (1%)

simplify282.0ms (2.3%)

prune89.0ms (0.7%)

regimes187.0ms (1.6%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample6.2s (51.8%)

Profiling