Details

analyze1.9s (14.4%)

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)

sample161.0ms (1.2%)

Algorithm

1×

intervals

Results

110.0ms	147×	body	1024	valid
25.0ms	45×	body	512	valid
6.0ms	24×	body	256	valid
5.0ms	39×	body	128	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify22.0ms (0.2%)

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: 0.6b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize26.0ms (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)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.3b	(cos.f64 (-.f64 lambda1 lambda2))
3.3b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cos-sum_binary64`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `associate-+r+_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 44

Calls

4 calls:

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

series348.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
72.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
37.0ms	(sin.f64 (-.f64 lambda1 lambda2))
28.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4999	1058
1	4999	1058

prune298.0ms (2.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	42	14	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	14	57

Merged error: 0.4b

Counts

57 → 14

Compiler

Compiled 5680 to 2928 computations (48.5% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.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 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
3.3b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
4×	`sin-sum_binary64`
3×	`associate-*r/_binary64` `cancel-sign-sub-inv_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`sin-diff_binary64` `sub-neg_binary64` `cos-mult_binary64` `frac-add_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 67

Calls

4 calls:

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

series805.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

443.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
255.0ms	(.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
73.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
33.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify86.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4903	1675
1	4903	1675

prune229.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	79	14	93

Merged error: 0.1b

Counts

93 → 14

Compiler

Compiled 5366 to 2009 computations (62.6% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite30.0ms (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`
3×	`associate-*r/_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`cos-mult_binary64` `frac-add_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 62

Calls

4 calls:

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

series880.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

448.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
260.0ms	(.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
101.0ms	(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 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
70.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5255	2097

prune107.0ms (0.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	74	14	88

Merged error: 0.1b

Counts

88 → 14

Compiler

Compiled 3471 to 622 computations (82.1% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.4b	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))
0.5b	(+.f64 (cos.f64 phi1) (/.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
3.3b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`pow1_binary64`
34×	`pow-prod-down_binary64`
28×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`pow-prod-up_binary64` `pow-sqr_binary64`
7×	`*-un-lft-identity_binary64`
6×	`add-log-exp_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`cos-mult_binary64` `sin-sum_binary64` `pow-plus_binary64` `sin-mult_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`swap-sqr_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `sub-neg_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

12.0ms	(+.f64 (cos.f64 phi1) (/.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
11.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
10.0ms	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series2.0s (14.8%)

Counts

4 → 12

Calls

4 calls:

1.7s	(+.f64 (cos.f64 phi1) (/.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
117.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
109.0ms	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))
31.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4965	2185
1	4965	2185

prune227.0ms (1.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	110	14	124

Merged error: 0.1b

Counts

124 → 14

Compiler

Compiled 6808 to 1746 computations (74.4% saved)

regimes219.0ms (1.6%)

Compiler: Compiled 2656 to 1660 computations (37.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	56
1	57	56

end0.0ms (0%)

sample5.7s (42.3%)

Algorithm

1×

intervals

Results

3.5s	4520×	body	1024	valid
759.0ms	1725×	body	512	valid
335.0ms	913×	body	128	valid
203.0ms	740×	body	256	valid
194.0ms	102×	body	2048	valid

Compiler

Compiled 495 to 308 computations (37.8% saved)

Details

analyze1.9s (14.4%)

sample161.0ms (1.2%)

simplify22.0ms (0.2%)

prune3.0ms (0%)

localize26.0ms (0.2%)

rewrite21.0ms (0.2%)

series348.0ms (2.6%)

simplify84.0ms (0.6%)

prune298.0ms (2.2%)

localize29.0ms (0.2%)

rewrite34.0ms (0.2%)

series805.0ms (5.9%)

simplify86.0ms (0.6%)

prune229.0ms (1.7%)

localize29.0ms (0.2%)

rewrite30.0ms (0.2%)

series880.0ms (6.5%)

simplify70.0ms (0.5%)

prune107.0ms (0.8%)

localize35.0ms (0.3%)

rewrite59.0ms (0.4%)

series2.0s (14.8%)

simplify61.0ms (0.5%)

prune227.0ms (1.7%)

regimes219.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.7s (42.3%)

Profiling