Details

analyze1.9s (15.6%)

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)

sample147.0ms (1.2%)

Algorithm

1×

intervals

Results

98.0ms	150×	body	1024	valid
23.0ms	56×	body	512	valid
7.0ms	27×	body	256	valid
4.0ms	3×	body	2048	valid
3.0ms	20×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify120.0ms (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

0.8b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize16.0ms (0.1%)

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))))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))
3.9b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms (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	(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))
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)))))

series653.0ms (5.3%)

Counts

4 → 52

Calls

4 calls:

423.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
115.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
58.0ms	(sin.f64 (-.f64 lambda1 lambda2))
57.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2159 to 1585 computations (26.6% saved)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4953	1902
1	4953	1902

prune136.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	81	15	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	15	97

Error

0.6b

Counts

97 → 15

Compiler

Compiled 2893 to 840 computations (71% saved)

localize23.0ms (0.2%)

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 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.2b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_441`
7×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
4×	`cos-sum_binary64_553`
3×	`associate-r_binary64_359` `associate-l_binary64_360` `cancel-sign-sub-inv_binary64_385` `cos-diff_binary64_556`
2×	`associate-+r+_binary64_351`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `sin-cos-mult_binary64_575` `sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sum-log_binary64_510` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 51

Calls

4 calls:

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

series769.0ms (6.2%)

Counts

4 → 48

Calls

4 calls:

434.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
149.0ms	(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) (cos.f64 (-.f64 lambda1 lambda2)))))
127.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
59.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2683 to 1980 computations (26.2% saved)

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4905	2118
1	4905	2118

prune126.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	101	13	114

Error

0.0b

Counts

114 → 13

Compiler

Compiled 3598 to 861 computations (76.1% saved)

localize25.0ms (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 (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)))))

rewrite22.0ms (0.2%)

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×	`associate-+r+_binary64_351` `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-cos-mult_binary64_575` `distribute-rgt-in_binary64_369` `sin-mult_binary64_574` `sum-log_binary64_510` `distribute-lft-in_binary64_368` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 58

Calls

4 calls:

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

series1.4s (11.3%)

Counts

4 → 46

Calls

4 calls:

946.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
188.0ms	(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))))))
132.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
123.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))

Compiler

Compiled 3317 to 2166 computations (34.7% saved)

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5101	2764

prune141.0ms (1.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Error

0.0b

Counts

117 → 13

Compiler

Compiled 4511 to 975 computations (78.4% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.7b	(cos.f64 (-.f64 lambda1 lambda2))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))
3.9b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite27.0ms (0.2%)

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:

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

series278.0ms (2.3%)

Counts

4 → 42

Calls

4 calls:

72.0ms	(cos.f64 (-.f64 lambda1 lambda2))
71.0ms	(sin.f64 (-.f64 lambda1 lambda2))
71.0ms	(cos.f64 (-.f64 lambda1 lambda2))
63.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3520 to 1952 computations (44.5% saved)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4847	1118
1	4847	1118

prune140.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	90	13	103

Error

0.0b

Counts

103 → 13

Compiler

Compiled 4845 to 1105 computations (77.2% saved)

regimes560.0ms (4.5%)

Accuracy

Total 0.1b remaining (60.3%)

Threshold costs 0.1b (60.3%)

Compiler

Compiled 7665 to 4735 computations (38.2% 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%)

sample5.4s (44%)

Algorithm

1×

intervals

Results

3.1s	4490×	body	1024	valid
705.0ms	1734×	body	512	valid
190.0ms	752×	body	256	valid
134.0ms	97×	body	2048	valid
115.0ms	927×	body	128	valid

Compiler

Compiled 1142 to 705 computations (38.3% saved)

Details

analyze1.9s (15.6%)

sample147.0ms (1.2%)

simplify120.0ms (1%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite19.0ms (0.2%)

series653.0ms (5.3%)

simplify75.0ms (0.6%)

prune136.0ms (1.1%)

localize23.0ms (0.2%)

rewrite20.0ms (0.2%)

series769.0ms (6.2%)

simplify94.0ms (0.8%)

prune126.0ms (1%)

localize25.0ms (0.2%)

rewrite22.0ms (0.2%)

series1.4s (11.3%)

simplify65.0ms (0.5%)

prune141.0ms (1.1%)

localize30.0ms (0.2%)

rewrite27.0ms (0.2%)

series278.0ms (2.3%)

simplify96.0ms (0.8%)

prune140.0ms (1.1%)

regimes560.0ms (4.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.4s (44%)

Profiling