Details

analyze5.6s (8.6%)

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)

sample637.0ms (1%)

Algorithm

1×

intervals

Results

443.0ms	146×	body	1024	valid
78.0ms	52×	body	512	valid
33.0ms	25×	body	256	valid
13.0ms	3×	body	2048	valid
10.0ms	30×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify303.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	271	32
1	271	32

prune10.0ms (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: 1.3b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize73.0ms (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)))))
0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))
3.6b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite89.0ms (0.1%)

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:

36.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
23.0ms	(sin.f64 (-.f64 lambda1 lambda2))
19.0ms	(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)))))

series744.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

470.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
125.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
89.0ms	(sin.f64 (-.f64 lambda1 lambda2))
58.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify293.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (230.0ms)

Iter	Nodes	Cost
0	5235	1058

prune689.0ms (1.1%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	28	28	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	29	57

Merged error: 1.1b

Counts

57 → 29

Compiler

Compiled 2292 to 740 computations (67.7% saved)

localize54.0ms (0.1%)

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) (cos.f64 (-.f64 lambda1 lambda2)))))
0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite53.0ms (0.1%)

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:

20.0ms	(cos.f64 (-.f64 lambda1 lambda2))
9.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
9.0ms	(*.f64 (sin.f64 lambda1) (cos.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) (cos.f64 (-.f64 lambda1 lambda2)))))

series409.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 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) (cos.f64 (-.f64 lambda1 lambda2)))))
70.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
28.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify169.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4818	1256
1	4818	1256

prune894.0ms (1.4%)

Pruning

56 alts after pruning (54 fresh and 2 done)

	Pruned	Kept	Total
New	36	27	63
Fresh	0	27	27
Picked	0	1	1
Done	0	1	1
Total	36	56	92

Merged error: 0.1b

Counts

92 → 56

Compiler

Compiled 3911 to 1408 computations (64% saved)

localize51.0ms (0.1%)

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)))))

rewrite44.0ms (0.1%)

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:

11.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
8.0ms	(+.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))))))

series704.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

452.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
118.0ms	(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))))))
68.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
65.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))

simplify208.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (172.0ms)

Iter	Nodes	Cost
0	4952	1640
1	4952	1640

prune1.9s (2.9%)

Pruning

81 alts after pruning (78 fresh and 3 done)

	Pruned	Kept	Total
New	42	28	70
Fresh	3	50	53
Picked	0	1	1
Done	0	2	2
Total	45	81	126

Merged error: 0.1b

Counts

126 → 81

Compiler

Compiled 5828 to 2057 computations (64.7% saved)

localize116.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)))))
26.5b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

rewrite124.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_441`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `cbrt-prod_binary64_450`
6×	`add-log-exp_binary64_458`
3×	`associate-r_binary64_359` `sin-mult_binary64_574` `associate-l_binary64_360` `pow-unpow_binary64_496`
2×	`associate-+r+_binary64_351` `pow-prod-down_binary64_490` `unpow-prod-down_binary64_498` `unpow3_binary64_485` `cube-mult_binary64_449` `rem-cube-cbrt_binary64_442` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `sqr-pow_binary64_391` `cube-div_binary64_448` `cube-prod_binary64_447` `pow-pow_binary64_491`
1×	`flip3-+_binary64_422` `pow1/3_binary64_501` `cbrt-div_binary64_451` `distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `sum-log_binary64_510` `rem-cbrt-cube_binary64_443` `pow-to-exp_binary64_488` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 73

Calls

4 calls:

26.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
23.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)))))
20.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))
19.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)

series1.5s (2.3%)

Counts

4 → 12

Calls

4 calls:

994.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)))))
308.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
107.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
105.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

simplify200.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	4949	1361
1	4949	1361

prune1.9s (3%)

Pruning

86 alts after pruning (82 fresh and 4 done)

	Pruned	Kept	Total
New	67	18	85
Fresh	13	64	77
Picked	0	1	1
Done	0	3	3
Total	80	86	166

Merged error: 0.1b

Counts

166 → 86

Compiler

Compiled 3499 to 733 computations (79.1% saved)

regimes10.8s (16.5%)

Compiler: Compiled 50946 to 30880 computations (39.4% saved)

bsearch9.4s (14.3%)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	56
1	59	56

end0.0ms (0%)

sample28.4s (43.4%)

Algorithm

1×

intervals

Results

7.6s	4474×	body	1024	valid
1.8s	1729×	body	512	valid
498.0ms	739×	body	256	valid
396.0ms	110×	body	2048	valid
286.0ms	948×	body	128	valid

Compiler

Compiled 7362 to 4462 computations (39.4% saved)

Pareto

Details

analyze5.6s (8.6%)

sample637.0ms (1%)

simplify303.0ms (0.5%)

prune10.0ms (0%)

localize73.0ms (0.1%)

rewrite89.0ms (0.1%)

series744.0ms (1.1%)

simplify293.0ms (0.4%)

prune689.0ms (1.1%)

localize54.0ms (0.1%)

rewrite53.0ms (0.1%)

series409.0ms (0.6%)

simplify169.0ms (0.3%)

prune894.0ms (1.4%)

localize51.0ms (0.1%)

rewrite44.0ms (0.1%)

series704.0ms (1.1%)

simplify208.0ms (0.3%)

prune1.9s (2.9%)

localize116.0ms (0.2%)

rewrite124.0ms (0.2%)

series1.5s (2.3%)

simplify200.0ms (0.3%)

prune1.9s (3%)

regimes10.8s (16.5%)

bsearch9.4s (14.3%)

simplify11.0ms (0%)

end0.0ms (0%)

sample28.4s (43.4%)

Profiling