Details

analyze2.1s (14.6%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample93.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	191×	body	128	valid
14.0ms	27×	body	512	valid
13.0ms	25×	body	1024	valid
9.0ms	85×	body	128	invalid
7.0ms	14×	body	1024	invalid
5.0ms	14×	body	512	invalid
3.0ms	12×	body	256	valid
2.0ms	7×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify300.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4986	49
1	4986	49

prune4.0ms (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: 38.4b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite84.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_710`
102×	`flip--_binary64_742` `flip3--_binary64_771`
68×	`frac-times_binary64_777`
66×	`sqrt-div_binary64_784`
64×	`frac-add_binary64_775`
44×	`pow1_binary64_828`
34×	`associate-*r/_binary64_709`
17×	`pow-prod-down_binary64_838`
16×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
8×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816`
6×	`add-sqr-sqrt_binary64_789`
5×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
4×	`pow-prod-up_binary64_837` `add-log-exp_binary64_806` `pow-sqr_binary64_740`
3×	`sqrt-prod_binary64_783`
2×	`pow-plus_binary64_830`
1×	`associate-l_binary64_708` `pow2_binary64_848` `associate-r_binary64_707` `swap-sqr_binary64_734` `rem-sqrt-square_binary64_780` `*-commutative_binary64_698` `flip-+_binary64_741` `pow1/2_binary64_847` `flip3-+_binary64_770` `sqrt-pow1_binary64_785`

Counts

4 → 135

Calls

4 calls:

23.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
15.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.6s (11.5%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
288.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5222	10334

prune413.0ms (2.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 25.3b

Counts

148 → 8

Compiler

Compiled 11471 to 4559 computations (60.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite115.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip--_binary64_742` `flip3--_binary64_771`
196×	`frac-times_binary64_777`
138×	`sqrt-div_binary64_784`
136×	`frac-add_binary64_775`
130×	`associate-*l/_binary64_710`
74×	`associate-*r/_binary64_709`
73×	`cos-mult_binary64_921`
12×	`pow1_binary64_828` `add-sqr-sqrt_binary64_789`
9×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
6×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
4×	`add-log-exp_binary64_806`
3×	`associate-l_binary64_708` `associate-r_binary64_707` `swap-sqr_binary64_734` `sqrt-prod_binary64_783`
1×	`pow2_binary64_848` `unswap-sqr_binary64_735` `rem-sqrt-square_binary64_780` `cbrt-unprod_binary64_800` `pow-prod-up_binary64_837` `pow-plus_binary64_830` `prod-exp_binary64_816` `*-commutative_binary64_698` `flip-+_binary64_741` `pow1/2_binary64_847` `sqr-cos-a_binary64_916` `flip3-+_binary64_770` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `pow-sqr_binary64_740`

Counts

4 → 192

Calls

4 calls:

34.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

series1.4s (9.8%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
60.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify190.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5086	17276

prune543.0ms (3.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	199	5	204
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	204	8	212

Merged error: 24.5b

Counts

212 → 8

Compiler

Compiled 15645 to 5722 computations (63.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
0.3b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))

rewrite57.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_805`
12×	`add-sqr-sqrt_binary64_789`
10×	`associate-*l/_binary64_710`
9×	`prod-exp_binary64_816` `*-un-lft-identity_binary64_767` `add-cbrt-cube_binary64_803` `add-cube-cbrt_binary64_802`
8×	`associate-r_binary64_707`
7×	`unpow-prod-down_binary64_846`
6×	`pow1_binary64_828` `flip--_binary64_742` `flip3--_binary64_771`
4×	`frac-times_binary64_777` `unswap-sqr_binary64_735` `add-log-exp_binary64_806`
3×	`pow-to-exp_binary64_836` `cbrt-unprod_binary64_800` `sqr-pow_binary64_739` `pow-exp_binary64_835` `pow-unpow_binary64_844` `unpow2_binary64_832` `sqrt-prod_binary64_783`
2×	`associate-*r/_binary64_709` `sqrt-div_binary64_784`
1×	`associate-l_binary64_708` `pow2_binary64_848` `rem-sqrt-square_binary64_780` `*-commutative_binary64_698` `flip-+_binary64_741` `pow1/2_binary64_847` `flip3-+_binary64_770` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `pow-pow_binary64_839`

Counts

4 → 78

Calls

4 calls:

20.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
19.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)

series1.7s (12%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
298.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
63.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
25.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4986	2059
1	4986	2059

prune170.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	89	9	98

Merged error: 24.5b

Counts

98 → 9

Compiler

Compiled 3659 to 2170 computations (40.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
0.3b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.7b	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_789`
19×	`unpow-prod-down_binary64_846`
17×	`add-exp-log_binary64_805`
16×	`unswap-sqr_binary64_735`
13×	`*-un-lft-identity_binary64_767`
11×	`sqr-pow_binary64_739` `unpow2_binary64_832` `add-cube-cbrt_binary64_802`
10×	`associate-l_binary64_708`
9×	`prod-exp_binary64_816`
8×	`associate-r_binary64_707`
7×	`pow-to-exp_binary64_836` `pow-exp_binary64_835`
6×	`pow1_binary64_828` `add-cbrt-cube_binary64_803`
4×	`add-log-exp_binary64_806`
3×	`pow-unpow_binary64_844` `sqrt-prod_binary64_783`
2×	`sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `cbrt-unprod_binary64_800` `*-commutative_binary64_698` `flip-+_binary64_741` `distribute-lft-out--_binary64_719` `pow1/2_binary64_847` `flip3-+_binary64_770` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `pow-pow_binary64_839` `difference-of-squares_binary64_736`

Counts

4 → 93

Calls

4 calls:

15.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
12.0ms	(*.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)

series1.7s (12.1%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
285.0ms	(*.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
61.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4939	2424
1	4939	2424

prune152.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	105	9	114

Merged error: 24.5b

Counts

114 → 9

Compiler

Compiled 3248 to 1929 computations (40.6% saved)

regimes265.0ms (1.9%)

Compiler: Compiled 1618 to 1308 computations (19.2% saved)

bsearch66.0ms (0.5%)

Steps

Iters	Range		Point
8	-1.9564235207466203e+94	-1.9901349408174056e+91	-3.716661685574004e+93

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	48
1	55	48

end0.0ms (0%)

sample2.9s (20.1%)

Algorithm

1×

intervals

Results

628.0ms	6037×	body	128	valid
446.0ms	787×	body	1024	valid
269.0ms	745×	body	512	valid
260.0ms	483×	body	1024	invalid
242.0ms	2385×	body	128	invalid
128.0ms	362×	body	512	invalid
103.0ms	425×	body	256	valid
38.0ms	169×	body	256	invalid
7.0ms	6×	body	2048	valid

Compiler

Compiled 306 to 236 computations (22.9% saved)

Details

analyze2.1s (14.6%)

sample93.0ms (0.7%)

simplify300.0ms (2.1%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite84.0ms (0.6%)

series1.6s (11.5%)

simplify96.0ms (0.7%)

prune413.0ms (2.9%)

localize17.0ms (0.1%)

rewrite115.0ms (0.8%)

series1.4s (9.8%)

simplify190.0ms (1.3%)

prune543.0ms (3.8%)

localize19.0ms (0.1%)

rewrite57.0ms (0.4%)

series1.7s (12%)

simplify81.0ms (0.6%)

prune170.0ms (1.2%)

localize20.0ms (0.1%)

rewrite49.0ms (0.3%)

series1.7s (12.1%)

simplify78.0ms (0.5%)

prune152.0ms (1.1%)

regimes265.0ms (1.9%)

bsearch66.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (20.1%)

Profiling