Details

analyze2.2s (12.2%)

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)

sample80.0ms (0.4%)

Algorithm

1×

intervals

Results

20.0ms	193×	body	128	valid
13.0ms	24×	body	1024	valid
8.0ms	23×	body	512	valid
7.0ms	73×	body	128	invalid
4.0ms	8×	body	1024	invalid
4.0ms	16×	body	256	valid
3.0ms	9×	body	512	invalid
2.0ms	9×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify322.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (151.0ms)

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: 37.1b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize17.0ms (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))))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.4b	(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))))

rewrite89.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_1054`
102×	`flip3--_binary64_1115` `flip--_binary64_1086`
68×	`frac-times_binary64_1121`
66×	`sqrt-div_binary64_1128`
64×	`frac-add_binary64_1119`
44×	`pow1_binary64_1172`
34×	`associate-*r/_binary64_1053`
17×	`pow-prod-down_binary64_1182`
16×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
8×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144`
6×	`add-sqr-sqrt_binary64_1133`
5×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
4×	`pow-prod-up_binary64_1181` `pow-sqr_binary64_1084` `add-log-exp_binary64_1150`
3×	`sqrt-prod_binary64_1127`
2×	`pow-plus_binary64_1174`
1×	`pow1/2_binary64_1191` `-commutative_binary64_1042` `rem-sqrt-square_binary64_1124` `flip-+_binary64_1085` `associate-r_binary64_1051` `flip3-+_binary64_1114` `swap-sqr_binary64_1078` `associate-l*_binary64_1052` `pow2_binary64_1192` `sqrt-pow1_binary64_1129`

Counts

4 → 135

Calls

4 calls:

27.0ms	(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))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.7s (9%)

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))))
293.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
25.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify100.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5222	10334

prune534.0ms (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: 25.1b

Counts

148 → 8

Compiler

Compiled 15215 to 6332 computations (58.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.4b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite76.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`associate-*l/_binary64_1054`
97×	`flip3--_binary64_1115` `flip--_binary64_1086`
66×	`sqrt-div_binary64_1128`
64×	`frac-times_binary64_1121` `frac-add_binary64_1119`
32×	`associate-*r/_binary64_1053`
12×	`add-sqr-sqrt_binary64_1133`
9×	`*-un-lft-identity_binary64_1111`
7×	`add-cube-cbrt_binary64_1146` `pow1_binary64_1172`
6×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
5×	`associate-l_binary64_1052`
4×	`add-log-exp_binary64_1150`
3×	`associate-r_binary64_1051` `sqrt-prod_binary64_1127`
1×	`pow1/2_binary64_1191` `*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `rem-sqrt-square_binary64_1124` `flip-+_binary64_1085` `flip3-+_binary64_1114` `pow-prod-down_binary64_1182` `unswap-sqr_binary64_1079` `difference-of-squares_binary64_1080` `sqrt-pow1_binary64_1129` `distribute-lft-out--_binary64_1063`

Counts

4 → 115

Calls

4 calls:

24.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
8.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.5s (8.4%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
181.0ms	(*.f64 (-.f64 lambda1 lambda2) (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))

simplify116.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4988	9691
1	4988	9691

prune259.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	127	8	135

Merged error: 25.1b

Counts

135 → 8

Compiler

Compiled 8348 to 2774 computations (66.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.4b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.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))))

rewrite114.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip3--_binary64_1115` `flip--_binary64_1086`
196×	`frac-times_binary64_1121`
138×	`sqrt-div_binary64_1128`
136×	`frac-add_binary64_1119`
98×	`associate-l/_binary64_1054` `associate-r/_binary64_1053`
73×	`cos-mult_binary64_1265`
12×	`add-sqr-sqrt_binary64_1133` `pow1_binary64_1172`
9×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
6×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
4×	`add-log-exp_binary64_1150`
3×	`associate-r_binary64_1051` `swap-sqr_binary64_1078` `associate-l_binary64_1052` `sqrt-prod_binary64_1127`
1×	`pow1/2_binary64_1191` `*-commutative_binary64_1042` `pow-prod-up_binary64_1181` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `rem-sqrt-square_binary64_1124` `flip-+_binary64_1085` `flip3-+_binary64_1114` `sqr-cos-a_binary64_1260` `pow-plus_binary64_1174` `pow-sqr_binary64_1084` `pow-prod-down_binary64_1182` `unswap-sqr_binary64_1079` `pow2_binary64_1192` `sqrt-pow1_binary64_1129`

Counts

4 → 192

Calls

4 calls:

28.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.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)))

series1.5s (7.9%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.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))))
71.0ms	(*.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))

simplify198.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5085	17276

prune559.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	2	4	6
Picked	1	0	1
Done	1	0	1
Total	204	8	212

Merged error: 24.8b

Counts

212 → 8

Compiler

Compiled 15873 to 5793 computations (63.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))
0.6b	(+.f64 1 (cos.f64 (+.f64 phi1 phi2)))
3.4b	(cos.f64 (+.f64 phi1 phi2))
34.4b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite125.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

200×	`flip3--_binary64_1115` `flip--_binary64_1086`
198×	`frac-times_binary64_1121`
138×	`sqrt-div_binary64_1128`
136×	`frac-add_binary64_1119`
100×	`associate-*l/_binary64_1054`
99×	`associate-*r/_binary64_1053`
24×	`*-un-lft-identity_binary64_1111`
22×	`add-sqr-sqrt_binary64_1133`
16×	`associate-r_binary64_1051`
14×	`add-cube-cbrt_binary64_1146`
13×	`times-frac_binary64_1117`
9×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
7×	`pow1_binary64_1172`
6×	`add-log-exp_binary64_1150`
5×	`associate-l_binary64_1052`
4×	`distribute-lft-out_binary64_1062`
3×	`sqrt-prod_binary64_1127`
2×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `flip-+_binary64_1085` `flip3-+_binary64_1114` `unswap-sqr_binary64_1079` `cos-sum_binary64_1245`
1×	`pow1/2_binary64_1191` `*-commutative_binary64_1042` `rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `+-commutative_binary64_1041` `div-exp_binary64_1162` `pow-prod-down_binary64_1182` `cbrt-undiv_binary64_1145` `difference-of-squares_binary64_1080` `sqrt-pow1_binary64_1129` `sum-log_binary64_1202` `associate-+r-_binary64_1045` `distribute-lft-out--_binary64_1063`

Counts

4 → 213

Calls

4 calls:

32.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(*.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))
6.0ms	(+.f64 1 (cos.f64 (+.f64 phi1 phi2)))
5.0ms	(cos.f64 (+.f64 phi1 phi2))

series4.8s (26.1%)

Counts

4 → 12

Calls

4 calls:

4.5s	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
210.0ms	(*.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))
28.0ms	(+.f64 1 (cos.f64 (+.f64 phi1 phi2)))
21.0ms	(cos.f64 (+.f64 phi1 phi2))

simplify191.0ms (1%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5177	18230

prune568.0ms (3.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	221	4	225
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	223	10	233

Merged error: 24.6b

Counts

233 → 10

Compiler

Compiled 16106 to 5584 computations (65.3% saved)

regimes310.0ms (1.7%)

Compiler: Compiled 2774 to 1868 computations (32.7% saved)

bsearch58.0ms (0.3%)

Steps

Iters	Range		Point
9	4.207808836155575e-14	2.640972555690998e-05	2.5973862171465132e-05

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	89	66
1	89	66

end0.0ms (0%)

sample2.9s (15.9%)

Algorithm

1×

intervals

Results

622.0ms	6021×	body	128	valid
427.0ms	789×	body	1024	valid
269.0ms	2453×	body	128	invalid
264.0ms	743×	body	512	valid
220.0ms	415×	body	1024	invalid
131.0ms	363×	body	512	invalid
110.0ms	441×	body	256	valid
42.0ms	185×	body	256	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 523 to 346 computations (33.8% saved)

Details

analyze2.2s (12.2%)

sample80.0ms (0.4%)

simplify322.0ms (1.7%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite89.0ms (0.5%)

series1.7s (9%)

simplify100.0ms (0.5%)

prune534.0ms (2.9%)

localize19.0ms (0.1%)

rewrite76.0ms (0.4%)

series1.5s (8.4%)

simplify116.0ms (0.6%)

prune259.0ms (1.4%)

localize21.0ms (0.1%)

rewrite114.0ms (0.6%)

series1.5s (7.9%)

simplify198.0ms (1.1%)

prune559.0ms (3%)

localize17.0ms (0.1%)

rewrite125.0ms (0.7%)

series4.8s (26.1%)

simplify191.0ms (1%)

prune568.0ms (3.1%)

regimes310.0ms (1.7%)

bsearch58.0ms (0.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (15.9%)

Profiling