Details

analyze2.1s (9.9%)

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)

sample96.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	181×	body	128	valid
20.0ms	36×	body	1024	valid
9.0ms	25×	body	512	valid
7.0ms	13×	body	1024	invalid
7.0ms	65×	body	128	invalid
4.0ms	12×	body	512	invalid
3.0ms	14×	body	256	valid
2.0ms	7×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify308.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (141.0ms)

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: 39.1b

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 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.8b	(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))))

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`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:

22.0ms	(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))))
8.0ms	(*.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))

series1.5s (7%)

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))))
164.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5141	9677

prune310.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	122	6	128

Merged error: 27.1b

Counts

128 → 6

Compiler

Compiled 9087 to 3282 computations (63.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
36.9b	(cbrt.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))))
36.9b	(cbrt.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))))

rewrite123.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_1054`
192×	`flip3--_binary64_1115` `flip--_binary64_1086`
132×	`cbrt-div_binary64_1143`
128×	`frac-times_binary64_1121` `frac-add_binary64_1119`
64×	`associate-*r/_binary64_1053`
6×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `cbrt-prod_binary64_1142` `add-cube-cbrt_binary64_1146`
4×	`add-cbrt-cube_binary64_1147` `add-log-exp_binary64_1150` `pow1_binary64_1172` `add-exp-log_binary64_1149`
2×	`pow1/3_binary64_1193` `flip-+_binary64_1085` `flip3-+_binary64_1114`

Counts

4 → 168

Calls

4 calls:

22.0ms	(cbrt.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))))
22.0ms	(cbrt.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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.5s (16.4%)

Counts

4 → 12

Calls

4 calls:

1.7s	(cbrt.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))))
1.7s	(cbrt.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))))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify151.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4993	18474
1	4993	18474

prune769.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	179	7	186

Merged error: 27.1b

Counts

186 → 7

Compiler

Compiled 20655 to 7379 computations (64.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.2b	(exp.f64 (log.f64 (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))))))
35.8b	(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))))

rewrite127.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_1054`
192×	`flip3--_binary64_1115` `flip--_binary64_1086`
132×	`sqrt-div_binary64_1128`
128×	`frac-times_binary64_1121` `frac-add_binary64_1119`
66×	`exp-diff_binary64_1159` `log-div_binary64_1198`
64×	`associate-*r/_binary64_1053`
9×	`add-sqr-sqrt_binary64_1133`
8×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
7×	`pow1_binary64_1172`
6×	`log-prod_binary64_1197` `exp-sum_binary64_1157` `exp-prod_binary64_1163` `sqrt-prod_binary64_1127`
4×	`add-cbrt-cube_binary64_1147` `add-log-exp_binary64_1150` `add-exp-log_binary64_1149`
3×	`log-pow_binary64_1200`
2×	`pow1/2_binary64_1191` `flip-+_binary64_1085` `flip3-+_binary64_1114` `sqrt-pow1_binary64_1129`
1×	`rem-sqrt-square_binary64_1124` `rem-exp-log_binary64_1151`

Counts

4 → 179

Calls

4 calls:

30.0ms	(exp.f64 (log.f64 (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))))))
22.0ms	(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))))
9.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.2s (14.8%)

Counts

4 → 12

Calls

4 calls:

1.8s	(exp.f64 (log.f64 (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))))))
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))))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify156.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5220	18510

prune692.0ms (3.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	182	9	191
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	185	13	198

Merged error: 17.6b

Counts

198 → 13

Compiler

Compiled 18231 to 7204 computations (60.5% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.4b	(pow.f64 (exp.f64 1/2) (log.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)))))
37.3b	(log.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))))

rewrite126.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_1054`
192×	`flip3--_binary64_1115` `flip--_binary64_1086`
132×	`log-div_binary64_1198`
128×	`frac-times_binary64_1121` `frac-add_binary64_1119`
66×	`pow-sub_binary64_1187`
64×	`associate-*r/_binary64_1053`
9×	`*-un-lft-identity_binary64_1111` `add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
7×	`pow1_binary64_1172`
6×	`log-prod_binary64_1197`
5×	`add-exp-log_binary64_1149`
4×	`add-cbrt-cube_binary64_1147` `pow-unpow_binary64_1188` `pow-pow_binary64_1183` `add-log-exp_binary64_1150`
3×	`unpow-prod-down_binary64_1190` `unpow-prod-up_binary64_1189` `exp-prod_binary64_1163`
2×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `log-pow_binary64_1200`
1×	`pow-exp_binary64_1179` `sqr-pow_binary64_1083` `rem-log-exp_binary64_1152` `pow-to-exp_binary64_1180`

Counts

4 → 182

Calls

4 calls:

32.0ms	(pow.f64 (exp.f64 1/2) (log.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)))))
23.0ms	(log.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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.3s (15.5%)

Counts

4 → 12

Calls

4 calls:

2.1s	(pow.f64 (exp.f64 1/2) (log.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)))))
1.1s	(log.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))))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify168.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5021	20063

prune777.0ms (3.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	187	7	194
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	190	17	207

Merged error: 17.6b

Counts

207 → 17

Compiler

Compiled 19024 to 7999 computations (58% saved)

regimes609.0ms (2.8%)

Compiler: Compiled 4732 to 3653 computations (22.8% saved)

bsearch3.0ms (0%)

Compiler: Compiled 32 to 21 computations (34.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	166
1	61	166

end0.0ms (0%)

sample3.2s (14.9%)

Algorithm

1×

intervals

Results

649.0ms	5974×	body	128	valid
494.0ms	880×	body	1024	valid
272.0ms	2433×	body	128	invalid
266.0ms	747×	body	512	valid
265.0ms	489×	body	1024	invalid
135.0ms	371×	body	512	invalid
103.0ms	391×	body	256	valid
52.0ms	201×	body	256	invalid
8.0ms	8×	body	2048	valid

Compiler

Compiled 595 to 432 computations (27.4% saved)

Details

analyze2.1s (9.9%)

sample96.0ms (0.4%)

simplify308.0ms (1.4%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite75.0ms (0.3%)

series1.5s (7%)

simplify91.0ms (0.4%)

prune310.0ms (1.4%)

localize21.0ms (0.1%)

rewrite123.0ms (0.6%)

series3.5s (16.4%)

simplify151.0ms (0.7%)

prune769.0ms (3.6%)

localize21.0ms (0.1%)

rewrite127.0ms (0.6%)

series3.2s (14.8%)

simplify156.0ms (0.7%)

prune692.0ms (3.2%)

localize27.0ms (0.1%)

rewrite126.0ms (0.6%)

series3.3s (15.5%)

simplify168.0ms (0.8%)

prune777.0ms (3.6%)

regimes609.0ms (2.8%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.2s (14.9%)

Profiling