Details

analyze2.1s (16%)

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)

sample79.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	203×	body	128	valid
9.0ms	21×	body	1024	valid
8.0ms	13×	body	256	valid
7.0ms	76×	body	128	invalid
7.0ms	15×	body	1024	invalid
6.0ms	19×	body	512	valid
2.0ms	6×	body	512	invalid
1.0ms	6×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify223.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

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

36.9b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize15.0ms (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))))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
33.9b	(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))))

rewrite78.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_1044`
102×	`flip--_binary64_1076` `flip3--_binary64_1105`
68×	`frac-times_binary64_1111`
66×	`sqrt-div_binary64_1118`
64×	`frac-add_binary64_1109`
44×	`pow1_binary64_1162`
34×	`associate-*r/_binary64_1043`
17×	`pow-prod-down_binary64_1172`
16×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
6×	`add-sqr-sqrt_binary64_1123`
5×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
4×	`pow-prod-up_binary64_1171` `add-log-exp_binary64_1140` `pow-sqr_binary64_1074`
3×	`sqrt-prod_binary64_1117`
2×	`pow-plus_binary64_1164`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `flip-+_binary64_1075` `associate-l*_binary64_1042` `pow2_binary64_1182` `pow1/2_binary64_1181`

Counts

4 → 135

Calls

4 calls:

24.0ms	(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))))
14.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series922.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

729.0ms	(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))))
160.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5228	10334

prune312.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	138	9	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	138	10	148

Error

22.8b

Counts

148 → 10

Compiler

Compiled 8917 to 3005 computations (66.3% saved)

localize23.0ms (0.2%)

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))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
33.9b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite82.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/_binary64_1044`
96×	`flip--_binary64_1076` `flip3--_binary64_1105`
66×	`sqrt-div_binary64_1118`
64×	`frac-times_binary64_1111` `frac-add_binary64_1109`
32×	`associate-*r/_binary64_1043`
6×	`add-sqr-sqrt_binary64_1123`
5×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`sqrt-prod_binary64_1117`
1×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

4 → 100

Calls

4 calls:

30.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series759.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

712.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5066	9368

prune264.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	112	10	122

Error

22.8b

Counts

122 → 10

Compiler

Compiled 8416 to 2974 computations (64.7% saved)

localize27.0ms (0.2%)

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))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
33.9b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite79.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/_binary64_1044`
96×	`flip--_binary64_1076` `flip3--_binary64_1105`
66×	`sqrt-div_binary64_1118`
64×	`frac-times_binary64_1111` `frac-add_binary64_1109`
32×	`associate-*r/_binary64_1043`
6×	`add-sqr-sqrt_binary64_1123`
5×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`sqrt-prod_binary64_1117`
1×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

4 → 100

Calls

4 calls:

30.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.0s (7.8%)

Counts

4 → 12

Calls

4 calls:

947.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (cbrt.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
18.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
18.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify107.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5066	9368

prune293.0ms (2.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	112	10	122

Error

22.8b

Counts

122 → 10

Compiler

Compiled 8945 to 3316 computations (62.9% saved)

localize19.0ms (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))
33.9b	(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))))
33.9b	(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))))

rewrite115.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_1044`
192×	`flip--_binary64_1076` `flip3--_binary64_1105`
132×	`sqrt-div_binary64_1118`
128×	`frac-times_binary64_1111` `frac-add_binary64_1109`
64×	`associate-*r/_binary64_1043`
8×	`add-sqr-sqrt_binary64_1123`
6×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

4 → 172

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))))
21.0ms	(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))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.5s (11.3%)

Counts

4 → 12

Calls

4 calls:

715.0ms	(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))))
709.0ms	(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))))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify144.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5001	18224

prune713.0ms (5.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	184	10	194

Error

22.8b

Counts

194 → 10

Compiler

Compiled 19450 to 6566 computations (66.2% saved)

regimes820.0ms (6.4%)

Accuracy

Total 3.7b remaining (12.7%)

Threshold costs 0b (0%)

Compiler

Compiled 9650 to 5676 computations (41.2% saved)

bsearch3.0ms (0%)

Compiler: Compiled 29 to 19 computations (34.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	91
1	58	91

end0.0ms (0%)

sample3.1s (23.8%)

Algorithm

1×

intervals

Results

626.0ms	6046×	body	128	valid
373.0ms	833×	body	1024	valid
239.0ms	2465×	body	128	invalid
229.0ms	709×	body	512	valid
226.0ms	474×	body	1024	invalid
119.0ms	360×	body	512	invalid
89.0ms	401×	body	256	valid
39.0ms	162×	body	256	invalid
8.0ms	11×	body	2048	valid

Compiler

Compiled 1086 to 635 computations (41.5% saved)

Details

analyze2.1s (16%)

sample79.0ms (0.6%)

simplify223.0ms (1.7%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite78.0ms (0.6%)

series922.0ms (7.2%)

simplify94.0ms (0.7%)

prune312.0ms (2.4%)

localize23.0ms (0.2%)

rewrite82.0ms (0.6%)

series759.0ms (5.9%)

simplify94.0ms (0.7%)

prune264.0ms (2.1%)

localize27.0ms (0.2%)

rewrite79.0ms (0.6%)

series1.0s (7.8%)

simplify107.0ms (0.8%)

prune293.0ms (2.3%)

localize19.0ms (0.1%)

rewrite115.0ms (0.9%)

series1.5s (11.3%)

simplify144.0ms (1.1%)

prune713.0ms (5.6%)

regimes820.0ms (6.4%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (23.8%)

Profiling