Details

analyze2.1s (10%)

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 (0.4%)

Algorithm

1×

intervals

Results

24.0ms	192×	body	128	valid
15.0ms	28×	body	1024	valid
9.0ms	25×	body	512	valid
8.0ms	22×	body	512	invalid
7.0ms	13×	body	1024	invalid
7.0ms	69×	body	128	invalid
3.0ms	11×	body	256	valid
2.0ms	9×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify307.0ms (1.5%)

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: 40.7b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize18.0ms (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))))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
36.8b	(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))))

rewrite89.0ms (0.4%)

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:

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))))
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))

series1.6s (7.8%)

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))))
301.0ms	(.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))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify92.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5222	10334

prune296.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	141	6	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	141	7	148

Merged error: 25.9b

Counts

148 → 7

Compiler

Compiled 8721 to 2899 computations (66.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
36.8b	(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))))
36.8b	(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))))

rewrite129.0ms (0.6%)

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:

26.0ms	(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))))
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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.7s (12.6%)

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))))
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))))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify148.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4997	18224
1	4997	18224

prune683.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	184	7	191

Merged error: 25.9b

Counts

191 → 7

Compiler

Compiled 19576 to 6658 computations (66% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.1b	(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))))))
36.8b	(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))))

rewrite150.0ms (0.7%)

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`
66×	`exp-diff_binary64_1149` `log-div_binary64_1188`
64×	`associate-*r/_binary64_1043`
9×	`add-sqr-sqrt_binary64_1123`
8×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
7×	`pow1_binary64_1162`
6×	`exp-sum_binary64_1147` `exp-prod_binary64_1153` `sqrt-prod_binary64_1117` `log-prod_binary64_1187`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`log-pow_binary64_1190`
2×	`sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181`
1×	`rem-sqrt-square_binary64_1114` `rem-exp-log_binary64_1141`

Counts

4 → 179

Calls

4 calls:

39.0ms	(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))))
36.0ms	(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))))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.2s (15.3%)

Counts

4 → 12

Calls

4 calls:

1.9s	(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))))
29.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify151.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5220	18510

prune480.0ms (2.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	182	9	191
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	183	15	198

Merged error: 18.1b

Counts

198 → 15

Compiler

Compiled 14328 to 4638 computations (67.6% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.6b	(pow.f64 E.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))))))
36.8b	(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))))

rewrite137.0ms (0.7%)

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`
66×	`pow-sub_binary64_1177` `log-div_binary64_1188`
64×	`associate-*r/_binary64_1043`
10×	`add-sqr-sqrt_binary64_1123`
9×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
8×	`pow1_binary64_1162`
6×	`unpow-prod-up_binary64_1179` `pow-unpow_binary64_1178` `sqrt-prod_binary64_1117` `log-prod_binary64_1187`
5×	`add-exp-log_binary64_1139`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`unpow-prod-down_binary64_1180` `log-pow_binary64_1190`
2×	`pow-exp_binary64_1169` `sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `flip-+_binary64_1075` `pow1/2_binary64_1181`
1×	`rem-sqrt-square_binary64_1114` `pow-pow_binary64_1173` `sqr-pow_binary64_1073` `e-exp-1_binary64_1146` `pow-to-exp_binary64_1170`

Counts

4 → 186

Calls

4 calls:

37.0ms	(pow.f64 E.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))))))
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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.4s (16%)

Counts

4 → 12

Calls

4 calls:

2.0s	(pow.f64 E.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))))))
1.4s	(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))
25.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify161.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4997	20128
1	4997	20128

prune535.0ms (2.5%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	192	6	198
Fresh	3	9	12
Picked	1	0	1
Done	0	2	2
Total	196	17	213

Merged error: 18.1b

Counts

213 → 17

Compiler

Compiled 14918 to 4754 computations (68.1% saved)

regimes1.1s (5%)

Compiler: Compiled 13392 to 8244 computations (38.4% saved)

bsearch4.0ms (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%)

sample3.4s (16.3%)

Algorithm

1×

intervals

Results

642.0ms	6044×	body	128	valid
442.0ms	793×	body	1024	valid
260.0ms	737×	body	512	valid
244.0ms	2342×	body	128	invalid
242.0ms	438×	body	1024	invalid
136.0ms	399×	body	512	invalid
109.0ms	420×	body	256	valid
47.0ms	207×	body	256	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 1315 to 810 computations (38.4% saved)

Details

analyze2.1s (10%)

sample93.0ms (0.4%)

simplify307.0ms (1.5%)

prune4.0ms (0%)

localize18.0ms (0.1%)

rewrite89.0ms (0.4%)

series1.6s (7.8%)

simplify92.0ms (0.4%)

prune296.0ms (1.4%)

localize22.0ms (0.1%)

rewrite129.0ms (0.6%)

series2.7s (12.6%)

simplify148.0ms (0.7%)

prune683.0ms (3.2%)

localize22.0ms (0.1%)

rewrite150.0ms (0.7%)

series3.2s (15.3%)

simplify151.0ms (0.7%)

prune480.0ms (2.3%)

localize27.0ms (0.1%)

rewrite137.0ms (0.7%)

series3.4s (16%)

simplify161.0ms (0.8%)

prune535.0ms (2.5%)

regimes1.1s (5%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.4s (16.3%)

Profiling