Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 42 to 29 computations (31% saved)

sample33.0ms (0.1%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
9.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify425.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (260.0ms)

Iter	Nodes	Cost
0	5111	37

prune11.0ms (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: 1.0b

Counts

2 → 2

Compiler

Compiled 145 to 102 computations (29.7% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
7.6b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
9.0b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))

rewrite115.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1111`
34×	`add-cbrt-cube_binary64_1147` `distribute-lft-out_binary64_1062` `add-exp-log_binary64_1149`
24×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
21×	`add-sqr-sqrt_binary64_1133` `associate-r_binary64_1051`
18×	`associate-/r/_binary64_1057`
16×	`frac-times_binary64_1121`
15×	`add-cube-cbrt_binary64_1146`
14×	`times-frac_binary64_1117`
13×	`pow1_binary64_1172`
11×	`swap-sqr_binary64_1078`
10×	`prod-exp_binary64_1160` `associate-*l/_binary64_1054` `cbrt-unprod_binary64_1144` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
9×	`associate-l_binary64_1052`
8×	`associate-*r/_binary64_1053`
7×	`associate-/l/_binary64_1058`
6×	`associate-/r*_binary64_1055`
5×	`associate-/l*_binary64_1056`
4×	`add-log-exp_binary64_1150`
3×	`div-inv_binary64_1108` `unswap-sqr_binary64_1079`
2×	`*-commutative_binary64_1042` `frac-2neg_binary64_1122` `pow-prod-down_binary64_1182` `clear-num_binary64_1110`
1×	`pow-prod-up_binary64_1181` `distribute-lft-in_binary64_1060` `pow-plus_binary64_1174` `pow-sqr_binary64_1084` `pow2_binary64_1192` `distribute-rgt-in_binary64_1061`

Counts

4 → 158

Calls

4 calls:

31.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
27.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
19.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
18.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series533.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
182.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
103.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
33.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify87.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4982	3959
1	4982	3959

prune630.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	6	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0.0b

Counts

172 → 7

Compiler

Compiled 12830 to 9181 computations (28.4% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))

rewrite120.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64_1111`
89×	`times-frac_binary64_1117`
82×	`distribute-lft-out_binary64_1062`
60×	`add-sqr-sqrt_binary64_1133`
48×	`add-cube-cbrt_binary64_1146`
38×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
26×	`associate-r_binary64_1051` `associate-l_binary64_1052`
15×	`associate-/r*_binary64_1055` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
10×	`associate-/r/_binary64_1057`
9×	`associate-/l*_binary64_1056`
8×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144`
7×	`flip-+_binary64_1085` `associate-/l/_binary64_1058` `flip3-+_binary64_1114`
6×	`pow1_binary64_1172`
5×	`div-inv_binary64_1108`
4×	`unswap-sqr_binary64_1079` `add-log-exp_binary64_1150`
3×	`frac-2neg_binary64_1122` `clear-num_binary64_1110`
2×	`associate-l/_binary64_1054` `frac-times_binary64_1121` `associate-r/_binary64_1053`
1×	`*-commutative_binary64_1042` `pow-prod-down_binary64_1182`

Counts

4 → 202

Calls

4 calls:

41.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
31.0ms	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))

series512.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

225.0ms	(/.f64 (*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
187.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
50.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
50.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))

simplify120.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4963	5499
1	4963	5499

prune412.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	215	6	221

Merged error: 0.0b

Counts

221 → 6

Compiler

Compiled 8126 to 5261 computations (35.3% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
0.1b	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))

rewrite1.4s (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

15581×	`*-un-lft-identity_binary64_1111`
12730×	`times-frac_binary64_1117`
6938×	`distribute-lft-out_binary64_1062`
3552×	`add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
587×	`associate-/r/_binary64_1057`
308×	`div-inv_binary64_1108`
282×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
171×	`associate-/r*_binary64_1055`
39×	`associate-/l*_binary64_1056`
34×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
20×	`div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
7×	`associate-/l/_binary64_1058`
4×	`frac-2neg_binary64_1122` `add-log-exp_binary64_1150` `pow1_binary64_1172` `clear-num_binary64_1110`

Counts

4 → 3963

Calls

4 calls:

139.0ms	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))
22.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
21.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

series414.0ms (1%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))
82.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
59.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))
51.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify2.2s (5.1%)

Algorithm

1×	egg-herbie

Counts

3975 → 3975

Iterations

Useful iterations: 0 (181.0ms)

Iter	Nodes	Cost
0	5532	269388

prune34.2s (78.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	3974	1	3975
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	3975	6	3981

Merged error: 0b

Counts

3981 → 6

Compiler

Compiled 188387 to 121400 computations (35.6% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
0.1b	(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
9.0b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))

rewrite138.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

133×	`*-un-lft-identity_binary64_1111`
103×	`add-exp-log_binary64_1149`
67×	`times-frac_binary64_1117`
61×	`add-cbrt-cube_binary64_1147`
54×	`add-sqr-sqrt_binary64_1133` `distribute-lft-out_binary64_1062`
42×	`prod-exp_binary64_1160`
37×	`add-cube-cbrt_binary64_1146`
35×	`div-exp_binary64_1162`
27×	`associate-r_binary64_1051`
25×	`associate-l_binary64_1052`
22×	`cbrt-unprod_binary64_1144`
19×	`frac-times_binary64_1121` `cbrt-undiv_binary64_1145`
13×	`flip-+_binary64_1085` `associate-/l/_binary64_1058` `flip3-+_binary64_1114` `associate-*r/_binary64_1053`
11×	`associate-*l/_binary64_1054` `pow1_binary64_1172`
10×	`associate-/r*_binary64_1055`
8×	`associate-/r/_binary64_1057`
6×	`1-exp_binary64_1155` `rec-exp_binary64_1161` `unswap-sqr_binary64_1079`
5×	`associate-/l*_binary64_1056`
4×	`div-inv_binary64_1108` `pow-prod-down_binary64_1182` `add-log-exp_binary64_1150`
2×	`*-commutative_binary64_1042` `frac-2neg_binary64_1122` `clear-num_binary64_1110`

Counts

4 → 212

Calls

4 calls:

39.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
33.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
27.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))
11.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

series611.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
196.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))))
152.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
49.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify112.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4960	5833
1	4960	5833

prune349.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	224	6	230

Merged error: 0b

Counts

230 → 6

Compiler

Compiled 7069 to 4573 computations (35.3% saved)

regimes35.0ms (0.1%)

Compiler: Compiled 368 to 276 computations (25% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

end0.0ms (0%)

sample946.0ms (2.2%)

Algorithm

1×

intervals

Results

489.0ms	8000×	body	128	valid
135.0ms	8000×	pre	128	true

Compiler

Compiled 249 to 183 computations (26.5% saved)

Details

analyze5.0ms (0%)

sample33.0ms (0.1%)

simplify425.0ms (1%)

prune11.0ms (0%)

localize13.0ms (0%)

rewrite115.0ms (0.3%)

series533.0ms (1.2%)

simplify87.0ms (0.2%)

prune630.0ms (1.4%)

localize14.0ms (0%)

rewrite120.0ms (0.3%)

series512.0ms (1.2%)

simplify120.0ms (0.3%)

prune412.0ms (0.9%)

localize12.0ms (0%)

rewrite1.4s (3.2%)

series414.0ms (1%)

simplify2.2s (5.1%)

prune34.2s (78.6%)

localize16.0ms (0%)

rewrite138.0ms (0.3%)

series611.0ms (1.4%)

simplify112.0ms (0.3%)

prune349.0ms (0.8%)

regimes35.0ms (0.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample946.0ms (2.2%)

Profiling