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)

sample27.0ms (0.2%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify427.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (257.0ms)

Iter	Nodes	Cost
0	5111	37

prune8.0ms (0.1%)

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: 0.8b

Counts

2 → 2

Compiler

Compiled 145 to 102 computations (29.7% saved)

localize13.0ms (0.1%)

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)))
7.3b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
12.2b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite116.0ms (0.9%)

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:

29.0ms	(/.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)))
25.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
21.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
16.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series545.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(/.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)))
194.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
101.0ms	(/.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))

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4982	3959
1	4982	3959

prune618.0ms (4.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	163	7	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0.0b

Counts

172 → 7

Compiler

Compiled 12686 to 9108 computations (28.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
7.3b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite209.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

826×	`*-un-lft-identity_binary64_1111`
508×	`times-frac_binary64_1117`
374×	`distribute-lft-out_binary64_1062`
191×	`add-sqr-sqrt_binary64_1133`
182×	`add-cube-cbrt_binary64_1146`
136×	`associate-r_binary64_1051`
34×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
31×	`associate-/l*_binary64_1056`
30×	`associate-/r/_binary64_1057`
20×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
15×	`div-inv_binary64_1108` `associate-/r*_binary64_1055`
14×	`div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
8×	`associate-/l/_binary64_1058`
6×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `pow1_binary64_1172`
4×	`associate-l/_binary64_1054` `frac-times_binary64_1121` `associate-l*_binary64_1052` `add-log-exp_binary64_1150`
3×	`frac-2neg_binary64_1122` `unswap-sqr_binary64_1079` `clear-num_binary64_1110`
2×	`associate-*r/_binary64_1053`
1×	`*-commutative_binary64_1042` `pow-prod-down_binary64_1182`

Counts

4 → 422

Calls

4 calls:

59.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
37.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
26.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

series579.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
193.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
103.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
61.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

simplify162.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4941	12598
1	4941	12598

prune1.2s (9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	430	4	434
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	435	6	441

Merged error: 0.0b

Counts

441 → 6

Compiler

Compiled 17851 to 11556 computations (35.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta)))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
7.3b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2)))

rewrite535.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

2828×	`*-un-lft-identity_binary64_1111`
2522×	`times-frac_binary64_1117`
1137×	`distribute-lft-out_binary64_1062`
890×	`add-sqr-sqrt_binary64_1133`
869×	`add-cube-cbrt_binary64_1146`
421×	`associate-r_binary64_1051`
100×	`add-exp-log_binary64_1149`
92×	`associate-/r/_binary64_1057`
87×	`associate-/l*_binary64_1056`
58×	`div-exp_binary64_1162`
52×	`add-cbrt-cube_binary64_1147` `div-inv_binary64_1108`
44×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
36×	`associate-/r*_binary64_1055`
26×	`cbrt-undiv_binary64_1145`
16×	`prod-exp_binary64_1160`
8×	`cbrt-unprod_binary64_1144` `1-exp_binary64_1155` `rec-exp_binary64_1161`
7×	`pow1_binary64_1172`
6×	`associate-/l/_binary64_1058` `unswap-sqr_binary64_1079`
4×	`associate-l/_binary64_1054` `frac-times_binary64_1121` `associate-l*_binary64_1052` `add-log-exp_binary64_1150`
3×	`frac-2neg_binary64_1122` `clear-num_binary64_1110`
2×	`associate-*r/_binary64_1053`
1×	`*-commutative_binary64_1042` `pow-flip_binary64_1185` `pow-prod-down_binary64_1182` `inv-pow_binary64_1196`

Counts

4 → 1153

Calls

4 calls:

144.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2)))
68.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
38.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))
15.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta)))

series655.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
203.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2)))
155.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))
75.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta)))

simplify382.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1165 → 1165

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4991	39634
1	4991	39634

prune4.7s (35.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1165	0	1165
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	1165	6	1171

Merged error: 0.0b

Counts

1171 → 6

Compiler

Compiled 46996 to 31082 computations (33.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
0.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
7.3b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

rewrite194.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

829×	`*-un-lft-identity_binary64_1111`
394×	`times-frac_binary64_1117`
355×	`distribute-lft-out_binary64_1062`
248×	`sqrt-prod_binary64_1127`
224×	`add-sqr-sqrt_binary64_1133`
149×	`add-cube-cbrt_binary64_1146`
127×	`swap-sqr_binary64_1078`
45×	`associate-l_binary64_1052`
42×	`associate-r_binary64_1051`
38×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
16×	`pow1_binary64_1172`
14×	`associate-/l*_binary64_1056`
13×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144`
12×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `associate-/r/_binary64_1057`
10×	`frac-times_binary64_1121` `associate-/r*_binary64_1055` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `unswap-sqr_binary64_1079`
7×	`associate-*r/_binary64_1053`
6×	`associate-*l/_binary64_1054` `div-inv_binary64_1108`
4×	`sqrt-div_binary64_1128` `associate-/l/_binary64_1058` `pow-prod-down_binary64_1182` `add-log-exp_binary64_1150`
2×	`*-commutative_binary64_1042` `frac-2neg_binary64_1122` `clear-num_binary64_1110`
1×	`pow-prod-up_binary64_1181` `pow-plus_binary64_1174` `pow-sqr_binary64_1084` `pow2_binary64_1192`

Counts

4 → 405

Calls

4 calls:

57.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
33.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
12.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
12.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

series408.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
93.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
62.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
62.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

simplify141.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5792	11833

prune1.1s (8.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	418	5	423

Merged error: 0.0b

Counts

423 → 5

Compiler

Compiled 15365 to 10329 computations (32.8% saved)

regimes33.0ms (0.3%)

Compiler: Compiled 272 to 216 computations (20.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	40
1	25	40

end0.0ms (0%)

sample1.1s (8%)

Algorithm

1×

intervals

Results

471.0ms	8000×	body	128	valid
281.0ms	8000×	pre	128	true

Compiler

Compiled 203 to 155 computations (23.6% saved)

Details

analyze5.0ms (0%)

sample27.0ms (0.2%)

simplify427.0ms (3.2%)

prune8.0ms (0.1%)

localize13.0ms (0.1%)

rewrite116.0ms (0.9%)

series545.0ms (4.1%)

simplify83.0ms (0.6%)

prune618.0ms (4.7%)

localize14.0ms (0.1%)

rewrite209.0ms (1.6%)

series579.0ms (4.4%)

simplify162.0ms (1.2%)

prune1.2s (9%)

localize14.0ms (0.1%)

rewrite535.0ms (4%)

series655.0ms (4.9%)

simplify382.0ms (2.9%)

prune4.7s (35.5%)

localize14.0ms (0.1%)

rewrite194.0ms (1.5%)

series408.0ms (3.1%)

simplify141.0ms (1.1%)

prune1.1s (8.5%)

regimes33.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (8%)

Profiling