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

19.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify416.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (250.0ms)

Iter	Nodes	Cost
0	5111	37

prune5.0ms (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: 1.3b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize15.0ms (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)))
7.9b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
9.1b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))

rewrite111.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1425`
34×	`distribute-lft-out_binary64_1378` `add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
24×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
21×	`associate-r_binary64_1367` `add-sqr-sqrt_binary64_1446`
18×	`associate-/r/_binary64_1373`
16×	`frac-times_binary64_1435`
15×	`add-cube-cbrt_binary64_1457`
14×	`times-frac_binary64_1431`
13×	`pow1_binary64_1483`
11×	`swap-sqr_binary64_1392`
10×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `div-exp_binary64_1473` `associate-*l/_binary64_1370` `cbrt-undiv_binary64_1456`
9×	`associate-l_binary64_1368`
8×	`associate-*r/_binary64_1369`
7×	`associate-/l/_binary64_1374`
6×	`associate-/r*_binary64_1371`
5×	`associate-/l*_binary64_1372`
4×	`add-log-exp_binary64_1461`
3×	`unswap-sqr_binary64_1393` `div-inv_binary64_1422`
2×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`
1×	`distribute-lft-in_binary64_1376` `pow-plus_binary64_1485` `pow2_binary64_1503` `distribute-rgt-in_binary64_1377` `pow-sqr_binary64_1398` `pow-prod-up_binary64_1492`

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))))
20.0ms	(*.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)))

series554.0ms (1.2%)

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)))
204.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
100.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
32.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify104.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4939	3959
1	4939	3959

prune291.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	162	8	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	164	8	172

Merged error: 0.0b

Counts

172 → 8

Compiler

Compiled 5303 to 3436 computations (35.2% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite113.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64_1425`
89×	`times-frac_binary64_1431`
82×	`distribute-lft-out_binary64_1378`
60×	`add-sqr-sqrt_binary64_1446`
48×	`add-cube-cbrt_binary64_1457`
38×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
26×	`associate-l_binary64_1368` `associate-r_binary64_1367`
15×	`associate-/r*_binary64_1371` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
10×	`associate-/r/_binary64_1373`
9×	`associate-/l*_binary64_1372`
8×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455`
7×	`flip3-+_binary64_1428` `flip-+_binary64_1399` `associate-/l/_binary64_1374`
6×	`pow1_binary64_1483`
5×	`div-inv_binary64_1422`
4×	`unswap-sqr_binary64_1393` `add-log-exp_binary64_1461`
3×	`frac-2neg_binary64_1436` `clear-num_binary64_1424`
2×	`associate-r/_binary64_1369` `associate-l/_binary64_1370` `frac-times_binary64_1435`
1×	`*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 202

Calls

4 calls:

37.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
29.0ms	(/.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 alpha 1) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

series528.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.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)))
194.0ms	(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
61.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
51.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))

simplify79.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5289	5499

prune357.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	215	7	222

Merged error: 0.0b

Counts

222 → 7

Compiler

Compiled 7050 to 4455 computations (36.8% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
0.5b	(/.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))))

rewrite1.5s (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

15581×	`*-un-lft-identity_binary64_1425`
12730×	`times-frac_binary64_1431`
6938×	`distribute-lft-out_binary64_1378`
3552×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446`
587×	`associate-/r/_binary64_1373`
308×	`div-inv_binary64_1422`
282×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
171×	`associate-/r*_binary64_1371`
39×	`associate-/l*_binary64_1372`
34×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
20×	`div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
7×	`associate-/l/_binary64_1374`
4×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `pow1_binary64_1483` `add-log-exp_binary64_1461`

Counts

4 → 3963

Calls

4 calls:

129.0ms	(/.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))))
30.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
11.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
10.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))

series442.0ms (1%)

Counts

4 → 12

Calls

4 calls:

229.0ms	(/.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))))
94.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)))
59.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))
59.0ms	(/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2))

simplify2.1s (4.6%)

Algorithm

1×	egg-herbie

Counts

3975 → 3975

Iterations

Useful iterations: 0 (183.0ms)

Iter	Nodes	Cost
0	5539	269388

prune30.8s (67%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	3974	1	3975
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	3975	7	3982

Merged error: 0b

Counts

3982 → 7

Compiler

Compiled 186961 to 120337 computations (35.6% saved)

localize15.0ms (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 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
0.5b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
0.6b	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))

rewrite896.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

2156×	`*-un-lft-identity_binary64_1425`
1592×	`times-frac_binary64_1431`
917×	`distribute-lft-out_binary64_1378`
679×	`add-sqr-sqrt_binary64_1446`
569×	`add-cube-cbrt_binary64_1457`
550×	`sqrt-prod_binary64_1440`
214×	`associate-l_binary64_1368` `associate-r_binary64_1367`
78×	`associate-/r/_binary64_1373`
56×	`associate-/l*_binary64_1372`
52×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
40×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
39×	`div-inv_binary64_1422`
25×	`unswap-sqr_binary64_1393` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
21×	`associate-/r*_binary64_1371`
9×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455`
8×	`sqrt-div_binary64_1441`
6×	`pow1_binary64_1483`
4×	`associate-/l/_binary64_1374` `add-log-exp_binary64_1461`
3×	`frac-2neg_binary64_1436` `clear-num_binary64_1424`
1×	`associate-r/_binary64_1369` `associate-l/_binary64_1370` `*-commutative_binary64_1358` `frac-times_binary64_1435` `pow-prod-down_binary64_1493`

Counts

4 → 1046

Calls

4 calls:

588.0ms	(*.f64 (/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
28.0ms	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
24.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
13.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

series465.0ms (1%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(*.f64 (/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
99.0ms	(/.f64 (/.f64 (+.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
95.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
58.0ms	(/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2))

simplify400.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1058 → 1058

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4982	48084
1	4982	48084

prune5.6s (12.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1058	0	1058
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	1058	7	1065

Merged error: 0b

Counts

1065 → 7

Compiler

Compiled 50601 to 33711 computations (33.4% saved)

regimes45.0ms (0.1%)

Compiler: Compiled 564 to 396 computations (29.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

end0.0ms (0%)

sample991.0ms (2.2%)

Algorithm

1×

intervals

Results

472.0ms	8000×	body	128	valid
140.0ms	8000×	pre	128	true

Compiler

Compiled 347 to 243 computations (30% saved)

Details

analyze5.0ms (0%)

sample33.0ms (0.1%)

simplify416.0ms (0.9%)

prune5.0ms (0%)

localize15.0ms (0%)

rewrite111.0ms (0.2%)

series554.0ms (1.2%)

simplify104.0ms (0.2%)

prune291.0ms (0.6%)

localize13.0ms (0%)

rewrite113.0ms (0.2%)

series528.0ms (1.1%)

simplify79.0ms (0.2%)

prune357.0ms (0.8%)

localize13.0ms (0%)

rewrite1.5s (3.3%)

series442.0ms (1%)

simplify2.1s (4.6%)

prune30.8s (67%)

localize15.0ms (0%)

rewrite896.0ms (2%)

series465.0ms (1%)

simplify400.0ms (0.9%)

prune5.6s (12.3%)

regimes45.0ms (0.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample991.0ms (2.2%)

Profiling