Details

analyze6.0ms (0.1%)

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)

sample28.0ms (0.4%)

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)

simplify422.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (257.0ms)

Iter	Nodes	Cost
0	5111	37

prune5.0ms (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 85 to 60 computations (29.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.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)))
7.2b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.7b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite115.0ms (1.6%)

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:

34.0ms	(/.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)))
26.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.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)))
16.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series557.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(/.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)))
195.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
107.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
37.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4939	3959
1	4939	3959

prune302.0ms (4.2%)

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 5237 to 3395 computations (35.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite116.0ms (1.6%)

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:

38.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
30.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

series531.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
197.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
54.0ms	(/.f64 (+.f64 1 alpha) (+.f64 (+.f64 beta alpha) 2))
52.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

simplify117.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4937	5499
1	4937	5499

prune368.0ms (5.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	214	7	221

Merged error: 0b

Counts

221 → 7

Compiler

Compiled 7022 to 4444 computations (36.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha))))
0.1b	(/.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
0.2b	(/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))

rewrite217.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

808×	`*-un-lft-identity_binary64_1425`
627×	`times-frac_binary64_1431`
352×	`sqrt-prod_binary64_1440`
307×	`distribute-lft-out_binary64_1378`
265×	`add-cube-cbrt_binary64_1457` `add-sqr-sqrt_binary64_1446`
58×	`associate-/r*_binary64_1371`
42×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
23×	`associate-/r/_binary64_1373`
21×	`div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
20×	`sqrt-div_binary64_1441`
17×	`associate-/l*_binary64_1372`
14×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
12×	`div-inv_binary64_1422`
9×	`associate-/l/_binary64_1374`
6×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455`
4×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `pow1_binary64_1483` `add-log-exp_binary64_1461`
1×	`associate-r/_binary64_1369` `associate-l/_binary64_1370` `frac-times_binary64_1435`

Counts

4 → 500

Calls

4 calls:

58.0ms	(/.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
26.0ms	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha))))
13.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))
12.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

series390.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(/.f64 (*.f64 (/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
74.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha)))
50.0ms	(/.f64 (sqrt.f64 (+.f64 1 alpha)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 1 alpha))))
47.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

simplify187.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

512 → 512

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4973	16854
1	4973	16854

prune1.6s (22.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	512	0	512
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	512	7	519

Merged error: 0b

Counts

519 → 7

Compiler

Compiled 20572 to 13791 computations (33% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (+.f64 beta 1))
0.2b	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
7.2b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

rewrite123.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`*-un-lft-identity_binary64_1425`
58×	`add-sqr-sqrt_binary64_1446`
56×	`add-exp-log_binary64_1460`
50×	`cbrt-prod_binary64_1453`
49×	`associate-r_binary64_1367`
47×	`times-frac_binary64_1431`
40×	`add-cbrt-cube_binary64_1458`
37×	`distribute-lft-out_binary64_1378`
34×	`add-cube-cbrt_binary64_1457`
24×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455`
22×	`associate-l_binary64_1368`
18×	`pow1_binary64_1483`
14×	`cbrt-div_binary64_1454` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456` `frac-times_binary64_1435`
13×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
10×	`unswap-sqr_binary64_1393`
9×	`associate-*r/_binary64_1369` `swap-sqr_binary64_1392`
8×	`associate-*l/_binary64_1370`
7×	`pow1/3_binary64_1504`
6×	`pow-prod-down_binary64_1493`
4×	`associate-/r/_binary64_1373` `add-log-exp_binary64_1461`
3×	`*-commutative_binary64_1358`
2×	`div-inv_binary64_1422` `pow-sqr_binary64_1398` `pow-prod-up_binary64_1492`
1×	`pow-plus_binary64_1485` `pow2_binary64_1503`

Counts

4 → 189

Calls

4 calls:

38.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
34.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
12.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
3.0ms	(cbrt.f64 (+.f64 beta 1))

series397.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
101.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
54.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
40.0ms	(cbrt.f64 (+.f64 beta 1))

simplify119.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4933	5176
1	4933	5176

prune411.0ms (5.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	201	7	208

Merged error: 0b

Counts

208 → 7

Compiler

Compiled 7728 to 5214 computations (32.5% saved)

regimes41.0ms (0.6%)

Compiler: Compiled 436 to 330 computations (24.3% 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%)

sample976.0ms (13.5%)

Algorithm

1×

intervals

Results

480.0ms	8000×	body	128	valid
137.0ms	8000×	pre	128	true

Compiler

Compiled 283 to 210 computations (25.8% saved)

Details

analyze6.0ms (0.1%)

sample28.0ms (0.4%)

simplify422.0ms (5.8%)

prune5.0ms (0.1%)

localize13.0ms (0.2%)

rewrite115.0ms (1.6%)

series557.0ms (7.7%)

simplify101.0ms (1.4%)

prune302.0ms (4.2%)

localize15.0ms (0.2%)

rewrite116.0ms (1.6%)

series531.0ms (7.3%)

simplify117.0ms (1.6%)

prune368.0ms (5.1%)

localize14.0ms (0.2%)

rewrite217.0ms (3%)

series390.0ms (5.4%)

simplify187.0ms (2.6%)

prune1.6s (22.6%)

localize19.0ms (0.3%)

rewrite123.0ms (1.7%)

series397.0ms (5.5%)

simplify119.0ms (1.7%)

prune411.0ms (5.7%)

regimes41.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample976.0ms (13.5%)

Profiling