Details

analyze5.0ms (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)

sample27.0ms (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)

simplify416.0ms (6.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (252.0ms)

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)

localize12.0ms (0.2%)

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 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
8.6b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite108.0ms (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:

28.0ms	(/.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)))
24.0ms	(.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)))
15.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series555.0ms (8.4%)

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)))
205.0ms	(.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)))
34.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify95.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4939	3959
1	4939	3959

prune293.0ms (4.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	163	7	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	164	8	172

Merged error: 0b

Counts

172 → 8

Compiler

Compiled 5299 to 3441 computations (35.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
0.1b	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
7.9b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))

rewrite134.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

133×	`*-un-lft-identity_binary64_1425`
103×	`add-exp-log_binary64_1460`
67×	`times-frac_binary64_1431`
61×	`add-cbrt-cube_binary64_1458`
54×	`distribute-lft-out_binary64_1378` `add-sqr-sqrt_binary64_1446`
42×	`prod-exp_binary64_1471`
37×	`add-cube-cbrt_binary64_1457`
35×	`div-exp_binary64_1473`
27×	`associate-r_binary64_1367`
25×	`associate-l_binary64_1368`
22×	`cbrt-unprod_binary64_1455`
19×	`cbrt-undiv_binary64_1456` `frac-times_binary64_1435`
13×	`flip3-+_binary64_1428` `associate-*r/_binary64_1369` `flip-+_binary64_1399` `associate-/l/_binary64_1374`
11×	`pow1_binary64_1483` `associate-*l/_binary64_1370`
10×	`associate-/r*_binary64_1371`
8×	`associate-/r/_binary64_1373`
6×	`unswap-sqr_binary64_1393` `1-exp_binary64_1466` `rec-exp_binary64_1472`
5×	`associate-/l*_binary64_1372`
4×	`div-inv_binary64_1422` `add-log-exp_binary64_1461` `pow-prod-down_binary64_1493`
2×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `*-commutative_binary64_1358`

Counts

4 → 212

Calls

4 calls:

32.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
30.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
28.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

series574.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
192.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
107.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
50.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

simplify111.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4943	5836
1	4943	5836

prune382.0ms (5.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	225	7	232

Merged error: 0b

Counts

232 → 7

Compiler

Compiled 7287 to 4736 computations (35% saved)

localize14.0ms (0.2%)

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)))
7.9b	(.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))))

rewrite200.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

829×	`*-un-lft-identity_binary64_1425`
394×	`times-frac_binary64_1431`
355×	`distribute-lft-out_binary64_1378`
248×	`sqrt-prod_binary64_1440`
224×	`add-sqr-sqrt_binary64_1446`
149×	`add-cube-cbrt_binary64_1457`
127×	`swap-sqr_binary64_1392`
45×	`associate-l_binary64_1368`
42×	`associate-r_binary64_1367`
38×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
16×	`pow1_binary64_1483`
14×	`associate-/l*_binary64_1372`
13×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455`
12×	`flip3-+_binary64_1428` `associate-/r/_binary64_1373` `flip-+_binary64_1399`
10×	`associate-/r*_binary64_1371` `unswap-sqr_binary64_1393` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456` `frac-times_binary64_1435`
7×	`associate-*r/_binary64_1369`
6×	`div-inv_binary64_1422` `associate-*l/_binary64_1370`
4×	`sqrt-div_binary64_1441` `associate-/l/_binary64_1374` `add-log-exp_binary64_1461` `pow-prod-down_binary64_1493`
2×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `*-commutative_binary64_1358`
1×	`pow-plus_binary64_1485` `pow2_binary64_1503` `pow-sqr_binary64_1398` `pow-prod-up_binary64_1492`

Counts

4 → 405

Calls

4 calls:

51.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
35.0ms	(.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))))
15.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
12.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

series444.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(.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))))
110.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
74.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
61.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

simplify138.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5751	11883

prune947.0ms (14.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	417	0	417
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	417	7	424

Merged error: 0b

Counts

424 → 7

Compiler

Compiled 15196 to 10205 computations (32.8% saved)

localize14.0ms (0.2%)

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 1 (+.f64 alpha (+.f64 beta 3))))
7.9b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
8.6b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite129.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`*-un-lft-identity_binary64_1425`
80×	`add-exp-log_binary64_1460`
52×	`add-cbrt-cube_binary64_1458`
42×	`associate-r_binary64_1367`
38×	`prod-exp_binary64_1471`
37×	`distribute-lft-out_binary64_1378`
28×	`add-sqr-sqrt_binary64_1446`
26×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
24×	`times-frac_binary64_1431`
23×	`frac-times_binary64_1435`
22×	`add-cube-cbrt_binary64_1457` `cbrt-unprod_binary64_1455`
20×	`div-exp_binary64_1473`
18×	`associate-/r/_binary64_1373` `pow1_binary64_1483`
17×	`associate-*l/_binary64_1370`
12×	`cbrt-undiv_binary64_1456`
11×	`swap-sqr_binary64_1392`
10×	`associate-l_binary64_1368` `associate-*r/_binary64_1369`
5×	`pow-prod-down_binary64_1493`
4×	`associate-/l*_binary64_1372` `1-exp_binary64_1466` `add-log-exp_binary64_1461` `rec-exp_binary64_1472`
3×	`unswap-sqr_binary64_1393` `div-inv_binary64_1422` `*-commutative_binary64_1358`
2×	`associate-/l/_binary64_1374`
1×	`distribute-lft-in_binary64_1376` `frac-2neg_binary64_1436` `associate-/r*_binary64_1371` `pow-plus_binary64_1485` `un-div-inv_binary64_1423` `clear-num_binary64_1424` `pow2_binary64_1503` `distribute-rgt-in_binary64_1377` `pow-sqr_binary64_1398` `pow-prod-up_binary64_1492`

Counts

4 → 190

Calls

4 calls:

36.0ms	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.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))))
22.0ms	(/.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))

series543.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
196.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
98.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
36.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4989	5069
1	4989	5069

prune332.0ms (5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	202	7	209

Merged error: 0b

Counts

209 → 7

Compiler

Compiled 6205 to 4156 computations (33% saved)

regimes68.0ms (1%)

Compiler: Compiled 803 to 599 computations (25.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	40
1	26	40

end0.0ms (0%)

sample985.0ms (14.8%)

Algorithm

1×

intervals

Results

467.0ms	8000×	body	128	valid
145.0ms	8000×	pre	128	true

Compiler

Compiled 312 to 232 computations (25.6% saved)

Details

analyze5.0ms (0.1%)

sample27.0ms (0.4%)

simplify416.0ms (6.3%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

rewrite108.0ms (1.6%)

series555.0ms (8.4%)

simplify95.0ms (1.4%)

prune293.0ms (4.4%)

localize14.0ms (0.2%)

rewrite134.0ms (2%)

series574.0ms (8.6%)

simplify111.0ms (1.7%)

prune382.0ms (5.7%)

localize14.0ms (0.2%)

rewrite200.0ms (3%)

series444.0ms (6.7%)

simplify138.0ms (2.1%)

prune947.0ms (14.3%)

localize14.0ms (0.2%)

rewrite129.0ms (1.9%)

series543.0ms (8.2%)

simplify96.0ms (1.4%)

prune332.0ms (5%)

regimes68.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample985.0ms (14.8%)

Profiling