Details

analyze120.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 22 computations (31.3% saved)

sample23.0ms (0%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify129.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5054	46

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

Compiler

Compiled 62 to 42 computations (32.3% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
1.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64_1483` `add-exp-log_binary64_1460`
14×	`add-cbrt-cube_binary64_1458`
10×	`add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
8×	`add-cube-cbrt_binary64_1457`
7×	`associate-r_binary64_1367`
6×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `add-log-exp_binary64_1461` `pow-prod-down_binary64_1493`
4×	`associate-*r/_binary64_1369`
3×	`distribute-lft-in_binary64_1376` `pow-unpow_binary64_1499` `unpow-prod-down_binary64_1501` `distribute-rgt-in_binary64_1377`
2×	`unswap-sqr_binary64_1393` `associate-l_binary64_1368` `flip3-+_binary64_1428` `sub-neg_binary64_1418` `flip-+_binary64_1399` `associate-+r+_binary64_1359` `*-commutative_binary64_1358`
1×	`flip--_binary64_1400` `pow-pow_binary64_1494` `pow-to-exp_binary64_1491` `unpow2_binary64_1487` `pow-exp_binary64_1490` `distribute-lft-out_binary64_1378` `sum-log_binary64_1513` `+-commutative_binary64_1357` `flip3--_binary64_1429` `sqr-pow_binary64_1397`

Counts

4 → 78

Calls

4 calls:

10.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
9.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series169.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
33.0ms	(.f64 (.f64 a a) (+.f64 1 a))
33.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
29.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify42.0ms (0%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5085	1820

prune144.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	2	91

Merged error: 0.0b

Counts

91 → 2

Compiler

Compiled 3382 to 1827 computations (46% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
0.1b	(.f64 (.f64 a a) (+.f64 1 a))
1.1b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
3.0b	(.f64 (.f64 b b) (*.f64 a a))

rewrite68.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_1483`
32×	`associate-*r/_binary64_1369`
26×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
20×	`frac-add_binary64_1433` `pow-prod-down_binary64_1493`
14×	`prod-exp_binary64_1471` `flip3-+_binary64_1428` `cbrt-unprod_binary64_1455` `flip-+_binary64_1399`
13×	`add-log-exp_binary64_1461`
8×	`associate-r_binary64_1367` `add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
6×	`add-cube-cbrt_binary64_1457` `sum-log_binary64_1513`
5×	`flip--_binary64_1400` `flip3--_binary64_1429`
4×	`pow-plus_binary64_1485` `pow-prod-up_binary64_1492`
3×	`distribute-lft-in_binary64_1376` `unswap-sqr_binary64_1393` `associate-l_binary64_1368` `distribute-rgt-in_binary64_1377` `*-commutative_binary64_1358`
2×	`sub-neg_binary64_1418` `pow2_binary64_1503` `pow-sqr_binary64_1398` `associate-+r+_binary64_1359`
1×	`distribute-lft-out_binary64_1378` `associate-+l+_binary64_1360` `+-commutative_binary64_1357`

Counts

4 → 104

Calls

4 calls:

27.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))
8.0ms	(.f64 (.f64 a a) (+.f64 1 a))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series177.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
37.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
32.0ms	(.f64 (.f64 a a) (+.f64 1 a))
28.0ms	(.f64 (.f64 b b) (*.f64 a a))

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4949	4749
1	4949	4749

prune323.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	115	3	118

Merged error: 0b

Counts

118 → 3

Compiler

Compiled 6650 to 4065 computations (38.9% saved)

localize45.0ms (0%)

Local error

Found 4 expressions with local error:

1.2b	(+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
1.5b	(.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (*.f64 b b) (-.f64 1 a)))
2.4b	(*.f64 (pow.f64 b 4) (pow.f64 a 4))
41.5b	(/.f64 (+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))

rewrite13.2s (8.8%)

Algorithm

1×	rewrite-expression-head

Rules

33584×	`associate-*r/_binary64_1369`
28080×	`frac-times_binary64_1435`
21940×	`flip--_binary64_1400` `flip3--_binary64_1429`
20384×	`frac-add_binary64_1433`
14040×	`associate-*l/_binary64_1370`
7511×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
5202×	`associate-/l/_binary64_1374`
34×	`add-exp-log_binary64_1460`
26×	`associate-/r/_binary64_1373`
24×	`add-cbrt-cube_binary64_1458`
23×	`add-sqr-sqrt_binary64_1446`
18×	`prod-exp_binary64_1471`
13×	`pow1_binary64_1483`
12×	`unpow-prod-down_binary64_1501`
11×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
10×	`associate-l_binary64_1368` `cbrt-unprod_binary64_1455`
9×	`unswap-sqr_binary64_1393`
8×	`sub-neg_binary64_1418` `associate-r_binary64_1367` `sqr-pow_binary64_1397`
7×	`pow-prod-down_binary64_1493`
6×	`distribute-lft-in_binary64_1376` `pow-to-exp_binary64_1491` `pow-exp_binary64_1490` `distribute-rgt-in_binary64_1377` `add-log-exp_binary64_1461`
3×	`times-frac_binary64_1431` `div-exp_binary64_1473` `associate-/l*_binary64_1372` `cbrt-undiv_binary64_1456`
2×	`associate-+l+_binary64_1360` `associate-+r+_binary64_1359` `*-commutative_binary64_1358`
1×	`frac-2neg_binary64_1436` `associate-/r*_binary64_1371` `clear-num_binary64_1424` `div-inv_binary64_1422` `sum-log_binary64_1513` `+-commutative_binary64_1357`

Counts

4 → 10541

Calls

4 calls:

603.0ms	(/.f64 (+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
201.0ms	(+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
13.0ms	(.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (*.f64 b b) (-.f64 1 a)))
7.0ms	(*.f64 (pow.f64 b 4) (pow.f64 a 4))

series1.0s (0.7%)

Counts

4 → 12

Calls

4 calls:

562.0ms	(+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
409.0ms	(/.f64 (+.f64 (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (pow.f64 b 4) (pow.f64 a 4)) 4) (.f64 (+.f64 (pow.f64 b 4) (pow.f64 a 4)) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 4 (+.f64 (.f64 (.f64 (.f64 a a) (-.f64 1 (.f64 a a))) (+.f64 1 (.f64 a 3))) (.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (.f64 b b) (-.f64 1 a))))) (-.f64 (.f64 (.f64 (.f64 b a) (.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4))))) (.f64 (.f64 (+.f64 1 (.f64 a 3)) (-.f64 1 a)) (-.f64 (.f64 (.f64 (.f64 b a) (*.f64 b a)) 2) (+.f64 (pow.f64 b 4) (pow.f64 a 4)))))
48.0ms	(*.f64 (pow.f64 b 4) (pow.f64 a 4))
29.0ms	(.f64 (-.f64 1 (.f64 a (.f64 a 9))) (.f64 (*.f64 b b) (-.f64 1 a)))

simplify23.8s (15.8%)

Algorithm

1×	egg-herbie

Counts

10553 → 10553

Iterations

Useful iterations: 0 (579.0ms)

Iter	Nodes	Cost
0	27094	3858800

Details

analyze120.0ms (0.1%)

sample23.0ms (0%)

simplify129.0ms (0.1%)

prune3.0ms (0%)

localize16.0ms (0%)

rewrite42.0ms (0%)

series169.0ms (0.1%)

simplify42.0ms (0%)

prune144.0ms (0.1%)

localize23.0ms (0%)

rewrite68.0ms (0%)

series177.0ms (0.1%)

simplify75.0ms (0.1%)

prune323.0ms (0.2%)

localize45.0ms (0%)

rewrite13.2s (8.8%)

series1.0s (0.7%)

simplify23.8s (15.8%)

prune1.8min (73.7%)

Profiling