Details

analyze11.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample24.0ms (0.9%)

Algorithm

1×

intervals

Results

6.0ms	55×	body	512	valid
6.0ms	145×	body	128	valid
4.0ms	29×	body	1024	valid
3.0ms	27×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify167.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune3.0ms (0.1%)

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: 11.7b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite90.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64_1425`
58×	`add-sqr-sqrt_binary64_1446`
56×	`times-frac_binary64_1431`
25×	`add-cube-cbrt_binary64_1457`
18×	`distribute-lft-out--_binary64_1379`
17×	`distribute-lft-out_binary64_1378`
14×	`difference-of-squares_binary64_1394`
12×	`add-exp-log_binary64_1460`
11×	`associate-/r*_binary64_1371` `add-log-exp_binary64_1461`
8×	`add-cbrt-cube_binary64_1458` `div-inv_binary64_1422`
6×	`associate-/l*_binary64_1372` `pow1_binary64_1483`
4×	`difference-of-sqr-1_binary64_1395` `associate-/r/_binary64_1373` `div-exp_binary64_1473`
3×	`flip--_binary64_1400` `frac-add_binary64_1433` `flip3--_binary64_1429`
2×	`diff-log_binary64_1514` `frac-2neg_binary64_1436` `pow-flip_binary64_1496` `inv-pow_binary64_1507` `flip3-+_binary64_1428` `sub-neg_binary64_1418` `clear-num_binary64_1424` `sum-log_binary64_1513` `flip-+_binary64_1399` `frac-sub_binary64_1434` `1-exp_binary64_1466` `cbrt-undiv_binary64_1456` `rec-exp_binary64_1472`
1×	`associate-+l+_binary64_1360` `associate-+l-_binary64_1362` `+-commutative_binary64_1357`

Counts

4 → 135

Calls

4 calls:

42.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
9.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series172.0ms (6%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
26.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
18.0ms	(/.f64 1 (-.f64 x 1))
17.0ms	(/.f64 1 (+.f64 x 1))

simplify84.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5051	2576

prune201.0ms (7.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	3	148

Merged error: 0.3b

Counts

148 → 3

Compiler

Compiled 3244 to 2604 computations (19.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(*.f64 x (+.f64 1 x))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
16.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite67.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_1446`
42×	`associate-*r/_binary64_1369`
34×	`*-un-lft-identity_binary64_1425`
32×	`frac-add_binary64_1433`
27×	`times-frac_binary64_1431`
26×	`flip--_binary64_1400` `flip3--_binary64_1429`
20×	`add-cube-cbrt_binary64_1457`
19×	`flip3-+_binary64_1428` `flip-+_binary64_1399`
18×	`associate-/l/_binary64_1374`
16×	`difference-of-squares_binary64_1394` `frac-times_binary64_1435`
9×	`associate-/r*_binary64_1371`
8×	`add-cbrt-cube_binary64_1458` `associate-*l/_binary64_1370` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
6×	`pow1_binary64_1483`
4×	`distribute-lft-out--_binary64_1379` `distribute-rgt-out--_binary64_1381` `unpow-prod-down_binary64_1501` `associate-r_binary64_1367` `unpow3_binary64_1488` `cube-prod_binary64_1450` `sqr-pow_binary64_1397`
3×	`distribute-lft-in_binary64_1376` `associate-l_binary64_1368` `sub-neg_binary64_1418` `distribute-rgt-in_binary64_1377` `associate-/l*_binary64_1372`
2×	`associate-+l+_binary64_1360` `associate-/r/_binary64_1373` `associate-+r+_binary64_1359`
1×	`diff-log_binary64_1514` `frac-2neg_binary64_1436` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `cbrt-unprod_binary64_1455` `clear-num_binary64_1424` `distribute-lft-out_binary64_1378` `div-inv_binary64_1422` `sum-log_binary64_1513` `div-exp_binary64_1473` `+-commutative_binary64_1357` `cbrt-undiv_binary64_1456` `*-commutative_binary64_1358` `pow-prod-down_binary64_1493`

Counts

4 → 136

Calls

4 calls:

24.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
12.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
6.0ms	(*.f64 x (+.f64 1 x))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series147.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
53.0ms	(*.f64 x (+.f64 1 x))
29.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
8.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify99.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5450	6035

prune325.0ms (11.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	149	2	151

Merged error: 0.3b

Counts

151 → 2

Compiler

Compiled 6386 to 4474 computations (29.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (pow.f64 x 3) x)
0.3b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_1446`
31×	`*-un-lft-identity_binary64_1425`
27×	`times-frac_binary64_1431`
20×	`difference-of-squares_binary64_1394`
16×	`add-cube-cbrt_binary64_1457`
9×	`associate-/r*_binary64_1371`
5×	`distribute-lft-out--_binary64_1379` `distribute-rgt-out--_binary64_1381` `unpow-prod-down_binary64_1501` `unpow3_binary64_1488` `cube-prod_binary64_1450` `sqr-pow_binary64_1397`
4×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
3×	`associate-/l*_binary64_1372`
2×	`flip--_binary64_1400` `associate-/r/_binary64_1373` `pow1_binary64_1483` `flip3--_binary64_1429`
1×	`diff-log_binary64_1514` `frac-2neg_binary64_1436` `sub-neg_binary64_1418` `clear-num_binary64_1424` `div-inv_binary64_1422` `div-exp_binary64_1473` `cbrt-undiv_binary64_1456`

Counts

2 → 70

Calls

2 calls:

9.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))
7.0ms	(-.f64 (pow.f64 x 3) x)

series133.0ms (4.7%)

Counts

2 → 6

Calls

2 calls:

79.0ms	(-.f64 (pow.f64 x 3) x)
53.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify57.0ms (2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4894	1312
1	4894	1312

prune76.0ms (2.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	74	4	78

Merged error: 0.0b

Counts

78 → 4

Compiler

Compiled 1137 to 831 computations (26.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (/.f64 1 x) (/.f64 2 (-.f64 (.f64 x x) 1)))
0.2b	(/.f64 2 (-.f64 (*.f64 x x) 1))

rewrite36.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64_1446`
52×	`times-frac_binary64_1431`
39×	`*-un-lft-identity_binary64_1425`
30×	`add-cube-cbrt_binary64_1457`
26×	`add-exp-log_binary64_1460`
24×	`associate-r_binary64_1367`
16×	`add-cbrt-cube_binary64_1458`
14×	`difference-of-squares_binary64_1394`
13×	`associate-l_binary64_1368`
9×	`div-exp_binary64_1473`
8×	`prod-exp_binary64_1471`
7×	`difference-of-sqr-1_binary64_1395`
6×	`associate-/r*_binary64_1371` `unswap-sqr_binary64_1393`
5×	`cbrt-undiv_binary64_1456`
4×	`cbrt-unprod_binary64_1455` `associate-/r/_binary64_1373` `pow1_binary64_1483`
3×	`div-inv_binary64_1422` `associate-/l*_binary64_1372`
2×	`flip--_binary64_1400` `1-exp_binary64_1466` `flip3--_binary64_1429` `add-log-exp_binary64_1461` `rec-exp_binary64_1472`
1×	`frac-2neg_binary64_1436` `clear-num_binary64_1424` `associate-r/_binary64_1369` `associate-l/_binary64_1370` `*-commutative_binary64_1358` `frac-times_binary64_1435` `pow-prod-down_binary64_1493`

Counts

2 → 108

Calls

2 calls:

19.0ms	(.f64 (/.f64 1 x) (/.f64 2 (-.f64 (.f64 x x) 1)))
7.0ms	(/.f64 2 (-.f64 (*.f64 x x) 1))

series94.0ms (3.3%)

Counts

2 → 6

Calls

2 calls:

58.0ms	(.f64 (/.f64 1 x) (/.f64 2 (-.f64 (.f64 x x) 1)))
36.0ms	(/.f64 2 (-.f64 (*.f64 x x) 1))

simplify72.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5113	1864

prune107.0ms (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	114	4	118

Merged error: 0b

Counts

118 → 4

Compiler

Compiled 1894 to 1344 computations (29% saved)

regimes10.0ms (0.4%)

Compiler: Compiled 48 to 39 computations (18.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	13
1	18	13

end0.0ms (0%)

sample805.0ms (28.4%)

Algorithm

1×

intervals

Results

187.0ms	1282×	body	1024	valid
177.0ms	4437×	body	128	valid
169.0ms	1480×	body	512	valid
58.0ms	801×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 80 to 66 computations (17.5% saved)

Details

analyze11.0ms (0.4%)

sample24.0ms (0.9%)

simplify167.0ms (5.9%)

prune3.0ms (0.1%)

localize12.0ms (0.4%)

rewrite90.0ms (3.2%)

series172.0ms (6%)

simplify84.0ms (2.9%)

prune201.0ms (7.1%)

localize13.0ms (0.4%)

rewrite67.0ms (2.4%)

series147.0ms (5.2%)

simplify99.0ms (3.5%)

prune325.0ms (11.4%)

localize5.0ms (0.2%)

rewrite23.0ms (0.8%)

series133.0ms (4.7%)

simplify57.0ms (2%)

prune76.0ms (2.7%)

localize6.0ms (0.2%)

rewrite36.0ms (1.3%)

series94.0ms (3.3%)

simplify72.0ms (2.5%)

prune107.0ms (3.8%)

regimes10.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample805.0ms (28.4%)

Profiling