Details

analyze6.0ms (0.2%)

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)

sample28.0ms (0.9%)

Algorithm

1×

intervals

Results

9.0ms	37×	body	512	valid
6.0ms	42×	body	1024	valid
5.0ms	145×	body	128	valid
2.0ms	32×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify177.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

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: 10.8b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize9.0ms (0.3%)

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))
3.6b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite91.0ms (3%)

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:

43.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
19.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series173.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(+.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))
19.0ms	(/.f64 1 (+.f64 x 1))
18.0ms	(/.f64 1 (-.f64 x 1))

simplify83.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5051	2576

prune204.0ms (6.8%)

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: 0.2b

Counts

148 → 3

Compiler

Compiled 3250 to 2609 computations (19.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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))
0.2b	(-.f64 x (*.f64 (+.f64 1 x) 2))
14.5b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite67.0ms (2.3%)

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:

21.0ms	(/.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))

series149.0ms (5%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
55.0ms	(*.f64 x (+.f64 1 x))
26.0ms	(-.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)))

simplify239.0ms (8%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5450	6035

prune332.0ms (11.1%)

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: 0.2b

Counts

151 → 2

Compiler

Compiled 6364 to 4457 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (pow.f64 x 3) x)
0.2b	(/.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)

series148.0ms (5%)

Counts

2 → 6

Calls

2 calls:

96.0ms	(-.f64 (pow.f64 x 3) x)
52.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify56.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4894	1312
1	4894	1312

prune77.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	71	5	76
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	73	5	78

Merged error: 0b

Counts

78 → 5

Compiler

Compiled 1175 to 862 computations (26.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64_1431`
78×	`add-sqr-sqrt_binary64_1446` `*-un-lft-identity_binary64_1425`
64×	`add-cube-cbrt_binary64_1457`
28×	`difference-of-squares_binary64_1394`
14×	`difference-of-sqr-1_binary64_1395`
13×	`associate-/l*_binary64_1372`
8×	`div-inv_binary64_1422`
6×	`associate-/r*_binary64_1371` `add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
3×	`div-exp_binary64_1473` `cbrt-undiv_binary64_1456`
2×	`associate-/r/_binary64_1373`
1×	`flip--_binary64_1400` `frac-2neg_binary64_1436` `clear-num_binary64_1424` `associate-/l/_binary64_1374` `pow1_binary64_1483` `flip3--_binary64_1429` `add-log-exp_binary64_1461`

Counts

1 → 114

Calls

1 calls:

13.0ms

(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))

series51.0ms (1.7%)

Counts

1 → 3

Calls

1 calls:

51.0ms

(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))

simplify69.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4952	2916
1	4952	2916

prune110.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	117	5	122

Merged error: 0b

Counts

122 → 5

Compiler

Compiled 2168 to 1441 computations (33.5% saved)

regimes15.0ms (0.5%)

Compiler: Compiled 77 to 64 computations (16.9% 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%)

sample822.0ms (27.6%)

Algorithm

1×

intervals

Results

193.0ms	1344×	body	1024	valid
174.0ms	4435×	body	128	valid
154.0ms	1444×	body	512	valid
58.0ms	777×	body	256	valid

Compiler

Compiled 109 to 91 computations (16.5% saved)

Details

analyze6.0ms (0.2%)

sample28.0ms (0.9%)

simplify177.0ms (5.9%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

rewrite91.0ms (3%)

series173.0ms (5.8%)

simplify83.0ms (2.8%)

prune204.0ms (6.8%)

localize13.0ms (0.4%)

rewrite67.0ms (2.3%)

series149.0ms (5%)

simplify239.0ms (8%)

prune332.0ms (11.1%)

localize5.0ms (0.2%)

rewrite23.0ms (0.8%)

series148.0ms (5%)

simplify56.0ms (1.9%)

prune77.0ms (2.6%)

localize5.0ms (0.2%)

rewrite25.0ms (0.8%)

series51.0ms (1.7%)

simplify69.0ms (2.3%)

prune110.0ms (3.7%)

regimes15.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample822.0ms (27.6%)

Profiling