Details

analyze106.0ms (3.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22
0	1	1
1	1	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

10.0ms	147×	body	128	valid
6.0ms	41×	body	1024	valid
5.0ms	47×	body	512	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

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: 9.3b

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))
3.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite92.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_1442`
74×	`times-frac_binary64_1448`
72×	`add-sqr-sqrt_binary64_1464`
39×	`add-cube-cbrt_binary64_1477`
26×	`cancel-sign-sub-inv_binary64_1408`
18×	`distribute-lft-out--_binary64_1394`
17×	`distribute-lft-out_binary64_1393`
14×	`associate-+l+_binary64_1375` `difference-of-squares_binary64_1411`
12×	`add-exp-log_binary64_1480`
11×	`associate-/r*_binary64_1386` `add-log-exp_binary64_1481`
10×	`div-inv_binary64_1439`
8×	`add-cbrt-cube_binary64_1478`
6×	`associate-/l*_binary64_1387` `pow1_binary64_1503`
4×	`associate-/r/_binary64_1388` `difference-of-sqr-1_binary64_1412` `div-exp_binary64_1493`
3×	`flip3--_binary64_1446` `flip--_binary64_1417` `frac-add_binary64_1450`
2×	`inv-pow_binary64_1527` `cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `sub-neg_binary64_1435` `clear-num_binary64_1441` `1-exp_binary64_1486` `frac-sub_binary64_1451` `rec-exp_binary64_1492` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`+-commutative_binary64_1372` `associate-+l-_binary64_1377`

Counts

4 → 161

Calls

4 calls:

46.0ms	(+.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))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 1 (+.f64 x 1))

series81.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
13.0ms	(/.f64 1 (-.f64 x 1))
13.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
8.0ms	(/.f64 1 (+.f64 x 1))

simplify96.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4963	2797
1	4963	2797

prune218.0ms (6.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	3	174

Merged error: 0.0b

Counts

174 → 3

Compiler

Compiled 3616 to 2901 computations (19.8% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (pow.f64 x 3) 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))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
16.8b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite71.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64_1464`
42×	`associate-*r/_binary64_1384`
39×	`*-un-lft-identity_binary64_1442`
32×	`flip3--_binary64_1446` `flip--_binary64_1417` `frac-add_binary64_1450`
27×	`times-frac_binary64_1448`
22×	`difference-of-squares_binary64_1411`
21×	`add-cube-cbrt_binary64_1477`
20×	`frac-times_binary64_1452`
18×	`associate-/l/_binary64_1389` `flip3-+_binary64_1445` `flip-+_binary64_1416`
10×	`associate-*l/_binary64_1385`
9×	`associate-/r*_binary64_1386`
8×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
7×	`cancel-sign-sub-inv_binary64_1408` `associate-l_binary64_1383`
6×	`pow1_binary64_1503` `distribute-lft-out--_binary64_1394`
5×	`sub-neg_binary64_1435` `cube-prod_binary64_1470` `distribute-rgt-out--_binary64_1396` `distribute-lft-in_binary64_1391` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `distribute-rgt-in_binary64_1392` `unpow-prod-down_binary64_1521`
4×	`associate-+l+_binary64_1375`
3×	`associate-r_binary64_1382` `associate-/l*_binary64_1387`
2×	`associate-/r/_binary64_1388` `associate-+r+_binary64_1374`
1×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `difference-of-sqr-1_binary64_1412` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `prod-exp_binary64_1491` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`

Counts

4 → 158

Calls

4 calls:

19.0ms	(/.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)))
9.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
7.0ms	(-.f64 (pow.f64 x 3) x)

series85.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(-.f64 (pow.f64 x 3) x)
27.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
16.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
4.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify134.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4941	6742
1	4941	6742

prune380.0ms (11.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	170	3	173

Merged error: 0.0b

Counts

173 → 3

Compiler

Compiled 7167 to 4979 computations (30.5% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64_1464`
32×	`*-un-lft-identity_binary64_1442`
27×	`times-frac_binary64_1448`
20×	`difference-of-squares_binary64_1411`
17×	`add-cube-cbrt_binary64_1477`
9×	`associate-/r*_binary64_1386`
5×	`cube-prod_binary64_1470` `distribute-rgt-out--_binary64_1396` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `distribute-lft-out--_binary64_1394` `unpow-prod-down_binary64_1521`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
3×	`cancel-sign-sub-inv_binary64_1408` `associate-/l*_binary64_1387`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `div-exp_binary64_1493`

Counts

2 → 73

Calls

2 calls:

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

series66.0ms (2%)

Counts

2 → 6

Calls

2 calls:

39.0ms	(-.f64 (pow.f64 x 3) x)
27.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify88.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4973	1321
1	4973	1321

prune72.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Merged error: 0b

Counts

82 → 4

Compiler

Compiled 1157 to 843 computations (27.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (*.f64 x x) 1)
0.0b	(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64_1448`
81×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
66×	`add-cube-cbrt_binary64_1477`
30×	`difference-of-squares_binary64_1411`
15×	`difference-of-sqr-1_binary64_1412`
13×	`associate-/l*_binary64_1387`
8×	`div-inv_binary64_1439`
7×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
6×	`associate-/r*_binary64_1386`
4×	`add-log-exp_binary64_1481`
3×	`cbrt-undiv_binary64_1476` `cancel-sign-sub-inv_binary64_1408` `div-exp_binary64_1493`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503`
1×	`associate-/l/_binary64_1389` `sub-neg_binary64_1435` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `diff-log_binary64_1534`

Counts

2 → 131

Calls

2 calls:

12.0ms	(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))
4.0ms	(-.f64 (*.f64 x x) 1)

series48.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

25.0ms	(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))
23.0ms	(-.f64 (*.f64 x x) 1)

simplify74.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5210	3083

prune119.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	137	4	141

Merged error: 0b

Counts

141 → 4

Compiler

Compiled 2406 to 1590 computations (33.9% saved)

regimes112.0ms (3.4%)

Compiler: Compiled 1416 to 1162 computations (17.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms (0%)

sample1.3s (39.7%)

Algorithm

1×

intervals

Results

172.0ms	1285×	body	1024	valid
166.0ms	4421×	body	128	valid
165.0ms	1540×	body	512	valid
52.0ms	754×	body	256	valid

Compiler

Compiled 724 to 595 computations (17.8% saved)

Details

analyze106.0ms (3.2%)

sample28.0ms (0.9%)

simplify14.0ms (0.4%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

rewrite92.0ms (2.8%)

series81.0ms (2.5%)

simplify96.0ms (2.9%)

prune218.0ms (6.7%)

localize13.0ms (0.4%)

rewrite71.0ms (2.2%)

series85.0ms (2.6%)

simplify134.0ms (4.1%)

prune380.0ms (11.6%)

localize4.0ms (0.1%)

rewrite22.0ms (0.7%)

series66.0ms (2%)

simplify88.0ms (2.7%)

prune72.0ms (2.2%)

localize5.0ms (0.2%)

rewrite29.0ms (0.9%)

series48.0ms (1.5%)

simplify74.0ms (2.3%)

prune119.0ms (3.6%)

regimes112.0ms (3.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (39.7%)

Profiling