Details

analyze451.0ms (5.5%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample38.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	38×	body	2048	valid
9.0ms	175×	body	128	valid
5.0ms	24×	body	1024	valid
2.0ms	11×	body	512	valid
1.0ms	4×	body	4096	valid
1.0ms	18×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify234.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 34.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite43.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1464`
14×	`*-un-lft-identity_binary64_1442`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
8×	`add-log-exp_binary64_1481` `add-cube-cbrt_binary64_1477`
6×	`times-frac_binary64_1448` `associate-/l*_binary64_1387` `sqrt-prod_binary64_1458` `difference-of-squares_binary64_1411`
5×	`pow1_binary64_1503`
4×	`cancel-sign-sub-inv_binary64_1408` `flip3--_binary64_1446` `flip--_binary64_1417`
3×	`distribute-lft-out--_binary64_1394`
2×	`cbrt-undiv_binary64_1476` `associate-/l/_binary64_1389` `sub-neg_binary64_1435` `sqrt-div_binary64_1459` `diff-log_binary64_1534` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-/r*_binary64_1386` `rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `div-sub_binary64_1447`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series516.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5031	1979

prune118.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Merged error: 5.7b

Counts

87 → 7

Compiler

Compiled 2119 to 1264 computations (40.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2))
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.1b	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1442`
14×	`add-sqr-sqrt_binary64_1464`
11×	`times-frac_binary64_1448` `add-cube-cbrt_binary64_1477`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `sqrt-prod_binary64_1458`
8×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481`
6×	`associate-/l*_binary64_1387`
5×	`pow1_binary64_1503`
4×	`div-inv_binary64_1439` `flip3--_binary64_1446` `sqrt-div_binary64_1459` `flip--_binary64_1417`
2×	`cbrt-undiv_binary64_1476` `associate-/l/_binary64_1389` `sub-neg_binary64_1435` `diff-log_binary64_1534` `distribute-lft-out--_binary64_1394` `div-exp_binary64_1493`
1×	`sqrt-pow1_binary64_1460` `associate-/r*_binary64_1386` `rem-sqrt-square_binary64_1455` `sub-div_binary64_1449` `cbrt-unprod_binary64_1475` `clear-num_binary64_1441` `frac-sub_binary64_1451` `frac-2neg_binary64_1453` `distribute-rgt-out--_binary64_1396` `pow1/2_binary64_1522` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411`

Counts

4 → 80

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
9.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series613.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

271.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2))
157.0ms	(-.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (.f64 a 2)) (/.f64 b (*.f64 a 2)))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5035	2187

prune115.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	91	8	99

Merged error: 5.7b

Counts

99 → 8

Compiler

Compiled 2604 to 1610 computations (38.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite118.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_1448`
439×	`add-sqr-sqrt_binary64_1464`
364×	`*-un-lft-identity_binary64_1442`
290×	`add-cube-cbrt_binary64_1477`
74×	`difference-of-squares_binary64_1411`
71×	`associate-/r*_binary64_1386`
40×	`sqrt-prod_binary64_1458`
37×	`distribute-lft-out--_binary64_1394`
25×	`add-exp-log_binary64_1480`
17×	`div-inv_binary64_1439`
15×	`div-exp_binary64_1493`
13×	`add-cbrt-cube_binary64_1478`
8×	`add-log-exp_binary64_1481`
6×	`cbrt-undiv_binary64_1476` `pow1_binary64_1503`
5×	`associate-/r/_binary64_1388`
4×	`cancel-sign-sub-inv_binary64_1408`
3×	`associate-/l*_binary64_1387` `1-exp_binary64_1486` `flip3--_binary64_1446` `rec-exp_binary64_1492` `flip--_binary64_1417`
2×	`sub-neg_binary64_1435` `sqrt-div_binary64_1459` `diff-log_binary64_1534`
1×	`sqrt-pow1_binary64_1460` `inv-pow_binary64_1527` `rem-sqrt-square_binary64_1455` `clear-num_binary64_1441` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`

Counts

4 → 356

Calls

4 calls:

28.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series551.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) 2)))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
114.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify199.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4947	16295
1	4947	16295

prune775.0ms (9.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	367	1	368
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	367	9	376

Merged error: 5.6b

Counts

376 → 9

Compiler

Compiled 12756 to 7700 computations (39.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
10.7b	(-.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) a) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 b (.f64 a 2)))
24.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`cbrt-prod_binary64_1473`
4×	`add-cbrt-cube_binary64_1478` `cbrt-div_binary64_1474` `flip3--_binary64_1446` `add-exp-log_binary64_1480` `flip--_binary64_1417` `pow1_binary64_1503`
3×	`times-frac_binary64_1448` `frac-sub_binary64_1451`
2×	`sub-neg_binary64_1435` `diff-log_binary64_1534` `frac-times_binary64_1452` `pow1/3_binary64_1524`
1×	`associate-r/_binary64_1384` `sub-div_binary64_1449` `div-inv_binary64_1439` `associate-l/_binary64_1385`

Counts

4 → 60

Calls

4 calls:

15.0ms	(-.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) a) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 b (.f64 a 2)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series999.0ms (12.1%)

Counts

4 → 12

Calls

4 calls:

581.0ms	(-.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) a) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) 2)) (/.f64 b (.f64 a 2)))
181.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
166.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
71.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify84.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4959	2148
1	4959	2148

prune118.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	72	9	81

Merged error: 5.6b

Counts

81 → 9

Compiler

Compiled 2939 to 1827 computations (37.8% saved)

regimes884.0ms (10.7%)

Compiler: Compiled 4068 to 3120 computations (23.3% saved)

bsearch59.0ms (0.7%)

Steps

Iters	Range		Point
8	3.000591128364517e-86	3.8061952448547226e-83	2.6283193000196084e-84
8	-4.420005681040467e+157	-5.368815422905672e+153	-6.135258149216111e+153

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	58
1	101	58

end0.0ms (0%)

sample2.0s (24.8%)

Algorithm

1×

intervals

Results

277.0ms	1126×	body	2048	valid
276.0ms	5180×	body	128	valid
148.0ms	730×	body	1024	valid
145.0ms	446×	body	4096	valid
50.0ms	351×	body	512	valid
34.0ms	681×	body	128	nan
21.0ms	400×	body	128	invalid
17.0ms	167×	body	256	valid

Compiler

Compiled 1093 to 829 computations (24.2% saved)

Details

analyze451.0ms (5.5%)

sample38.0ms (0.5%)

simplify234.0ms (2.8%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite43.0ms (0.5%)

series516.0ms (6.3%)

simplify78.0ms (0.9%)

prune118.0ms (1.4%)

localize14.0ms (0.2%)

rewrite42.0ms (0.5%)

series613.0ms (7.4%)

simplify61.0ms (0.7%)

prune115.0ms (1.4%)

localize12.0ms (0.1%)

rewrite118.0ms (1.4%)

series551.0ms (6.7%)

simplify199.0ms (2.4%)

prune775.0ms (9.4%)

localize18.0ms (0.2%)

rewrite36.0ms (0.4%)

series999.0ms (12.1%)

simplify84.0ms (1%)

prune118.0ms (1.4%)

regimes884.0ms (10.7%)

bsearch59.0ms (0.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (24.8%)

Profiling