Details

analyze600.0ms (10.3%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	174×	body	128	valid
8.0ms	35×	body	2048	valid
3.0ms	12×	body	4096	valid
3.0ms	18×	body	1024	valid
1.0ms	11×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	6×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify189.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	309	20
1	309	20

prune10.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 34.2b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.6b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series453.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
121.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
121.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
58.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4922	2470
1	4922	2470

prune113.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	92	9	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	9	102

Merged error: 6.3b

Counts

102 → 9

Compiler

Compiled 2316 to 461 computations (80.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.1b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.6b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`associate-/r/_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 126

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
12.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series896.0ms (15.3%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
296.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
101.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify91.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4936	4018
1	4936	4018

prune126.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	139	8	147

Merged error: 6.2b

Counts

147 → 8

Compiler

Compiled 3607 to 609 computations (83.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 81

Calls

4 calls:

11.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series678.0ms (11.6%)

Counts

4 → 12

Calls

4 calls:

356.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
153.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
101.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
68.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5200	2111

prune85.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	93	8	101

Merged error: 6.2b

Counts

101 → 8

Compiler

Compiled 2338 to 774 computations (66.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.1b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))) (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
24.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`add-cube-cbrt_binary64`
7×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-div_binary64`
3×	`associate-/l/_binary64` `associate-/r*_binary64` `flip3--_binary64` `times-frac_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 74

Calls

4 calls:

29.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))) (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series639.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

302.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))) (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
107.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
107.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5078	1740

prune77.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	86	8	94

Merged error: 6.2b

Counts

94 → 8

Compiler

Compiled 2543 to 460 computations (81.9% saved)

regimes143.0ms (2.5%)

Compiler: Compiled 357 to 276 computations (22.7% saved)

bsearch95.0ms (1.6%)

Steps

Iters	Range	Point
7	1.8636084122990392e+97	1.9135304727080364e+99	1.7712927136614406e+99
9	7.342863312857922e-248	7.37490432424297e-239	2.4652136646182423e-246
9	-2.6124887179107254e+101	-5.233603415107368e+95	-9.077412142073874e+100

Iters

Range

Point

1.8636084122990392e+97

1.9135304727080364e+99

1.7712927136614406e+99

7.342863312857922e-248

7.37490432424297e-239

2.4652136646182423e-246

-2.6124887179107254e+101

-5.233603415107368e+95

-9.077412142073874e+100

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	175	80
1	175	80

end0.0ms (0%)

sample1.2s (20.2%)

Algorithm

1×

intervals

Results

233.0ms	5163×	body	128	valid
232.0ms	1126×	body	2048	valid
122.0ms	768×	body	1024	valid
104.0ms	395×	body	4096	valid
43.0ms	359×	body	512	valid
36.0ms	826×	body	128	nan
15.0ms	189×	body	256	valid
11.0ms	254×	body	128	invalid

Compiler

Compiled 185 to 131 computations (29.2% saved)

Details

analyze600.0ms (10.3%)

sample41.0ms (0.7%)

simplify189.0ms (3.2%)

prune10.0ms (0.2%)

localize11.0ms (0.2%)

rewrite42.0ms (0.7%)

series453.0ms (7.7%)

simplify78.0ms (1.3%)

prune113.0ms (1.9%)

localize9.0ms (0.2%)

rewrite57.0ms (1%)

series896.0ms (15.3%)

simplify91.0ms (1.6%)

prune126.0ms (2.2%)

localize10.0ms (0.2%)

rewrite36.0ms (0.6%)

series678.0ms (11.6%)

simplify65.0ms (1.1%)

prune85.0ms (1.5%)

localize16.0ms (0.3%)

rewrite56.0ms (1%)

series639.0ms (10.9%)

simplify44.0ms (0.7%)

prune77.0ms (1.3%)

regimes143.0ms (2.5%)

bsearch95.0ms (1.6%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.2s (20.2%)

Profiling