Details

analyze603.0ms (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 30 to 30 computations (0% saved)

sample92.0ms (0.6%)

Algorithm

1×

intervals

Results

34.0ms	197×	body	80	valid
21.0ms	27×	body	640	valid
15.0ms	14×	body	1280	valid
7.0ms	12×	body	320	valid
3.0ms	6×	body	160	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5326	39

prune5.0ms (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: 1.8b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
0.3b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
4.3b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.7b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
24×	`add-exp-log_binary64` `times-frac_binary64`
17×	`unpow-prod-down_binary64`
15×	`sqrt-prod_binary64`
12×	`associate-l_binary64`
8×	`add-cbrt-cube_binary64`
7×	`prod-exp_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `pow-exp_binary64`
5×	`associate-r_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `associate-/r/_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 123

Calls

4 calls:

19.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
7.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series2.1s (13.5%)

Counts

4 → 12

Calls

4 calls:

1.1s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
668.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
321.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
46.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5011	4397

prune290.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	3	136

Merged error: 0.0b

Counts

136 → 3

Compiler

Compiled 4742 to 3610 computations (23.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
0.8b	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.8b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.7b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

rewrite69.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
32×	`cbrt-unprod_binary64` `prod-exp_binary64`
29×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
15×	`sqrt-prod_binary64`
14×	`associate-l_binary64`
12×	`pow1_binary64`
11×	`associate-*r/_binary64` `frac-times_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
6×	`associate-/r_binary64` `associate-r*_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `insert-posit16` `sqrt-div_binary64` `associate-*l/_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`distribute-lft-out_binary64` `associate-/r/_binary64` `unpow-prod-down_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 152

Calls

4 calls:

25.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
22.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
5.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

series2.4s (15.6%)

Counts

4 → 12

Calls

4 calls:

1.1s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
658.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
355.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
331.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

simplify192.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4954	5958
1	4954	5958

prune358.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	164	3	167

Merged error: 0.0b

Counts

167 → 3

Compiler

Compiled 6104 to 4230 computations (30.7% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
4.3b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.3b	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
8.7b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
39×	`times-frac_binary64`
38×	`add-cube-cbrt_binary64`
25×	`log-pow_binary64`
24×	`sqrt-prod_binary64` `exp-prod_binary64`
18×	`add-exp-log_binary64`
12×	`associate-l_binary64`
10×	`unpow-prod-down_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `prod-exp_binary64` `sqrt-div_binary64`
5×	`associate-r_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `insert-posit16` `flip-+_binary64`
3×	`log-prod_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`
2×	`distribute-lft-out_binary64` `unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

19.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
8.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series3.2s (20.2%)

Counts

4 → 12

Calls

4 calls:

1.1s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
1.1s	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
663.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
324.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify135.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5037	5414

prune368.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	147	3	150

Merged error: 0.0b

Counts

150 → 3

Compiler

Compiled 5787 to 4464 computations (22.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1/2 (posit16->binary64 (binary64->posit16 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
4.3b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.7b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
23.5b	(posit16->binary64 (binary64->posit16 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
18×	`add-exp-log_binary64`
17×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64` `times-frac_binary64`
10×	`unpow-prod-down_binary64`
8×	`add-cbrt-cube_binary64`
6×	`prod-exp_binary64`
5×	`pow1_binary64` `associate-r_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`associate-/r_binary64` `associate-/l_binary64` `div-exp_binary64` `sqrt-prod_binary64` `pow-exp_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `remove-posit16` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

19.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.0ms	(/.f64 1/2 (posit16->binary64 (binary64->posit16 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
1.0ms	(posit16->binary64 (binary64->posit16 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))

series1.6s (10.5%)

Counts

4 → 12

Calls

4 calls:

657.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
497.0ms	(/.f64 1/2 (posit16->binary64 (binary64->posit16 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
328.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
149.0ms	(posit16->binary64 (binary64->posit16 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))

simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4976	3810
1	4976	3810

prune222.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	105	3	108

Merged error: 0.0b

Counts

108 → 3

Compiler

Compiled 3776 to 2887 computations (23.5% saved)

regimes291.0ms (1.9%)

Compiler: Compiled 1779 to 1819 computations (-2.2% saved)

bsearch83.0ms (0.5%)

Steps

Iters	Range		Point
10	4.7434592279872615e+296	#hash((type . real) (value . +inf))	1.7807741941626171e+308

Compiler

Compiled 7 to 9 computations (-28.6% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	101
1	41	101

end0.0ms (0%)

sample3.0s (19.3%)

Algorithm

1×

intervals

Results

1.1s	6197×	body	80	valid
620.0ms	548×	body	1280	valid
551.0ms	670×	body	640	valid
209.0ms	366×	body	320	valid
82.0ms	219×	body	160	valid

Compiler

Compiled 177 to 171 computations (3.4% saved)

Details

analyze603.0ms (3.9%)

sample92.0ms (0.6%)

simplify96.0ms (0.6%)

prune5.0ms (0%)

localize20.0ms (0.1%)

rewrite44.0ms (0.3%)

series2.1s (13.5%)

simplify133.0ms (0.8%)

prune290.0ms (1.9%)

localize20.0ms (0.1%)

rewrite69.0ms (0.4%)

series2.4s (15.6%)

simplify192.0ms (1.2%)

prune358.0ms (2.3%)

localize23.0ms (0.1%)

rewrite48.0ms (0.3%)

series3.2s (20.2%)

simplify135.0ms (0.9%)

prune368.0ms (2.4%)

localize22.0ms (0.1%)

rewrite31.0ms (0.2%)

series1.6s (10.5%)

simplify123.0ms (0.8%)

prune222.0ms (1.4%)

regimes291.0ms (1.9%)

bsearch83.0ms (0.5%)

simplify6.0ms (0%)

end0.0ms (0%)

sample3.0s (19.3%)

Profiling