Details

analyze606.0ms (4.8%)

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)

sample87.0ms (0.7%)

Algorithm

1×

intervals

Results

37.0ms	200×	body	128	valid
22.0ms	25×	body	1024	valid
12.0ms	20×	body	512	valid
4.0ms	11×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify47.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5325	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)

localize21.0ms (0.2%)

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)))))

rewrite55.0ms (0.4%)

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` `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 → 119

Calls

4 calls:

18.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms	(/.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))))))
8.0ms	(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 (16.2%)

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))))))
651.0ms	(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)))))
296.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
36.0ms	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5005	4288

prune280.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	3	132

Merged error: 0.0b

Counts

132 → 3

Compiler

Compiled 4611 to 3507 computations (23.9% saved)

localize21.0ms (0.2%)

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))))))

rewrite76.0ms (0.6%)

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` `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 → 148

Calls

4 calls:

22.0ms	(.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))))
19.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms	(/.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)))))))
4.0ms	(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 (19.1%)

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)))))))
674.0ms	(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))))))
345.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
297.0ms	(.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))))

simplify120.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4948	5827
1	4948	5827

prune366.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	160	3	163

Merged error: 0.0b

Counts

163 → 3

Compiler

Compiled 5963 to 4131 computations (30.7% saved)

localize24.0ms (0.2%)

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)))))

rewrite58.0ms (0.5%)

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` `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 → 131

Calls

4 calls:

17.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms	(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))))))))
7.0ms	(/.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)))))

series2.8s (22.4%)

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))))))
772.0ms	(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))))))))
664.0ms	(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)))))
325.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5032	5281

prune355.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	143	3	146

Merged error: 0.0b

Counts

146 → 3

Compiler

Compiled 5650 to 4355 computations (22.9% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Merged error: 0.0b

Counts

3 → 3

Compiler

Compiled 0 to 0 computations (0% saved)

regimes259.0ms (2%)

Compiler: Compiled 1342 to 1458 computations (-8.6% saved)

bsearch66.0ms (0.5%)

Steps

Iters	Range		Point
9	1.1403897104606272e+234	4.3084504751607156e+240	3.952622994141695e+240

Compiler

Compiled 7 to 9 computations (-28.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	61
1	35	61

end0.0ms (0%)

sample2.7s (21.5%)

Algorithm

1×

intervals

Results

1.1s	6338×	body	128	valid
702.0ms	792×	body	1024	valid
358.0ms	569×	body	512	valid
115.0ms	301×	body	256	valid

Compiler

Compiled 129 to 133 computations (-3.1% saved)

Details

analyze606.0ms (4.8%)

sample87.0ms (0.7%)

simplify47.0ms (0.4%)

prune5.0ms (0%)

localize21.0ms (0.2%)

rewrite55.0ms (0.4%)

series2.1s (16.2%)

simplify80.0ms (0.6%)

prune280.0ms (2.2%)

localize21.0ms (0.2%)

rewrite76.0ms (0.6%)

series2.4s (19.1%)

simplify120.0ms (0.9%)

prune366.0ms (2.9%)

localize24.0ms (0.2%)

rewrite58.0ms (0.5%)

series2.8s (22.4%)

simplify87.0ms (0.7%)

prune355.0ms (2.8%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune1.0ms (0%)

regimes259.0ms (2%)

bsearch66.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (21.5%)

Profiling