Details

analyze634.0ms (0.2%)

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)

sample79.0ms (0%)

Algorithm

1×

intervals

Results

38.0ms	211×	body	128	valid
16.0ms	19×	body	1024	valid
9.0ms	15×	body	512	valid
4.0ms	11×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify141.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5325	39

prune4.0ms (0%)

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

Error

1.8b

Counts

2 → 2

Compiler

Compiled 25 to 25 computations (0% saved)

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (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)))))))))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(/.f64 1 (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))))))
3.8b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.1b	(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%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_441`
30×	`*-un-lft-identity_binary64_419`
26×	`add-cube-cbrt_binary64_454`
21×	`times-frac_binary64_425` `add-exp-log_binary64_457`
15×	`sqrt-prod_binary64_435`
13×	`unpow-prod-down_binary64_498`
12×	`associate-l_binary64_360`
8×	`add-cbrt-cube_binary64_455` `pow1_binary64_480`
6×	`prod-exp_binary64_468` `associate-/r*_binary64_363`
5×	`associate-r_binary64_359`
4×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `unswap-sqr_binary64_387` `pow-exp_binary64_487` `div-exp_binary64_470`
3×	`flip3-+_binary64_422` `sqr-pow_binary64_391` `pow-flip_binary64_493` `flip-+_binary64_393` `pow-unpow_binary64_496` `unpow2_binary64_484` `associate-/l*_binary64_364`
2×	`pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out_binary64_370` `associate-*r/_binary64_361` `associate-/r/_binary64_365` `pow-to-exp_binary64_488` `sqrt-pow1_binary64_437`
1×	`clear-num_binary64_418` `1-exp_binary64_463` `distribute-rgt-in_binary64_369` `inv-pow_binary64_504` `cbrt-unprod_binary64_452` `rec-exp_binary64_469` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `frac-2neg_binary64_430` `pow-pow_binary64_491` `rem-sqrt-square_binary64_432` `cbrt-undiv_binary64_453`

Counts

4 → 119

Calls

8 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)))
7.0ms	(/.f64 1 (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)))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (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)))))))))

series3.0s (1%)

Counts

4 → 52

Calls

4 calls:

1.3s	(/.f64 1 (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))))))
1.0s	(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)))))
571.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
22.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 4071 to 3786 computations (7% saved)

simplify81.0ms (0%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4987	5691
1	4987	5691

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (+.f64 1/2 (/.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))))))))
0.2b	(pow.f64 (sin.f64 ky) 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))))))
3.8b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.1b	(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)))))

rewrite45.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_441`
30×	`*-un-lft-identity_binary64_419`
26×	`add-cube-cbrt_binary64_454`
21×	`times-frac_binary64_425`
19×	`add-exp-log_binary64_457`
15×	`sqrt-prod_binary64_435`
13×	`unpow-prod-down_binary64_498`
12×	`associate-l_binary64_360`
8×	`add-cbrt-cube_binary64_455`
6×	`prod-exp_binary64_468` `associate-/r*_binary64_363` `pow1_binary64_480`
5×	`associate-r_binary64_359`
4×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `unswap-sqr_binary64_387` `pow-exp_binary64_487`
3×	`flip3-+_binary64_422` `sqr-pow_binary64_391` `flip-+_binary64_393` `pow-unpow_binary64_496` `unpow2_binary64_484` `div-exp_binary64_470` `associate-/l*_binary64_364`
2×	`div-inv_binary64_416` `distribute-lft-out_binary64_370` `associate-*r/_binary64_361` `associate-/r/_binary64_365` `pow-to-exp_binary64_488`
1×	`clear-num_binary64_418` `distribute-rgt-in_binary64_369` `pow1/2_binary64_499` `cbrt-unprod_binary64_452` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `frac-2neg_binary64_430` `pow-pow_binary64_491` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `cbrt-undiv_binary64_453`

Counts

4 → 113

Calls

8 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)))
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)))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(sqrt.f64 (+.f64 1/2 (/.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))))))))

series3.2s (1%)

Counts

4 → 52

Calls

4 calls:

1.5s	(/.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))))))
1.0s	(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)))))
597.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
21.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3731 to 3446 computations (7.6% saved)

simplify81.0ms (0%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4997	5689
1	4997	5689

prune4.0s (1.3%)

Pruning

126 alts after pruning (124 fresh and 2 done)

	Pruned	Kept	Total
New	212	124	336
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	212	126	338

Error

0.0b

Counts

338 → 126

Compiler

Compiled 13110 to 10477 computations (20.1% saved)

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))))
1.9b	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.1b	(sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))

rewrite52.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_419`
19×	`sqrt-prod_binary64_435`
18×	`add-sqr-sqrt_binary64_441`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
11×	`add-cube-cbrt_binary64_454`
10×	`sqrt-div_binary64_436`
9×	`pow1_binary64_480`
8×	`associate-r_binary64_359`
7×	`associate-l_binary64_360`
6×	`unpow-prod-down_binary64_498` `distribute-lft-out_binary64_370`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`times-frac_binary64_425` `pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
2×	`unswap-sqr_binary64_387` `frac-times_binary64_429` `associate-*r/_binary64_361` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `div-inv_binary64_416` `-commutative_binary64_350`

Counts

4 → 86

Calls

8 calls:

17.0ms	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
0.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))))

series2.1s (0.7%)

Counts

4 → 56

Calls

4 calls:

1.0s	(sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
665.0ms	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
218.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
195.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 4567 to 3849 computations (15.7% saved)

simplify101.0ms (0%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4960	3941
1	4960	3941

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (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))))))))))
0.3b	(/.f64 1 (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)))))))
0.6b	(.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))))
4.0b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.1b	(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))))))

rewrite71.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-exp-log_binary64_457`
69×	`add-cbrt-cube_binary64_455`
32×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
29×	`*-un-lft-identity_binary64_419`
28×	`add-sqr-sqrt_binary64_441`
25×	`add-cube-cbrt_binary64_454`
24×	`times-frac_binary64_425`
18×	`div-exp_binary64_470`
17×	`cbrt-undiv_binary64_453`
15×	`sqrt-prod_binary64_435`
14×	`associate-l_binary64_360` `pow1_binary64_480`
11×	`frac-times_binary64_429` `associate-*r/_binary64_361`
8×	`flip3-+_binary64_422` `flip-+_binary64_393`
6×	`associate-r_binary64_359` `associate-/r*_binary64_363`
5×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`associate-*l/_binary64_362` `pow-prod-down_binary64_490` `sqrt-div_binary64_436` `add-log-exp_binary64_458`
3×	`div-inv_binary64_416` `pow-flip_binary64_493` `associate-/l*_binary64_364`
2×	`unpow-prod-down_binary64_498` `pow1/2_binary64_499` `distribute-lft-out_binary64_370` `associate-/r/_binary64_365` `*-commutative_binary64_350` `sqrt-pow1_binary64_437`
1×	`clear-num_binary64_418` `1-exp_binary64_463` `inv-pow_binary64_504` `unswap-sqr_binary64_387` `rec-exp_binary64_469` `frac-2neg_binary64_430` `rem-sqrt-square_binary64_432`

Counts

4 → 154

Calls

8 calls:

20.0ms	(.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))))
16.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms	(/.f64 1 (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))))))
0.0ms	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (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))))))))))

series3.5s (1.1%)

Counts

4 → 63

Calls

4 calls:

1.3s	(/.f64 1 (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)))))))
1.0s	(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))))))
608.0ms	(.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))))
510.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 4797 to 4445 computations (7.3% saved)

simplify163.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4986	7811
1	4986	7811

localize32.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)
0.0b	(.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)
0.0b	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)))) (/.f64 (.f64 (.f64 l l) (.f64 kx kx)) (*.f64 Om Om)))))))))
0.0b	(+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)))) (/.f64 (.f64 (.f64 l l) (.f64 kx kx)) (.f64 Om Om)))))))
9.4b	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
9.4b	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
12.8b	(/.f64 (.f64 (.f64 l l) (.f64 kx kx)) (.f64 Om Om))
14.0b	(.f64 (.f64 l l) (*.f64 kx kx))

rewrite90.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-exp-log_binary64_457`
76×	`add-sqr-sqrt_binary64_441`
61×	`add-cbrt-cube_binary64_455`
58×	`unpow-prod-down_binary64_498`
53×	`prod-exp_binary64_468`
41×	`unswap-sqr_binary64_387`
37×	`associate-r_binary64_359`
32×	`pow1_binary64_480`
31×	`cbrt-unprod_binary64_452`
27×	`times-frac_binary64_425`
24×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
22×	`sqr-pow_binary64_391` `unpow2_binary64_484`
20×	`pow-exp_binary64_487`
17×	`associate-l_binary64_360`
16×	`pow-prod-down_binary64_490` `div-exp_binary64_470`
14×	`pow-to-exp_binary64_488`
10×	`cbrt-undiv_binary64_453`
4×	`add-log-exp_binary64_458` `pow-plus_binary64_482` `pow-prod-up_binary64_489`
3×	`div-inv_binary64_416` `*-commutative_binary64_350`
2×	`pow-sqr_binary64_392` `pow2_binary64_500`
1×	`clear-num_binary64_418` `frac-2neg_binary64_430` `associate-/r_binary64_363` `associate-/l_binary64_364`

Counts

4 → 198

Calls

8 calls:

17.0ms	(/.f64 (.f64 (.f64 l l) (.f64 kx kx)) (.f64 Om Om))
13.0ms	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
13.0ms	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
9.0ms	(.f64 (.f64 l l) (*.f64 kx kx))
0.0ms	(+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)))) (/.f64 (.f64 (.f64 l l) (.f64 kx kx)) (.f64 Om Om)))))))

series818.0ms (0.3%)

Counts

4 → 33

Calls

4 calls:

258.0ms	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
257.0ms	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
210.0ms	(/.f64 (.f64 (.f64 l l) (.f64 kx kx)) (.f64 Om Om))
93.0ms	(.f64 (.f64 l l) (*.f64 kx kx))

Compiler

Compiled 3792 to 3244 computations (14.5% saved)

simplify95.0ms (0%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5053	3484

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))))))))))
10.1b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))))
18.3b	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
18.3b	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
18.3b	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))

rewrite22.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_450`
12×	`add-sqr-sqrt_binary64_441`
11×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`unpow-prod-down_binary64_498`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow1/3_binary64_501` `sqr-pow_binary64_391` `unpow2_binary64_484` `sqrt-prod_binary64_435`
2×	`sqrt-div_binary64_436`
1×	`flip3-+_binary64_422` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 63

Calls

8 calls:

3.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
0.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))))))))))

series1.3s (0.4%)

Counts

4 → 29

Calls

4 calls:

1.0s	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))))
92.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
89.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
77.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))

Compiler

Compiled 2363 to 2114 computations (10.5% saved)

simplify64.0ms (0%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5336	1981

prune21.5s (7%)

Pruning

269 alts after pruning (263 fresh and 6 done)

	Pruned	Kept	Total
New	515	167	682
Fresh	23	96	119
Picked	0	0	0
Done	1	6	7
Total	539	269	808

Error

0.0b

Counts

808 → 269

Compiler

Compiled 31254 to 22959 computations (26.5% saved)

localize32.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (*.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))))))
10.1b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
17.7b	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
17.7b	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
17.7b	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite60.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-div_binary64_451`
7×	`flip3-+_binary64_422` `flip-+_binary64_393`
6×	`frac-times_binary64_429` `add-sqr-sqrt_binary64_441` `associate-*r/_binary64_361`
5×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `pow1_binary64_480`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`associate-*l/_binary64_362` `pow1/3_binary64_501` `cbrt-prod_binary64_450` `sqrt-prod_binary64_435`
2×	`sqrt-div_binary64_436`
1×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 57

Calls

8 calls:

17.0ms	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
13.0ms	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
13.0ms	(cbrt.f64 (.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 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
0.0ms	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (*.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))))))

series5.6s (1.8%)

Counts

4 → 62

Calls

4 calls:

1.9s	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
1.3s	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
1.2s	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
1.2s	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

Compiler

Compiled 8342 to 6952 computations (16.7% saved)

simplify105.0ms (0%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4979	4123
1	4979	4123

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 l) Om)) 2) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
0.1b	(.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 l) Om)) 2) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 l) Om)) 2) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))
0.2b	(pow.f64 (sin.f64 ky) 2)
4.0b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
5.1b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 l) Om)) 2) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
9.9b	(sqrt.f64 (/.f64 (*.f64 2 l) Om))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
14×	`add-exp-log_binary64_457`
13×	`add-cbrt-cube_binary64_455`
12×	`add-cube-cbrt_binary64_454`
10×	`sqrt-prod_binary64_435`
9×	`pow1_binary64_480`
7×	`associate-l_binary64_360`
6×	`times-frac_binary64_425`
5×	`unpow-prod-down_binary64_498` `associate-r_binary64_359`
4×	`add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `pow-unpow_binary64_496`
2×	`pow1/2_binary64_499` `div-inv_binary64_416` `frac-times_binary64_429` `distribute-lft-out_binary64_370` `associate-*r/_binary64_361` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `pow-exp_binary64_487` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `distribute-lft-in_binary64_368` `-commutative_binary64_350` `pow-pow_binary64_491` `unpow2_binary64_484`

Counts

4 → 86

Calls

8 calls:

16.0ms	(.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 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 l) Om)) 2) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
3.0ms	(sqrt.f64 (/.f64 (*.f64 2 l) Om))
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 l) Om)) 2) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))

series2.2s (0.7%)

Counts

4 → 41

Calls

4 calls:

1.6s	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 2 l) Om)) 2) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
526.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
64.0ms	(sqrt.f64 (/.f64 (*.f64 2 l) Om))
26.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3505 to 3199 computations (8.7% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5264	2915

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 (.f64 l (.f64 l 4)) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) Om) (.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))))
5.3b	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
5.3b	(.f64 (.f64 l (*.f64 l 4)) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
26.7b	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
27.0b	(sqrt.f64 (.f64 (.f64 l (*.f64 l 4)) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite78.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64_480`
18×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
16×	`*-un-lft-identity_binary64_419`
15×	`pow-prod-down_binary64_490`
10×	`associate-r_binary64_359` `add-sqr-sqrt_binary64_441` `sqrt-prod_binary64_435`
9×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`add-cube-cbrt_binary64_454` `associate-*r/_binary64_361`
5×	`sqrt-pow1_binary64_437`
4×	`flip3-+_binary64_422` `unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `distribute-lft-out_binary64_370` `flip-+_binary64_393`
3×	`sqrt-div_binary64_436` `times-frac_binary64_425`
2×	`distribute-rgt-in_binary64_369` `pow1/2_binary64_499` `associate-/r/_binary64_365` `distribute-lft-in_binary64_368` `-commutative_binary64_350` `associate-l*_binary64_360`
1×	`div-inv_binary64_416` `unswap-sqr_binary64_387` `rem-sqrt-square_binary64_432`

Counts

4 → 87

Calls

8 calls:

16.0ms	(.f64 (.f64 l (*.f64 l 4)) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
15.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
15.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
14.0ms	(sqrt.f64 (.f64 (.f64 l (*.f64 l 4)) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (/.f64 (sqrt.f64 (.f64 (.f64 l (.f64 l 4)) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) Om) (.f64 1/2 (.f64 Om (sqrt.f64 (/.f64 1/4 (.f64 (*.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))))

series1.6s (0.5%)

Counts

4 → 42

Calls

4 calls:

578.0ms	(sqrt.f64 (/.f64 1/4 (.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
397.0ms	(sqrt.f64 (.f64 (.f64 l (*.f64 l 4)) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
354.0ms	(.f64 (.f64 l (*.f64 l 4)) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
265.0ms	(.f64 (.f64 l l) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 3534 to 2952 computations (16.5% saved)

simplify59.0ms (0%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5093	2958

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(pow.f64 (/.f64 (*.f64 2 l) Om) 2)
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fabs.f64 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))))))))
10.1b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))))
18.3b	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
18.3b	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
18.3b	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_450`
12×	`add-sqr-sqrt_binary64_441`
11×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`unpow-prod-down_binary64_498`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow1/3_binary64_501` `sqr-pow_binary64_391` `unpow2_binary64_484` `sqrt-prod_binary64_435`
2×	`sqrt-div_binary64_436`
1×	`flip3-+_binary64_422` `pow1/2_binary64_499` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 63

Calls

8 calls:

3.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
0.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fabs.f64 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))))))))

series1.3s (0.4%)

Counts

4 → 29

Calls

4 calls:

1.1s	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))))
96.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
90.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
80.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))

Compiler

Compiled 2413 to 2164 computations (10.3% saved)

simplify68.0ms (0%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5336	1981

prune26.6s (8.6%)

Pruning

370 alts after pruning (359 fresh and 11 done)

	Pruned	Kept	Total
New	347	120	467
Fresh	19	239	258
Picked	0	0	0
Done	0	11	11
Total	366	370	736

Error

0.0b

Counts

736 → 370

Compiler

Compiled 33497 to 25854 computations (22.8% saved)

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (pow.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (*.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) 1/2)))))
10.1b	(pow.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) 1/2)
17.7b	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
17.7b	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
17.7b	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite59.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-div_binary64_451`
6×	`flip3-+_binary64_422` `-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `frac-times_binary64_429` `add-sqr-sqrt_binary64_441` `associate-r/_binary64_361` `flip-+_binary64_393`
5×	`add-exp-log_binary64_457` `pow1_binary64_480`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455`
3×	`associate-*l/_binary64_362` `pow1/3_binary64_501` `unpow-prod-down_binary64_498` `cbrt-prod_binary64_450` `pow-unpow_binary64_496`
1×	`pow-exp_binary64_487` `sqr-pow_binary64_391` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `unpow1/2_binary64_483`

Counts

4 → 60

Calls

8 calls:

14.0ms	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
13.0ms	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
13.0ms	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
5.0ms	(pow.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) 1/2)
0.0ms	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (pow.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (*.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) 1/2)))))

series7.2s (2.3%)

Counts

4 → 62

Calls

4 calls:

3.4s	(pow.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) 1/2)
1.3s	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
1.3s	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
1.2s	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

Compiler

Compiled 8760 to 7320 computations (16.4% saved)

simplify92.0ms (0%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4968	4414
1	4968	4414

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize39.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 1 (+.f64 1 (.f64 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om)) 4)))
0.0b	(.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om)) 4)))) (/.f64 (.f64 (.f64 ky ky) (.f64 l l)) (.f64 Om Om))))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (fabs.f64 (+.f64 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om)) 4))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om)) 4)))) (/.f64 (.f64 (.f64 ky ky) (.f64 l l)) (.f64 Om Om)))))))))
0.0b	(+.f64 1/2 (/.f64 1/2 (fabs.f64 (+.f64 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om)) 4))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om)) 4)))) (/.f64 (.f64 (.f64 ky ky) (.f64 l l)) (.f64 Om Om))))))))
11.5b	(/.f64 (.f64 (.f64 ky ky) (.f64 l l)) (.f64 Om Om))
13.5b	(/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (*.f64 Om Om))
13.5b	(/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (*.f64 Om Om))
20.0b	(.f64 (.f64 ky ky) (*.f64 l l))

rewrite71.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`add-exp-log_binary64_457`
99×	`add-cbrt-cube_binary64_455`
79×	`prod-exp_binary64_468`
47×	`cbrt-unprod_binary64_452`
38×	`div-exp_binary64_470`
32×	`pow1_binary64_480`
22×	`cbrt-undiv_binary64_453`
14×	`pow-prod-down_binary64_490`
8×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
4×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `pow-plus_binary64_482` `pow-prod-up_binary64_489`
3×	`clear-num_binary64_418` `times-frac_binary64_425` `div-inv_binary64_416` `frac-2neg_binary64_430` `associate-/r_binary64_363` `associate-/l_binary64_364`
2×	`pow-sqr_binary64_392` `pow2_binary64_500`
1×	`associate-r_binary64_359` `unswap-sqr_binary64_387` `-commutative_binary64_350` `associate-l*_binary64_360`

Counts

4 → 128

Calls

8 calls:

14.0ms	(/.f64 (.f64 (.f64 ky ky) (.f64 l l)) (.f64 Om Om))
11.0ms	(/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (*.f64 Om Om))
11.0ms	(/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (*.f64 Om Om))
9.0ms	(.f64 (.f64 ky ky) (*.f64 l l))
0.0ms	(+.f64 1/2 (/.f64 1/2 (fabs.f64 (+.f64 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om)) 4))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (.f64 Om Om)) 4)))) (/.f64 (.f64 (.f64 ky ky) (.f64 l l)) (.f64 Om Om))))))))

series838.0ms (0.3%)

Counts

4 → 33

Calls

4 calls:

268.0ms	(/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (*.f64 Om Om))
268.0ms	(/.f64 (.f64 (pow.f64 (sin.f64 kx) 2) (.f64 l l)) (*.f64 Om Om))
210.0ms	(/.f64 (.f64 (.f64 ky ky) (.f64 l l)) (.f64 Om Om))
91.0ms	(.f64 (.f64 ky ky) (*.f64 l l))

Compiler

Compiled 3786 to 2932 computations (22.6% saved)

simplify65.0ms (0%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5167	2132

localize36.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)
0.0b	(.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)
0.0b	(sqrt.f64 (.f64 (/.f64 1 2) (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)))) (.f64 (fabs.f64 (.f64 (/.f64 l Om) kx)) (fabs.f64 (.f64 (/.f64 l Om) kx))))))))))
0.0b	(+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)))) (.f64 (fabs.f64 (.f64 (/.f64 l Om) kx)) (fabs.f64 (*.f64 (/.f64 l Om) kx))))))))
8.6b	(sqrt.f64 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)))
8.7b	(sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4))))
9.4b	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
9.4b	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))

rewrite79.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-sqr-sqrt_binary64_441`
58×	`unpow-prod-down_binary64_498`
44×	`add-exp-log_binary64_457`
40×	`unswap-sqr_binary64_387`
37×	`times-frac_binary64_425`
36×	`associate-r_binary64_359`
33×	`*-un-lft-identity_binary64_419`
32×	`add-cube-cbrt_binary64_454`
24×	`prod-exp_binary64_468`
22×	`sqr-pow_binary64_391` `unpow2_binary64_484`
20×	`pow-exp_binary64_487`
18×	`sqrt-prod_binary64_435`
16×	`associate-l_binary64_360`
14×	`pow-to-exp_binary64_488`
8×	`add-cbrt-cube_binary64_455`
7×	`pow1_binary64_480`
6×	`div-exp_binary64_470`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
3×	`sqrt-div_binary64_436` `div-inv_binary64_416`
2×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `pow1/2_binary64_499` `cbrt-unprod_binary64_452` `associate-/r/_binary64_365` `*-commutative_binary64_350` `flip-+_binary64_393`
1×	`inv-pow_binary64_504` `pow-flip_binary64_493`

Counts

4 → 181

Calls

8 calls:

14.0ms	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
14.0ms	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
6.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)))
0.0ms	(+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4))) (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)))) (.f64 (fabs.f64 (.f64 (/.f64 l Om) kx)) (fabs.f64 (*.f64 (/.f64 l Om) kx))))))))

series1.2s (0.4%)

Counts

4 → 44

Calls

4 calls:

315.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4)))
306.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (.f64 (.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2)) 4))))
280.0ms	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))
271.0ms	(*.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (/.f64 l Om) 2))

Compiler

Compiled 4763 to 3685 computations (22.6% saved)

simplify89.0ms (0%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5043	4243

localize35.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 (.f64 l (pow.f64 (sin.f64 ky) 2)) Om))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 (.f64 l (pow.f64 (sin.f64 ky) 2)) Om))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
9.1b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 (.f64 l (pow.f64 (sin.f64 ky) 2)) Om))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
17.7b	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
17.7b	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
22.4b	(cbrt.f64 (/.f64 (*.f64 l (pow.f64 (sin.f64 ky) 2)) Om))

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-div_binary64_451`
9×	`cbrt-prod_binary64_450`
8×	`add-sqr-sqrt_binary64_441`
7×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
5×	`flip3-+_binary64_422` `flip-+_binary64_393` `pow1_binary64_480`
4×	`add-log-exp_binary64_458` `frac-times_binary64_429` `associate-*r/_binary64_361` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`pow1/3_binary64_501` `times-frac_binary64_425` `sqrt-prod_binary64_435`
2×	`associate-*l/_binary64_362` `sqrt-div_binary64_436`
1×	`pow1/2_binary64_499` `div-inv_binary64_416` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 59

Calls

8 calls:

16.0ms	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
13.0ms	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
4.0ms	(cbrt.f64 (/.f64 (*.f64 l (pow.f64 (sin.f64 ky) 2)) Om))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 (.f64 l (pow.f64 (sin.f64 ky) 2)) Om))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
0.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 (.f64 l (pow.f64 (sin.f64 ky) 2)) Om))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))

series5.3s (1.7%)

Counts

4 → 54

Calls

4 calls:

2.4s	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (.f64 (.f64 (cbrt.f64 2) (cbrt.f64 (/.f64 (.f64 l (pow.f64 (sin.f64 ky) 2)) Om))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
1.2s	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
1.2s	(cbrt.f64 (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
543.0ms	(cbrt.f64 (/.f64 (*.f64 l (pow.f64 (sin.f64 ky) 2)) Om))

Compiler

Compiled 6859 to 5804 computations (15.4% saved)

simplify89.0ms (0%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4961	4658
1	4961	4658

prune36.5s (11.9%)

Pruning

481 alts after pruning (466 fresh and 15 done)

	Pruned	Kept	Total
New	498	123	621
Fresh	11	343	354
Picked	0	0	0
Done	1	15	16
Total	510	481	991

Error

0.0b

Counts

991 → 481

Compiler

Compiled 23474 to 15232 computations (35.1% saved)

simplify1.5s (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	8961	98401

regimes1.3min (25.2%)

Compiler: Compiled 1093866 to 889915 computations (18.6% saved)

bsearch101.0ms (0%)

Compiler: Compiled 5 to 7 computations (-40% saved)

regimes55.3s (18%)

Compiler: Compiled 725466 to 599999 computations (17.3% saved)

bsearch72.0ms (0%)

Compiler: Compiled 7 to 9 computations (-28.6% saved)

regimes26.5s (8.6%)

Compiler: Compiled 336769 to 286561 computations (14.9% saved)

bsearch0.0ms (0%)

regimes2.0s (0.6%)

Compiler: Compiled 22201 to 20803 computations (6.3% saved)

bsearch0.0ms (0%)

regimes2.1s (0.7%)

Compiler: Compiled 21098 to 19811 computations (6.1% saved)

bsearch3.0ms (0%)

Compiler: Compiled 2 to 5 computations (-150% saved)

regimes1.4s (0.5%)

Compiler: Compiled 11566 to 11000 computations (4.9% saved)

bsearch2.0ms (0%)

Compiler: Compiled 2 to 5 computations (-150% saved)

regimes491.0ms (0.2%)

Compiler: Compiled 3818 to 3836 computations (-0.5% saved)

bsearch102.0ms (0%)

Steps

Iters	Range		Point
7	2.579158100260435e-191	7.222955987846852e-190	6.972013279243029e-190
9	-1.9923310761319195e-162	-3.16672658780068e-169	-2.7032954679589283e-163

Compiler

Compiled 2 to 5 computations (-150% saved)

regimes752.0ms (0.2%)

Compiler: Compiled 2840 to 2864 computations (-0.8% saved)

bsearch256.0ms (0.1%)

Steps

Iters	Range		Point
9	1.1533341732448266e+175	5.549053917952494e+181	5.230022574008346e+176
7	4.053251443937403e-206	1.7518554776576523e-204	1.7177684397412795e-204
9	-4.7339251338766036e-141	-1.6753290048274203e-147	-1.7015588124713997e-147
8	-2.4283709899968465e+207	-4.8758032293004596e+204	-4.9196336260896123e+204

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes445.0ms (0.1%)

Compiler: Compiled 2648 to 2680 computations (-1.2% saved)

bsearch173.0ms (0.1%)

Steps

Iters

Range

Point

4.053251443937403e-206

1.7518554776576523e-204

1.7177684397412795e-204

-4.7339251338766036e-141

-1.6753290048274203e-147

-2.1004755517664194e-146

-2.4283709899968465e+207

-4.8758032293004596e+204

-5.524097090692549e+204

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes275.0ms (0.1%)

Compiler: Compiled 1112 to 1208 computations (-8.6% saved)

bsearch175.0ms (0.1%)

Steps

Iters

Range

Point

2.985362870515833e-102

1.6088709269305315e-97

3.040136823878769e-102

-2.330470645778574e-306

2.3537975322901135e-301

4.535938700067649e-306

-9.755346650897043e-154

-1.6970347710731736e-159

-2.0017555155169974e-158

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes124.0ms (0%)

Compiler: Compiled 170 to 272 computations (-60% saved)

bsearch104.0ms (0%)

Steps

Iters	Range		Point
7	4.053251443937403e-206	1.7518554776576523e-204	1.7177684397412795e-204
9	-4.7339251338766036e-141	-1.6753290048274203e-147	-2.8558940119130246e-146

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes40.0ms (0%)

Compiler: Compiled 20 to 92 computations (-360% saved)

bsearch39.0ms (0%)

Compiler: Compiled 858 to 689 computations (19.7% saved)

simplify15.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	253	1214
1	253	1214

end0.0ms (0%)

sample6.9s (2.2%)

Algorithm

1×

intervals

Results

1.2s	6434×	body	128	valid
684.0ms	782×	body	1024	valid
325.0ms	513×	body	512	valid
105.0ms	271×	body	256	valid

Compiler

Compiled 63566 to 51544 computations (18.9% saved)