Details

analyze743.0ms (7.1%)

Algorithm

1×	search
2×	egg-herbie

Rules

582×	`associate-/l*_binary64`
500×	`unswap-sqr_binary64`
354×	`associate-/r/_binary64`
324×	`associate-*l/_binary64`
294×	`associate-*r/_binary64`
262×	`associate-l_binary64` `associate-r_binary64`
155×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
138×	`*-commutative_binary64`
126×	`associate-/l/_binary64`
60×	`distribute-rgt-out_binary64` `distribute-lft-out_binary64`
50×	`swap-sqr_binary64`
45×	`+-commutative_binary64`
40×	`sqr-pow_binary64`
19×	`associate-+l+_binary64` `associate-+r+_binary64`
10×	`unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `unpow1_binary64` `cube-unmult_binary64` `rem-sqrt-square_binary64`
1×	`1-exp_binary64` `swap-kx-ky`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate-/r_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	294
1	222	273
2	515	273
3	2273	273
4	4998	273
0	4	4
1	4	4

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

Symmetry

(sort kx ky)

Compiler

Compiled 30 to 30 computations (0% saved)

sample94.0ms (0.9%)

Algorithm

1×

intervals

Results

39.0ms	201×	body	128	valid
20.0ms	25×	body	1024	valid
11.0ms	18×	body	512	valid
4.0ms	12×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

575×	`associate-l_binary64`
512×	`unswap-sqr_binary64`
437×	`associate-r_binary64`
409×	`distribute-rgt-out_binary64`
369×	`associate-/r/_binary64`
368×	`associate-/r*_binary64`
334×	`associate-/l/_binary64`
328×	`associate-*l/_binary64`
299×	`associate-*r/_binary64`
197×	`times-frac_binary64`
128×	`*-commutative_binary64`
97×	`associate-/l*_binary64`
88×	`distribute-rgt-in_binary64`
82×	`swap-sqr_binary64`
70×	`distribute-lft-in_binary64`
52×	`distribute-lft-out_binary64`
41×	`sqr-pow_binary64`
15×	`cube-unmult_binary64`
12×	`pow-plus_binary64` `cube-prod_binary64`
7×	`+-commutative_binary64`
5×	`unpow3_binary64`
3×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
1×	`1-exp_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	42
1	56	39
2	107	39
3	429	39
4	2037	39
5	4844	39
6	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

Error

0.5b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
2.2b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.6b	(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)))))

rewrite211.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
17×	`*-un-lft-identity_binary64`
16×	`unpow-prod-down_binary64`
13×	`add-cube-cbrt_binary64`
12×	`associate-l_binary64`
7×	`pow1_binary64`
6×	`add-cbrt-cube_binary64` `prod-exp_binary64` `pow-unpow_binary64`
5×	`pow-exp_binary64` `associate-r_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `unpow2_binary64` `sqr-pow_binary64`
3×	`sqrt-prod_binary64` `pow-to-exp_binary64` `times-frac_binary64`
2×	`flip3-+_binary64` `sqrt-div_binary64` `flip-+_binary64` `div-exp_binary64` `associate-*r/_binary64` `distribute-lft-out_binary64` `pow-pow_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `cbrt-unprod_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

16.0ms	(.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)))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3003 to 2262 computations (24.7% saved)

series487.0ms (4.7%)

Error

0.2b

Counts

4 → 47

Calls

4 calls:

290.0ms	(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)))))
121.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(pow.f64 (sin.f64 kx) 2)
9.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 4643 to 4015 computations (13.5% saved)

simplify162.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

438×	`unswap-sqr_binary64`
367×	`distribute-rgt-in_binary64`
289×	`cancel-sign-sub-inv_binary64`
215×	`associate-r_binary64`
192×	`associate-l_binary64`
164×	`*-commutative_binary64`
125×	`sub-neg_binary64`
119×	`sqr-pow_binary64`
109×	`log-prod_binary64`
94×	`distribute-rgt-neg-in_binary64`
88×	`+-commutative_binary64`
84×	`associate-/l*_binary64`
77×	`distribute-lft-neg-in_binary64`
71×	`associate-*r/_binary64`
69×	`distribute-rgt-out_binary64`
68×	`distribute-lft-in_binary64`
67×	`times-frac_binary64`
60×	`associate-+r+_binary64`
58×	`associate-*l/_binary64`
55×	`associate-/r*_binary64`
51×	`exp-prod_binary64`
46×	`associate--r+_binary64` `associate-+l+_binary64`
42×	`distribute-lft-out_binary64`
37×	`associate--l+_binary64`
36×	`log-pow_binary64`
35×	`cube-prod_binary64`
33×	`distribute-neg-frac_binary64`
30×	`neg-sub0_binary64` `distribute-neg-in_binary64`
28×	`neg-mul-1_binary64`
20×	`pow-sqr_binary64`
19×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64`
18×	`*-lft-identity_binary64`
17×	`*-rgt-identity_binary64`
16×	`associate-/r/_binary64`
15×	`log-div_binary64` `unsub-neg_binary64` `swap-sqr_binary64`
14×	`unpow3_binary64` `distribute-lft-neg-out_binary64`
9×	`pow-plus_binary64` `cube-unmult_binary64` `cube-mult_binary64` `rem-sqrt-square_binary64` `distribute-rgt-out--_binary64`
7×	`cube-div_binary64`
6×	`distribute-rgt-neg-out_binary64` `distribute-rgt1-in_binary64`
5×	`difference-of-squares_binary64`
4×	`exp-sum_binary64` `rem-square-sqrt_binary64`
3×	`distribute-lft-out--_binary64`
2×	`rem-3cbrt-rft_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `difference-of-sqr-1_binary64` `associate-+r-_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `+-rgt-identity_binary64` `distribute-lft1-in_binary64` `associate-+l-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `div-sub_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `count-2_binary64` `associate-/l/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

137 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	4678
1	774	4424
2	2741	4247
3	4889	4247
4	5007	4247

prune143.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Error

0.0b

Counts

109 → 3

Compiler

Compiled 2756 to 1971 computations (28.5% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.2b	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
2.4b	(sqrt.f64 (cbrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
12.0b	(cbrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
12.0b	(cbrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

rewrite290.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

20×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64` `*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64` `associate-r_binary64`
10×	`cbrt-prod_binary64` `unpow-prod-down_binary64`
6×	`add-cbrt-cube_binary64` `cbrt-div_binary64` `sqrt-prod_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `flip3-+_binary64` `flip-+_binary64` `unswap-sqr_binary64`
3×	`pow1/3_binary64` `pow-exp_binary64` `times-frac_binary64`
2×	`sqrt-pow1_binary64` `sqrt-div_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-*l/_binary64` `distribute-lft-out_binary64`
1×	`pow1/2_binary64` `pow-to-exp_binary64` `cbrt-unprod_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

17.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
4.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
4.0ms	(cbrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
3.0ms	(cbrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

Compiler

Compiled 5180 to 3871 computations (25.3% saved)

series1.8s (17.2%)

Error

0.0b

Counts

4 → 92

Calls

4 calls:

500.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
495.0ms	(cbrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
495.0ms	(cbrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
138.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))

Compiler

Compiled 16430 to 13340 computations (18.8% saved)

simplify238.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

386×	`cancel-sign-sub-inv_binary64`
330×	`unswap-sqr_binary64`
251×	`associate-r_binary64`
228×	`sub-neg_binary64`
195×	`*-commutative_binary64`
162×	`associate-l_binary64`
155×	`+-commutative_binary64`
138×	`associate-+r+_binary64`
131×	`sqr-pow_binary64`
119×	`associate-*r/_binary64`
114×	`associate-/l*_binary64`
106×	`associate-*l/_binary64`
99×	`times-frac_binary64`
97×	`associate-+l+_binary64`
96×	`associate-/r*_binary64`
78×	`associate--r+_binary64`
62×	`associate--l+_binary64`
59×	`distribute-rgt-in_binary64`
57×	`distribute-lft-in_binary64`
45×	`log-prod_binary64` `neg-mul-1_binary64` `neg-sub0_binary64`
36×	`unsub-neg_binary64`
30×	`exp-prod_binary64`
29×	`exp-sum_binary64`
23×	`cube-prod_binary64`
20×	`*-lft-identity_binary64` `distribute-neg-in_binary64`
18×	`distribute-rgt-neg-in_binary64` `associate-/r/_binary64`
17×	`distribute-rgt-out_binary64`
15×	`swap-sqr_binary64`
14×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `*-rgt-identity_binary64`
13×	`pow-sqr_binary64` `distribute-lft-neg-in_binary64`
10×	`log-div_binary64` `unpow3_binary64`
9×	`unpow1/3_binary64`
8×	`log-pow_binary64` `cube-unmult_binary64`
7×	`cube-mult_binary64` `cube-div_binary64` `distribute-lft-out_binary64`
6×	`pow-plus_binary64` `rem-sqrt-square_binary64`
4×	`distribute-lft-neg-out_binary64`
3×	`exp-diff_binary64` `div-sub_binary64` `remove-double-neg_binary64` `difference-of-squares_binary64`
2×	`rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `distribute-rgt-neg-out_binary64` `distribute-rgt-out--_binary64`
1×	`log-rec_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-rft_binary64` `/-rgt-identity_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `distribute-lft-out--_binary64` `associate-+l-_binary64` `associate-+r-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

175 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	402	10481
1	998	10148
2	3612	10041
3	5078	10041

prune288.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	152	3	155

Error

0.0b

Counts

155 → 3

Compiler

Compiled 7893 to 5499 computations (30.3% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

5.0b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
5.0b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
27.5b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
28.0b	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))

rewrite402.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

51×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
40×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
24×	`unpow-prod-down_binary64`
16×	`associate-/l*_binary64`
15×	`sqrt-prod_binary64`
14×	`add-exp-log_binary64`
11×	`pow1_binary64`
8×	`add-cbrt-cube_binary64` `sqrt-div_binary64` `unpow2_binary64` `sqr-pow_binary64`
7×	`associate-/r/_binary64`
6×	`sqrt-pow1_binary64` `frac-times_binary64` `associate-r/_binary64` `div-exp_binary64` `associate-/r_binary64`
4×	`add-log-exp_binary64` `frac-add_binary64` `flip3-+_binary64` `flip-+_binary64`
3×	`div-inv_binary64`
2×	`pow1/2_binary64` `pow-prod-down_binary64` `pow-flip_binary64` `associate-*l/_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`inv-pow_binary64` `rem-sqrt-square_binary64`

Counts

4 → 144

Calls

4 calls:

50.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
43.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
6.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
6.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 8245 to 5463 computations (33.7% saved)

series345.0ms (3.3%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

135.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
110.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
33.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
31.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 3966 to 3088 computations (22.1% saved)

simplify154.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

473×	`associate-/l*_binary64`
425×	`times-frac_binary64`
338×	`associate-*l/_binary64`
336×	`associate-r_binary64`
335×	`associate-l_binary64`
298×	`associate-/r*_binary64`
286×	`associate-*r/_binary64`
157×	`associate-/r/_binary64`
133×	`associate-/l/_binary64`
68×	`*-commutative_binary64`
55×	`log-prod_binary64`
53×	`distribute-rgt-in_binary64`
50×	`distribute-rgt-neg-in_binary64`
48×	`distribute-neg-frac_binary64`
46×	`distribute-lft-neg-in_binary64` `distribute-lft-in_binary64`
42×	`sqr-pow_binary64`
33×	`log-div_binary64`
30×	`unswap-sqr_binary64`
25×	`cancel-sign-sub-inv_binary64`
22×	`sub-neg_binary64`
17×	`neg-mul-1_binary64` `neg-sub0_binary64`
15×	`unpow3_binary64` `pow-plus_binary64`
14×	`+-commutative_binary64`
11×	`log-pow_binary64`
10×	`cube-div_binary64`
9×	`distribute-lft-neg-out_binary64` `distribute-rgt-out_binary64`
8×	`cube-prod_binary64` `/-rgt-identity_binary64`
7×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `distribute-lft-out_binary64`
5×	`cube-unmult_binary64` `cube-mult_binary64` `*-rgt-identity_binary64` `distribute-rgt-neg-out_binary64`
3×	`rem-square-sqrt_binary64` `div-sub_binary64` `*-lft-identity_binary64`
2×	`log-rec_binary64` `distribute-rgt-out--_binary64`
1×	`1-exp_binary64` `rem-3cbrt-rft_binary64` `difference-of-squares_binary64` `associate-+l-_binary64` `associate-+r-_binary64` `associate-+l+_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+r+_binary64`

Counts

178 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	4064
1	470	3691
2	1178	3627
3	4855	3627
4	4956	3627

prune170.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	109	3	112

Error

0.0b

Counts

112 → 3

Compiler

Compiled 4990 to 3236 computations (35.2% saved)

regimes1.9s (18.3%)

Accuracy

Total 0.9b remaining (96%)

Threshold costs 0.9b (96%)

Compiler

Compiled 32230 to 28463 computations (11.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64` `+-commutative_binary64`
1×	`1-exp_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `unpow1_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	76
1	33	76
2	32	76

end10.0ms (0.1%)

Remove: (sort kx ky)
Compiler: Compiled 144 to 126 computations (12.5% saved)

sample2.9s (27.4%)

Algorithm

1×

intervals

Results

1.2s	6374×	body	128	valid
670.0ms	793×	body	1024	valid
300.0ms	507×	body	512	valid
133.0ms	325×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 204 to 198 computations (2.9% saved)

Details

analyze743.0ms (7.1%)

sample94.0ms (0.9%)

simplify50.0ms (0.5%)

prune5.0ms (0%)

localize25.0ms (0.2%)

rewrite211.0ms (2%)

series487.0ms (4.7%)

simplify162.0ms (1.6%)

prune143.0ms (1.4%)

localize28.0ms (0.3%)

rewrite290.0ms (2.8%)

series1.8s (17.2%)

simplify238.0ms (2.3%)

prune288.0ms (2.8%)

localize34.0ms (0.3%)

rewrite402.0ms (3.9%)

series345.0ms (3.3%)

simplify154.0ms (1.5%)

prune170.0ms (1.6%)

regimes1.9s (18.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end10.0ms (0.1%)

sample2.9s (27.4%)

Profiling