Details

Time bar (total: 9.1s)

analyze735.0ms (8.1%)

Algorithm
search
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-exp_binary64 swap-kx-ky
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)

IterNodesCost
088294
1222273
2515273
32273273
44998273
044
144
Search
TrueOtherFalseIter
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)

sample87.0ms (1%)

Algorithm
intervals
Results
36.0ms207×body128valid
16.0ms19×body1024valid
10.0ms17×body512valid
5.0ms13×body256valid
Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify48.0ms (0.5%)

Algorithm
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
+-commutative_binary64
unpow3_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 rem-sqrt-square_binary64 pow-sqr_binary64 associate-+l+_binary64 associate-+r+_binary64
1-exp_binary64
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)

IterNodesCost
02442
15639
210739
342939
4203739
5484439
6532539

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
1.3b
Counts
2 → 1
Compiler

Compiled 50 to 50 computations (0% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (sin.f64 kx) 2)
0.7b
(/.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))))))
2.4b
(*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.8b
(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)))))

rewrite383.0ms (4.2%)

Algorithm
rewrite-expression-head
Error
1.1b
Rules
33×add-sqr-sqrt_binary64
30×*-un-lft-identity_binary64
26×add-cube-cbrt_binary64
21×times-frac_binary64
19×add-exp-log_binary64
15×sqrt-prod_binary64
13×unpow-prod-down_binary64
12×associate-*l*_binary64
add-cbrt-cube_binary64
pow1_binary64 prod-exp_binary64 associate-/r*_binary64
associate-*r*_binary64
add-log-exp_binary64 sqrt-div_binary64 pow-exp_binary64 unswap-sqr_binary64
flip3-+_binary64 flip-+_binary64 div-exp_binary64 unpow2_binary64 sqr-pow_binary64 associate-/l*_binary64 pow-unpow_binary64
pow-to-exp_binary64 associate-*r/_binary64 div-inv_binary64 distribute-lft-out_binary64 associate-/r/_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 cbrt-unprod_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 *-commutative_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 pow-pow_binary64
Counts
4 → 113
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)))
6.0ms
(/.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))))))
3.0ms
(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 kx) 2)
Compiler

Compiled 4225 to 3201 computations (24.2% saved)

series698.0ms (7.7%)

Error
0.4b
Counts
4 → 52
Calls

4 calls:

288.0ms
(/.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))))))
224.0ms
(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)))))
123.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 4854 to 4340 computations (10.6% saved)

simplify155.0ms (1.7%)

Algorithm
egg-herbie
Rules
406×distribute-rgt-in_binary64
396×distribute-lft-in_binary64
347×times-frac_binary64
304×unswap-sqr_binary64
176×associate-*r*_binary64
168×associate-*l*_binary64
136×*-commutative_binary64
127×cancel-sign-sub-inv_binary64
108×distribute-rgt-neg-in_binary64
96×sqr-pow_binary64
91×distribute-lft-neg-in_binary64
61×associate-*r/_binary64
54×distribute-rgt-out_binary64
51×associate-/l*_binary64 associate-*l/_binary64
47×exp-prod_binary64
42×+-commutative_binary64
41×associate-/r*_binary64
39×cube-prod_binary64 sub-neg_binary64
33×neg-sub0_binary64
31×neg-mul-1_binary64 distribute-lft-out_binary64
29×log-prod_binary64
23×*-rgt-identity_binary64 swap-sqr_binary64
19×*-lft-identity_binary64 distribute-neg-frac_binary64
18×distribute-neg-in_binary64
16×unpow2_binary64 unpow1/2_binary64 unpow1_binary64
15×associate-/l/_binary64
14×unpow3_binary64 pow-sqr_binary64
12×log-pow_binary64 distribute-lft-neg-out_binary64 associate-/r/_binary64
log-div_binary64 cube-mult_binary64
pow-plus_binary64 cube-unmult_binary64 cube-div_binary64 distribute-rgt-out--_binary64 associate-+l+_binary64
rem-sqrt-square_binary64
distribute-rgt-neg-out_binary64 distribute-rgt1-in_binary64
/-rgt-identity_binary64 difference-of-squares_binary64 associate-+r+_binary64
exp-sum_binary64 unsub-neg_binary64 associate--r+_binary64
rem-square-sqrt_binary64 distribute-lft-out--_binary64 associate--l+_binary64
mul-1-neg_binary64 difference-of-sqr-1_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 distribute-lft1-in_binary64 associate-+l-_binary64 associate-+r-_binary64
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 +-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--r-_binary64 associate--l-_binary64
Counts
165 → 140
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02956235
16925850
221025689
349925689

prune155.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1391140
Fresh000
Picked011
Done000
Total1392141
Error
0.0b
Counts
141 → 2
Compiler

Compiled 3668 to 2692 computations (26.6% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.3b
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
4.3b
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
27.3b
(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
27.5b
(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)))))

rewrite372.0ms (4.1%)

Algorithm
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
add-cbrt-cube_binary64 sqrt-div_binary64 unpow2_binary64 sqr-pow_binary64
associate-/r/_binary64
sqrt-pow1_binary64 frac-times_binary64 associate-*r/_binary64 div-exp_binary64 associate-/r*_binary64
add-log-exp_binary64 frac-add_binary64 flip3-+_binary64 flip-+_binary64
div-inv_binary64
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
inv-pow_binary64 rem-sqrt-square_binary64
Counts
4 → 144
Calls

4 calls:

44.0ms
(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
44.0ms
(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)))))
6.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
5.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
Compiler

Compiled 8245 to 5463 computations (33.7% saved)

series349.0ms (3.8%)

Error
0.0b
Counts
4 → 34
Calls

4 calls:

128.0ms
(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)))))
119.0ms
(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
34.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
33.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
Compiler

Compiled 4021 to 3119 computations (22.4% saved)

simplify186.0ms (2%)

Algorithm
egg-herbie
Rules
510×times-frac_binary64
479×associate-/l*_binary64
349×associate-*l/_binary64
332×associate-/r*_binary64
331×associate-*l*_binary64
283×associate-*r/_binary64
167×associate-/r/_binary64
143×associate-/l/_binary64
73×neg-mul-1_binary64
70×*-commutative_binary64
57×distribute-neg-frac_binary64 associate-*r*_binary64
55×distribute-rgt-in_binary64
53×cancel-sign-sub-inv_binary64
47×log-prod_binary64 distribute-rgt-neg-in_binary64
46×distribute-lft-in_binary64
45×cube-prod_binary64
41×sqr-pow_binary64 distribute-lft-neg-in_binary64
38×cube-div_binary64
33×log-div_binary64
32×sub-neg_binary64
30×unswap-sqr_binary64
26×log-pow_binary64 div-sub_binary64
21×rem-sqrt-square_binary64
19×neg-sub0_binary64
18×cube-unmult_binary64
16×+-commutative_binary64
15×unpow3_binary64 pow-plus_binary64
11×distribute-lft-neg-out_binary64 distribute-rgt-out_binary64
cube-mult_binary64
/-rgt-identity_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 exp-prod_binary64 pow-sqr_binary64 distribute-lft-out_binary64
*-rgt-identity_binary64 distribute-rgt-neg-out_binary64
associate--l+_binary64 associate--r+_binary64
rem-square-sqrt_binary64 unsub-neg_binary64 *-lft-identity_binary64
log-rec_binary64 distribute-neg-in_binary64 distribute-rgt-out--_binary64 associate-+l+_binary64
1-exp_binary64 rem-3cbrt-rft_binary64 difference-of-squares_binary64 associate-+l-_binary64 associate-+r-_binary64
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 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 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-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate-+r+_binary64
Counts
178 → 109
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02364095
14803690
212243649
346523649
449953649
549633649

prune153.0ms (1.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1090109
Fresh000
Picked011
Done011
Total1092111
Error
0.0b
Counts
111 → 2
Compiler

Compiled 5006 to 3243 computations (35.2% saved)

regimes2.9s (32.3%)

Accuracy

Total 0.3b remaining (81.6%)

Threshold costs 0.3b (81.6%)

Compiler

Compiled 50714 to 46586 computations (8.1% saved)

bsearch4.0ms (0%)

Compiler

Compiled 7 to 9 computations (-28.6% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
1-exp_binary64
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)

IterNodesCost
044136
157136
256136

end13.0ms (0.1%)

Remove

(sort kx ky)

Compiler

Compiled 261 to 207 computations (20.7% saved)

sample2.8s (30.3%)

Algorithm
intervals
Results
1.1s6381×body128valid
622.0ms749×body1024valid
319.0ms534×body512valid
125.0ms336×body256valid
Compiler

Compiled 195 to 183 computations (6.2% saved)

Profiling

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