Details

Time bar (total: 9.1s)

analyze727.0ms (8%)

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)

sample91.0ms (1%)

Algorithm
intervals
Results
40.0ms213×body128valid
23.0ms28×body1024valid
4.0msbody512valid
3.0msbody256valid
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

prune4.0ms (0%)

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 ky) 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))))))
1.9b
(*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.4b
(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)))))

rewrite209.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
0.9b
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:

20.0ms
(*.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 ky) 2)
Compiler

Compiled 4225 to 3201 computations (24.2% saved)

series678.0ms (7.5%)

Error
0.4b
Counts
4 → 52
Calls

4 calls:

272.0ms
(/.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))))))
218.0ms
(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)))))
120.0ms
(*.f64 (pow.f64 (/.f64 (*.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
12.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 4854 to 4340 computations (10.6% saved)

simplify145.0ms (1.6%)

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
131×cancel-sign-sub-inv_binary64
110×distribute-rgt-neg-in_binary64
96×sqr-pow_binary64
93×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
349975689

prune178.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1382140
Fresh000
Picked011
Done000
Total1383141
Error
0b
Counts
141 → 3
Compiler

Compiled 3696 to 2717 computations (26.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.2b
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
4.3b
(*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
4.7b
(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
9.3b
(/.f64 (*.f64 l l) Om)

rewrite330.0ms (3.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
67×times-frac_binary64
61×*-un-lft-identity_binary64
51×add-sqr-sqrt_binary64
47×add-cube-cbrt_binary64
30×unpow-prod-down_binary64
28×add-exp-log_binary64
22×add-cbrt-cube_binary64
17×associate-/l*_binary64
11×associate-*r*_binary64
10×div-exp_binary64
associate-/r*_binary64
unpow2_binary64 sqr-pow_binary64
associate-*l*_binary64 distribute-lft-out_binary64
pow1_binary64 cbrt-undiv_binary64 div-inv_binary64
prod-exp_binary64 cbrt-unprod_binary64
add-log-exp_binary64
frac-2neg_binary64 clear-num_binary64 frac-times_binary64 associate-*r/_binary64
pow-to-exp_binary64 pow-exp_binary64 frac-add_binary64 flip3-+_binary64 flip-+_binary64 unswap-sqr_binary64
pow-prod-down_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-*l/_binary64 distribute-rgt-out_binary64 *-commutative_binary64
Counts
4 → 163
Calls

4 calls:

50.0ms
(*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
5.0ms
(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
5.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
5.0ms
(/.f64 (*.f64 l l) Om)
Compiler

Compiled 5887 to 3454 computations (41.3% saved)

series229.0ms (2.5%)

Error
0b
Counts
4 → 32
Calls

4 calls:

131.0ms
(*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
28.0ms
(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
26.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
23.0ms
(/.f64 (*.f64 l l) Om)
Compiler

Compiled 2088 to 1870 computations (10.4% saved)

simplify147.0ms (1.6%)

Algorithm
egg-herbie
Rules
497×associate-/l/_binary64
367×associate-/r/_binary64
338×distribute-rgt-in_binary64
320×distribute-lft-in_binary64
206×associate-*l/_binary64
159×associate-/l*_binary64 associate-*l*_binary64
155×associate-*r/_binary64
154×unswap-sqr_binary64
132×associate-*r*_binary64
116×log-prod_binary64
106×*-commutative_binary64
75×log-div_binary64
69×times-frac_binary64
59×sqr-pow_binary64
54×associate-/r*_binary64
37×sub-neg_binary64
31×cube-div_binary64
29×distribute-neg-frac_binary64
28×exp-prod_binary64
26×log-pow_binary64
25×distribute-rgt-neg-in_binary64
24×*-rgt-identity_binary64
23×cube-prod_binary64 *-lft-identity_binary64
21×/-rgt-identity_binary64 distribute-lft-neg-in_binary64
19×swap-sqr_binary64
18×distribute-rgt-out_binary64 +-commutative_binary64
16×neg-mul-1_binary64 neg-sub0_binary64
15×cancel-sign-sub-inv_binary64
12×unpow2_binary64 unpow1/2_binary64 unpow1_binary64 cube-unmult_binary64
11×pow-sqr_binary64
10×pow-plus_binary64 distribute-lft-neg-out_binary64
exp-sum_binary64
log-rec_binary64
unpow3_binary64 distribute-rgt-neg-out_binary64 distribute-lft-out_binary64
rem-sqrt-square_binary64
div-sub_binary64
associate-+l-_binary64 associate-+l+_binary64
cube-mult_binary64 rem-3cbrt-rft_binary64 rem-square-sqrt_binary64 distribute-rgt-out--_binary64 associate--l+_binary64 associate-+r-_binary64 associate-+r+_binary64
1-exp_binary64 exp-1-e_binary64 difference-of-squares_binary64 distribute-neg-in_binary64 count-2_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 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 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 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--r+_binary64
Counts
195 → 132
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02814132
16543532
221543442
348523442
449993442

prune134.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1311132
Fresh101
Picked101
Done011
Total1332135
Error
0b
Counts
135 → 2
Compiler

Compiled 3024 to 1740 computations (42.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b
(/.f64 1/2 (+.f64 1 (*.f64 2 (*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (*.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))
4.2b
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
4.3b
(*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (*.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om))))
9.3b
(/.f64 (*.f64 l l) Om)

rewrite231.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
40×times-frac_binary64
38×add-sqr-sqrt_binary64
34×add-cube-cbrt_binary64 *-un-lft-identity_binary64
25×add-exp-log_binary64
22×add-cbrt-cube_binary64
12×associate-/l*_binary64 unpow-prod-down_binary64
associate-/r*_binary64
div-exp_binary64
associate-*l*_binary64
pow1_binary64 cbrt-undiv_binary64
prod-exp_binary64 cbrt-unprod_binary64 associate-*r/_binary64
add-log-exp_binary64 div-inv_binary64 unpow2_binary64 sqr-pow_binary64
frac-2neg_binary64 clear-num_binary64 frac-times_binary64 flip3-+_binary64 flip-+_binary64 associate-*r*_binary64
frac-add_binary64 unswap-sqr_binary64 associate-/r/_binary64
pow-prod-down_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-*l/_binary64 *-commutative_binary64 pow-to-exp_binary64 pow-exp_binary64
Counts
4 → 135
Calls

4 calls:

19.0ms
(*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (*.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om))))
6.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
5.0ms
(/.f64 1/2 (+.f64 1 (*.f64 2 (*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (*.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))
5.0ms
(/.f64 (*.f64 l l) Om)
Compiler

Compiled 5580 to 2664 computations (52.3% saved)

series407.0ms (4.5%)

Error
0b
Counts
4 → 38
Calls

4 calls:

200.0ms
(/.f64 1/2 (+.f64 1 (*.f64 2 (*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (*.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om)))))))
131.0ms
(*.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (*.f64 (sin.f64 kx) (/.f64 (sin.f64 kx) Om))))
27.0ms
(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
22.0ms
(/.f64 (*.f64 l l) Om)
Compiler

Compiled 2742 to 2429 computations (11.4% saved)

simplify135.0ms (1.5%)

Algorithm
egg-herbie
Rules
622×distribute-rgt-in_binary64
592×distribute-lft-in_binary64
216×associate-*l*_binary64
207×associate-*l/_binary64
205×associate-*r*_binary64
169×associate-*r/_binary64
147×unswap-sqr_binary64
142×*-commutative_binary64
135×associate-/l*_binary64
100×distribute-rgt-neg-in_binary64
86×cancel-sign-sub-inv_binary64
85×distribute-lft-neg-in_binary64
66×times-frac_binary64
62×sqr-pow_binary64
57×associate-/r*_binary64
56×associate-/l/_binary64
54×distribute-rgt-out_binary64
52×distribute-neg-frac_binary64
44×cube-prod_binary64
40×sub-neg_binary64
39×associate-/r/_binary64
38×cube-div_binary64
34×+-commutative_binary64
33×log-prod_binary64
32×log-div_binary64 swap-sqr_binary64
30×exp-prod_binary64 neg-mul-1_binary64 neg-sub0_binary64
29×*-rgt-identity_binary64
27×distribute-neg-in_binary64
24×*-lft-identity_binary64
20×distribute-lft-neg-out_binary64
17×distribute-lft-out_binary64
14×/-rgt-identity_binary64
12×unpow3_binary64
10×cube-unmult_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 cube-mult_binary64
exp-sum_binary64
log-pow_binary64 pow-sqr_binary64
pow-plus_binary64 distribute-rgt-neg-out_binary64 distribute-rgt-out--_binary64 associate-+l+_binary64
associate-+r+_binary64
rem-sqrt-square_binary64 div-sub_binary64 associate-+l-_binary64
distribute-lft-out--_binary64 associate--l+_binary64 associate-+r-_binary64
log-rec_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-square-sqrt_binary64 unsub-neg_binary64 difference-of-squares_binary64 count-2_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 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 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 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate--r-_binary64 associate--l-_binary64
Counts
173 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02965277
17364585
225304567
354864567

prune134.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh000
Picked011
Done011
Total1292131
Error
0b
Counts
131 → 2
Compiler

Compiled 3540 to 1957 computations (44.7% saved)

regimes2.4s (26.3%)

Accuracy

Total 0.8b remaining (73.9%)

Threshold costs 0.8b (73.9%)

Compiler

Compiled 37884 to 34769 computations (8.2% saved)

bsearch3.0ms (0%)

Compiler

Compiled 7 to 9 computations (-28.6% saved)

simplify6.0ms (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
041100
155100
253100

end11.0ms (0.1%)

Remove

(sort kx ky)

Compiler

Compiled 195 to 156 computations (20% saved)

sample2.8s (30.6%)

Algorithm
intervals
Results
1.1s6304×body128valid
658.0ms825×body1024valid
330.0ms553×body512valid
123.0ms317×body256valid
2.0msbody2048valid
Compiler

Compiled 152 to 150 computations (1.3% saved)

Profiling

Loading profile data...