Details

Time bar (total: 12.1s)

analyze1.3s (11%)

Algorithm
search
egg-herbie
Rules
900×unswap-sqr_binary64
743×associate-/r/_binary64
640×associate-*r/_binary64
437×associate-*l*_binary64
374×associate-*r*_binary64
348×associate-*l/_binary64
249×associate-/l*_binary64
187×associate-/r*_binary64
139×*-commutative_binary64
105×sqr-pow_binary64
73×associate-/l/_binary64
72×cube-prod_binary64
39×unpow3_binary64
36×pow-plus_binary64
27×pow-sqr_binary64
21×cube-unmult_binary64
18×cube-mult_binary64
rem-sqrt-square_binary64
unpow2_binary64
unpow1/2_binary64 unpow1_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 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-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 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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 swap-sqr_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-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027104
151104
268104
3175104
4506104
51959104
64916104
74671104
85547104
033
133
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
25%74.9%0.1%8
54.6%45.2%0.1%9
56.2%43.7%0.1%10
62.4%37.4%0.1%11
65.9%33.9%0.1%12
66.3%33.5%0.1%13
69%30.8%0.1%14
Compiler

Compiled 17 to 15 computations (11.8% saved)

sample155.0ms (1.3%)

Algorithm
intervals
Results
115.0ms155×body1024valid
17.0ms38×body512valid
6.0ms50×body128valid
4.0ms13×body256valid
Compiler

Compiled 33 to 32 computations (3% saved)

simplify91.0ms (0.8%)

Algorithm
egg-herbie
Rules
868×unswap-sqr_binary64
626×associate-*r/_binary64
542×sqr-pow_binary64
394×associate-*l*_binary64
283×associate-/r/_binary64
262×associate-*r*_binary64
261×associate-/r*_binary64
250×*-commutative_binary64
244×associate-*l/_binary64
211×associate-/l/_binary64
208×associate-/l*_binary64
166×pow-sqr_binary64
164×cube-prod_binary64
86×pow-plus_binary64
84×unpow3_binary64
74×cube-mult_binary64
30×rem-sqrt-square_binary64
16×cube-unmult_binary64
14×unpow2_binary64 unpow1/2_binary64 unpow1_binary64
1-exp_binary64 +-commutative_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-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 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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 swap-sqr_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-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01426
12626
23626
36426
413326
533226
6102326
7242226
8299426
9399026
10431726
11474826
12517026

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
4.5b
Counts
1 → 1
Compiler

Compiled 16 to 14 computations (12.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b
(pow.f64 (sin.f64 kx) 2)
0.2b
(pow.f64 (sin.f64 ky) 2)
4.2b
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite208.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
4.4b
Rules
46×*-un-lft-identity_binary64
27×add-sqr-sqrt_binary64
26×add-cube-cbrt_binary64
25×sqrt-prod_binary64
24×times-frac_binary64
16×unpow-prod-down_binary64
10×distribute-lft-out_binary64
add-exp-log_binary64 associate-/r*_binary64
pow1_binary64
add-cbrt-cube_binary64 pow-unpow_binary64
add-log-exp_binary64 sqrt-div_binary64
associate-/l*_binary64
flip3-+_binary64 flip-+_binary64 pow-pow_binary64 pow-to-exp_binary64 pow-exp_binary64 unpow2_binary64 sqr-pow_binary64 associate-/r/_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 div-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64
Counts
4 → 102
Calls

4 calls:

17.0ms
(/.f64 (sin.f64 ky) (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)))
3.0ms
(pow.f64 (sin.f64 ky) 2)
3.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 2338 to 1310 computations (44% saved)

series178.0ms (1.5%)

Error
2.0b
Counts
4 → 35
Calls

4 calls:

79.0ms
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
44.0ms
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
11.0ms
(pow.f64 (sin.f64 kx) 2)
11.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 1941 to 1453 computations (25.1% saved)

simplify108.0ms (0.9%)

Algorithm
egg-herbie
Rules
765×associate-/l*_binary64
702×associate-/r*_binary64
375×cancel-sign-sub-inv_binary64
189×associate-/r/_binary64
158×sub-neg_binary64
143×associate-/l/_binary64
104×times-frac_binary64
103×distribute-rgt-neg-in_binary64
96×+-commutative_binary64
90×sqr-pow_binary64 distribute-lft-neg-in_binary64
76×unswap-sqr_binary64
74×distribute-neg-frac_binary64
66×associate-+r+_binary64
65×associate--l+_binary64
64×*-commutative_binary64
62×distribute-neg-in_binary64
61×associate-+l+_binary64
59×associate-*r*_binary64
47×distribute-rgt-in_binary64
46×neg-mul-1_binary64 neg-sub0_binary64
44×associate--r+_binary64
41×associate-*l/_binary64
37×associate-*r/_binary64
32×associate-*l*_binary64
28×unsub-neg_binary64
23×distribute-lft-in_binary64
21×distribute-rgt-out_binary64
17×pow-sqr_binary64
14×distribute-lft-neg-out_binary64
13×cube-prod_binary64
12×log-prod_binary64
10×log-pow_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64
cube-unmult_binary64 difference-of-squares_binary64
unpow3_binary64 exp-prod_binary64 *-rgt-identity_binary64
log-div_binary64 swap-sqr_binary64
pow-plus_binary64 cube-mult_binary64 cube-div_binary64 rem-sqrt-square_binary64 distribute-rgt-out--_binary64
/-rgt-identity_binary64 distribute-lft-out_binary64
rem-square-sqrt_binary64 distribute-lft-out--_binary64
rem-3cbrt-rft_binary64 distribute-rgt1-in_binary64
1-exp_binary64 *-lft-identity_binary64 distribute-rgt-neg-out_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 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 div-sub_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-lft1-in_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64
Counts
137 → 81
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02713329
16353203
220693116
353793116

prune82.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New72981
Fresh000
Picked101
Done000
Total73982
Error
2.0b
Counts
82 → 9
Compiler

Compiled 1664 to 988 computations (40.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (sin.f64 kx) 2)
0.2b
(pow.f64 (sin.f64 ky) 2)
0.3b
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.4b
(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite226.0ms (1.9%)

Algorithm
rewrite-expression-head
Error
2.0b
Rules
54×*-un-lft-identity_binary64
45×sqrt-prod_binary64
41×add-sqr-sqrt_binary64
34×times-frac_binary64
28×add-cube-cbrt_binary64
24×associate-*r*_binary64
18×unpow-prod-down_binary64
12×distribute-lft-out_binary64
10×pow1_binary64
add-exp-log_binary64
add-cbrt-cube_binary64 pow-unpow_binary64
add-log-exp_binary64 associate-/r/_binary64 unswap-sqr_binary64
sqrt-pow1_binary64 rem-sqrt-square_binary64 associate-*l*_binary64
sqrt-div_binary64 div-inv_binary64 flip3-+_binary64 flip-+_binary64 pow-pow_binary64 pow-to-exp_binary64 pow-exp_binary64 unpow2_binary64 sqr-pow_binary64
pow1/2_binary64 inv-pow_binary64 pow-flip_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*r/_binary64 *-commutative_binary64
Counts
4 → 115
Calls

4 calls:

18.0ms
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms
(sqrt.f64 (/.f64 1 (+.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 2868 to 1788 computations (37.7% saved)

series201.0ms (1.7%)

Error
2.0b
Counts
4 → 35
Calls

4 calls:

79.0ms
(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
63.0ms
(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
13.0ms
(pow.f64 (sin.f64 kx) 2)
11.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 2085 to 1597 computations (23.4% saved)

simplify105.0ms (0.9%)

Algorithm
egg-herbie
Rules
760×associate-/r*_binary64
664×associate-/l*_binary64
305×cancel-sign-sub-inv_binary64
155×sub-neg_binary64
108×associate-*r*_binary64
102×distribute-rgt-neg-in_binary64
99×times-frac_binary64 sqr-pow_binary64 +-commutative_binary64
98×distribute-neg-in_binary64
95×associate-*l*_binary64
90×distribute-lft-neg-in_binary64
86×*-commutative_binary64
83×unswap-sqr_binary64
64×distribute-neg-frac_binary64 associate-/r/_binary64 associate--l+_binary64
62×distribute-rgt-in_binary64
60×associate-+l+_binary64
58×associate-+r+_binary64
48×neg-mul-1_binary64 neg-sub0_binary64
46×associate--r+_binary64
34×distribute-lft-in_binary64 associate-/l/_binary64 associate-*r/_binary64
31×unsub-neg_binary64
29×associate-*l/_binary64
25×log-prod_binary64 cube-prod_binary64
24×exp-prod_binary64
18×pow-sqr_binary64
17×*-rgt-identity_binary64
16×*-lft-identity_binary64
13×distribute-rgt-out_binary64
12×swap-sqr_binary64
11×distribute-lft-neg-out_binary64
10×log-pow_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64
cube-unmult_binary64 difference-of-squares_binary64
unpow3_binary64 rem-sqrt-square_binary64
pow-plus_binary64 cube-mult_binary64
distribute-rgt-out--_binary64
distribute-lft-out_binary64
rem-square-sqrt_binary64 distribute-lft-out--_binary64
rem-3cbrt-rft_binary64 /-rgt-identity_binary64 distribute-rgt1-in_binary64
1-exp_binary64 exp-1-e_binary64 distribute-rgt-neg-out_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 log-div_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-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_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 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-lft1-in_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64
Counts
150 → 96
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02843538
16613346
221633295
352853295

prune105.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New93396
Fresh268
Picked101
Done000
Total969105
Error
2.0b
Counts
105 → 9
Compiler

Compiled 1993 to 1248 computations (37.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (sin.f64 kx) 2)
0.2b
(pow.f64 (sin.f64 ky) 2)
0.3b
(*.f64 (sin.f64 ky) (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2))
4.2b
(pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2)

rewrite157.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
2.0b
Rules
21×unpow-prod-down_binary64 *-un-lft-identity_binary64
18×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
12×add-exp-log_binary64
pow-unpow_binary64 associate-*r*_binary64
pow1_binary64
add-cbrt-cube_binary64
sqr-pow_binary64
distribute-lft-out_binary64 pow-to-exp_binary64 pow-exp_binary64 add-log-exp_binary64
pow-pow_binary64 prod-exp_binary64 unswap-sqr_binary64 associate-*l*_binary64
unpow2_binary64
cbrt-unprod_binary64 *-commutative_binary64
Counts
4 → 82
Calls

4 calls:

14.0ms
(*.f64 (sin.f64 ky) (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2))
9.0ms
(pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2)
3.0ms
(pow.f64 (sin.f64 ky) 2)
3.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 1914 to 1129 computations (41% saved)

series211.0ms (1.7%)

Error
2.0b
Counts
4 → 35
Calls

4 calls:

79.0ms
(*.f64 (sin.f64 ky) (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2))
76.0ms
(pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2)
11.0ms
(pow.f64 (sin.f64 ky) 2)
11.0ms
(pow.f64 (sin.f64 kx) 2)
Compiler

Compiled 2079 to 1583 computations (23.9% saved)

simplify90.0ms (0.7%)

Algorithm
egg-herbie
Rules
749×associate-/r*_binary64
645×associate-/l*_binary64
260×cancel-sign-sub-inv_binary64
173×unswap-sqr_binary64
141×sub-neg_binary64
124×sqr-pow_binary64
108×associate-*r*_binary64
98×times-frac_binary64 distribute-neg-in_binary64
95×associate-*l*_binary64
91×+-commutative_binary64
80×*-commutative_binary64
79×distribute-rgt-neg-in_binary64
73×distribute-lft-neg-in_binary64
64×distribute-neg-frac_binary64 associate--l+_binary64
60×associate-/r/_binary64
59×associate-+l+_binary64
58×associate-+r+_binary64
55×distribute-rgt-in_binary64
46×associate--r+_binary64
42×neg-mul-1_binary64 neg-sub0_binary64
34×log-prod_binary64
32×unsub-neg_binary64
31×exp-prod_binary64 distribute-lft-in_binary64
30×associate-*r/_binary64
28×cube-prod_binary64 associate-/l/_binary64
27×associate-*l/_binary64
23×pow-sqr_binary64
14×log-pow_binary64
13×cube-unmult_binary64 swap-sqr_binary64
11×unpow1/2_binary64 unpow1_binary64 *-lft-identity_binary64
10×unpow2_binary64 *-rgt-identity_binary64
distribute-rgt-out_binary64
rem-sqrt-square_binary64
unpow3_binary64 pow-plus_binary64 distribute-lft-neg-out_binary64
cube-mult_binary64 distribute-lft-out_binary64
pow-base-1_binary64
rem-3cbrt-rft_binary64 rem-square-sqrt_binary64 distribute-rgt1-in_binary64 count-2_binary64
unpow-1_binary64 1-exp_binary64 exp-1-e_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_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 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 unpow0_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-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_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 mul-1-neg_binary64 /-rgt-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_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 distribute-lft1-in_binary64 associate--r-_binary64 associate--l-_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
117 → 71
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02532652
16142532
220842487
352962487

prune77.0ms (0.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New70171
Fresh178
Picked011
Done000
Total71980
Error
2.0b
Counts
80 → 9
Compiler

Compiled 1502 to 923 computations (38.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(pow.f64 (sin.f64 ky) 2)
0.3b
(/.f64 (sin.f64 ky) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.7b
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.7b
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite150.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
2.0b
Rules
24×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64 add-sqr-sqrt_binary64
10×cbrt-prod_binary64
times-frac_binary64
add-exp-log_binary64 unpow-prod-down_binary64
add-cbrt-cube_binary64
pow1_binary64
add-log-exp_binary64 cbrt-div_binary64 distribute-lft-out_binary64
associate-/l*_binary64 associate-/r*_binary64 pow-unpow_binary64
pow1/3_binary64 flip3-+_binary64 flip-+_binary64
div-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64 pow-pow_binary64 pow-to-exp_binary64 pow-exp_binary64 unpow2_binary64 sqr-pow_binary64
Counts
4 → 75
Calls

4 calls:

8.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms
(/.f64 (sin.f64 ky) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 2852 to 1739 computations (39% saved)

series297.0ms (2.5%)

Error
2.0b
Counts
4 → 39
Calls

4 calls:

90.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
89.0ms
(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
51.0ms
(/.f64 (sin.f64 ky) (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
14.0ms
(pow.f64 (sin.f64 ky) 2)
Compiler

Compiled 3741 to 2867 computations (23.4% saved)

simplify169.0ms (1.4%)

Algorithm
egg-herbie
Rules
817×associate-*l*_binary64
424×cancel-sign-sub-inv_binary64
185×associate-/l*_binary64
182×times-frac_binary64
171×unswap-sqr_binary64
136×sub-neg_binary64
123×distribute-rgt-neg-in_binary64
122×associate-/r*_binary64
118×neg-sub0_binary64
115×neg-mul-1_binary64
109×distribute-lft-neg-in_binary64
104×associate-*r*_binary64
94×sqr-pow_binary64
81×associate-*l/_binary64
80×log-prod_binary64
74×associate-/l/_binary64
70×*-commutative_binary64
57×associate-*r/_binary64
53×+-commutative_binary64
45×associate-/r/_binary64
40×cube-unmult_binary64
39×distribute-rgt-out_binary64
38×cube-prod_binary64 associate--l+_binary64
35×log-pow_binary64 exp-prod_binary64
28×log-div_binary64 unsub-neg_binary64
27×associate-+l+_binary64
26×associate-+r+_binary64
25×cube-div_binary64
24×pow-plus_binary64 distribute-rgt-in_binary64 associate--r+_binary64
22×rem-sqrt-square_binary64
20×distribute-lft-out_binary64
15×distribute-lft-neg-out_binary64
14×distribute-neg-frac_binary64
12×pow-sqr_binary64 distribute-neg-in_binary64
11×unpow3_binary64
10×distribute-rgt-out--_binary64 distribute-lft-in_binary64
unpow1/3_binary64 difference-of-squares_binary64 swap-sqr_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64
log-rec_binary64 cube-mult_binary64
/-rgt-identity_binary64 *-rgt-identity_binary64
distribute-lft-out--_binary64
div-sub_binary64
1-exp_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 *-lft-identity_binary64 distribute-rgt-neg-out_binary64 distribute-rgt1-in_binary64 count-2_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 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-cbrt-cube_binary64 rem-cube-cbrt_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-lft1-in_binary64 associate--r-_binary64 associate--l-_binary64
Counts
114 → 98
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02133499
15073267
214953220
344343220
449783220
549353220

prune122.0ms (1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New98098
Fresh077
Picked011
Done011
Total989107
Error
2.0b
Counts
107 → 9
Compiler

Compiled 3156 to 1986 computations (37.1% saved)

regimes2.6s (21.7%)

Accuracy

Total 1.4b remaining (44.4%)

Threshold costs 0b (0%)

Compiler

Compiled 36821 to 29912 computations (18.8% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64 *-rgt-identity_binary64 +-commutative_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 *-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
02465
12965
22765

end1.0ms (0%)

Compiler

Compiled 40 to 26 computations (35% saved)

sample5.3s (44.1%)

Algorithm
intervals
Results
3.4s4558×body1024valid
903.0ms1426×body512valid
189.0ms1441×body128valid
177.0ms561×body256valid
20.0ms14×body2048valid
Compiler

Compiled 253 to 214 computations (15.4% saved)

Profiling

Loading profile data...