Details

analyze1.1s (6.9%)

Algorithm

1×	search
2×	egg-herbie

Rules

70×	`*-commutative_binary64_691`
57×	`associate-/l*_binary64_705`
30×	`associate-/r/_binary64_706`
26×	`distribute-rgt-out_binary64_713`
24×	`associate-*r/_binary64_702`
18×	`associate-r_binary64_700`
16×	`associate-*l/_binary64_703`
12×	`associate-/l/_binary64_707` `associate-l_binary64_701`
9×	`+-commutative_binary64_690`
6×	`distribute-rgt-in_binary64_710`
4×	`distribute-lft-out_binary64_711`
3×	`associate-/r*_binary64_704`
1×	`swap-a1-a2`
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_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `log-pow_binary64_849` `log-rec_binary64_848` `log-div_binary64_847` `log-prod_binary64_846` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `unpow3_binary64_826` `unpow2_binary64_825` `unpow1/2_binary64_824` `pow-plus_binary64_823` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow1_binary64_818` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `exp-prod_binary64_812` `div-exp_binary64_811` `rec-exp_binary64_810` `prod-exp_binary64_809` `exp-diff_binary64_808` `exp-neg_binary64_807` `exp-sum_binary64_806` `e-exp-1_binary64_805` `1-exp_binary64_804` `exp-1-e_binary64_803` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-unmult_binary64_797` `cube-mult_binary64_790` `cube-div_binary64_789` `cube-prod_binary64_788` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `rem-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `times-frac_binary64_766` `div-sub_binary64_765` `neg-mul-1_binary64_756` `neg-sub0_binary64_755` `unsub-neg_binary64_754` `sub-neg_binary64_753` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-rgt-identity_binary64_745` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `*-inverses_binary64_740` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `pow-sqr_binary64_733` `sqr-pow_binary64_732` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `unswap-sqr_binary64_728` `swap-sqr_binary64_727` `cancel-sign-sub-inv_binary64_726` `cancel-sign-sub_binary64_725` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-lft-out--_binary64_712` `distribute-lft-in_binary64_709` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--l+_binary64_697` `associate--r+_binary64_696` `associate-+l-_binary64_695` `associate-+r-_binary64_694` `associate-+l+_binary64_693` `associate-+r+_binary64_692`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	65	80
2	120	80
3	174	80
4	228	80
5	258	80
6	285	80
7	279	80
8	279	80
0	3	3
1	3	3

Search

True	Other	False	Iter
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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Symmetry

(sort a1 a2)

Compiler

Compiled 20 to 16 computations (20% saved)

sample86.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms	42×	body	1024	invalid
16.0ms	48×	body	1024	valid
11.0ms	155×	body	128	valid
7.0ms	32×	body	512	valid
4.0ms	17×	body	512	invalid
3.0ms	20×	body	256	valid
1.0ms	9×	body	256	invalid
1.0ms	16×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64_691`
20×	`associate-/l*_binary64_705`
11×	`associate-/r/_binary64_706`
9×	`distribute-rgt-out_binary64_713` `associate-*r/_binary64_702`
6×	`associate-r_binary64_700`
5×	`associate-*l/_binary64_703`
4×	`associate-/l/_binary64_707` `associate-l_binary64_701`
3×	`+-commutative_binary64_690`
2×	`distribute-rgt-in_binary64_710` `associate-/r*_binary64_704`
1×	`distribute-lft-out_binary64_711`
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_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `log-pow_binary64_849` `log-rec_binary64_848` `log-div_binary64_847` `log-prod_binary64_846` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `unpow3_binary64_826` `unpow2_binary64_825` `unpow1/2_binary64_824` `pow-plus_binary64_823` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow1_binary64_818` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `exp-prod_binary64_812` `div-exp_binary64_811` `rec-exp_binary64_810` `prod-exp_binary64_809` `exp-diff_binary64_808` `exp-neg_binary64_807` `exp-sum_binary64_806` `e-exp-1_binary64_805` `1-exp_binary64_804` `exp-1-e_binary64_803` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-unmult_binary64_797` `cube-mult_binary64_790` `cube-div_binary64_789` `cube-prod_binary64_788` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `rem-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `times-frac_binary64_766` `div-sub_binary64_765` `neg-mul-1_binary64_756` `neg-sub0_binary64_755` `unsub-neg_binary64_754` `sub-neg_binary64_753` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-rgt-identity_binary64_745` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `*-inverses_binary64_740` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `pow-sqr_binary64_733` `sqr-pow_binary64_732` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `unswap-sqr_binary64_728` `swap-sqr_binary64_727` `cancel-sign-sub-inv_binary64_726` `cancel-sign-sub_binary64_725` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-lft-out--_binary64_712` `distribute-lft-in_binary64_709` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--l+_binary64_697` `associate--r+_binary64_696` `associate-+l-_binary64_695` `associate-+r-_binary64_694` `associate-+l+_binary64_693` `associate-+r+_binary64_692`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	26	20
2	46	20
3	66	20
4	85	20
5	97	20
6	108	20
7	106	20
8	106	20

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite191.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

40×	`add-sqr-sqrt_binary64_782`
38×	`times-frac_binary64_766`
32×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
22×	`sqrt-prod_binary64_776` `associate-r_binary64_700`
10×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
6×	`associate-/r*_binary64_704`
5×	`pow1_binary64_821` `add-log-exp_binary64_799`
3×	`associate-/l_binary64_705` `unswap-sqr_binary64_728` `associate-l*_binary64_701`
2×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `pow-prod-down_binary64_831` `associate-r/_binary64_702` `-commutative_binary64_691` `sum-log_binary64_851` `+-commutative_binary64_690`

Counts

3 → 94

Calls

3 calls:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2096 to 762 computations (63.6% saved)

series1.1s (6.7%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

631.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
269.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
124.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1297 to 1213 computations (6.5% saved)

simplify129.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

367×	`sub-neg_binary64_753`
341×	`unswap-sqr_binary64_728`
336×	`associate-/l*_binary64_705`
303×	`*-commutative_binary64_691`
272×	`associate-*r/_binary64_702`
269×	`associate-*l/_binary64_703`
169×	`associate--l+_binary64_697`
153×	`distribute-rgt-in_binary64_710`
148×	`associate-+l+_binary64_693`
138×	`associate--r+_binary64_696`
133×	`distribute-lft-in_binary64_709`
131×	`associate-/r*_binary64_704`
129×	`associate-/r/_binary64_706`
118×	`associate-l_binary64_701`
115×	`associate-r_binary64_700`
109×	`associate-/l/_binary64_707`
100×	`cancel-sign-sub-inv_binary64_726`
98×	`times-frac_binary64_766`
96×	`associate-+r+_binary64_692`
81×	`unsub-neg_binary64_754`
70×	`sqr-pow_binary64_732`
54×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
46×	`*-rgt-identity_binary64_750`
44×	`*-lft-identity_binary64_749` `difference-of-squares_binary64_729`
40×	`+-commutative_binary64_690`
35×	`distribute-rgt-neg-in_binary64_718`
30×	`/-rgt-identity_binary64_751`
29×	`associate-+l-_binary64_695`
28×	`cube-prod_binary64_788` `distribute-lft-neg-in_binary64_717`
26×	`distribute-neg-in_binary64_721` `associate-+r-_binary64_694`
24×	`log-prod_binary64_846` `exp-prod_binary64_812`
20×	`log-div_binary64_847`
19×	`div-sub_binary64_765`
18×	`cube-div_binary64_789`
17×	`+-rgt-identity_binary64_745` `distribute-neg-frac_binary64_724`
16×	`distribute-rgt-out_binary64_713`
15×	`pow-sqr_binary64_733`
12×	`unpow3_binary64_826`
10×	`cube-unmult_binary64_797` `distribute-lft-neg-out_binary64_719`
9×	`sub0-neg_binary64_747`
7×	`pow-plus_binary64_823` `distribute-rgt-out--_binary64_714` `distribute-lft-out_binary64_711`
6×	`cube-mult_binary64_790` `swap-sqr_binary64_727` `associate--l-_binary64_698`
4×	`unpow1/2_binary64_824` `rem-sqrt-square_binary64_773`
3×	`log-rec_binary64_848` `unpow2_binary64_825` `unpow1_binary64_818` `distribute-rgt-neg-out_binary64_720`
2×	`remove-double-div_binary64_736`
1×	`prod-exp_binary64_809` `exp-sum_binary64_806` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-square-sqrt_binary64_772` `distribute-lft-out--_binary64_712`
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_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `log-pow_binary64_849` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `div-exp_binary64_811` `rec-exp_binary64_810` `exp-diff_binary64_808` `exp-neg_binary64_807` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `*-inverses_binary64_740` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `count-2_binary64_708` `associate--r-_binary64_699`

Counts

136 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3337
1	445	3089
2	1498	2993
3	4168	2993
4	5044	2993

prune143.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	119	7	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	121	7	128

Error

Counts

128 → 7

Compiler

Compiled 1838 to 768 computations (58.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
5.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.1b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite525.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

84×	`sqrt-prod_binary64_776`
72×	`times-frac_binary64_766`
61×	`add-sqr-sqrt_binary64_782`
59×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
40×	`associate-r_binary64_700`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
11×	`pow1_binary64_821`
10×	`sqrt-div_binary64_777`
6×	`associate-/l_binary64_705` `associate-/r_binary64_704` `prod-exp_binary64_809` `cbrt-unprod_binary64_793`
5×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-*r/_binary64_702`
4×	`add-log-exp_binary64_799`
3×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `pow-prod-down_binary64_831`
2×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `div-inv_binary64_757` `associate-/l/_binary64_707` `frac-times_binary64_770` `associate-*l/_binary64_703`
1×	`sqrt-undiv_binary64_781` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

4 → 157

Calls

4 calls:

23.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 4768 to 1200 computations (74.8% saved)

series1.1s (7.2%)

Error

Counts

4 → 54

Calls

4 calls:

637.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
209.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
117.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
115.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 2838 to 2183 computations (23.1% saved)

simplify230.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

794×	`times-frac_binary64_766`
242×	`associate-l_binary64_701`
214×	`associate-/l/_binary64_707`
207×	`associate-r_binary64_700`
182×	`distribute-rgt-in_binary64_710`
174×	`cancel-sign-sub-inv_binary64_726`
160×	`*-commutative_binary64_691`
156×	`distribute-lft-in_binary64_709`
139×	`associate-/l*_binary64_705`
114×	`associate-*r/_binary64_702`
106×	`sub-neg_binary64_753`
97×	`unswap-sqr_binary64_728`
87×	`distribute-rgt-neg-in_binary64_718`
75×	`distribute-lft-neg-in_binary64_717`
73×	`associate-*l/_binary64_703`
57×	`+-commutative_binary64_690`
50×	`distribute-neg-frac_binary64_724`
45×	`log-prod_binary64_846` `associate-/r*_binary64_704`
40×	`cube-prod_binary64_788` `sqr-pow_binary64_732`
39×	`neg-sub0_binary64_755`
35×	`neg-mul-1_binary64_756`
34×	`exp-prod_binary64_812`
33×	`unpow3_binary64_826`
30×	`associate--l+_binary64_697`
28×	`log-div_binary64_847` `distribute-neg-in_binary64_721` `associate-+l+_binary64_693`
27×	`*-rgt-identity_binary64_750`
24×	`cube-div_binary64_789`
23×	`*-lft-identity_binary64_749` `associate--r+_binary64_696`
22×	`associate-+r+_binary64_692`
18×	`swap-sqr_binary64_727`
17×	`unsub-neg_binary64_754` `associate-/r/_binary64_706`
15×	`cube-unmult_binary64_797`
14×	`distribute-lft-neg-out_binary64_719`
13×	`cube-mult_binary64_790`
12×	`difference-of-squares_binary64_729` `distribute-rgt-out--_binary64_714`
10×	`distribute-rgt-out_binary64_713`
8×	`/-rgt-identity_binary64_751`
7×	`pow-plus_binary64_823` `associate-+r-_binary64_694`
4×	`unpow1/2_binary64_824` `rem-sqrt-square_binary64_773` `mul-1-neg_binary64_752` `pow-sqr_binary64_733` `distribute-lft-out_binary64_711`
3×	`unpow2_binary64_825` `unpow1_binary64_818` `rem-square-sqrt_binary64_772` `div-sub_binary64_765` `associate-+l-_binary64_695`
2×	`log-rec_binary64_848` `+-rgt-identity_binary64_745` `distribute-rgt-neg-out_binary64_720` `distribute-lft-out--_binary64_712`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `count-2_binary64_708`
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_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `log-pow_binary64_849` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `div-exp_binary64_811` `rec-exp_binary64_810` `prod-exp_binary64_809` `exp-diff_binary64_808` `exp-neg_binary64_807` `exp-sum_binary64_806` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `*-inverses_binary64_740` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `associate--r-_binary64_699` `associate--l-_binary64_698`

Counts

211 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	5812
1	674	5509
2	2332	5413
3	4885	5413
4	4977	5413
5	4965	5413

prune172.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	151	7	158

Error

Counts

158 → 7

Compiler

Compiled 2890 to 997 computations (65.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
5.1b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
5.1b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite614.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

149×	`add-sqr-sqrt_binary64_782`
146×	`times-frac_binary64_766`
127×	`sqrt-prod_binary64_776`
90×	`cbrt-prod_binary64_791`
87×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
58×	`associate-r_binary64_700`
27×	`add-exp-log_binary64_798`
21×	`unswap-sqr_binary64_728`
19×	`add-cbrt-cube_binary64_796`
10×	`associate-l_binary64_701`
9×	`associate-/r*_binary64_704`
8×	`pow1_binary64_821` `div-exp_binary64_811` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `cbrt-undiv_binary64_794`
6×	`sqrt-div_binary64_777` `associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `div-inv_binary64_757`
2×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-/l/_binary64_707`
1×	`pow-prod-down_binary64_831` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `*-commutative_binary64_691` `frac-2neg_binary64_771` `clear-num_binary64_759`

Counts

4 → 226

Calls

4 calls:

39.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 8391 to 3621 computations (56.8% saved)

series1.0s (6.5%)

Error

Counts

4 → 48

Calls

4 calls:

419.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
299.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
126.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
117.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3244 to 2660 computations (18% saved)

simplify346.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

785×	`times-frac_binary64_766`
397×	`associate-/r*_binary64_704`
219×	`associate-*r/_binary64_702`
213×	`associate-*l/_binary64_703`
196×	`associate-/r/_binary64_706`
168×	`associate-l_binary64_701`
157×	`associate-/l*_binary64_705`
152×	`associate-r_binary64_700`
151×	`*-commutative_binary64_691`
134×	`cancel-sign-sub-inv_binary64_726`
104×	`neg-sub0_binary64_755`
101×	`neg-mul-1_binary64_756`
97×	`sub-neg_binary64_753`
95×	`associate-/l/_binary64_707`
93×	`distribute-rgt-neg-in_binary64_718`
84×	`distribute-lft-neg-in_binary64_717`
73×	`unswap-sqr_binary64_728`
65×	`distribute-rgt-in_binary64_710`
62×	`log-div_binary64_847`
56×	`distribute-lft-in_binary64_709`
53×	`log-prod_binary64_846`
48×	`cube-prod_binary64_788`
43×	`*-rgt-identity_binary64_750`
39×	`cube-div_binary64_789`
34×	`*-lft-identity_binary64_749`
33×	`sqr-pow_binary64_732`
30×	`distribute-neg-frac_binary64_724`
24×	`+-commutative_binary64_690`
22×	`exp-prod_binary64_812`
20×	`swap-sqr_binary64_727`
18×	`unpow3_binary64_826`
17×	`unsub-neg_binary64_754`
16×	`distribute-rgt-out--_binary64_714`
14×	`cube-unmult_binary64_797` `div-sub_binary64_765`
12×	`/-rgt-identity_binary64_751`
11×	`cube-mult_binary64_790` `distribute-rgt-out_binary64_713`
10×	`distribute-neg-in_binary64_721`
9×	`associate-+l-_binary64_695`
8×	`pow-plus_binary64_823` `distribute-lft-neg-out_binary64_719` `associate--r+_binary64_696`
7×	`rem-sqrt-square_binary64_773` `difference-of-squares_binary64_729` `associate-+r-_binary64_694`
6×	`associate--l+_binary64_697` `associate-+l+_binary64_693`
5×	`pow-sqr_binary64_733`
4×	`log-rec_binary64_848` `mul-1-neg_binary64_752`
3×	`unpow1/2_binary64_824` `rem-square-sqrt_binary64_772` `distribute-lft-out--_binary64_712`
2×	`log-pow_binary64_849` `unpow2_binary64_825` `unpow1_binary64_818` `+-rgt-identity_binary64_745` `count-2_binary64_708`
1×	`unpow1/3_binary64_827` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-3cbrt-lft_binary64_785` `distribute-rgt-neg-out_binary64_720` `distribute-lft-out_binary64_711` `associate--r-_binary64_699` `associate-+r+_binary64_692`
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_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `pow-base-0_binary64_844` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `div-exp_binary64_811` `rec-exp_binary64_810` `prod-exp_binary64_809` `exp-diff_binary64_808` `exp-neg_binary64_807` `exp-sum_binary64_806` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `*-inverses_binary64_740` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `associate--l-_binary64_698`

Counts

274 → 252

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	10662
1	659	9706
2	2392	9242
3	4637	9022
4	4996	9022
5	4954	9022

prune381.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	252	7	259

Error

Counts

259 → 7

Compiler

Compiled 6152 to 2857 computations (53.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.2b	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
0.4b	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))

rewrite119.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`add-sqr-sqrt_binary64_782`
10×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
9×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
6×	`times-frac_binary64_766` `sqrt-prod_binary64_776` `associate-/r*_binary64_704`
5×	`pow1_binary64_821` `add-log-exp_binary64_799`
4×	`associate-*l/_binary64_703`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-l_binary64_701` `associate-r_binary64_700`
2×	`prod-exp_binary64_809` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `cbrt-unprod_binary64_793` `associate-/l/_binary64_707`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l_binary64_705` `pow-prod-down_binary64_831` `unswap-sqr_binary64_728` `-commutative_binary64_691` `sum-log_binary64_851` `+-commutative_binary64_690`

Counts

3 → 60

Calls

3 calls:

9.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1281 to 397 computations (69% saved)

series1.2s (7.4%)

Error

Counts

3 → 48

Calls

3 calls:

631.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
384.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
118.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1644 to 1488 computations (9.5% saved)

simplify132.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-/l*_binary64_705`
361×	`cancel-sign-sub-inv_binary64_726`
355×	`times-frac_binary64_766`
279×	`distribute-rgt-in_binary64_710`
254×	`distribute-lft-in_binary64_709`
194×	`associate-/l/_binary64_707`
163×	`associate-/r/_binary64_706`
130×	`sub-neg_binary64_753`
105×	`distribute-rgt-neg-in_binary64_718`
103×	`associate-l_binary64_701`
97×	`associate-r_binary64_700`
96×	`unswap-sqr_binary64_728`
92×	`distribute-lft-neg-in_binary64_717`
74×	`*-commutative_binary64_691`
63×	`+-commutative_binary64_690`
58×	`associate--l+_binary64_697`
50×	`distribute-neg-in_binary64_721`
47×	`distribute-rgt-out_binary64_713`
45×	`log-div_binary64_847`
40×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755` `associate-+l+_binary64_693`
38×	`associate-+r+_binary64_692`
37×	`log-prod_binary64_846`
36×	`sqr-pow_binary64_732` `associate-*l/_binary64_703` `associate--r+_binary64_696`
28×	`associate-*r/_binary64_702`
27×	`unsub-neg_binary64_754`
22×	`distribute-neg-frac_binary64_724` `distribute-lft-out_binary64_711`
21×	`exp-prod_binary64_812`
17×	`*-rgt-identity_binary64_750` `distribute-lft-neg-out_binary64_719`
16×	`associate-/r*_binary64_704`
15×	`cube-div_binary64_789`
13×	`log-rec_binary64_848`
12×	`/-rgt-identity_binary64_751` `distribute-rgt-out--_binary64_714`
11×	`*-lft-identity_binary64_749`
10×	`cube-prod_binary64_788`
7×	`exp-sum_binary64_806` `pow-sqr_binary64_733` `difference-of-squares_binary64_729` `swap-sqr_binary64_727`
6×	`cube-unmult_binary64_797`
5×	`unpow3_binary64_826`
4×	`div-sub_binary64_765` `distribute-rgt-neg-out_binary64_720`
3×	`unpow2_binary64_825` `unpow1/2_binary64_824` `unpow1_binary64_818` `cube-mult_binary64_790` `distribute-rgt1-in_binary64_716`
2×	`pow-plus_binary64_823`
1×	`prod-exp_binary64_809` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `distribute-lft-out--_binary64_712` `associate-+l-_binary64_695` `associate-+r-_binary64_694`
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_1023` `erf-erfc_binary64_1022` `erf-odd_binary64_1021` `if-if-and-not_binary64_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `not-gte_binary64_1012` `not-lte_binary64_1011` `not-gt_binary64_1010` `not-lt_binary64_1009` `gte-same_binary64_1008` `lte-same_binary64_1007` `gt-same_binary64_1006` `lt-same_binary64_1005` `sinh---cosh_binary64_952` `sinh-+-cosh_binary64_951` `sinh-cosh_binary64_950` `tanh-def-c_binary64_949` `tanh-def-b_binary64_948` `tanh-def-a_binary64_947` `cosh-def_binary64_946` `sinh-def_binary64_945` `tan-neg_binary64_892` `cos-neg_binary64_891` `sin-neg_binary64_890` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `hang-m-tan_binary64_886` `hang-p-tan_binary64_885` `hang-m0-tan_binary64_884` `hang-p0-tan_binary64_883` `hang-0m-tan_binary64_882` `hang-0p-tan_binary64_881` `tan-+PI/2_binary64_880` `tan-+PI_binary64_879` `tan-PI_binary64_878` `tan-PI/3_binary64_877` `tan-PI/4_binary64_876` `tan-PI/6_binary64_875` `cos-+PI/2_binary64_874` `cos-+PI_binary64_873` `cos-PI_binary64_872` `cos-PI/2_binary64_871` `cos-PI/3_binary64_870` `cos-PI/4_binary64_869` `cos-PI/6_binary64_868` `sin-+PI/2_binary64_867` `sin-+PI_binary64_866` `sin-PI_binary64_865` `sin-PI/2_binary64_864` `sin-PI/3_binary64_863` `sin-PI/4_binary64_862` `sin-PI/6_binary64_861` `sub-1-sin_binary64_860` `sub-1-cos_binary64_859` `-1-add-sin_binary64_858` `-1-add-cos_binary64_857` `1-sub-sin_binary64_856` `1-sub-cos_binary64_855` `cos-sin-sum_binary64_854` `log-E_binary64_850` `log-pow_binary64_849` `pow-base-0_binary64_844` `unpow1/3_binary64_827` `exp-to-pow_binary64_822` `pow-base-1_binary64_820` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-lft-sqr_binary64_815` `exp-cbrt_binary64_814` `exp-sqrt_binary64_813` `div-exp_binary64_811` `rec-exp_binary64_810` `exp-diff_binary64_808` `exp-neg_binary64_807` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-neg_binary64_787` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785` `rem-cbrt-cube_binary64_784` `rem-cube-cbrt_binary64_783` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `mul-1-neg_binary64_752` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-rgt-identity_binary64_745` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `*-inverses_binary64_740` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `rgt-mult-inverse_binary64_737` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-lft1-in_binary64_715` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698`

Counts

108 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2493
1	461	2188
2	1748	2050
3	4938	2050
4	5000	2050
5	4967	2050

prune83.0ms (0.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	97	7	104

Error

Counts

104 → 7

Compiler

Compiled 1102 to 444 computations (59.7% saved)

regimes4.3s (27.7%)

Accuracy

Total 0.3b remaining (76.8%)

Threshold costs 0.3b (76.8%)

Compiler

Compiled 49740 to 36083 computations (27.5% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64_691`
1×	`+-commutative_binary64_690`
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_1020` `if-if-and_binary64_1019` `if-if-or-not_binary64_1018` `if-if-or_binary64_1017` `if-not_binary64_1016` `if-same_binary64_1015` `if-false_binary64_1014` `if-true_binary64_1013` `tan-0_binary64_889` `cos-0_binary64_888` `sin-0_binary64_887` `unpow1_binary64_818` `e-exp-1_binary64_805` `1-exp_binary64_804` `exp-1-e_binary64_803` `exp-0_binary64_802` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `neg-mul-1_binary64_756` `neg-sub0_binary64_755` `unsub-neg_binary64_754` `sub-neg_binary64_753` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `+-rgt-identity_binary64_745` `+-lft-identity_binary64_744` `cancel-sign-sub-inv_binary64_726` `cancel-sign-sub_binary64_725` `distribute-neg-frac_binary64_724` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719` `distribute-rgt-neg-in_binary64_718` `distribute-lft-neg-in_binary64_717`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	17	34
2	17	34

end9.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 66 to 39 computations (40.9% saved)

sample2.7s (16.9%)

Algorithm

1×

intervals

Results

581.0ms	1832×	body	1024	valid
483.0ms	1553×	body	1024	invalid
357.0ms	4806×	body	128	valid
209.0ms	904×	body	512	valid
179.0ms	801×	body	512	invalid
68.0ms	455×	body	256	valid
59.0ms	378×	body	256	invalid
57.0ms	693×	body	128	invalid
1.0ms	3×	body	2048	valid

Compiler

Compiled 204 to 159 computations (22.1% saved)

Details

analyze1.1s (6.9%)

sample86.0ms (0.5%)

simplify12.0ms (0.1%)

prune5.0ms (0%)

localize10.0ms (0.1%)

rewrite191.0ms (1.2%)

series1.1s (6.7%)

simplify129.0ms (0.8%)

prune143.0ms (0.9%)

localize15.0ms (0.1%)

rewrite525.0ms (3.3%)

series1.1s (7.2%)

simplify230.0ms (1.5%)

prune172.0ms (1.1%)

localize20.0ms (0.1%)

rewrite614.0ms (3.9%)

series1.0s (6.5%)

simplify346.0ms (2.2%)

prune381.0ms (2.4%)

localize11.0ms (0.1%)

rewrite119.0ms (0.8%)

series1.2s (7.4%)

simplify132.0ms (0.8%)

prune83.0ms (0.5%)

regimes4.3s (27.7%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end9.0ms (0.1%)

sample2.7s (16.9%)

Profiling