Details

analyze3.0s (14.9%)

Algorithm

1×	search
2×	egg-herbie

Rules

668×	`times-frac_binary64_766`
359×	`cancel-sign-sub-inv_binary64_726`
300×	`associate-/l*_binary64_705`
286×	`*-commutative_binary64_691`
260×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
226×	`distribute-rgt-neg-in_binary64_718`
200×	`distribute-neg-frac_binary64_724`
197×	`distribute-lft-neg-in_binary64_717`
155×	`associate-/r/_binary64_706`
122×	`associate-/l/_binary64_707`
109×	`sub-neg_binary64_753`
93×	`associate-/r*_binary64_704`
85×	`swap-sqr_binary64_727`
81×	`associate-*r/_binary64_702`
65×	`associate-*l/_binary64_703`
49×	`sqr-pow_binary64_732`
42×	`associate-l_binary64_701`
30×	`div-sub_binary64_765`
29×	`distribute-lft-neg-out_binary64_719`
28×	`associate-r_binary64_700`
15×	`sub0-neg_binary64_747` `associate-+l-_binary64_695` `+-commutative_binary64_690`
13×	`unpow2_binary64_825`
12×	`unpow1/2_binary64_824` `unpow1_binary64_818` `rem-sqrt-square_binary64_773`
1×	`1-exp_binary64_804` `swap-M-D`
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` `pow-plus_binary64_823` `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` `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` `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-square-sqrt_binary64_772` `unsub-neg_binary64_754` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `remove-double-neg_binary64_748` `--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` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `unswap-sqr_binary64_728` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `distribute-rgt-in_binary64_710` `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-+r-_binary64_694` `associate-+l+_binary64_693` `associate-+r+_binary64_692`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	432
1	374	432
2	1139	432
3	2964	432
4	5015	432
0	6	6
1	6	6

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Symmetry

(sort M D)

Compiler

Compiled 19 to 19 computations (0% saved)

sample66.0ms (0.3%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
11.0ms	95×	body	128	nan
3.0ms	31×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

893×	`div-sub_binary64_765`
645×	`distribute-neg-frac_binary64_724`
581×	`distribute-rgt-neg-in_binary64_718`
569×	`distribute-lft-neg-in_binary64_717`
418×	`associate-/l*_binary64_705`
372×	`cancel-sign-sub-inv_binary64_726`
263×	`associate-/l/_binary64_707`
254×	`*-commutative_binary64_691`
227×	`times-frac_binary64_766`
189×	`associate-/r/_binary64_706`
163×	`associate-/r*_binary64_704`
133×	`neg-mul-1_binary64_756`
132×	`neg-sub0_binary64_755`
91×	`associate-*l/_binary64_703`
78×	`associate-*r/_binary64_702`
77×	`associate-l_binary64_701`
69×	`associate-r_binary64_700`
31×	`sub-neg_binary64_753`
22×	`distribute-lft-neg-out_binary64_719`
20×	`swap-sqr_binary64_727`
18×	`distribute-rgt-neg-out_binary64_720`
15×	`distribute-frac-neg_binary64_723`
8×	`unswap-sqr_binary64_728`
7×	`sqr-pow_binary64_732`
4×	`unsub-neg_binary64_754`
3×	`pow-plus_binary64_823` `cube-unmult_binary64_797` `+-commutative_binary64_690`
2×	`mul0-rgt_binary64_743` `mul0-lft_binary64_742` `div0_binary64_741` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709`
1×	`unpow3_binary64_826` `unpow2_binary64_825` `unpow1/2_binary64_824` `unpow1_binary64_818` `1-exp_binary64_804` `rem-sqrt-square_binary64_773` `sub0-neg_binary64_747` `associate-+l-_binary64_695` `associate-+l+_binary64_693`
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` `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` `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` `exp-1-e_binary64_803` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `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-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `-rgt-identity_binary64_750` `-lft-identity_binary64_749` `remove-double-neg_binary64_748` `--rgt-identity_binary64_746` `+-rgt-identity_binary64_745` `+-lft-identity_binary64_744` `*-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` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `cancel-sign-sub_binary64_725` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate--l+_binary64_697` `associate--r+_binary64_696` `associate-+r-_binary64_694` `associate-+r+_binary64_692`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	718	27
4	2816	27
5	4686	27
6	6100	27

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

12.7b

Counts

1 → 1

Compiler

Compiled 18 to 18 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
10.7b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite324.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

7.7b

Rules

67×	`add-exp-log_binary64_798`
38×	`add-sqr-sqrt_binary64_782`
27×	`prod-exp_binary64_809`
23×	`add-cbrt-cube_binary64_796`
19×	`div-exp_binary64_811` `associate-r_binary64_700`
17×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
15×	`times-frac_binary64_766`
13×	`associate-l_binary64_701`
10×	`pow-exp_binary64_828` `unswap-sqr_binary64_728`
7×	`pow1_binary64_821` `cbrt-unprod_binary64_793` `unpow-prod-down_binary64_839` `sqrt-prod_binary64_776`
5×	`cbrt-undiv_binary64_794`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777`
3×	`unpow2_binary64_825` `sqr-pow_binary64_732` `associate-*r/_binary64_702` `div-inv_binary64_757`
2×	`pow-to-exp_binary64_829` `*-commutative_binary64_691` `flip3--_binary64_764` `flip--_binary64_735`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-/r_binary64_704` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `pow-prod-down_binary64_831`

Counts

4 → 116

Calls

4 calls:

12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
9.0ms	(/.f64 (.f64 M D) (.f64 2 d))
9.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

Compiler

Compiled 3226 to 1835 computations (43.1% saved)

series2.1s (10.3%)

Error

7.2b

Counts

4 → 57

Calls

4 calls:

842.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
697.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
325.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
179.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2684 to 2575 computations (4.1% saved)

simplify114.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

628×	`associate-/l/_binary64_707`
278×	`associate-l_binary64_701`
253×	`distribute-rgt-neg-in_binary64_718`
250×	`times-frac_binary64_766`
239×	`associate-r_binary64_700`
234×	`distribute-lft-neg-in_binary64_717`
209×	`associate-/l*_binary64_705`
153×	`distribute-neg-frac_binary64_724`
150×	`associate-r/_binary64_702` `-commutative_binary64_691`
137×	`cancel-sign-sub-inv_binary64_726`
126×	`associate-/r*_binary64_704`
125×	`associate-*l/_binary64_703`
83×	`unswap-sqr_binary64_728`
82×	`log-prod_binary64_846`
73×	`cube-prod_binary64_788`
66×	`swap-sqr_binary64_727`
59×	`exp-prod_binary64_812` `distribute-rgt-in_binary64_710`
58×	`sqr-pow_binary64_732`
55×	`neg-sub0_binary64_755`
54×	`distribute-lft-in_binary64_709`
50×	`neg-mul-1_binary64_756`
48×	`log-div_binary64_847`
46×	`sub-neg_binary64_753`
39×	`cube-div_binary64_789`
36×	`-rgt-identity_binary64_750` `-lft-identity_binary64_749`
28×	`+-commutative_binary64_690`
22×	`associate-/r/_binary64_706`
12×	`distribute-lft-neg-out_binary64_719`
10×	`distribute-rgt-out_binary64_713`
9×	`log-pow_binary64_849`
8×	`unpow2_binary64_825` `unpow1/2_binary64_824` `pow-plus_binary64_823` `unpow1_binary64_818` `cube-unmult_binary64_797`
7×	`distribute-rgt1-in_binary64_716`
6×	`/-rgt-identity_binary64_751` `associate-+r-_binary64_694`
5×	`unpow3_binary64_826` `mul-1-neg_binary64_752` `pow-sqr_binary64_733` `distribute-lft-out_binary64_711`
4×	`exp-sqrt_binary64_813` `rem-sqrt-square_binary64_773` `distribute-rgt-neg-out_binary64_720` `associate--l+_binary64_697` `associate--r+_binary64_696` `associate-+l+_binary64_693`
3×	`cube-mult_binary64_790` `unsub-neg_binary64_754`
2×	`rem-square-sqrt_binary64_772` `distribute-neg-in_binary64_721` `distribute-lft1-in_binary64_715` `associate-+r+_binary64_692`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `associate-+l-_binary64_695`
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-rec_binary64_848` `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` `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` `div-sub_binary64_765` `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` `difference-of-squares_binary64_729` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-rgt-out--_binary64_714` `distribute-lft-out--_binary64_712` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698`

Counts

173 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	3951
1	662	3696
2	2842	3695
3	5385	3695

prune194.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	120	9	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	9	130

Error

5.3b

Counts

130 → 9

Compiler

Compiled 2227 to 1309 computations (41.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
4.2b	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.9b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))

rewrite298.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

4.9b

Rules

67×	`add-exp-log_binary64_798`
26×	`prod-exp_binary64_809`
23×	`add-cbrt-cube_binary64_796`
20×	`div-exp_binary64_811` `add-sqr-sqrt_binary64_782`
13×	`*-un-lft-identity_binary64_760`
10×	`pow-exp_binary64_828` `add-cube-cbrt_binary64_795` `associate-r_binary64_700`
6×	`cbrt-unprod_binary64_793` `unpow-prod-down_binary64_839` `cbrt-undiv_binary64_794` `sqrt-prod_binary64_776`
5×	`pow1_binary64_821` `times-frac_binary64_766`
4×	`add-log-exp_binary64_799` `unswap-sqr_binary64_728` `associate-/r*_binary64_704`
3×	`associate-l_binary64_701` `div-inv_binary64_757`
2×	`pow-to-exp_binary64_829` `unpow2_binary64_825` `sqr-pow_binary64_732` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l*_binary64_705` `sqrt-div_binary64_777` `difference-of-squares_binary64_729`
1×	`*-commutative_binary64_691` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `distribute-lft-out--_binary64_712` `rem-sqrt-square_binary64_773`

Counts

4 → 99

Calls

4 calls:

8.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
8.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
7.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2610 to 1612 computations (38.2% saved)

series1.9s (9.5%)

Error

5.3b

Counts

4 → 51

Calls

4 calls:

828.0ms	(/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)
544.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
355.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) l)))
167.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2328 to 2277 computations (2.2% saved)

simplify92.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

803×	`associate-/r/_binary64_706`
261×	`times-frac_binary64_766`
215×	`associate-/l*_binary64_705`
204×	`distribute-rgt-neg-in_binary64_718`
192×	`distribute-lft-neg-in_binary64_717`
156×	`distribute-neg-frac_binary64_724`
153×	`associate-l_binary64_701`
142×	`associate-r_binary64_700`
128×	`associate-/r*_binary64_704`
97×	`cancel-sign-sub-inv_binary64_726`
93×	`associate-*l/_binary64_703`
91×	`associate-*r/_binary64_702`
87×	`*-commutative_binary64_691`
75×	`unswap-sqr_binary64_728`
71×	`log-prod_binary64_846`
63×	`swap-sqr_binary64_727`
62×	`log-div_binary64_847`
55×	`sub-neg_binary64_753`
52×	`exp-prod_binary64_812`
51×	`cube-prod_binary64_788`
50×	`sqr-pow_binary64_732`
48×	`cube-div_binary64_789`
46×	`neg-sub0_binary64_755`
43×	`neg-mul-1_binary64_756`
30×	`distribute-rgt-in_binary64_710`
26×	`associate-/l/_binary64_707`
24×	`distribute-lft-in_binary64_709`
22×	`+-commutative_binary64_690`
20×	`*-rgt-identity_binary64_750`
19×	`*-lft-identity_binary64_749`
12×	`/-rgt-identity_binary64_751`
11×	`associate--l+_binary64_697`
10×	`log-pow_binary64_849`
8×	`unpow2_binary64_825` `unpow1/2_binary64_824` `pow-plus_binary64_823` `unpow1_binary64_818`
7×	`cube-unmult_binary64_797` `distribute-lft-neg-out_binary64_719`
5×	`unpow3_binary64_826` `distribute-rgt1-in_binary64_716`
4×	`log-rec_binary64_848` `exp-sqrt_binary64_813` `rem-sqrt-square_binary64_773` `unsub-neg_binary64_754` `pow-sqr_binary64_733` `associate--r+_binary64_696` `associate-+l+_binary64_693`
3×	`cube-mult_binary64_790` `div-sub_binary64_765` `mul-1-neg_binary64_752` `distribute-lft-out_binary64_711`
2×	`rem-square-sqrt_binary64_772` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720` `distribute-rgt-out_binary64_713` `associate-+r+_binary64_692`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `rem-3cbrt-rft_binary64_786` `rem-3cbrt-lft_binary64_785`
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` `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` `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-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` `+-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` `difference-of-squares_binary64_729` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-lft-out--_binary64_712` `count-2_binary64_708` `associate--r-_binary64_699` `associate--l-_binary64_698` `associate-+l-_binary64_695` `associate-+r-_binary64_694`

Counts

150 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	3053
1	518	2867
2	2269	2858
3	4987	2858

prune108.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Error

4.4b

Counts

104 → 8

Compiler

Compiled 1103 to 715 computations (35.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.2b	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2))) l)
4.6b	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))
5.5b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite425.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

307×	`add-exp-log_binary64_798`
146×	`prod-exp_binary64_809`
107×	`div-exp_binary64_811`
79×	`add-cbrt-cube_binary64_796`
32×	`cbrt-unprod_binary64_793`
30×	`pow-exp_binary64_828`
23×	`cbrt-undiv_binary64_794`
10×	`add-sqr-sqrt_binary64_782`
8×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
6×	`pow1_binary64_821` `times-frac_binary64_766` `pow-to-exp_binary64_829`
5×	`associate-/r_binary64_704` `associate-r*_binary64_700`
4×	`add-log-exp_binary64_799` `div-inv_binary64_757`
3×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l_binary64_705` `associate-l*_binary64_701`
2×	`associate-*r/_binary64_702`
1×	`pow-prod-down_binary64_831` `unswap-sqr_binary64_728` `-commutative_binary64_691` `associate-l/_binary64_703` `associate-/l/_binary64_707`

Counts

4 → 139

Calls

4 calls:

16.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2))) l)
11.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4988 to 2891 computations (42% saved)

series1.5s (7.7%)

Error

4.4b

Counts

4 → 45

Calls

4 calls:

855.0ms	(/.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2))) l)
336.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 2 d)))
183.0ms	(/.f64 (.f64 M D) (.f64 2 d))
167.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 2446 to 2198 computations (10.1% saved)

simplify164.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

307×	`times-frac_binary64_766`
272×	`associate-/l*_binary64_705`
268×	`log-prod_binary64_846`
243×	`associate-l_binary64_701`
204×	`associate-r_binary64_700`
200×	`log-div_binary64_847`
193×	`associate-+l+_binary64_693`
161×	`associate-*r/_binary64_702`
159×	`cube-prod_binary64_788`
150×	`unpow3_binary64_826`
140×	`associate-/r*_binary64_704` `associate--l+_binary64_697`
125×	`cube-div_binary64_789` `associate-*l/_binary64_703`
122×	`neg-mul-1_binary64_756`
110×	`associate-+l-_binary64_695`
103×	`*-commutative_binary64_691`
97×	`sub-neg_binary64_753`
96×	`associate-+r+_binary64_692`
83×	`swap-sqr_binary64_727`
75×	`distribute-rgt-neg-in_binary64_718`
73×	`associate-+r-_binary64_694`
70×	`distribute-lft-neg-in_binary64_717`
60×	`unswap-sqr_binary64_728` `+-commutative_binary64_690`
59×	`distribute-neg-frac_binary64_724`
58×	`associate--l-_binary64_698`
57×	`cube-mult_binary64_790`
51×	`exp-prod_binary64_812` `associate-/l/_binary64_707`
50×	`associate--r+_binary64_696`
47×	`associate-/r/_binary64_706`
34×	`cancel-sign-sub-inv_binary64_726`
31×	`div-sub_binary64_765`
30×	`sqr-pow_binary64_732`
27×	`*-rgt-identity_binary64_750` `associate--r-_binary64_699`
25×	`distribute-rgt-in_binary64_710`
21×	`log-pow_binary64_849`
20×	`neg-sub0_binary64_755` `distribute-lft-in_binary64_709`
17×	`*-lft-identity_binary64_749`
13×	`cube-unmult_binary64_797`
12×	`pow-plus_binary64_823`
10×	`log-rec_binary64_848`
9×	`exp-sqrt_binary64_813`
7×	`/-rgt-identity_binary64_751`
6×	`distribute-lft-neg-out_binary64_719`
5×	`unpow1/2_binary64_824` `unsub-neg_binary64_754`
4×	`unpow1_binary64_818` `rem-sqrt-square_binary64_773` `pow-sqr_binary64_733`
3×	`unpow2_binary64_825` `distribute-rgt-neg-out_binary64_720`
2×	`distribute-neg-in_binary64_721` `distribute-rgt-out_binary64_713`
1×	`1-exp_binary64_804` `exp-1-e_binary64_803` `remove-double-div_binary64_736` `distribute-rgt1-in_binary64_716` `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` `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` `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` `rem-square-sqrt_binary64_772` `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` `difference-of-sqr--1_binary64_731` `difference-of-sqr-1_binary64_730` `difference-of-squares_binary64_729` `cancel-sign-sub_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711`

Counts

184 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	3627
1	464	3087
2	2393	3084
3	4241	3084
4	4907	3084
5	5064	3084

prune149.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	142	7	149

Error

4.4b

Counts

149 → 7

Compiler

Compiled 1711 to 1074 computations (37.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(.f64 h (/.f64 (.f64 M D) (*.f64 d 2)))
5.2b	(/.f64 (/.f64 (.f64 M D) (.f64 d 2)) l)
5.5b	(/.f64 (.f64 M D) (.f64 d 2))
5.5b	(/.f64 (.f64 M D) (.f64 d 2))

rewrite318.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

64×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
22×	`times-frac_binary64_766`
21×	`prod-exp_binary64_809` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `cbrt-unprod_binary64_793`
18×	`add-sqr-sqrt_binary64_782`
16×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
8×	`div-inv_binary64_757`
7×	`associate-/l*_binary64_705`
6×	`pow1_binary64_821`
5×	`associate-/r_binary64_704` `associate-r*_binary64_700`
4×	`add-log-exp_binary64_799`
3×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-l_binary64_701`
1×	`associate-/l/_binary64_707` `pow-prod-down_binary64_831` `unswap-sqr_binary64_728` `associate-r/_binary64_702` `-commutative_binary64_691`

Counts

4 → 115

Calls

4 calls:

9.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 d 2)))
8.0ms	(/.f64 (.f64 M D) (.f64 d 2))
8.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 d 2)) l)
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 3632 to 1939 computations (46.6% saved)

series1.0s (5.2%)

Error

4.4b

Counts

4 → 42

Calls

4 calls:

347.0ms	(/.f64 (/.f64 (.f64 M D) (.f64 d 2)) l)
310.0ms	(.f64 h (/.f64 (.f64 M D) (*.f64 d 2)))
185.0ms	(/.f64 (.f64 M D) (.f64 d 2))
184.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 2112 to 1763 computations (16.5% saved)

simplify155.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

926×	`associate-/r/_binary64_706`
570×	`*-commutative_binary64_691`
253×	`times-frac_binary64_766`
242×	`log-prod_binary64_846`
190×	`sub-neg_binary64_753`
170×	`associate-/l*_binary64_705`
163×	`cube-prod_binary64_788`
162×	`log-div_binary64_847`
141×	`associate-l_binary64_701`
133×	`associate-/r*_binary64_704`
121×	`associate-r_binary64_700`
108×	`cube-div_binary64_789` `associate-*r/_binary64_702`
101×	`sqr-pow_binary64_732` `associate-/l/_binary64_707`
100×	`exp-prod_binary64_812`
97×	`associate-*l/_binary64_703`
93×	`swap-sqr_binary64_727`
53×	`associate--l+_binary64_697`
44×	`cancel-sign-sub-inv_binary64_726`
42×	`unpow3_binary64_826` `cube-mult_binary64_790`
40×	`associate-+l+_binary64_693`
36×	`+-commutative_binary64_690`
34×	`unswap-sqr_binary64_728` `associate-+l-_binary64_695`
32×	`neg-mul-1_binary64_756`
30×	`neg-sub0_binary64_755`
28×	`div-sub_binary64_765`
27×	`distribute-rgt-neg-in_binary64_718`
26×	`distribute-lft-neg-in_binary64_717` `associate-+r+_binary64_692`
25×	`distribute-neg-frac_binary64_724` `associate--l-_binary64_698`
24×	`distribute-neg-in_binary64_721`
21×	`associate-+r-_binary64_694`
19×	`associate--r+_binary64_696`
18×	`/-rgt-identity_binary64_751`
17×	`unsub-neg_binary64_754` `-rgt-identity_binary64_750` `-lft-identity_binary64_749`
14×	`distribute-rgt-in_binary64_710`
11×	`exp-sqrt_binary64_813`
10×	`cube-unmult_binary64_797`
7×	`+-rgt-identity_binary64_745`
5×	`log-rec_binary64_848` `pow-sqr_binary64_733`
4×	`div0_binary64_741` `distribute-lft-in_binary64_709`
3×	`distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722`
2×	`remove-double-neg_binary64_748` `sub0-neg_binary64_747` `--rgt-identity_binary64_746` `associate--r-_binary64_699`
1×	`unpow1/2_binary64_824` `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` `unpow2_binary64_825` `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` `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` `rem-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `+-lft-identity_binary64_744` `mul0-rgt_binary64_743` `mul0-lft_binary64_742` `*-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` `difference-of-squares_binary64_729` `cancel-sign-sub_binary64_725` `distribute-rgt-neg-out_binary64_720` `distribute-lft-neg-out_binary64_719` `distribute-rgt1-in_binary64_716` `distribute-lft1-in_binary64_715` `distribute-rgt-out--_binary64_714` `distribute-rgt-out_binary64_713` `distribute-lft-out--_binary64_712` `distribute-lft-out_binary64_711`

Counts

157 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	2791
1	421	2237
2	2004	2236
3	3563	2236
4	4968	2236
5	4996	2236
6	5019	2236

prune94.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	88	7	95

Error

4.4b

Counts

95 → 7

Compiler

Compiled 1136 to 604 computations (46.8% saved)

regimes6.0s (30%)

Accuracy

Total 3.4b remaining (39.9%)

Threshold costs 0b (0%)

Compiler

Compiled 69467 to 63427 computations (8.7% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64_691`
10×	`sub-neg_binary64_753` `+-commutative_binary64_690`
9×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755`
6×	`distribute-rgt-neg-in_binary64_718`
5×	`distribute-lft-neg-in_binary64_717`
3×	`distribute-neg-frac_binary64_724`
2×	`cancel-sign-sub-inv_binary64_726`
1×	`unpow1_binary64_818` `1-exp_binary64_804` `distribute-lft-neg-out_binary64_719`
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` `e-exp-1_binary64_805` `exp-1-e_binary64_803` `exp-0_binary64_802` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `unsub-neg_binary64_754` `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_binary64_725` `distribute-frac-neg_binary64_723` `distribute-neg-out_binary64_722` `distribute-neg-in_binary64_721` `distribute-rgt-neg-out_binary64_720`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	48
1	35	48
2	46	48
3	61	48
4	73	48
5	87	48
6	95	48
7	100	48
8	102	48
9	100	48

end10.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 93 to 69 computations (25.8% saved)

sample1.9s (9.3%)

Algorithm

1×

intervals

Results

688.0ms	8000×	body	128	valid
244.0ms	3072×	body	128	nan
114.0ms	1325×	body	128	invalid

Compiler

Compiled 201 to 202 computations (-0.5% saved)

Details

analyze3.0s (14.9%)

sample66.0ms (0.3%)

simplify42.0ms (0.2%)

prune2.0ms (0%)

localize14.0ms (0.1%)

rewrite324.0ms (1.6%)

series2.1s (10.3%)

simplify114.0ms (0.6%)

prune194.0ms (1%)

localize16.0ms (0.1%)

rewrite298.0ms (1.5%)

series1.9s (9.5%)

simplify92.0ms (0.5%)

prune108.0ms (0.5%)

localize17.0ms (0.1%)

rewrite425.0ms (2.1%)

series1.5s (7.7%)

simplify164.0ms (0.8%)

prune149.0ms (0.7%)

localize15.0ms (0.1%)

rewrite318.0ms (1.6%)

series1.0s (5.2%)

simplify155.0ms (0.8%)

prune94.0ms (0.5%)

regimes6.0s (30%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end10.0ms (0.1%)

sample1.9s (9.3%)

Profiling