Details

analyze3.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25%	13
74.9%	0%	25.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample11.0ms (1%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

128

valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify443.0ms (40.5%)

Algorithm

1×	egg-herbie

Rules

647×	`exp-diff_binary64_808`
609×	`exp-prod_binary64_812`
509×	`associate-/l/_binary64_707`
444×	`div-sub_binary64_765`
387×	`times-frac_binary64_766`
233×	`associate-/r*_binary64_704`
179×	`associate-+r-_binary64_694`
170×	`associate-+r+_binary64_692`
167×	`swap-sqr_binary64_727`
160×	`unsub-neg_binary64_754`
141×	`associate-+l-_binary64_695`
139×	`associate--r-_binary64_699`
127×	`associate--l-_binary64_698`
126×	`associate-+l+_binary64_693`
122×	`associate--r+_binary64_696`
113×	`associate--l+_binary64_697`
100×	`pow-plus_binary64_823` `distribute-rgt-neg-in_binary64_718`
79×	`distribute-rgt-in_binary64_710`
76×	`exp-sum_binary64_806`
64×	`distribute-rgt1-in_binary64_716`
62×	`associate-/l*_binary64_705`
61×	`distribute-lft-neg-in_binary64_717`
53×	`distribute-neg-in_binary64_721`
49×	`sub-neg_binary64_753`
42×	`distribute-neg-out_binary64_722` `distribute-rgt-neg-out_binary64_720`
40×	`distribute-rgt-out_binary64_713`
39×	`distribute-lft-neg-out_binary64_719` `associate-/r/_binary64_706` `associate-r_binary64_700`
38×	`associate-l_binary64_701`
36×	`neg-sub0_binary64_755`
35×	`cancel-sign-sub-inv_binary64_726` `distribute-frac-neg_binary64_723`
32×	`neg-mul-1_binary64_756`
29×	`distribute-lft-in_binary64_709`
28×	`sqr-pow_binary64_732` `distribute-rgt-out--_binary64_714` `*-commutative_binary64_691`
27×	`pow-sqr_binary64_733`
25×	`distribute-lft-out_binary64_711`
23×	`exp-sqrt_binary64_813`
22×	`distribute-lft-out--_binary64_712`
19×	`pow-base-1_binary64_820`
15×	`+-commutative_binary64_690`
12×	`exp-lft-sqr_binary64_815`
10×	`mul0-rgt_binary64_743` `mul0-lft_binary64_742`
9×	`*-lft-identity_binary64_749` `remove-double-neg_binary64_748` `unswap-sqr_binary64_728`
8×	`sqr-neg_binary64_774`
7×	`/-rgt-identity_binary64_751`
6×	`exp-neg_binary64_807` `cube-unmult_binary64_797` `cube-prod_binary64_788` `*-rgt-identity_binary64_750` `sub0-neg_binary64_747` `difference-of-squares_binary64_729`
5×	`+-rgt-identity_binary64_745` `cancel-sign-sub_binary64_725` `count-2_binary64_708`
4×	`+-inverses_binary64_739` `distribute-neg-frac_binary64_724` `distribute-lft1-in_binary64_715`
2×	`--rgt-identity_binary64_746` `+-lft-identity_binary64_744` `div0_binary64_741` `*-inverses_binary64_740` `difference-of-sqr-1_binary64_730`
1×	`prod-exp_binary64_809` `1-exp_binary64_804` `exp-1-e_binary64_803` `rgt-mult-inverse_binary64_737`
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` `exp-to-pow_binary64_822` `unpow0_binary64_819` `unpow1_binary64_818` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-cbrt_binary64_814` `div-exp_binary64_811` `rec-exp_binary64_810` `e-exp-1_binary64_805` `exp-0_binary64_802` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `cube-mult_binary64_790` `cube-div_binary64_789` `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` `rem-sqrt-square_binary64_773` `rem-square-sqrt_binary64_772` `mul-1-neg_binary64_752` `lft-mult-inverse_binary64_738` `remove-double-div_binary64_736` `difference-of-sqr--1_binary64_731` `associate-l/_binary64_703` `associate-r/_binary64_702`

Counts

1 → 3

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	14	10
2	20	10
3	26	10
4	54	10
5	77	10
6	190	10
7	423	10
8	900	10
9	4032	10

prune3.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	0	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	1	4

Error

Counts

4 → 1

Compiler

Compiled 28 to 21 computations (25% saved)

localize4.0ms (0.4%)

Local error

Found 1 expressions with local error:

0.0b	(.f64 (.f64 x x) 2)

rewrite21.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`pow1_binary64_821` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
3×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `add-sqr-sqrt_binary64_782` `associate-r_binary64_700`
2×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
1×	`add-log-exp_binary64_799` `unswap-sqr_binary64_728` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

1 → 19

Calls

1 calls:

6.0ms

(*.f64 (*.f64 x x) 2)

Compiler

Compiled 231 to 151 computations (34.6% saved)

series35.0ms (3.2%)

Error

Counts

1 → 3

Calls

1 calls:

33.0ms

(*.f64 (*.f64 x x) 2)

Compiler

Compiled 63 to 61 computations (3.2% saved)

simplify160.0ms (14.6%)

Algorithm

1×	egg-herbie

Rules

340×	`times-frac_binary64_766`
278×	`*-commutative_binary64_691`
257×	`associate-r_binary64_700`
215×	`associate--l+_binary64_697`
206×	`exp-prod_binary64_812`
202×	`associate--r+_binary64_696`
200×	`log-prod_binary64_846`
192×	`cube-prod_binary64_788` `distribute-rgt-out_binary64_713`
189×	`sqr-pow_binary64_732`
186×	`associate-+l-_binary64_695`
175×	`associate-*l/_binary64_703`
158×	`distribute-rgt-in_binary64_710`
155×	`unswap-sqr_binary64_728`
154×	`associate-/l*_binary64_705`
147×	`swap-sqr_binary64_727` `associate--r-_binary64_699`
145×	`associate--l-_binary64_698`
134×	`associate-*r/_binary64_702`
111×	`cancel-sign-sub-inv_binary64_726`
104×	`pow-sqr_binary64_733`
99×	`log-div_binary64_847`
96×	`cube-div_binary64_789`
85×	`associate-l_binary64_701`
74×	`sub-neg_binary64_753`
63×	`*-lft-identity_binary64_749`
61×	`*-rgt-identity_binary64_750`
60×	`distribute-lft-in_binary64_709`
54×	`count-2_binary64_708` `associate-+l+_binary64_693`
47×	`distribute-rgt1-in_binary64_716`
46×	`distribute-neg-in_binary64_721`
44×	`pow-plus_binary64_823`
31×	`associate-/r*_binary64_704`
30×	`associate-+r+_binary64_692`
29×	`/-rgt-identity_binary64_751`
27×	`unpow3_binary64_826` `div-sub_binary64_765`
26×	`exp-sqrt_binary64_813`
25×	`cube-mult_binary64_790` `associate-/r/_binary64_706`
24×	`exp-sum_binary64_806` `distribute-rgt-neg-in_binary64_718`
22×	`distribute-lft-out_binary64_711`
21×	`log-pow_binary64_849`
19×	`distribute-rgt-out--_binary64_714`
18×	`exp-lft-sqr_binary64_815` `distribute-lft-neg-in_binary64_717`
13×	`rem-sqrt-square_binary64_773` `distribute-lft1-in_binary64_715`
12×	`neg-mul-1_binary64_756` `associate-/l/_binary64_707`
11×	`associate-+r-_binary64_694`
10×	`distribute-neg-frac_binary64_724`
8×	`log-rec_binary64_848`
7×	`exp-diff_binary64_808` `cube-unmult_binary64_797` `distribute-lft-neg-out_binary64_719` `+-commutative_binary64_690`
6×	`neg-sub0_binary64_755` `unsub-neg_binary64_754` `distribute-lft-out--_binary64_712`
5×	`distribute-neg-out_binary64_722`
4×	`distribute-rgt-neg-out_binary64_720`
3×	`exp-to-pow_binary64_822` `prod-exp_binary64_809` `mul0-rgt_binary64_743`
2×	`pow-base-1_binary64_820` `sub0-neg_binary64_747` `mul0-lft_binary64_742` `distribute-frac-neg_binary64_723`
1×	`unpow2_binary64_825` `unpow1_binary64_818` `div-exp_binary64_811` `1-exp_binary64_804` `exp-1-e_binary64_803` `rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `remove-double-neg_binary64_748` `*-inverses_binary64_740` `rgt-mult-inverse_binary64_737`
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` `unpow1/2_binary64_824` `unpow0_binary64_819` `unpow-1_binary64_817` `exp-lft-cube_binary64_816` `exp-cbrt_binary64_814` `rec-exp_binary64_810` `exp-neg_binary64_807` `e-exp-1_binary64_805` `exp-0_binary64_802` `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_746` `+-rgt-identity_binary64_745` `+-lft-identity_binary64_744` `div0_binary64_741` `+-inverses_binary64_739` `lft-mult-inverse_binary64_738` `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`

Counts

22 → 50

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	236
1	86	191
2	310	191
3	561	191
4	1761	191
5	2666	191

prune39.0ms (3.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	50	1	51

Error

Counts

51 → 1

Compiler

Compiled 642 to 337 computations (47.5% saved)

simplify3.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`neg-mul-1_binary64_756` `neg-sub0_binary64_755` `sub-neg_binary64_753` `-rgt-identity_binary64_750` `-commutative_binary64_691` `+-commutative_binary64_690`
1×	`1-exp_binary64_804` `unsub-neg_binary64_754` `distribute-rgt-neg-out_binary64_720`
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` `exp-1-e_binary64_803` `exp-0_binary64_802` `sqr-abs_binary64_775` `sqr-neg_binary64_774` `mul-1-neg_binary64_752` `/-rgt-identity_binary64_751` `*-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-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	7	10
1	12	10
2	16	10
3	18	10
4	21	10
5	20	10

Proof

(=> (- f64 (* f64 (* f64 h0 h0) 2) 1))
sub-neg_binary64_753 =>
(+ f64 (* f64 (* f64 h0 h0) 2) (=> (neg f64 1)))
neg-mul-1_binary64_756 =>
(+ f64 (* f64 (* f64 h0 h0) 2) (=> (* f64 -1 1)))
*-rgt-identity_binary64_750 =>
(+ f64 (* f64 (* f64 h0 h0) 2) -1)

end0.0ms (0%)

sample372.0ms (34%)

Algorithm

1×

intervals

Results

152.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 22 to 20 computations (9.1% saved)

Details

analyze3.0ms (0.3%)

sample11.0ms (1%)

simplify443.0ms (40.5%)

prune3.0ms (0.3%)

localize4.0ms (0.4%)

rewrite21.0ms (1.9%)

series35.0ms (3.2%)

simplify160.0ms (14.6%)

prune39.0ms (3.5%)

simplify3.0ms (0.3%)

end0.0ms (0%)

sample372.0ms (34%)

Profiling