Details

analyze149.0ms (4.6%)

Algorithm

1×	search
2×	egg-herbie

Rules

1× 1-exp_binary64_6942 sub-neg_binary64_6891 +-commutative_binary64_6828

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_7161 erf-erfc_binary64_7160 erf-odd_binary64_7159 if-if-and-not_binary64_7158 if-if-and_binary64_7157 if-if-or-not_binary64_7156 if-if-or_binary64_7155 if-not_binary64_7154 if-same_binary64_7153 if-false_binary64_7152 if-true_binary64_7151 not-gte_binary64_7150 not-lte_binary64_7149 not-gt_binary64_7148 not-lt_binary64_7147 gte-same_binary64_7146 lte-same_binary64_7145 gt-same_binary64_7144 lt-same_binary64_7143 sinh---cosh_binary64_7090 sinh-+-cosh_binary64_7089 sinh-cosh_binary64_7088 tanh-def-c_binary64_7087 tanh-def-b_binary64_7086 tanh-def-a_binary64_7085 cosh-def_binary64_7084 sinh-def_binary64_7083 tan-neg_binary64_7030 cos-neg_binary64_7029 sin-neg_binary64_7028 tan-0_binary64_7027 cos-0_binary64_7026 sin-0_binary64_7025 hang-m-tan_binary64_7024 hang-p-tan_binary64_7023 hang-m0-tan_binary64_7022 hang-p0-tan_binary64_7021 hang-0m-tan_binary64_7020 hang-0p-tan_binary64_7019 tan-+PI/2_binary64_7018 tan-+PI_binary64_7017 tan-PI_binary64_7016 tan-PI/3_binary64_7015 tan-PI/4_binary64_7014 tan-PI/6_binary64_7013 cos-+PI/2_binary64_7012 cos-+PI_binary64_7011 cos-PI_binary64_7010 cos-PI/2_binary64_7009 cos-PI/3_binary64_7008 cos-PI/4_binary64_7007 cos-PI/6_binary64_7006 sin-+PI/2_binary64_7005 sin-+PI_binary64_7004 sin-PI_binary64_7003 sin-PI/2_binary64_7002 sin-PI/3_binary64_7001 sin-PI/4_binary64_7000 sin-PI/6_binary64_6999 sub-1-sin_binary64_6998 sub-1-cos_binary64_6997 -1-add-sin_binary64_6996 -1-add-cos_binary64_6995 1-sub-sin_binary64_6994 1-sub-cos_binary64_6993 cos-sin-sum_binary64_6992 log-E_binary64_6988 log-pow_binary64_6987 log-rec_binary64_6986 log-div_binary64_6985 log-prod_binary64_6984 pow-base-0_binary64_6982 unpow1/3_binary64_6965 unpow3_binary64_6964 unpow2_binary64_6963 unpow1/2_binary64_6962 pow-plus_binary64_6961 exp-to-pow_binary64_6960 pow-base-1_binary64_6958 unpow0_binary64_6957 unpow1_binary64_6956 unpow-1_binary64_6955 exp-lft-cube_binary64_6954 exp-lft-sqr_binary64_6953 exp-cbrt_binary64_6952 exp-sqrt_binary64_6951 exp-prod_binary64_6950 div-exp_binary64_6949 rec-exp_binary64_6948 prod-exp_binary64_6947 exp-diff_binary64_6946 exp-neg_binary64_6945 exp-sum_binary64_6944 e-exp-1_binary64_6943 exp-1-e_binary64_6941 exp-0_binary64_6940 rem-log-exp_binary64_6939 rem-exp-log_binary64_6938 cube-unmult_binary64_6935 cube-mult_binary64_6928 cube-div_binary64_6927 cube-prod_binary64_6926 cube-neg_binary64_6925 rem-3cbrt-rft_binary64_6924 rem-3cbrt-lft_binary64_6923 rem-cbrt-cube_binary64_6922 rem-cube-cbrt_binary64_6921 sqr-abs_binary64_6913 sqr-neg_binary64_6912 rem-sqrt-square_binary64_6911 rem-square-sqrt_binary64_6910 times-frac_binary64_6904 div-sub_binary64_6903 neg-mul-1_binary64_6894 neg-sub0_binary64_6893 unsub-neg_binary64_6892 mul-1-neg_binary64_6890 /-rgt-identity_binary64_6889 *-rgt-identity_binary64_6888 *-lft-identity_binary64_6887 remove-double-neg_binary64_6886 sub0-neg_binary64_6885 --rgt-identity_binary64_6884 +-rgt-identity_binary64_6883 +-lft-identity_binary64_6882 mul0-rgt_binary64_6881 mul0-lft_binary64_6880 div0_binary64_6879 *-inverses_binary64_6878 +-inverses_binary64_6877 lft-mult-inverse_binary64_6876 rgt-mult-inverse_binary64_6875 remove-double-div_binary64_6874 pow-sqr_binary64_6871 sqr-pow_binary64_6870 difference-of-sqr--1_binary64_6869 difference-of-sqr-1_binary64_6868 difference-of-squares_binary64_6867 unswap-sqr_binary64_6866 swap-sqr_binary64_6865 cancel-sign-sub-inv_binary64_6864 cancel-sign-sub_binary64_6863 distribute-neg-frac_binary64_6862 distribute-frac-neg_binary64_6861 distribute-neg-out_binary64_6860 distribute-neg-in_binary64_6859 distribute-rgt-neg-out_binary64_6858 distribute-lft-neg-out_binary64_6857 distribute-rgt-neg-in_binary64_6856 distribute-lft-neg-in_binary64_6855 distribute-rgt1-in_binary64_6854 distribute-lft1-in_binary64_6853 distribute-rgt-out--_binary64_6852 distribute-rgt-out_binary64_6851 distribute-lft-out--_binary64_6850 distribute-lft-out_binary64_6849 distribute-rgt-in_binary64_6848 distribute-lft-in_binary64_6847 count-2_binary64_6846 associate-/l/_binary64_6845 associate-/r/_binary64_6844 associate-/l*_binary64_6843 associate-/r*_binary64_6842 associate-*l/_binary64_6841 associate-*r/_binary64_6840 associate-*l*_binary64_6839 associate-*r*_binary64_6838 associate--r-_binary64_6837 associate--l-_binary64_6836 associate--l+_binary64_6835 associate--r+_binary64_6834 associate-+l-_binary64_6833 associate-+r-_binary64_6832 associate-+l+_binary64_6831 associate-+r+_binary64_6830 *-commutative_binary64_6829

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	12	4
2	13	4
3	10	4
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
75%	25%	0%	3
87.5%	12.5%	0%	4
93.7%	6.2%	0%	5
96.8%	3.1%	0%	6
98.4%	1.6%	0%	7
99.2%	0.8%	0%	8
99.6%	0.4%	0%	9
99.8%	0.2%	0%	10
99.9%	0.1%	0%	11
99.9%	0%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 6 to 6 computations (0% saved)

sample11.0ms (0.4%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 11 to 12 computations (-9.1% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1× 1-exp_binary64_6942 sub-neg_binary64_6891 +-commutative_binary64_6828

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	12	4
2	13	4
3	10	4

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 6 to 6 computations (0% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 x 1/3)

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

4×	`add-sqr-sqrt_binary64_6920` `*-un-lft-identity_binary64_6898`
3×	`add-log-exp_binary64_6937` `cancel-sign-sub-inv_binary64_6864`
2×	`add-cube-cbrt_binary64_6933`
1×	`diff-log_binary64_6990` `pow1_binary64_6959` `add-exp-log_binary64_6936` `add-cbrt-cube_binary64_6934` `flip3--_binary64_6902` `sub-neg_binary64_6891` `flip--_binary64_6873` `difference-of-squares_binary64_6867` `distribute-lft-out--_binary64_6850`

Counts

1 → 16

Calls

1 calls:

4.0ms

(-.f64 x 1/3)

Compiler

Compiled 136 to 108 computations (20.6% saved)

series29.0ms (0.9%)

Error

0.0b

Counts

1 → 6

Calls

1 calls:

26.0ms

(-.f64 x 1/3)

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify108.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

502×	`distribute-lft-out_binary64_6849`
470×	`cancel-sign-sub-inv_binary64_6864`
388×	`*-commutative_binary64_6829`
374×	`unswap-sqr_binary64_6866`
344×	`distribute-rgt-in_binary64_6848`
341×	`neg-mul-1_binary64_6894` `neg-sub0_binary64_6893`
298×	`sub-neg_binary64_6891`
256×	`associate-+l+_binary64_6831`
255×	`+-commutative_binary64_6828`
237×	`unsub-neg_binary64_6892`
212×	`associate-+r+_binary64_6830`
202×	`distribute-rgt-out_binary64_6851`
199×	`sqr-pow_binary64_6870`
198×	`distribute-neg-in_binary64_6859`
197×	`distribute-lft-neg-out_binary64_6857`
190×	`associate-l_binary64_6839`
166×	`distribute-lft-in_binary64_6847`
145×	`distribute-rgt-neg-out_binary64_6858`
105×	`associate-r_binary64_6838`
102×	`cube-prod_binary64_6926`
84×	`distribute-rgt-neg-in_binary64_6856`
79×	`remove-double-neg_binary64_6886`
67×	`associate-+l-_binary64_6833`
60×	`pow-sqr_binary64_6871`
57×	`distribute-lft-neg-in_binary64_6855` `associate--r+_binary64_6834`
54×	`associate--l+_binary64_6835`
50×	`associate-+r-_binary64_6832`
44×	`pow-plus_binary64_6961`
43×	`unpow3_binary64_6964` `associate--r-_binary64_6837`
38×	`cube-mult_binary64_6928` `associate--l-_binary64_6836`
30×	`distribute-neg-out_binary64_6860`
19×	`mul0-lft_binary64_6880`
16×	`distribute-rgt-out--_binary64_6852`
14×	`exp-prod_binary64_6950` `cube-unmult_binary64_6935`
12×	`exp-sum_binary64_6944` `rem-sqrt-square_binary64_6911`
9×	`count-2_binary64_6846`
8×	`unpow2_binary64_6963` `unpow1/2_binary64_6962` `unpow1_binary64_6956` `exp-diff_binary64_6946` `sub0-neg_binary64_6885`
7×	`log-prod_binary64_6984`
5×	`div-sub_binary64_6903` `distribute-lft-out--_binary64_6850`
4×	`cube-neg_binary64_6925` `*-lft-identity_binary64_6887` `--rgt-identity_binary64_6884` `+-rgt-identity_binary64_6883`
3×	`+-lft-identity_binary64_6882` `swap-sqr_binary64_6865`
2×	`sqr-neg_binary64_6912` `*-rgt-identity_binary64_6888` `mul0-rgt_binary64_6881` `distribute-rgt1-in_binary64_6854`
1×	`div-exp_binary64_6949` `1-exp_binary64_6942` `exp-1-e_binary64_6941` `rem-3cbrt-lft_binary64_6923` `rem-square-sqrt_binary64_6910` `mul-1-neg_binary64_6890` `distribute-lft1-in_binary64_6853`
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_7161` `erf-erfc_binary64_7160` `erf-odd_binary64_7159` `if-if-and-not_binary64_7158` `if-if-and_binary64_7157` `if-if-or-not_binary64_7156` `if-if-or_binary64_7155` `if-not_binary64_7154` `if-same_binary64_7153` `if-false_binary64_7152` `if-true_binary64_7151` `not-gte_binary64_7150` `not-lte_binary64_7149` `not-gt_binary64_7148` `not-lt_binary64_7147` `gte-same_binary64_7146` `lte-same_binary64_7145` `gt-same_binary64_7144` `lt-same_binary64_7143` `sinh---cosh_binary64_7090` `sinh-+-cosh_binary64_7089` `sinh-cosh_binary64_7088` `tanh-def-c_binary64_7087` `tanh-def-b_binary64_7086` `tanh-def-a_binary64_7085` `cosh-def_binary64_7084` `sinh-def_binary64_7083` `tan-neg_binary64_7030` `cos-neg_binary64_7029` `sin-neg_binary64_7028` `tan-0_binary64_7027` `cos-0_binary64_7026` `sin-0_binary64_7025` `hang-m-tan_binary64_7024` `hang-p-tan_binary64_7023` `hang-m0-tan_binary64_7022` `hang-p0-tan_binary64_7021` `hang-0m-tan_binary64_7020` `hang-0p-tan_binary64_7019` `tan-+PI/2_binary64_7018` `tan-+PI_binary64_7017` `tan-PI_binary64_7016` `tan-PI/3_binary64_7015` `tan-PI/4_binary64_7014` `tan-PI/6_binary64_7013` `cos-+PI/2_binary64_7012` `cos-+PI_binary64_7011` `cos-PI_binary64_7010` `cos-PI/2_binary64_7009` `cos-PI/3_binary64_7008` `cos-PI/4_binary64_7007` `cos-PI/6_binary64_7006` `sin-+PI/2_binary64_7005` `sin-+PI_binary64_7004` `sin-PI_binary64_7003` `sin-PI/2_binary64_7002` `sin-PI/3_binary64_7001` `sin-PI/4_binary64_7000` `sin-PI/6_binary64_6999` `sub-1-sin_binary64_6998` `sub-1-cos_binary64_6997` `-1-add-sin_binary64_6996` `-1-add-cos_binary64_6995` `1-sub-sin_binary64_6994` `1-sub-cos_binary64_6993` `cos-sin-sum_binary64_6992` `log-E_binary64_6988` `log-pow_binary64_6987` `log-rec_binary64_6986` `log-div_binary64_6985` `pow-base-0_binary64_6982` `unpow1/3_binary64_6965` `exp-to-pow_binary64_6960` `pow-base-1_binary64_6958` `unpow0_binary64_6957` `unpow-1_binary64_6955` `exp-lft-cube_binary64_6954` `exp-lft-sqr_binary64_6953` `exp-cbrt_binary64_6952` `exp-sqrt_binary64_6951` `rec-exp_binary64_6948` `prod-exp_binary64_6947` `exp-neg_binary64_6945` `e-exp-1_binary64_6943` `exp-0_binary64_6940` `rem-log-exp_binary64_6939` `rem-exp-log_binary64_6938` `cube-div_binary64_6927` `rem-3cbrt-rft_binary64_6924` `rem-cbrt-cube_binary64_6922` `rem-cube-cbrt_binary64_6921` `sqr-abs_binary64_6913` `times-frac_binary64_6904` `/-rgt-identity_binary64_6889` `div0_binary64_6879` `-inverses_binary64_6878` `+-inverses_binary64_6877` `lft-mult-inverse_binary64_6876` `rgt-mult-inverse_binary64_6875` `remove-double-div_binary64_6874` `difference-of-sqr--1_binary64_6869` `difference-of-sqr-1_binary64_6868` `difference-of-squares_binary64_6867` `cancel-sign-sub_binary64_6863` `distribute-neg-frac_binary64_6862` `distribute-frac-neg_binary64_6861` `associate-/l/_binary64_6845` `associate-/r/_binary64_6844` `associate-/l_binary64_6843` `associate-/r_binary64_6842` `associate-l/_binary64_6841` `associate-*r/_binary64_6840`

Counts

22 → 16

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	136
1	81	127
2	123	124
3	169	124
4	265	124
5	478	124
6	1025	124
7	1622	124
8	1940	124
9	2785	124
10	4193	124
11	4894	124
12	4802	124

prune12.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	2	17

Error

0.0b

Counts

17 → 2

Compiler

Compiled 105 to 81 computations (22.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x 1/3)
0.0b	(+.f64 1/9 (*.f64 x (+.f64 x 1/3)))
0.2b	(*.f64 x (+.f64 x 1/3))
20.0b	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (+.f64 1/9 (*.f64 x (+.f64 x 1/3))))

rewrite192.0ms (6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

49×	`add-sqr-sqrt_binary64_6920`
31×	`*-un-lft-identity_binary64_6898`
24×	`times-frac_binary64_6904`
19×	`add-cube-cbrt_binary64_6933`
16×	`difference-of-squares_binary64_6867`
8×	`add-exp-log_binary64_6936` `add-log-exp_binary64_6937` `add-cbrt-cube_binary64_6934` `associate-/l*_binary64_6843`
6×	`pow1_binary64_6959`
4×	`unpow-prod-down_binary64_6977` `cube-prod_binary64_6926` `sqr-pow_binary64_6870` `distribute-lft-out--_binary64_6850` `flip3-+_binary64_6901` `flip-+_binary64_6872` `associate-r_binary64_6838`
3×	`associate-/r_binary64_6842` `associate-l*_binary64_6839`
2×	`associate-/l/_binary64_6845` `associate-/r/_binary64_6844` `distribute-rgt-in_binary64_6848` `distribute-lft-in_binary64_6847` `associate-*r/_binary64_6840` `distribute-lft-out_binary64_6849` `sum-log_binary64_6989` `associate-+r+_binary64_6830` `+-commutative_binary64_6828`
1×	`div-exp_binary64_6949` `cbrt-undiv_binary64_6932` `frac-2neg_binary64_6909` `div-sub_binary64_6903` `clear-num_binary64_6897` `div-inv_binary64_6895` `flip3--_binary64_6902` `flip--_binary64_6873` `pow-prod-down_binary64_6969` `prod-exp_binary64_6947` `cbrt-unprod_binary64_6931` `unswap-sqr_binary64_6866` `*-commutative_binary64_6829`

Counts

4 → 100

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (+.f64 1/9 (*.f64 x (+.f64 x 1/3))))
7.0ms	(*.f64 x (+.f64 x 1/3))
4.0ms	(+.f64 1/9 (*.f64 x (+.f64 x 1/3)))
3.0ms	(+.f64 x 1/3)

Compiler

Compiled 2365 to 1856 computations (21.5% saved)

series320.0ms (9.9%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

127.0ms	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (+.f64 1/9 (*.f64 x (+.f64 x 1/3))))
90.0ms	(+.f64 1/9 (*.f64 x (+.f64 x 1/3)))
55.0ms	(*.f64 x (+.f64 x 1/3))
28.0ms	(+.f64 x 1/3)

Compiler

Compiled 676 to 567 computations (16.1% saved)

simplify110.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

673×	`distribute-rgt-in_binary64_6848`
660×	`distribute-lft-in_binary64_6847`
637×	`times-frac_binary64_6904`
181×	`associate-/l*_binary64_6843`
176×	`associate-+l+_binary64_6831`
149×	`associate-+r+_binary64_6830`
126×	`associate-*l/_binary64_6841`
99×	`associate-/r*_binary64_6842`
97×	`associate-*r/_binary64_6840`
81×	`associate-l_binary64_6839`
80×	`associate-/l/_binary64_6845`
67×	`associate-r_binary64_6838`
59×	`associate--r+_binary64_6834`
58×	`cancel-sign-sub-inv_binary64_6864`
53×	`associate-/r/_binary64_6844`
52×	`sub-neg_binary64_6891`
49×	`distribute-rgt-neg-in_binary64_6856`
47×	`*-commutative_binary64_6829`
42×	`distribute-neg-in_binary64_6859`
41×	`div-sub_binary64_6903`
38×	`unswap-sqr_binary64_6866`
37×	`distribute-lft-neg-in_binary64_6855`
35×	`associate--l+_binary64_6835`
33×	`+-commutative_binary64_6828`
28×	`exp-prod_binary64_6950`
26×	`neg-mul-1_binary64_6894` `neg-sub0_binary64_6893`
23×	`sqr-pow_binary64_6870`
21×	`distribute-rgt-out_binary64_6851`
16×	`*-rgt-identity_binary64_6888` `associate-+l-_binary64_6833`
15×	`log-prod_binary64_6984` `distribute-neg-frac_binary64_6862`
12×	`cube-prod_binary64_6926` `associate-+r-_binary64_6832`
11×	`exp-sum_binary64_6944` `*-lft-identity_binary64_6887`
10×	`distribute-rgt-out--_binary64_6852`
8×	`cube-unmult_binary64_6935` `/-rgt-identity_binary64_6889` `swap-sqr_binary64_6865` `distribute-lft-neg-out_binary64_6857`
6×	`unsub-neg_binary64_6892` `distribute-lft-out_binary64_6849`
5×	`unpow3_binary64_6964` `pow-plus_binary64_6961` `cube-mult_binary64_6928`
3×	`log-div_binary64_6985` `rem-sqrt-square_binary64_6911` `distribute-rgt-neg-out_binary64_6858`
2×	`log-pow_binary64_6987` `unpow1/2_binary64_6962` `prod-exp_binary64_6947` `exp-diff_binary64_6946` `pow-sqr_binary64_6871` `associate--l-_binary64_6836`
1×	`unpow1/3_binary64_6965` `unpow2_binary64_6963` `unpow1_binary64_6956` `1-exp_binary64_6942` `exp-1-e_binary64_6941` `cube-div_binary64_6927` `rem-square-sqrt_binary64_6910` `distribute-lft-out--_binary64_6850` `associate--r-_binary64_6837`
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_7161` `erf-erfc_binary64_7160` `erf-odd_binary64_7159` `if-if-and-not_binary64_7158` `if-if-and_binary64_7157` `if-if-or-not_binary64_7156` `if-if-or_binary64_7155` `if-not_binary64_7154` `if-same_binary64_7153` `if-false_binary64_7152` `if-true_binary64_7151` `not-gte_binary64_7150` `not-lte_binary64_7149` `not-gt_binary64_7148` `not-lt_binary64_7147` `gte-same_binary64_7146` `lte-same_binary64_7145` `gt-same_binary64_7144` `lt-same_binary64_7143` `sinh---cosh_binary64_7090` `sinh-+-cosh_binary64_7089` `sinh-cosh_binary64_7088` `tanh-def-c_binary64_7087` `tanh-def-b_binary64_7086` `tanh-def-a_binary64_7085` `cosh-def_binary64_7084` `sinh-def_binary64_7083` `tan-neg_binary64_7030` `cos-neg_binary64_7029` `sin-neg_binary64_7028` `tan-0_binary64_7027` `cos-0_binary64_7026` `sin-0_binary64_7025` `hang-m-tan_binary64_7024` `hang-p-tan_binary64_7023` `hang-m0-tan_binary64_7022` `hang-p0-tan_binary64_7021` `hang-0m-tan_binary64_7020` `hang-0p-tan_binary64_7019` `tan-+PI/2_binary64_7018` `tan-+PI_binary64_7017` `tan-PI_binary64_7016` `tan-PI/3_binary64_7015` `tan-PI/4_binary64_7014` `tan-PI/6_binary64_7013` `cos-+PI/2_binary64_7012` `cos-+PI_binary64_7011` `cos-PI_binary64_7010` `cos-PI/2_binary64_7009` `cos-PI/3_binary64_7008` `cos-PI/4_binary64_7007` `cos-PI/6_binary64_7006` `sin-+PI/2_binary64_7005` `sin-+PI_binary64_7004` `sin-PI_binary64_7003` `sin-PI/2_binary64_7002` `sin-PI/3_binary64_7001` `sin-PI/4_binary64_7000` `sin-PI/6_binary64_6999` `sub-1-sin_binary64_6998` `sub-1-cos_binary64_6997` `-1-add-sin_binary64_6996` `-1-add-cos_binary64_6995` `1-sub-sin_binary64_6994` `1-sub-cos_binary64_6993` `cos-sin-sum_binary64_6992` `log-E_binary64_6988` `log-rec_binary64_6986` `pow-base-0_binary64_6982` `exp-to-pow_binary64_6960` `pow-base-1_binary64_6958` `unpow0_binary64_6957` `unpow-1_binary64_6955` `exp-lft-cube_binary64_6954` `exp-lft-sqr_binary64_6953` `exp-cbrt_binary64_6952` `exp-sqrt_binary64_6951` `div-exp_binary64_6949` `rec-exp_binary64_6948` `exp-neg_binary64_6945` `e-exp-1_binary64_6943` `exp-0_binary64_6940` `rem-log-exp_binary64_6939` `rem-exp-log_binary64_6938` `cube-neg_binary64_6925` `rem-3cbrt-rft_binary64_6924` `rem-3cbrt-lft_binary64_6923` `rem-cbrt-cube_binary64_6922` `rem-cube-cbrt_binary64_6921` `sqr-abs_binary64_6913` `sqr-neg_binary64_6912` `mul-1-neg_binary64_6890` `remove-double-neg_binary64_6886` `sub0-neg_binary64_6885` `--rgt-identity_binary64_6884` `+-rgt-identity_binary64_6883` `+-lft-identity_binary64_6882` `mul0-rgt_binary64_6881` `mul0-lft_binary64_6880` `div0_binary64_6879` `*-inverses_binary64_6878` `+-inverses_binary64_6877` `lft-mult-inverse_binary64_6876` `rgt-mult-inverse_binary64_6875` `remove-double-div_binary64_6874` `difference-of-sqr--1_binary64_6869` `difference-of-sqr-1_binary64_6868` `difference-of-squares_binary64_6867` `cancel-sign-sub_binary64_6863` `distribute-frac-neg_binary64_6861` `distribute-neg-out_binary64_6860` `distribute-rgt1-in_binary64_6854` `distribute-lft1-in_binary64_6853` `count-2_binary64_6846`

Counts

127 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	165	2461
1	407	2351
2	1251	2346
3	4881	2304
4	5604	2304

prune122.0ms (3.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	91	3	94

Error

Counts

94 → 3

Compiler

Compiled 1957 to 1536 computations (21.5% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) (pow.f64 x 3))
0.2b	(*.f64 x (+.f64 x 1/3))
0.5b	(.f64 (+.f64 (.f64 x (+.f64 x 1/3)) 1/9) (+.f64 (pow.f64 x 3) 1/27))
26.8b	(/.f64 (-.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (.f64 1/27 1/27)) (.f64 (+.f64 (.f64 x (+.f64 x 1/3)) 1/9) (+.f64 (pow.f64 x 3) 1/27)))

rewrite488.0ms (15.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

54×	`add-sqr-sqrt_binary64_6920`
30×	`*-un-lft-identity_binary64_6898`
26×	`add-cube-cbrt_binary64_6933` `unpow-prod-down_binary64_6977` `cube-prod_binary64_6926`
25×	`add-exp-log_binary64_6936`
20×	`associate-r_binary64_6838`
18×	`unswap-sqr_binary64_6866` `associate-l_binary64_6839` `swap-sqr_binary64_6865`
15×	`add-cbrt-cube_binary64_6934`
13×	`flip3-+_binary64_6901` `flip-+_binary64_6872`
12×	`prod-exp_binary64_6947` `sqr-pow_binary64_6870`
8×	`pow1_binary64_6959` `frac-times_binary64_6908` `associate-/r/_binary64_6844`
6×	`associate-*r/_binary64_6840` `pow-to-exp_binary64_6967` `pow-exp_binary64_6966`
4×	`add-log-exp_binary64_6937` `cbrt-unprod_binary64_6931` `times-frac_binary64_6904` `associate-l/_binary64_6841` `associate-/l_binary64_6843` `unpow3_binary64_6964` `cube-mult_binary64_6928`
3×	`pow-prod-down_binary64_6969` `*-commutative_binary64_6829`
2×	`div-exp_binary64_6949` `cbrt-undiv_binary64_6932` `difference-of-squares_binary64_6867` `associate-/l/_binary64_6845` `distribute-rgt-in_binary64_6848` `distribute-lft-in_binary64_6847` `distribute-lft-out_binary64_6849`
1×	`frac-2neg_binary64_6909` `div-sub_binary64_6903` `clear-num_binary64_6897` `div-inv_binary64_6895` `flip3--_binary64_6902` `flip--_binary64_6873` `associate-/r*_binary64_6842` `pow2_binary64_6979` `pow-prod-up_binary64_6968` `pow-sqr_binary64_6871`

Counts

4 → 166

Calls

4 calls:

26.0ms	(/.f64 (-.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (.f64 1/27 1/27)) (.f64 (+.f64 (.f64 x (+.f64 x 1/3)) 1/9) (+.f64 (pow.f64 x 3) 1/27)))
19.0ms	(.f64 (+.f64 (.f64 x (+.f64 x 1/3)) 1/9) (+.f64 (pow.f64 x 3) 1/27))
11.0ms	(*.f64 (pow.f64 x 3) (pow.f64 x 3))
7.0ms	(*.f64 x (+.f64 x 1/3))

Compiler

Compiled 6039 to 4736 computations (21.6% saved)

series388.0ms (12.1%)

Error

Counts

4 → 27

Calls

4 calls:

176.0ms	(/.f64 (-.f64 (.f64 (pow.f64 x 3) (pow.f64 x 3)) (.f64 1/27 1/27)) (.f64 (+.f64 (.f64 x (+.f64 x 1/3)) 1/9) (+.f64 (pow.f64 x 3) 1/27)))
63.0ms	(.f64 (+.f64 (.f64 x (+.f64 x 1/3)) 1/9) (+.f64 (pow.f64 x 3) 1/27))
59.0ms	(*.f64 x (+.f64 x 1/3))
56.0ms	(*.f64 (pow.f64 x 3) (pow.f64 x 3))

Compiler

Compiled 1151 to 970 computations (15.7% saved)

simplify146.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

377×	`associate-l_binary64_6839`
319×	`associate-r_binary64_6838`
311×	`log-prod_binary64_6984`
207×	`distribute-rgt-in_binary64_6848`
196×	`distribute-lft-in_binary64_6847`
149×	`cancel-sign-sub-inv_binary64_6864`
145×	`associate-/l/_binary64_6845`
128×	`*-commutative_binary64_6829`
123×	`exp-prod_binary64_6950` `distribute-rgt-neg-in_binary64_6856`
111×	`distribute-lft-neg-in_binary64_6855`
107×	`associate-/r*_binary64_6842`
99×	`distribute-rgt-out_binary64_6851`
93×	`distribute-lft-out_binary64_6849`
85×	`associate-/r/_binary64_6844`
84×	`times-frac_binary64_6904`
74×	`cube-prod_binary64_6926`
72×	`associate-/l*_binary64_6843`
68×	`swap-sqr_binary64_6865`
60×	`sqr-pow_binary64_6870`
54×	`unswap-sqr_binary64_6866`
51×	`+-commutative_binary64_6828`
48×	`sub-neg_binary64_6891`
43×	`div-sub_binary64_6903`
38×	`distribute-neg-in_binary64_6859`
36×	`log-pow_binary64_6987`
33×	`neg-mul-1_binary64_6894` `neg-sub0_binary64_6893`
31×	`distribute-neg-frac_binary64_6862`
30×	`*-lft-identity_binary64_6887`
29×	`exp-sum_binary64_6944`
27×	`*-rgt-identity_binary64_6888` `associate-+l+_binary64_6831`
24×	`associate-+r+_binary64_6830`
19×	`pow-plus_binary64_6961`
18×	`log-div_binary64_6985`
17×	`/-rgt-identity_binary64_6889`
16×	`pow-sqr_binary64_6871` `distribute-rgt-out--_binary64_6852`
15×	`cube-unmult_binary64_6935`
13×	`associate-*l/_binary64_6841`
11×	`associate-*r/_binary64_6840`
10×	`rem-sqrt-square_binary64_6911` `distribute-lft-out--_binary64_6850`
9×	`unpow3_binary64_6964`
7×	`unsub-neg_binary64_6892`
6×	`cube-mult_binary64_6928` `distribute-lft-neg-out_binary64_6857` `count-2_binary64_6846`
4×	`distribute-rgt-neg-out_binary64_6858` `associate--r+_binary64_6834`
3×	`associate--l+_binary64_6835`
2×	`cube-div_binary64_6927` `rem-square-sqrt_binary64_6910` `associate-+l-_binary64_6833` `associate-+r-_binary64_6832`
1×	`unpow2_binary64_6963` `unpow1/2_binary64_6962` `unpow1_binary64_6956` `exp-diff_binary64_6946` `1-exp_binary64_6942` `exp-1-e_binary64_6941` `rem-cbrt-cube_binary64_6922` `rem-cube-cbrt_binary64_6921` `*-inverses_binary64_6878` `associate--r-_binary64_6837`
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_7161` `erf-erfc_binary64_7160` `erf-odd_binary64_7159` `if-if-and-not_binary64_7158` `if-if-and_binary64_7157` `if-if-or-not_binary64_7156` `if-if-or_binary64_7155` `if-not_binary64_7154` `if-same_binary64_7153` `if-false_binary64_7152` `if-true_binary64_7151` `not-gte_binary64_7150` `not-lte_binary64_7149` `not-gt_binary64_7148` `not-lt_binary64_7147` `gte-same_binary64_7146` `lte-same_binary64_7145` `gt-same_binary64_7144` `lt-same_binary64_7143` `sinh---cosh_binary64_7090` `sinh-+-cosh_binary64_7089` `sinh-cosh_binary64_7088` `tanh-def-c_binary64_7087` `tanh-def-b_binary64_7086` `tanh-def-a_binary64_7085` `cosh-def_binary64_7084` `sinh-def_binary64_7083` `tan-neg_binary64_7030` `cos-neg_binary64_7029` `sin-neg_binary64_7028` `tan-0_binary64_7027` `cos-0_binary64_7026` `sin-0_binary64_7025` `hang-m-tan_binary64_7024` `hang-p-tan_binary64_7023` `hang-m0-tan_binary64_7022` `hang-p0-tan_binary64_7021` `hang-0m-tan_binary64_7020` `hang-0p-tan_binary64_7019` `tan-+PI/2_binary64_7018` `tan-+PI_binary64_7017` `tan-PI_binary64_7016` `tan-PI/3_binary64_7015` `tan-PI/4_binary64_7014` `tan-PI/6_binary64_7013` `cos-+PI/2_binary64_7012` `cos-+PI_binary64_7011` `cos-PI_binary64_7010` `cos-PI/2_binary64_7009` `cos-PI/3_binary64_7008` `cos-PI/4_binary64_7007` `cos-PI/6_binary64_7006` `sin-+PI/2_binary64_7005` `sin-+PI_binary64_7004` `sin-PI_binary64_7003` `sin-PI/2_binary64_7002` `sin-PI/3_binary64_7001` `sin-PI/4_binary64_7000` `sin-PI/6_binary64_6999` `sub-1-sin_binary64_6998` `sub-1-cos_binary64_6997` `-1-add-sin_binary64_6996` `-1-add-cos_binary64_6995` `1-sub-sin_binary64_6994` `1-sub-cos_binary64_6993` `cos-sin-sum_binary64_6992` `log-E_binary64_6988` `log-rec_binary64_6986` `pow-base-0_binary64_6982` `unpow1/3_binary64_6965` `exp-to-pow_binary64_6960` `pow-base-1_binary64_6958` `unpow0_binary64_6957` `unpow-1_binary64_6955` `exp-lft-cube_binary64_6954` `exp-lft-sqr_binary64_6953` `exp-cbrt_binary64_6952` `exp-sqrt_binary64_6951` `div-exp_binary64_6949` `rec-exp_binary64_6948` `prod-exp_binary64_6947` `exp-neg_binary64_6945` `e-exp-1_binary64_6943` `exp-0_binary64_6940` `rem-log-exp_binary64_6939` `rem-exp-log_binary64_6938` `cube-neg_binary64_6925` `rem-3cbrt-rft_binary64_6924` `rem-3cbrt-lft_binary64_6923` `sqr-abs_binary64_6913` `sqr-neg_binary64_6912` `mul-1-neg_binary64_6890` `remove-double-neg_binary64_6886` `sub0-neg_binary64_6885` `--rgt-identity_binary64_6884` `+-rgt-identity_binary64_6883` `+-lft-identity_binary64_6882` `mul0-rgt_binary64_6881` `mul0-lft_binary64_6880` `div0_binary64_6879` `+-inverses_binary64_6877` `lft-mult-inverse_binary64_6876` `rgt-mult-inverse_binary64_6875` `remove-double-div_binary64_6874` `difference-of-sqr--1_binary64_6869` `difference-of-sqr-1_binary64_6868` `difference-of-squares_binary64_6867` `cancel-sign-sub_binary64_6863` `distribute-frac-neg_binary64_6861` `distribute-neg-out_binary64_6860` `distribute-rgt1-in_binary64_6854` `distribute-lft1-in_binary64_6853` `associate--l-_binary64_6836`

Counts

193 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	3410
1	659	3017
2	3030	2931
3	4753	2931
4	5023	2931

prune311.0ms (9.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	162	3	165

Error

Counts

165 → 3

Compiler

Compiled 4629 to 3636 computations (21.5% saved)

regimes234.0ms (7.3%)

Accuracy

Total 0.0b remaining (94%)

Threshold costs 0.0b (94%)

Compiler

Compiled 298 to 268 computations (10.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`sub-neg_binary64_6891` `+-commutative_binary64_6828`
1×	`1-exp_binary64_6942` `neg-mul-1_binary64_6894` `neg-sub0_binary64_6893` `*-commutative_binary64_6829`
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_7158` `if-if-and_binary64_7157` `if-if-or-not_binary64_7156` `if-if-or_binary64_7155` `if-not_binary64_7154` `if-same_binary64_7153` `if-false_binary64_7152` `if-true_binary64_7151` `tan-0_binary64_7027` `cos-0_binary64_7026` `sin-0_binary64_7025` `unpow1_binary64_6956` `e-exp-1_binary64_6943` `exp-1-e_binary64_6941` `exp-0_binary64_6940` `sqr-abs_binary64_6913` `sqr-neg_binary64_6912` `unsub-neg_binary64_6892` `mul-1-neg_binary64_6890` `/-rgt-identity_binary64_6889` `-rgt-identity_binary64_6888` `-lft-identity_binary64_6887` `remove-double-neg_binary64_6886` `sub0-neg_binary64_6885` `--rgt-identity_binary64_6884` `+-rgt-identity_binary64_6883` `+-lft-identity_binary64_6882` `cancel-sign-sub-inv_binary64_6864` `cancel-sign-sub_binary64_6863` `distribute-neg-frac_binary64_6862` `distribute-frac-neg_binary64_6861` `distribute-neg-out_binary64_6860` `distribute-neg-in_binary64_6859` `distribute-rgt-neg-out_binary64_6858` `distribute-lft-neg-out_binary64_6857` `distribute-rgt-neg-in_binary64_6856` `distribute-lft-neg-in_binary64_6855`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	11	4
2	15	4
3	17	4
4	18	4
5	16	4

end0.0ms (0%)

sample540.0ms (16.8%)

Algorithm

1×

intervals

Results

140.0ms

8000×

body

128

valid

Compiler

Compiled 152 to 138 computations (9.2% saved)

Details

analyze149.0ms (4.6%)

sample11.0ms (0.4%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

rewrite18.0ms (0.5%)

series29.0ms (0.9%)

simplify108.0ms (3.4%)

prune12.0ms (0.4%)

localize8.0ms (0.3%)

rewrite192.0ms (6%)

series320.0ms (9.9%)

simplify110.0ms (3.4%)

prune122.0ms (3.8%)

localize14.0ms (0.4%)

rewrite488.0ms (15.2%)

series388.0ms (12.1%)

simplify146.0ms (4.5%)

prune311.0ms (9.7%)

regimes234.0ms (7.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample540.0ms (16.8%)

Profiling