Details

analyze68.0ms (1.1%)

Algorithm

1×

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
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample19.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	8×	body	128	nan

Compiler

Compiled 13 to 13 computations (0% saved)

simplify148.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1× +-commutative_binary64_21832

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_22165 erf-erfc_binary64_22164 erf-odd_binary64_22163 if-if-and-not_binary64_22162 if-if-and_binary64_22161 if-if-or-not_binary64_22160 if-if-or_binary64_22159 if-not_binary64_22158 if-same_binary64_22157 if-false_binary64_22156 if-true_binary64_22155 not-gte_binary64_22154 not-lte_binary64_22153 not-gt_binary64_22152 not-lt_binary64_22151 gte-same_binary64_22150 lte-same_binary64_22149 gt-same_binary64_22148 lt-same_binary64_22147 sinh---cosh_binary64_22094 sinh-+-cosh_binary64_22093 sinh-cosh_binary64_22092 tanh-def-c_binary64_22091 tanh-def-b_binary64_22090 tanh-def-a_binary64_22089 cosh-def_binary64_22088 sinh-def_binary64_22087 tan-neg_binary64_22034 cos-neg_binary64_22033 sin-neg_binary64_22032 tan-0_binary64_22031 cos-0_binary64_22030 sin-0_binary64_22029 hang-m-tan_binary64_22028 hang-p-tan_binary64_22027 hang-m0-tan_binary64_22026 hang-p0-tan_binary64_22025 hang-0m-tan_binary64_22024 hang-0p-tan_binary64_22023 tan-+PI/2_binary64_22022 tan-+PI_binary64_22021 tan-PI_binary64_22020 tan-PI/3_binary64_22019 tan-PI/4_binary64_22018 tan-PI/6_binary64_22017 cos-+PI/2_binary64_22016 cos-+PI_binary64_22015 cos-PI_binary64_22014 cos-PI/2_binary64_22013 cos-PI/3_binary64_22012 cos-PI/4_binary64_22011 cos-PI/6_binary64_22010 sin-+PI/2_binary64_22009 sin-+PI_binary64_22008 sin-PI_binary64_22007 sin-PI/2_binary64_22006 sin-PI/3_binary64_22005 sin-PI/4_binary64_22004 sin-PI/6_binary64_22003 sub-1-sin_binary64_22002 sub-1-cos_binary64_22001 -1-add-sin_binary64_22000 -1-add-cos_binary64_21999 1-sub-sin_binary64_21998 1-sub-cos_binary64_21997 cos-sin-sum_binary64_21996 log-E_binary64_21992 log-pow_binary64_21991 log-rec_binary64_21990 log-div_binary64_21989 log-prod_binary64_21988 pow-base-0_binary64_21986 unpow1/3_binary64_21969 unpow3_binary64_21968 unpow2_binary64_21967 unpow1/2_binary64_21966 pow-plus_binary64_21965 exp-to-pow_binary64_21964 pow-base-1_binary64_21962 unpow0_binary64_21961 unpow1_binary64_21960 unpow-1_binary64_21959 exp-lft-cube_binary64_21958 exp-lft-sqr_binary64_21957 exp-cbrt_binary64_21956 exp-sqrt_binary64_21955 exp-prod_binary64_21954 div-exp_binary64_21953 rec-exp_binary64_21952 prod-exp_binary64_21951 exp-diff_binary64_21950 exp-neg_binary64_21949 exp-sum_binary64_21948 e-exp-1_binary64_21947 1-exp_binary64_21946 exp-1-e_binary64_21945 exp-0_binary64_21944 rem-log-exp_binary64_21943 rem-exp-log_binary64_21942 cube-unmult_binary64_21939 cube-mult_binary64_21932 cube-div_binary64_21931 cube-prod_binary64_21930 cube-neg_binary64_21929 rem-3cbrt-rft_binary64_21928 rem-3cbrt-lft_binary64_21927 rem-cbrt-cube_binary64_21926 rem-cube-cbrt_binary64_21925 sqr-abs_binary64_21917 sqr-neg_binary64_21916 rem-sqrt-square_binary64_21915 rem-square-sqrt_binary64_21914 times-frac_binary64_21908 div-sub_binary64_21907 neg-mul-1_binary64_21898 neg-sub0_binary64_21897 unsub-neg_binary64_21896 sub-neg_binary64_21895 mul-1-neg_binary64_21894 /-rgt-identity_binary64_21893 *-rgt-identity_binary64_21892 *-lft-identity_binary64_21891 remove-double-neg_binary64_21890 sub0-neg_binary64_21889 --rgt-identity_binary64_21888 +-rgt-identity_binary64_21887 +-lft-identity_binary64_21886 mul0-rgt_binary64_21885 mul0-lft_binary64_21884 div0_binary64_21883 *-inverses_binary64_21882 +-inverses_binary64_21881 lft-mult-inverse_binary64_21880 rgt-mult-inverse_binary64_21879 remove-double-div_binary64_21878 pow-sqr_binary64_21875 sqr-pow_binary64_21874 difference-of-sqr--1_binary64_21873 difference-of-sqr-1_binary64_21872 difference-of-squares_binary64_21871 unswap-sqr_binary64_21870 swap-sqr_binary64_21869 cancel-sign-sub-inv_binary64_21868 cancel-sign-sub_binary64_21867 distribute-neg-frac_binary64_21866 distribute-frac-neg_binary64_21865 distribute-neg-out_binary64_21864 distribute-neg-in_binary64_21863 distribute-rgt-neg-out_binary64_21862 distribute-lft-neg-out_binary64_21861 distribute-rgt-neg-in_binary64_21860 distribute-lft-neg-in_binary64_21859 distribute-rgt1-in_binary64_21858 distribute-lft1-in_binary64_21857 distribute-rgt-out--_binary64_21856 distribute-rgt-out_binary64_21855 distribute-lft-out--_binary64_21854 distribute-lft-out_binary64_21853 distribute-rgt-in_binary64_21852 distribute-lft-in_binary64_21851 count-2_binary64_21850 associate-/l/_binary64_21849 associate-/r/_binary64_21848 associate-/l*_binary64_21847 associate-/r*_binary64_21846 associate-*l/_binary64_21845 associate-*r/_binary64_21844 associate-*l*_binary64_21843 associate-*r*_binary64_21842 associate--r-_binary64_21841 associate--l-_binary64_21840 associate--l+_binary64_21839 associate--r+_binary64_21838 associate-+l-_binary64_21837 associate-+r-_binary64_21836 associate-+l+_binary64_21835 associate-+r+_binary64_21834 *-commutative_binary64_21833

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	7	9

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

20.1b

Counts

1 → 1

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) y)
18.7b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

20.1b

Rules

4×	`add-log-exp_binary64_21941` `add-sqr-sqrt_binary64_21924`
3×	`pow1_binary64_21963` `add-cube-cbrt_binary64_21937` `sqrt-prod_binary64_21918` `*-un-lft-identity_binary64_21902`
2×	`add-exp-log_binary64_21940` `add-cbrt-cube_binary64_21938` `flip3-+_binary64_21905` `sqrt-div_binary64_21919` `flip-+_binary64_21876`
1×	`pow1/2_binary64_21982` `sqrt-pow1_binary64_21920` `rem-sqrt-square_binary64_21915` `sum-log_binary64_21993` `+-commutative_binary64_21832`

Counts

2 → 26

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
4.0ms	(+.f64 (*.f64 x x) y)

Compiler

Compiled 355 to 89 computations (74.9% saved)

series219.0ms (3.5%)

Error

0.0b

Counts

2 → 27

Calls

2 calls:

113.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
88.0ms	(+.f64 (*.f64 x x) y)

Compiler

Compiled 563 to 464 computations (17.6% saved)

simplify109.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

828×	`times-frac_binary64_21908`
437×	`associate-/l*_binary64_21847`
339×	`cancel-sign-sub-inv_binary64_21868`
212×	`unswap-sqr_binary64_21870`
207×	`distribute-rgt-in_binary64_21852`
178×	`distribute-lft-in_binary64_21851`
160×	`associate-l_binary64_21843`
153×	`associate-r_binary64_21842`
148×	`distribute-rgt-neg-in_binary64_21860`
143×	`distribute-lft-neg-in_binary64_21859`
106×	`distribute-neg-frac_binary64_21866`
101×	`sub-neg_binary64_21895` `associate-/l/_binary64_21849`
100×	`associate-/r/_binary64_21848`
91×	`distribute-rgt-out_binary64_21855`
74×	`sqr-pow_binary64_21874`
66×	`distribute-lft-out_binary64_21853`
60×	`*-commutative_binary64_21833`
54×	`neg-sub0_binary64_21897`
51×	`neg-mul-1_binary64_21898`
47×	`pow-sqr_binary64_21875`
44×	`associate-/r*_binary64_21846`
32×	`+-commutative_binary64_21832`
29×	`associate-+l+_binary64_21835`
28×	`pow-plus_binary64_21965`
27×	`associate-*l/_binary64_21845`
26×	`distribute-lft-neg-out_binary64_21861`
25×	`associate-*r/_binary64_21844`
22×	`associate-+l-_binary64_21837`
20×	`distribute-neg-in_binary64_21863`
19×	`unsub-neg_binary64_21896` `associate-+r-_binary64_21836`
18×	`associate-+r+_binary64_21834`
17×	`+-rgt-identity_binary64_21887`
15×	`distribute-rgt-neg-out_binary64_21862` `associate--r+_binary64_21838`
13×	`div-sub_binary64_21907` `distribute-rgt-out--_binary64_21856`
11×	`sub0-neg_binary64_21889`
10×	`cube-unmult_binary64_21939`
8×	`exp-prod_binary64_21954` `difference-of-squares_binary64_21871` `associate--l+_binary64_21839`
7×	`cube-prod_binary64_21930`
5×	`unpow3_binary64_21968` `cancel-sign-sub_binary64_21867` `distribute-lft-out--_binary64_21854`
3×	`cube-mult_binary64_21932` `rem-sqrt-square_binary64_21915` `count-2_binary64_21850`
2×	`unpow2_binary64_21967` `unpow1_binary64_21960` `swap-sqr_binary64_21869` `associate--l-_binary64_21840`
1×	`log-prod_binary64_21988` `prod-exp_binary64_21951` `1-exp_binary64_21946` `rem-square-sqrt_binary64_21914` `mul-1-neg_binary64_21894` `-rgt-identity_binary64_21892` `-inverses_binary64_21882` `rgt-mult-inverse_binary64_21879` `distribute-neg-out_binary64_21864` `distribute-rgt1-in_binary64_21858`
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_22165` `erf-erfc_binary64_22164` `erf-odd_binary64_22163` `if-if-and-not_binary64_22162` `if-if-and_binary64_22161` `if-if-or-not_binary64_22160` `if-if-or_binary64_22159` `if-not_binary64_22158` `if-same_binary64_22157` `if-false_binary64_22156` `if-true_binary64_22155` `not-gte_binary64_22154` `not-lte_binary64_22153` `not-gt_binary64_22152` `not-lt_binary64_22151` `gte-same_binary64_22150` `lte-same_binary64_22149` `gt-same_binary64_22148` `lt-same_binary64_22147` `sinh---cosh_binary64_22094` `sinh-+-cosh_binary64_22093` `sinh-cosh_binary64_22092` `tanh-def-c_binary64_22091` `tanh-def-b_binary64_22090` `tanh-def-a_binary64_22089` `cosh-def_binary64_22088` `sinh-def_binary64_22087` `tan-neg_binary64_22034` `cos-neg_binary64_22033` `sin-neg_binary64_22032` `tan-0_binary64_22031` `cos-0_binary64_22030` `sin-0_binary64_22029` `hang-m-tan_binary64_22028` `hang-p-tan_binary64_22027` `hang-m0-tan_binary64_22026` `hang-p0-tan_binary64_22025` `hang-0m-tan_binary64_22024` `hang-0p-tan_binary64_22023` `tan-+PI/2_binary64_22022` `tan-+PI_binary64_22021` `tan-PI_binary64_22020` `tan-PI/3_binary64_22019` `tan-PI/4_binary64_22018` `tan-PI/6_binary64_22017` `cos-+PI/2_binary64_22016` `cos-+PI_binary64_22015` `cos-PI_binary64_22014` `cos-PI/2_binary64_22013` `cos-PI/3_binary64_22012` `cos-PI/4_binary64_22011` `cos-PI/6_binary64_22010` `sin-+PI/2_binary64_22009` `sin-+PI_binary64_22008` `sin-PI_binary64_22007` `sin-PI/2_binary64_22006` `sin-PI/3_binary64_22005` `sin-PI/4_binary64_22004` `sin-PI/6_binary64_22003` `sub-1-sin_binary64_22002` `sub-1-cos_binary64_22001` `-1-add-sin_binary64_22000` `-1-add-cos_binary64_21999` `1-sub-sin_binary64_21998` `1-sub-cos_binary64_21997` `cos-sin-sum_binary64_21996` `log-E_binary64_21992` `log-pow_binary64_21991` `log-rec_binary64_21990` `log-div_binary64_21989` `pow-base-0_binary64_21986` `unpow1/3_binary64_21969` `unpow1/2_binary64_21966` `exp-to-pow_binary64_21964` `pow-base-1_binary64_21962` `unpow0_binary64_21961` `unpow-1_binary64_21959` `exp-lft-cube_binary64_21958` `exp-lft-sqr_binary64_21957` `exp-cbrt_binary64_21956` `exp-sqrt_binary64_21955` `div-exp_binary64_21953` `rec-exp_binary64_21952` `exp-diff_binary64_21950` `exp-neg_binary64_21949` `exp-sum_binary64_21948` `e-exp-1_binary64_21947` `exp-1-e_binary64_21945` `exp-0_binary64_21944` `rem-log-exp_binary64_21943` `rem-exp-log_binary64_21942` `cube-div_binary64_21931` `cube-neg_binary64_21929` `rem-3cbrt-rft_binary64_21928` `rem-3cbrt-lft_binary64_21927` `rem-cbrt-cube_binary64_21926` `rem-cube-cbrt_binary64_21925` `sqr-abs_binary64_21917` `sqr-neg_binary64_21916` `/-rgt-identity_binary64_21893` `*-lft-identity_binary64_21891` `remove-double-neg_binary64_21890` `--rgt-identity_binary64_21888` `+-lft-identity_binary64_21886` `mul0-rgt_binary64_21885` `mul0-lft_binary64_21884` `div0_binary64_21883` `+-inverses_binary64_21881` `lft-mult-inverse_binary64_21880` `remove-double-div_binary64_21878` `difference-of-sqr--1_binary64_21873` `difference-of-sqr-1_binary64_21872` `distribute-frac-neg_binary64_21865` `distribute-lft1-in_binary64_21857` `associate--r-_binary64_21841`

Counts

53 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	644
1	196	623
2	595	623
3	1643	611

prune83.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Error

Counts

90 → 4

Compiler

Compiled 1556 to 590 computations (62.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) y))) (sqrt.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
18.7b	(sqrt.f64 (+.f64 y (*.f64 x x)))
18.7b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite142.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

52×	`sqrt-prod_binary64_21918`
36×	`add-sqr-sqrt_binary64_21924`
32×	`sqrt-div_binary64_21919`
14×	`pow1_binary64_21963` `add-cube-cbrt_binary64_21937` `sqrt-pow1_binary64_21920` `*-un-lft-identity_binary64_21902`
9×	`flip3-+_binary64_21905` `flip-+_binary64_21876` `unswap-sqr_binary64_21870` `associate-l_binary64_21843` `associate-r_binary64_21842`
8×	`pow1/2_binary64_21982`
6×	`add-exp-log_binary64_21940` `add-cbrt-cube_binary64_21938`
5×	`pow-prod-down_binary64_21973`
4×	`add-log-exp_binary64_21941` `rem-sqrt-square_binary64_21915` `frac-times_binary64_21912`
2×	`associate-l/_binary64_21845` `associate-r/_binary64_21844`
1×	`prod-exp_binary64_21951` `cbrt-unprod_binary64_21935` `sqrt-unprod_binary64_21922` `*-commutative_binary64_21833`

Counts

4 → 102

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) y))) (sqrt.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
7.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
3.0ms	(sqrt.f64 (+.f64 y (*.f64 x x)))

Compiler

Compiled 2661 to 390 computations (85.3% saved)

series622.0ms (10%)

Error

Counts

4 → 56

Calls

4 calls:

172.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 x x) y))) (sqrt.f64 (sqrt.f64 (+.f64 y (*.f64 x x)))))
172.0ms	(sqrt.f64 (sqrt.f64 (+.f64 (*.f64 x x) y)))
114.0ms	(sqrt.f64 (+.f64 y (*.f64 x x)))
111.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 2528 to 1749 computations (30.8% saved)

simplify474.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

522×	`cancel-sign-sub-inv_binary64_21868`
344×	`associate-r_binary64_21842`
327×	`associate-l_binary64_21843`
325×	`unswap-sqr_binary64_21870`
154×	`distribute-neg-frac_binary64_21866`
151×	`times-frac_binary64_21908`
145×	`sub-neg_binary64_21895`
141×	`associate-/l_binary64_21847` `-commutative_binary64_21833`
116×	`associate-/r*_binary64_21846`
107×	`sqr-pow_binary64_21874`
84×	`associate-*r/_binary64_21844`
83×	`associate-*l/_binary64_21845`
76×	`neg-sub0_binary64_21897`
70×	`neg-mul-1_binary64_21898`
66×	`pow-sqr_binary64_21875`
61×	`distribute-rgt-neg-in_binary64_21860`
58×	`distribute-rgt-in_binary64_21852`
52×	`+-commutative_binary64_21832`
47×	`distribute-lft-neg-in_binary64_21859`
43×	`associate-/r/_binary64_21848`
39×	`distribute-lft-in_binary64_21851` `associate-+l+_binary64_21835`
31×	`pow-plus_binary64_21965`
30×	`associate-+l-_binary64_21837`
28×	`associate-+r-_binary64_21836`
27×	`exp-prod_binary64_21954` `unsub-neg_binary64_21896`
26×	`associate-+r+_binary64_21834`
25×	`div-sub_binary64_21907`
22×	`*-rgt-identity_binary64_21892` `+-rgt-identity_binary64_21887`
18×	`log-prod_binary64_21988` `cube-prod_binary64_21930` `*-lft-identity_binary64_21891` `distribute-lft-neg-out_binary64_21861`
17×	`exp-sum_binary64_21948` `associate--l+_binary64_21839` `associate--r+_binary64_21838`
15×	`sub0-neg_binary64_21889`
14×	`cube-unmult_binary64_21939`
12×	`rem-sqrt-square_binary64_21915` `swap-sqr_binary64_21869` `distribute-neg-in_binary64_21863` `associate-/l/_binary64_21849`
10×	`difference-of-squares_binary64_21871`
9×	`log-div_binary64_21989` `exp-diff_binary64_21950`
8×	`exp-sqrt_binary64_21955`
7×	`cube-div_binary64_21931` `rem-square-sqrt_binary64_21914` `distribute-rgt-out--_binary64_21856` `distribute-rgt-out_binary64_21855`
6×	`unpow3_binary64_21968`
5×	`cancel-sign-sub_binary64_21867`
4×	`distribute-lft-out_binary64_21853`
3×	`rem-exp-log_binary64_21942` `cube-mult_binary64_21932` `distribute-rgt-neg-out_binary64_21862`
2×	`log-pow_binary64_21991` `unpow2_binary64_21967` `exp-to-pow_binary64_21964` `unpow1_binary64_21960` `exp-neg_binary64_21949` `mul0-rgt_binary64_21885` `mul0-lft_binary64_21884` `associate--r-_binary64_21841` `associate--l-_binary64_21840`
1×	`exp-lft-sqr_binary64_21957` `prod-exp_binary64_21951` `1-exp_binary64_21946` `exp-1-e_binary64_21945` `rem-log-exp_binary64_21943` `mul-1-neg_binary64_21894` `/-rgt-identity_binary64_21893` `remove-double-neg_binary64_21890` `*-inverses_binary64_21882` `+-inverses_binary64_21881` `rgt-mult-inverse_binary64_21879` `distribute-lft-out--_binary64_21854` `count-2_binary64_21850`
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_22165` `erf-erfc_binary64_22164` `erf-odd_binary64_22163` `if-if-and-not_binary64_22162` `if-if-and_binary64_22161` `if-if-or-not_binary64_22160` `if-if-or_binary64_22159` `if-not_binary64_22158` `if-same_binary64_22157` `if-false_binary64_22156` `if-true_binary64_22155` `not-gte_binary64_22154` `not-lte_binary64_22153` `not-gt_binary64_22152` `not-lt_binary64_22151` `gte-same_binary64_22150` `lte-same_binary64_22149` `gt-same_binary64_22148` `lt-same_binary64_22147` `sinh---cosh_binary64_22094` `sinh-+-cosh_binary64_22093` `sinh-cosh_binary64_22092` `tanh-def-c_binary64_22091` `tanh-def-b_binary64_22090` `tanh-def-a_binary64_22089` `cosh-def_binary64_22088` `sinh-def_binary64_22087` `tan-neg_binary64_22034` `cos-neg_binary64_22033` `sin-neg_binary64_22032` `tan-0_binary64_22031` `cos-0_binary64_22030` `sin-0_binary64_22029` `hang-m-tan_binary64_22028` `hang-p-tan_binary64_22027` `hang-m0-tan_binary64_22026` `hang-p0-tan_binary64_22025` `hang-0m-tan_binary64_22024` `hang-0p-tan_binary64_22023` `tan-+PI/2_binary64_22022` `tan-+PI_binary64_22021` `tan-PI_binary64_22020` `tan-PI/3_binary64_22019` `tan-PI/4_binary64_22018` `tan-PI/6_binary64_22017` `cos-+PI/2_binary64_22016` `cos-+PI_binary64_22015` `cos-PI_binary64_22014` `cos-PI/2_binary64_22013` `cos-PI/3_binary64_22012` `cos-PI/4_binary64_22011` `cos-PI/6_binary64_22010` `sin-+PI/2_binary64_22009` `sin-+PI_binary64_22008` `sin-PI_binary64_22007` `sin-PI/2_binary64_22006` `sin-PI/3_binary64_22005` `sin-PI/4_binary64_22004` `sin-PI/6_binary64_22003` `sub-1-sin_binary64_22002` `sub-1-cos_binary64_22001` `-1-add-sin_binary64_22000` `-1-add-cos_binary64_21999` `1-sub-sin_binary64_21998` `1-sub-cos_binary64_21997` `cos-sin-sum_binary64_21996` `log-E_binary64_21992` `log-rec_binary64_21990` `pow-base-0_binary64_21986` `unpow1/3_binary64_21969` `unpow1/2_binary64_21966` `pow-base-1_binary64_21962` `unpow0_binary64_21961` `unpow-1_binary64_21959` `exp-lft-cube_binary64_21958` `exp-cbrt_binary64_21956` `div-exp_binary64_21953` `rec-exp_binary64_21952` `e-exp-1_binary64_21947` `exp-0_binary64_21944` `cube-neg_binary64_21929` `rem-3cbrt-rft_binary64_21928` `rem-3cbrt-lft_binary64_21927` `rem-cbrt-cube_binary64_21926` `rem-cube-cbrt_binary64_21925` `sqr-abs_binary64_21917` `sqr-neg_binary64_21916` `--rgt-identity_binary64_21888` `+-lft-identity_binary64_21886` `div0_binary64_21883` `lft-mult-inverse_binary64_21880` `remove-double-div_binary64_21878` `difference-of-sqr--1_binary64_21873` `difference-of-sqr-1_binary64_21872` `distribute-frac-neg_binary64_21865` `distribute-neg-out_binary64_21864` `distribute-rgt1-in_binary64_21858` `distribute-lft1-in_binary64_21857`

Counts

158 → 304

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2779
1	367	2747
2	1087	2685
3	3204	2685

prune382.0ms (6.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	304	0	304
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	304	4	308

Error

Counts

308 → 4

Compiler

Compiled 8252 to 2612 computations (68.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (.f64 (/.f64 y x) (-.f64 (/.f64 1/8 (/.f64 (.f64 x x) y)) 1/2)))
0.1b	(.f64 (/.f64 y x) (-.f64 (/.f64 1/8 (/.f64 (.f64 x x) y)) 1/2))
0.4b	(/.f64 1/8 (/.f64 (*.f64 x x) y))
5.4b	(/.f64 (*.f64 x x) y)

rewrite209.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

49×	`times-frac_binary64_21908`
47×	`add-sqr-sqrt_binary64_21924`
36×	`*-un-lft-identity_binary64_21902`
34×	`add-cube-cbrt_binary64_21937`
23×	`add-exp-log_binary64_21940` `add-cbrt-cube_binary64_21938`
13×	`cancel-sign-sub-inv_binary64_21868` `associate-l_binary64_21843`
10×	`associate-/r*_binary64_21846`
8×	`div-exp_binary64_21953` `cbrt-undiv_binary64_21936` `distribute-rgt-in_binary64_21852` `distribute-lft-in_binary64_21851` `associate--r+_binary64_21838`
7×	`div-inv_binary64_21899` `associate-r_binary64_21842`
6×	`pow1_binary64_21963` `add-log-exp_binary64_21941`
5×	`sub-neg_binary64_21895`
4×	`prod-exp_binary64_21951` `cbrt-unprod_binary64_21935` `associate-/l*_binary64_21847`
3×	`flip3--_binary64_21906` `flip--_binary64_21877` `difference-of-squares_binary64_21871`
2×	`frac-2neg_binary64_21913` `clear-num_binary64_21901` `frac-times_binary64_21912` `unswap-sqr_binary64_21870` `associate-*r/_binary64_21844`
1×	`associate-/r/_binary64_21848` `pow-prod-down_binary64_21973` `associate-l/_binary64_21845` `distribute-lft-out--_binary64_21854` `-commutative_binary64_21833` `diff-log_binary64_21994`

Counts

4 → 137

Calls

4 calls:

25.0ms	(.f64 (/.f64 y x) (-.f64 (/.f64 1/8 (/.f64 (.f64 x x) y)) 1/2))
6.0ms	(/.f64 1/8 (/.f64 (*.f64 x x) y))
5.0ms	(/.f64 (*.f64 x x) y)
5.0ms	(-.f64 x (.f64 (/.f64 y x) (-.f64 (/.f64 1/8 (/.f64 (.f64 x x) y)) 1/2)))

Compiler

Compiled 3343 to 1523 computations (54.4% saved)

series873.0ms (14.1%)

Error

Counts

4 → 39

Calls

4 calls:

413.0ms	(-.f64 x (.f64 (/.f64 y x) (-.f64 (/.f64 1/8 (/.f64 (.f64 x x) y)) 1/2)))
198.0ms	(.f64 (/.f64 y x) (-.f64 (/.f64 1/8 (/.f64 (.f64 x x) y)) 1/2))
123.0ms	(/.f64 1/8 (/.f64 (*.f64 x x) y))
108.0ms	(/.f64 (*.f64 x x) y)

Compiler

Compiled 1350 to 1023 computations (24.2% saved)

simplify729.0ms (11.8%)

Algorithm

1×	egg-herbie

Rules

460×	`associate-/l/_binary64_21849`
344×	`distribute-rgt-in_binary64_21852`
334×	`distribute-lft-in_binary64_21851`
151×	`associate-*l/_binary64_21845`
143×	`associate-l_binary64_21843`
133×	`distribute-rgt-neg-in_binary64_21860`
124×	`*-commutative_binary64_21833`
121×	`associate-/r/_binary64_21848` `associate-/l*_binary64_21847`
112×	`cancel-sign-sub-inv_binary64_21868`
109×	`associate-r_binary64_21842`
108×	`distribute-lft-neg-in_binary64_21859`
96×	`times-frac_binary64_21908`
91×	`associate-*r/_binary64_21844`
87×	`distribute-neg-frac_binary64_21866`
70×	`distribute-lft-neg-out_binary64_21861`
62×	`log-div_binary64_21989` `associate-/r*_binary64_21846`
54×	`log-prod_binary64_21988` `distribute-rgt-neg-out_binary64_21862`
53×	`sub-neg_binary64_21895`
52×	`neg-sub0_binary64_21897`
50×	`neg-mul-1_binary64_21898` `+-commutative_binary64_21832`
47×	`sqr-pow_binary64_21874`
38×	`unswap-sqr_binary64_21870`
34×	`*-rgt-identity_binary64_21892`
33×	`distribute-rgt-out_binary64_21855`
29×	`exp-prod_binary64_21954` `associate-+l+_binary64_21835`
27×	`cube-prod_binary64_21930`
26×	`associate-+r+_binary64_21834`
25×	`cube-div_binary64_21931` `*-lft-identity_binary64_21891` `swap-sqr_binary64_21869`
24×	`unpow3_binary64_21968` `pow-plus_binary64_21965` `div-sub_binary64_21907`
22×	`associate--r+_binary64_21838`
21×	`pow-sqr_binary64_21875` `distribute-neg-in_binary64_21863`
18×	`associate-+l-_binary64_21837`
15×	`associate-+r-_binary64_21836`
10×	`div-exp_binary64_21953` `exp-sum_binary64_21948`
9×	`prod-exp_binary64_21951`
8×	`log-pow_binary64_21991`
7×	`unsub-neg_binary64_21896` `/-rgt-identity_binary64_21893` `difference-of-squares_binary64_21871`
6×	`cube-mult_binary64_21932` `distribute-lft-out_binary64_21853`
5×	`exp-diff_binary64_21950` `cube-unmult_binary64_21939`
4×	`log-rec_binary64_21990` `distribute-rgt-out--_binary64_21856`
3×	`rec-exp_binary64_21952` `associate--r-_binary64_21841` `associate--l-_binary64_21840` `associate--l+_binary64_21839`
2×	`unpow2_binary64_21967` `unpow1_binary64_21960` `remove-double-neg_binary64_21890` `+-rgt-identity_binary64_21887` `div0_binary64_21883` `distribute-frac-neg_binary64_21865`
1×	`exp-sqrt_binary64_21955` `1-exp_binary64_21946` `exp-1-e_binary64_21945` `rem-log-exp_binary64_21943` `rem-3cbrt-lft_binary64_21927` `rem-sqrt-square_binary64_21915` `rem-square-sqrt_binary64_21914` `*-inverses_binary64_21882` `cancel-sign-sub_binary64_21867` `count-2_binary64_21850`
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_22165` `erf-erfc_binary64_22164` `erf-odd_binary64_22163` `if-if-and-not_binary64_22162` `if-if-and_binary64_22161` `if-if-or-not_binary64_22160` `if-if-or_binary64_22159` `if-not_binary64_22158` `if-same_binary64_22157` `if-false_binary64_22156` `if-true_binary64_22155` `not-gte_binary64_22154` `not-lte_binary64_22153` `not-gt_binary64_22152` `not-lt_binary64_22151` `gte-same_binary64_22150` `lte-same_binary64_22149` `gt-same_binary64_22148` `lt-same_binary64_22147` `sinh---cosh_binary64_22094` `sinh-+-cosh_binary64_22093` `sinh-cosh_binary64_22092` `tanh-def-c_binary64_22091` `tanh-def-b_binary64_22090` `tanh-def-a_binary64_22089` `cosh-def_binary64_22088` `sinh-def_binary64_22087` `tan-neg_binary64_22034` `cos-neg_binary64_22033` `sin-neg_binary64_22032` `tan-0_binary64_22031` `cos-0_binary64_22030` `sin-0_binary64_22029` `hang-m-tan_binary64_22028` `hang-p-tan_binary64_22027` `hang-m0-tan_binary64_22026` `hang-p0-tan_binary64_22025` `hang-0m-tan_binary64_22024` `hang-0p-tan_binary64_22023` `tan-+PI/2_binary64_22022` `tan-+PI_binary64_22021` `tan-PI_binary64_22020` `tan-PI/3_binary64_22019` `tan-PI/4_binary64_22018` `tan-PI/6_binary64_22017` `cos-+PI/2_binary64_22016` `cos-+PI_binary64_22015` `cos-PI_binary64_22014` `cos-PI/2_binary64_22013` `cos-PI/3_binary64_22012` `cos-PI/4_binary64_22011` `cos-PI/6_binary64_22010` `sin-+PI/2_binary64_22009` `sin-+PI_binary64_22008` `sin-PI_binary64_22007` `sin-PI/2_binary64_22006` `sin-PI/3_binary64_22005` `sin-PI/4_binary64_22004` `sin-PI/6_binary64_22003` `sub-1-sin_binary64_22002` `sub-1-cos_binary64_22001` `-1-add-sin_binary64_22000` `-1-add-cos_binary64_21999` `1-sub-sin_binary64_21998` `1-sub-cos_binary64_21997` `cos-sin-sum_binary64_21996` `log-E_binary64_21992` `pow-base-0_binary64_21986` `unpow1/3_binary64_21969` `unpow1/2_binary64_21966` `exp-to-pow_binary64_21964` `pow-base-1_binary64_21962` `unpow0_binary64_21961` `unpow-1_binary64_21959` `exp-lft-cube_binary64_21958` `exp-lft-sqr_binary64_21957` `exp-cbrt_binary64_21956` `exp-neg_binary64_21949` `e-exp-1_binary64_21947` `exp-0_binary64_21944` `rem-exp-log_binary64_21942` `cube-neg_binary64_21929` `rem-3cbrt-rft_binary64_21928` `rem-cbrt-cube_binary64_21926` `rem-cube-cbrt_binary64_21925` `sqr-abs_binary64_21917` `sqr-neg_binary64_21916` `mul-1-neg_binary64_21894` `sub0-neg_binary64_21889` `--rgt-identity_binary64_21888` `+-lft-identity_binary64_21886` `mul0-rgt_binary64_21885` `mul0-lft_binary64_21884` `+-inverses_binary64_21881` `lft-mult-inverse_binary64_21880` `rgt-mult-inverse_binary64_21879` `remove-double-div_binary64_21878` `difference-of-sqr--1_binary64_21873` `difference-of-sqr-1_binary64_21872` `distribute-neg-out_binary64_21864` `distribute-rgt1-in_binary64_21858` `distribute-lft1-in_binary64_21857` `distribute-lft-out--_binary64_21854`

Counts

176 → 630

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	3327
1	653	3180
2	2209	3135
3	4913	3135

prune1.2s (19.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	630	0	630
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	630	4	634

Error

Counts

634 → 4

Compiler

Compiled 15578 to 7750 computations (50.3% saved)

localize2.0ms (0%)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

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

Error

Counts

4 → 4

Compiler

Compiled 0 to 0 computations (0% saved)

regimes209.0ms (3.4%)

Accuracy

Total 0.0b remaining (79.1%)

Threshold costs 0.0b (79.1%)

Compiler

Compiled 516 to 422 computations (18.2% saved)

bsearch23.0ms (0.4%)

Steps

Iters	Range		Point
3	5.1480053557963014e+135	6.593620608877907e+135	5.2140153461603685e+135
10	-3.2165725474231095e+157	-1.2289960017047064e+146	-1.3411284397379803e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64_21832`
2×	`*-commutative_binary64_21833`
1×	`neg-sub0_binary64_21897` `sub-neg_binary64_21895` `mul-1-neg_binary64_21894`
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_22162` `if-if-and_binary64_22161` `if-if-or-not_binary64_22160` `if-if-or_binary64_22159` `if-not_binary64_22158` `if-same_binary64_22157` `if-false_binary64_22156` `if-true_binary64_22155` `tan-0_binary64_22031` `cos-0_binary64_22030` `sin-0_binary64_22029` `unpow1_binary64_21960` `e-exp-1_binary64_21947` `1-exp_binary64_21946` `exp-1-e_binary64_21945` `exp-0_binary64_21944` `sqr-abs_binary64_21917` `sqr-neg_binary64_21916` `neg-mul-1_binary64_21898` `unsub-neg_binary64_21896` `/-rgt-identity_binary64_21893` `-rgt-identity_binary64_21892` `-lft-identity_binary64_21891` `remove-double-neg_binary64_21890` `sub0-neg_binary64_21889` `--rgt-identity_binary64_21888` `+-rgt-identity_binary64_21887` `+-lft-identity_binary64_21886` `cancel-sign-sub-inv_binary64_21868` `cancel-sign-sub_binary64_21867` `distribute-neg-frac_binary64_21866` `distribute-frac-neg_binary64_21865` `distribute-neg-out_binary64_21864` `distribute-neg-in_binary64_21863` `distribute-rgt-neg-out_binary64_21862` `distribute-lft-neg-out_binary64_21861` `distribute-rgt-neg-in_binary64_21860` `distribute-lft-neg-in_binary64_21859`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	34
1	24	34
2	26	34
3	27	34
4	28	34

Proof

(if real (<= f64 h0 -13411284397379802924545990801038831822307222629253063495936935408657244621287948110130908140256944424278430502387446460929054526414745438475780569251708928) (=> (* f64 -1 h0)) (if real (<= f64 h0 5214015346160368497777214983101959924248522932840924733231724370154238628919799715416334993000874916267028150835605751258882519922114560) (sqrt f64 (+ f64 (* f64 h0 h0) h1)) (+ f64 h0 (* f64 1/2 (/ f64 h1 h0)))))
mul-1-neg_binary64_21894 =>
(if real (<= f64 h0 -13411284397379802924545990801038831822307222629253063495936935408657244621287948110130908140256944424278430502387446460929054526414745438475780569251708928) (neg f64 h0) (if real (<= f64 h0 5214015346160368497777214983101959924248522932840924733231724370154238628919799715416334993000874916267028150835605751258882519922114560) (sqrt f64 (+ f64 (* f64 h0 h0) h1)) (+ f64 h0 (* f64 1/2 (/ f64 h1 h0)))))

end0.0ms (0%)

sample613.0ms (9.9%)

Algorithm

1×

intervals

Results

210.0ms	8000×	body	128	valid
4.0ms	176×	body	128	nan

Compiler

Compiled 133 to 105 computations (21.1% saved)

Details

analyze68.0ms (1.1%)

sample19.0ms (0.3%)

simplify148.0ms (2.4%)

prune2.0ms (0%)

localize4.0ms (0.1%)

rewrite31.0ms (0.5%)

series219.0ms (3.5%)

simplify109.0ms (1.8%)

prune83.0ms (1.3%)

localize10.0ms (0.2%)

rewrite142.0ms (2.3%)

series622.0ms (10%)

simplify474.0ms (7.7%)

prune382.0ms (6.2%)

localize10.0ms (0.2%)

rewrite209.0ms (3.4%)

series873.0ms (14.1%)

simplify729.0ms (11.8%)

prune1.2s (19.2%)

localize2.0ms (0%)

rewrite8.0ms (0.1%)

series0.0ms (0%)

simplify9.0ms (0.1%)

prune1.0ms (0%)

regimes209.0ms (3.4%)

bsearch23.0ms (0.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample613.0ms (9.9%)

Profiling