Details

Time bar (total: 9.9s)

analyze529.0ms (5.4%)

Algorithm
search
egg-herbie
Rules
756×neg-mul-1_binary64
741×neg-sub0_binary64
638×associate-/l*_binary64
470×distribute-frac-neg_binary64
468×div-sub_binary64
448×unsub-neg_binary64
352×sub-neg_binary64
260×distribute-rgt-in_binary64
256×times-frac_binary64
236×distribute-lft-neg-out_binary64
234×distribute-rgt-neg-out_binary64
198×distribute-lft-in_binary64 associate-*l/_binary64
187×associate-*l*_binary64
177×cancel-sign-sub-inv_binary64
173×associate-*r/_binary64
172×distribute-neg-frac_binary64
170×associate-*r*_binary64
155×associate-/r/_binary64
149×associate-/r*_binary64
122×*-lft-identity_binary64
117×associate-/l/_binary64
103×*-rgt-identity_binary64
97×*-commutative_binary64
90×remove-double-neg_binary64
82×distribute-rgt-neg-in_binary64
78×cancel-sign-sub_binary64
77×/-rgt-identity_binary64
53×div0_binary64
44×distribute-rgt-out_binary64 associate--r+_binary64 +-commutative_binary64
42×distribute-lft-neg-in_binary64
40×distribute-rgt-out--_binary64
34×+-lft-identity_binary64
32×associate-+l-_binary64 associate-+r+_binary64
29×distribute-neg-in_binary64
28×sub0-neg_binary64 distribute-neg-out_binary64
24×associate-+r-_binary64
22×associate-+l+_binary64
19×+-rgt-identity_binary64
17×remove-double-div_binary64
16×difference-of-squares_binary64
15×mul0-rgt_binary64 mul0-lft_binary64
12×distribute-lft-out_binary64
10×associate--r-_binary64
associate--l+_binary64
swap-sqr_binary64
associate--l-_binary64
sqr-neg_binary64 --rgt-identity_binary64
mul-1-neg_binary64
1-exp_binary64
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 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 unswap-sqr_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 count-2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
054208
1161200
2483200
31371192
42735192
53995192
64316192
74707192
85013192
033
133
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
12.5%68.6%18.9%6
18.7%62.4%18.9%7
18.7%59.3%22%8
28.1%39%32.9%9
32.8%34.3%32.9%10
32.8%32%35.3%11
38.2%20.7%41.1%12
41%17.9%41.1%13
41%16.6%42.5%14
Compiler

Compiled 38 to 24 computations (36.8% saved)

sample56.0ms (0.6%)

Algorithm
intervals
Results
38.0ms239×body256valid
3.0ms43×body128nan
1.0ms17×body128valid
Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify234.0ms (2.4%)

Algorithm
egg-herbie
Rules
637×associate-/l*_binary64
634×div-sub_binary64
582×unsub-neg_binary64
519×sub-neg_binary64
502×times-frac_binary64
356×distribute-rgt-out--_binary64
307×neg-mul-1_binary64
295×distribute-rgt-neg-in_binary64
286×associate-/l/_binary64
280×neg-sub0_binary64
252×associate-/r/_binary64
250×distribute-lft-neg-out_binary64
246×distribute-neg-out_binary64
212×associate-/r*_binary64 *-commutative_binary64
210×+-commutative_binary64
208×distribute-rgt-out_binary64
203×distribute-rgt-in_binary64
199×distribute-rgt-neg-out_binary64
186×distribute-neg-frac_binary64
160×associate-*r/_binary64
145×cancel-sign-sub-inv_binary64
137×associate-*l/_binary64
133×distribute-neg-in_binary64
123×distribute-lft-in_binary64
113×associate-+l+_binary64
106×distribute-lft-out--_binary64
100×distribute-frac-neg_binary64
98×associate-+l-_binary64
90×associate-*l*_binary64
81×associate-+r+_binary64
78×associate-*r*_binary64 associate--r-_binary64
63×associate--r+_binary64
59×distribute-lft-neg-in_binary64
46×*-lft-identity_binary64
44×associate-+r-_binary64
43×*-rgt-identity_binary64 distribute-lft-out_binary64
35×remove-double-neg_binary64 sub0-neg_binary64
34×associate--l+_binary64
27×mul0-rgt_binary64 swap-sqr_binary64
25×mul0-lft_binary64
24×distribute-rgt1-in_binary64
23×associate--l-_binary64
20×mul-1-neg_binary64
18×div0_binary64
14×cancel-sign-sub_binary64
+-lft-identity_binary64
+-rgt-identity_binary64
sqr-neg_binary64
/-rgt-identity_binary64 --rgt-identity_binary64 +-inverses_binary64
difference-of-squares_binary64 distribute-lft1-in_binary64
1-exp_binary64
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 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 unswap-sqr_binary64 count-2_binary64
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02052
15350
213950
338148
473548
5118948
6140948
7189348
8185348
9223548
10288948
11345748
12363948
13374948
14379748
15382148
16387148
17485848
18479948
19498048
20483448

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
34.1b
Counts
2 → 2
Compiler

Compiled 99 to 59 computations (40.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.0b
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
7.4b
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
27.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
27.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite176.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
29.6b
Rules
14×add-sqr-sqrt_binary64
11×cbrt-prod_binary64
10×*-un-lft-identity_binary64
sqrt-prod_binary64
add-cube-cbrt_binary64
pow1_binary64 times-frac_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64 difference-of-squares_binary64
pow1/2_binary64 sqrt-pow1_binary64 flip3--_binary64 flip--_binary64 rem-sqrt-square_binary64 pow1/3_binary64 cbrt-div_binary64
distribute-lft-out--_binary64 div-inv_binary64 associate-*l/_binary64
Counts
4 → 61
Calls

4 calls:

8.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
8.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2345 to 702 computations (70.1% saved)

series351.0ms (3.6%)

Error
29.5b
Counts
4 → 45
Calls

4 calls:

125.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
91.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
29.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
27.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 4535 to 3309 computations (27% saved)

simplify82.0ms (0.8%)

Algorithm
egg-herbie
Rules
644×associate-/l*_binary64
500×associate-/r*_binary64
407×associate-*l*_binary64
131×associate-*l/_binary64
125×associate-*r/_binary64
111×associate-/r/_binary64
102×sub-neg_binary64
101×cancel-sign-sub-inv_binary64
88×*-commutative_binary64
86×distribute-rgt-in_binary64
79×distribute-lft-in_binary64
78×associate-*r*_binary64
77×times-frac_binary64
73×distribute-rgt-neg-in_binary64
68×distribute-lft-neg-in_binary64
67×sqr-pow_binary64
61×exp-sum_binary64
52×unswap-sqr_binary64
49×distribute-neg-frac_binary64
46×exp-prod_binary64
45×+-commutative_binary64
38×neg-sub0_binary64
35×neg-mul-1_binary64
33×div-sub_binary64
29×exp-diff_binary64
22×unsub-neg_binary64
17×log-div_binary64
16×distribute-neg-in_binary64 distribute-lft-neg-out_binary64
13×unpow1/3_binary64
11×pow-sqr_binary64 difference-of-squares_binary64 distribute-rgt-neg-out_binary64 distribute-rgt-out_binary64 associate-+l-_binary64
10×log-prod_binary64 associate-+l+_binary64
exp-to-pow_binary64
associate-+r-_binary64 associate-+r+_binary64
associate--r+_binary64
associate--l+_binary64
cube-unmult_binary64
unpow3_binary64 exp-neg_binary64 cube-prod_binary64 associate--r-_binary64 associate--l-_binary64
log-pow_binary64 log-rec_binary64 pow-plus_binary64 cube-mult_binary64 rem-sqrt-square_binary64 mul-1-neg_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 rem-3cbrt-lft_binary64 remove-double-neg_binary64 distribute-lft-out_binary64
exp-lft-sqr_binary64 1-exp_binary64 rem-square-sqrt_binary64 +-rgt-identity_binary64
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 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 count-2_binary64 associate-/l/_binary64
Counts
106 → 65
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02552641
15532611
214732562
350862562

prune135.0ms (1.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New521365
Fresh011
Picked101
Done000
Total531467
Error
29.1b
Counts
67 → 14
Compiler

Compiled 2793 to 1325 computations (52.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b
(+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))
7.0b
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
27.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
27.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite217.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
29.1b
Rules
add-sqr-sqrt_binary64 sqrt-prod_binary64 *-un-lft-identity_binary64
pow1_binary64 add-log-exp_binary64 add-cube-cbrt_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
pow1/2_binary64 sqrt-pow1_binary64 flip3--_binary64 flip--_binary64 difference-of-squares_binary64 rem-sqrt-square_binary64
pow1/3_binary64 associate-*l/_binary64 cbrt-div_binary64 cbrt-prod_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 distribute-lft-out_binary64 +-commutative_binary64
Counts
4 → 54
Calls

4 calls:

8.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
7.0ms
(+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2128 to 634 computations (70.2% saved)

series306.0ms (3.1%)

Error
28.7b
Counts
4 → 42
Calls

4 calls:

90.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
35.0ms
(+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))
31.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
30.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 3665 to 2609 computations (28.8% saved)

simplify104.0ms (1.1%)

Algorithm
egg-herbie
Rules
306×cancel-sign-sub-inv_binary64
287×unswap-sqr_binary64
212×sub-neg_binary64
208×div-sub_binary64
188×associate-*r*_binary64
183×exp-sum_binary64
172×associate-*l*_binary64
147×times-frac_binary64
131×associate-/l*_binary64
121×*-commutative_binary64
105×distribute-rgt-in_binary64
103×unsub-neg_binary64
98×exp-diff_binary64
95×sqr-pow_binary64 distribute-lft-in_binary64
91×log-prod_binary64
76×associate-/r*_binary64 +-commutative_binary64
66×exp-prod_binary64
63×neg-sub0_binary64 associate-+l+_binary64
58×associate-+r-_binary64
54×associate-+r+_binary64
53×neg-mul-1_binary64
49×log-div_binary64
44×difference-of-squares_binary64
37×associate-*l/_binary64
36×associate-+l-_binary64
35×distribute-rgt-neg-in_binary64
30×distribute-lft-neg-in_binary64
25×associate--l+_binary64
23×associate-*r/_binary64
20×+-rgt-identity_binary64
19×exp-to-pow_binary64 rem-exp-log_binary64 associate--r-_binary64
18×log-pow_binary64 unpow1/3_binary64
16×cube-prod_binary64 sub0-neg_binary64 associate-/r/_binary64
15×cube-unmult_binary64 pow-sqr_binary64
14×distribute-neg-in_binary64 distribute-rgt-out_binary64
13×distribute-lft-neg-out_binary64
12×associate--r+_binary64
11×associate--l-_binary64
10×pow-plus_binary64 remove-double-neg_binary64
exp-neg_binary64 distribute-rgt-neg-out_binary64
unpow3_binary64 swap-sqr_binary64
--rgt-identity_binary64
log-rec_binary64
cube-mult_binary64 rem-sqrt-square_binary64 mul-1-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-neg-frac_binary64
distribute-rgt-out--_binary64 distribute-lft-out_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 *-lft-identity_binary64 +-inverses_binary64 cancel-sign-sub_binary64
prod-exp_binary64 1-exp_binary64 cube-neg_binary64 rem-3cbrt-lft_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 distribute-neg-out_binary64 count-2_binary64
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 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 +-lft-identity_binary64 div0_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 associate-/l/_binary64
Counts
96 → 60
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01711729
13861674
28881647
329181603
449231603
549351603

prune197.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New57360
Fresh21113
Picked101
Done000
Total601474
Error
28.7b
Counts
74 → 14
Compiler

Compiled 2520 to 1119 computations (55.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b
(+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))
7.4b
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
27.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
27.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite188.0ms (1.9%)

Algorithm
rewrite-expression-head
Error
28.7b
Rules
14×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64
10×cbrt-prod_binary64
sqrt-prod_binary64
add-cube-cbrt_binary64
pow1_binary64 add-log-exp_binary64 times-frac_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64 difference-of-squares_binary64
pow1/2_binary64 sqrt-pow1_binary64 flip3--_binary64 flip--_binary64 rem-sqrt-square_binary64
pow1/3_binary64 cbrt-div_binary64 distribute-lft-out--_binary64 div-inv_binary64 sum-log_binary64 flip3-+_binary64 flip-+_binary64 distribute-lft-out_binary64 +-commutative_binary64
Counts
4 → 63
Calls

4 calls:

8.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
6.0ms
(+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2468 to 747 computations (69.7% saved)

series358.0ms (3.6%)

Error
28.7b
Counts
4 → 47
Calls

4 calls:

126.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) (*.f64 2 a)))
32.0ms
(+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))))
30.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
28.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 4455 to 3215 computations (27.8% saved)

simplify82.0ms (0.8%)

Algorithm
egg-herbie
Rules
639×associate-/l*_binary64
499×associate-/r*_binary64
407×associate-*l*_binary64
130×associate-*l/_binary64
125×associate-*r/_binary64
114×cancel-sign-sub-inv_binary64 distribute-rgt-in_binary64
108×associate-/r/_binary64
105×sub-neg_binary64
98×distribute-lft-in_binary64
82×distribute-rgt-neg-in_binary64
78×associate-*r*_binary64 *-commutative_binary64
77×times-frac_binary64
74×distribute-lft-neg-in_binary64
54×sqr-pow_binary64 unswap-sqr_binary64
51×+-commutative_binary64
49×distribute-neg-frac_binary64
44×neg-sub0_binary64
41×neg-mul-1_binary64
39×exp-sum_binary64
34×exp-prod_binary64
26×distribute-neg-in_binary64
23×div-sub_binary64
19×exp-diff_binary64
18×unsub-neg_binary64 distribute-lft-neg-out_binary64
17×log-div_binary64
13×difference-of-squares_binary64 distribute-rgt-out_binary64
12×associate-+l+_binary64
11×distribute-rgt-neg-out_binary64
10×log-prod_binary64
associate-+l-_binary64
unpow1/3_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r+_binary64
exp-to-pow_binary64 pow-sqr_binary64 associate-+r-_binary64
unpow3_binary64
exp-neg_binary64 cube-unmult_binary64 cube-mult_binary64 cube-prod_binary64 associate--r-_binary64 associate--l-_binary64
log-pow_binary64 log-rec_binary64 pow-plus_binary64 rem-sqrt-square_binary64 mul-1-neg_binary64 distribute-rgt-out--_binary64 distribute-lft-out_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 remove-double-neg_binary64 cancel-sign-sub_binary64
exp-lft-sqr_binary64 prod-exp_binary64 1-exp_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 +-rgt-identity_binary64 +-inverses_binary64 distribute-neg-out_binary64 count-2_binary64
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 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 swap-sqr_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 associate-/l/_binary64
Counts
110 → 63
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02332579
15322540
214412487
350382487

prune200.0ms (2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New57663
Fresh21113
Picked101
Done000
Total601777
Error
28.7b
Counts
77 → 17
Compiler

Compiled 2889 to 1404 computations (51.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.0b
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
7.4b
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) a))
27.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
27.6b
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))

rewrite307.0ms (3.1%)

Algorithm
rewrite-expression-head
Error
28.6b
Rules
30×add-sqr-sqrt_binary64
23×cbrt-prod_binary64
22×*-un-lft-identity_binary64
18×times-frac_binary64
16×add-cube-cbrt_binary64
11×sqrt-prod_binary64
difference-of-squares_binary64
pow1_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
distribute-lft-out--_binary64
pow1/2_binary64 sqrt-pow1_binary64 flip3--_binary64 flip--_binary64 rem-sqrt-square_binary64 pow1/3_binary64 cbrt-div_binary64
div-inv_binary64 associate-*l/_binary64
Counts
4 → 73
Calls

4 calls:

8.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
8.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) a))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
4.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 2812 to 755 computations (73.2% saved)

series407.0ms (4.1%)

Error
28.7b
Counts
4 → 45
Calls

4 calls:

108.0ms
(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h))) g) a))
90.0ms
(cbrt.f64 (*.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))) a) -1/2))
30.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
28.0ms
(sqrt.f64 (-.f64 (*.f64 g g) (*.f64 h h)))
Compiler

Compiled 4552 to 3292 computations (27.7% saved)

simplify125.0ms (1.3%)

Algorithm
egg-herbie
Rules
524×associate-/l*_binary64
452×associate-/r*_binary64
301×associate-*l*_binary64
197×exp-sum_binary64
141×associate-*l/_binary64
133×associate-*r/_binary64
110×associate-/r/_binary64
104×sub-neg_binary64
94×cancel-sign-sub-inv_binary64
90×exp-prod_binary64
86×distribute-rgt-in_binary64
79×distribute-lft-in_binary64
74×exp-diff_binary64 times-frac_binary64 *-commutative_binary64
67×sqr-pow_binary64
64×distribute-rgt-neg-in_binary64
59×distribute-lft-neg-in_binary64
54×unswap-sqr_binary64
52×associate-*r*_binary64
47×distribute-neg-frac_binary64
45×+-commutative_binary64
41×neg-sub0_binary64
38×neg-mul-1_binary64
35×div-sub_binary64
32×log-div_binary64
30×unpow1/3_binary64
24×log-prod_binary64
22×unsub-neg_binary64
20×exp-to-pow_binary64
16×distribute-neg-in_binary64 distribute-lft-neg-out_binary64 associate-/l/_binary64
14×exp-neg_binary64
11×pow-sqr_binary64 difference-of-squares_binary64 distribute-rgt-neg-out_binary64 distribute-rgt-out_binary64 associate-+l-_binary64
10×pow-plus_binary64 associate-+l+_binary64
associate-+r-_binary64 associate-+r+_binary64
associate--r+_binary64
unpow3_binary64 cube-unmult_binary64
log-pow_binary64 associate--l+_binary64
cube-prod_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 associate--r-_binary64 associate--l-_binary64
log-rec_binary64 cube-mult_binary64 rem-sqrt-square_binary64 mul-1-neg_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 exp-lft-sqr_binary64 rem-3cbrt-lft_binary64 remove-double-neg_binary64 distribute-lft-out_binary64
prod-exp_binary64 1-exp_binary64 rem-square-sqrt_binary64 *-lft-identity_binary64 +-rgt-identity_binary64
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 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 count-2_binary64
Counts
118 → 69
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02713067
15693037
214392988
347352947
450652947

prune228.0ms (2.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New64569
Fresh21416
Picked101
Done000
Total671986
Error
28.6b
Counts
86 → 19
Compiler

Compiled 2419 to 995 computations (58.9% saved)

regimes3.2s (32.5%)

Accuracy

Total 2.4b remaining (7.9%)

Threshold costs 0b (0%)

Compiler

Compiled 63886 to 40304 computations (36.9% saved)

bsearch16.0ms (0.2%)

Compiler

Compiled 37 to 23 computations (37.8% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
13×*-commutative_binary64 +-commutative_binary64
10×sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64
distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64
1-exp_binary64 unsub-neg_binary64 cancel-sign-sub-inv_binary64 distribute-neg-frac_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-in_binary64
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 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
037114
158114
269114
383114
492112
599112
6102112
7103112
8101112

end2.0ms (0%)

Compiler

Compiled 72 to 37 computations (48.6% saved)

sample2.3s (23.1%)

Algorithm
intervals
Results
1.2s7577×body256valid
96.0ms1116×body128nan
35.0ms423×body128valid
Compiler

Compiled 865 to 531 computations (38.6% saved)

Profiling

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