Details

Time bar (total: 4.0s)

analyze262.0ms (6.6%)

Algorithm
search
egg-herbie
Rules
1298×associate--r-_binary64
588×div-sub_binary64
492×unsub-neg_binary64
469×sub-neg_binary64
405×distribute-rgt-in_binary64
381×neg-mul-1_binary64
352×neg-sub0_binary64
318×distribute-frac-neg_binary64
292×distribute-lft-in_binary64
270×distribute-rgt-neg-in_binary64
246×distribute-lft-neg-in_binary64
219×associate--r+_binary64
209×*-commutative_binary64
194×cancel-sign-sub-inv_binary64
188×associate-/l*_binary64
166×+-commutative_binary64
157×associate-/r/_binary64
144×remove-double-neg_binary64
142×distribute-rgt-out--_binary64
137×distribute-neg-in_binary64
126×distribute-rgt-neg-out_binary64
124×distribute-lft-neg-out_binary64
118×distribute-lft-out--_binary64
116×distribute-lft-out_binary64 associate-/l/_binary64
114×distribute-neg-out_binary64
98×distribute-neg-frac_binary64
96×associate-+l-_binary64
77×associate-*r*_binary64
69×associate-+l+_binary64
66×associate-+r+_binary64
65×associate-/r*_binary64
56×associate-*l/_binary64
52×distribute-rgt-out_binary64
48×associate--l+_binary64
46×associate-+r-_binary64
38×associate-*l*_binary64
31×/-rgt-identity_binary64
29×sub0-neg_binary64
28×associate-*r/_binary64
19×*-lft-identity_binary64
17×mul0-lft_binary64
16×mul0-rgt_binary64
15×+-rgt-identity_binary64
14×+-lft-identity_binary64
12×*-rgt-identity_binary64
div0_binary64
+-inverses_binary64 associate--l-_binary64
sqr-neg_binary64 swap-sqr_binary64
*-inverses_binary64 difference-of-squares_binary64
1-exp_binary64 distribute-rgt1-in_binary64 distribute-lft1-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 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 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 mul-1-neg_binary64 --rgt-identity_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 cancel-sign-sub_binary64 count-2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01544
13644
28644
316444
435344
587844
6131244
7155644
8190044
9247744
10284744
11317644
12339244
13340744
14374044
15352044
16356844
17356044
18359244
19359244
20579044
022
122
Search
TrueOtherFalseIter
0%18.7%81.3%0
0%18.7%81.3%1
0%18.7%81.3%2
0%18.7%81.3%3
0%18.7%81.3%4
4.7%14%81.3%5
5.3%13.5%81.3%6
18.1%0.6%81.3%7
18.1%0.6%81.3%8
18.6%0.1%81.3%9
18.6%0.1%81.3%10
18.7%0%81.3%11
18.7%0%81.3%12
18.7%0%81.3%13
18.7%0%81.3%14
Compiler

Compiled 23 to 15 computations (34.8% saved)

sample25.0ms (0.6%)

Algorithm
intervals
Results
9.0ms256×body128valid
5.0ms256×pre128true
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify181.0ms (4.5%)

Algorithm
egg-herbie
Rules
917×times-frac_binary64
687×unsub-neg_binary64
552×sub-neg_binary64
367×distribute-lft-neg-in_binary64
317×associate-*l/_binary64
287×associate-/l*_binary64
271×neg-sub0_binary64
267×distribute-rgt-in_binary64
256×distribute-neg-in_binary64
251×+-commutative_binary64
239×div-sub_binary64
236×distribute-neg-out_binary64
223×*-commutative_binary64
222×distribute-rgt-out--_binary64
208×neg-mul-1_binary64
204×distribute-rgt-neg-in_binary64
188×associate-/r*_binary64
184×cancel-sign-sub-inv_binary64
180×distribute-rgt-neg-out_binary64
173×associate-/l/_binary64
160×associate--r+_binary64
158×associate-+l-_binary64
153×distribute-lft-in_binary64
139×distribute-frac-neg_binary64 distribute-lft-neg-out_binary64
137×distribute-neg-frac_binary64
128×associate--l+_binary64
122×associate-*r*_binary64
120×*-lft-identity_binary64
119×mul-1-neg_binary64 distribute-rgt-out_binary64
95×associate-/r/_binary64
85×associate-+r-_binary64
80×associate--l-_binary64
74×associate--r-_binary64
72×remove-double-neg_binary64
71×distribute-lft-out_binary64
69×distribute-lft-out--_binary64
57×associate-+l+_binary64
55×associate-+r+_binary64
51×associate-*l*_binary64
41×sub0-neg_binary64
39×/-rgt-identity_binary64
19×*-rgt-identity_binary64
18×associate-*r/_binary64
17×mul0-lft_binary64
15×mul0-rgt_binary64
11×distribute-rgt1-in_binary64
10×+-rgt-identity_binary64
div0_binary64
+-lft-identity_binary64 swap-sqr_binary64
sqr-neg_binary64 cancel-sign-sub_binary64 distribute-lft1-in_binary64
+-inverses_binary64
--rgt-identity_binary64
remove-double-div_binary64 count-2_binary64
1-exp_binary64 difference-of-squares_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 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_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
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01022
12322
25122
310022
421822
549922
689722
7195422
8263122
9433422
10392622
11414022
12422622
13422822
14422822
15497922

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
18.1b
Counts
1 → 1
Compiler

Compiled 15 to 9 computations (40% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 x x) (*.f64 y y))
17.8b
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))

rewrite52.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
17.8b
Rules
associate-/l/_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
flip3-+_binary64 flip-+_binary64
add-log-exp_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64 frac-times_binary64
times-frac_binary64 flip3--_binary64 flip--_binary64 associate-/r*_binary64
pow1_binary64 div-exp_binary64 cbrt-undiv_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-/r/_binary64
prod-exp_binary64 cbrt-unprod_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64 sum-log_binary64 +-commutative_binary64
Counts
2 → 42
Calls

2 calls:

12.0ms
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))
4.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 1154 to 190 computations (83.5% saved)

series61.0ms (1.5%)

Error
0.0b
Counts
2 → 24
Calls

2 calls:

29.0ms
(/.f64 (*.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (*.f64 x x) (*.f64 y y)))
26.0ms
(+.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 505 to 415 computations (17.8% saved)

simplify51.0ms (1.3%)

Algorithm
egg-herbie
Rules
945×distribute-rgt-in_binary64
893×distribute-lft-in_binary64
355×times-frac_binary64
127×div-sub_binary64
65×associate-*l*_binary64
58×associate-*r*_binary64
57×associate-/l*_binary64
55×sub-neg_binary64 *-commutative_binary64
52×cancel-sign-sub-inv_binary64
47×unswap-sqr_binary64
38×distribute-rgt-neg-in_binary64
33×distribute-lft-neg-in_binary64
32×associate-*l/_binary64
27×distribute-lft-neg-out_binary64
25×sqr-pow_binary64 associate-/r*_binary64 associate-*r/_binary64
24×neg-mul-1_binary64 neg-sub0_binary64
22×associate-/l/_binary64
20×distribute-rgt-neg-out_binary64
19×+-commutative_binary64
17×distribute-neg-frac_binary64 distribute-neg-in_binary64
14×log-div_binary64
12×*-rgt-identity_binary64 associate-/r/_binary64
11×cube-div_binary64
distribute-rgt-out--_binary64
unsub-neg_binary64
cube-unmult_binary64 difference-of-squares_binary64 distribute-rgt-out_binary64
/-rgt-identity_binary64 pow-sqr_binary64
exp-prod_binary64 cube-prod_binary64 associate-+l+_binary64
unpow3_binary64 associate--r+_binary64 associate-+r+_binary64
swap-sqr_binary64 distribute-lft-out_binary64 associate--l+_binary64
log-prod_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 unpow1_binary64 exp-diff_binary64 cube-mult_binary64 remove-double-neg_binary64 *-inverses_binary64 associate-+l-_binary64 associate-+r-_binary64
log-rec_binary64 prod-exp_binary64 exp-sum_binary64 1-exp_binary64 *-lft-identity_binary64 distribute-lft-out--_binary64 associate--r-_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 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_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 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 sub0-neg_binary64 --rgt-identity_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 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--l-_binary64
Counts
66 → 45
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0981322
13341124
213341122
352371122

prune23.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New44145
Fresh000
Picked011
Done000
Total44246
Error
9.3b
Counts
46 → 2
Compiler

Compiled 670 to 161 computations (76% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

18.4b
(/.f64 (*.f64 x x) (*.f64 y y))

rewrite24.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
4.2b
Rules
13×add-exp-log_binary64 add-cbrt-cube_binary64
prod-exp_binary64 div-exp_binary64 cbrt-undiv_binary64 cbrt-unprod_binary64
pow1_binary64 add-log-exp_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 frac-2neg_binary64 times-frac_binary64 *-un-lft-identity_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64 associate-/r*_binary64
Counts
1 → 21
Calls

1 calls:

6.0ms
(/.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 375 to 150 computations (60% saved)

series21.0ms (0.5%)

Error
9.3b
Counts
1 → 6
Calls

1 calls:

20.0ms
(/.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 143 to 143 computations (0% saved)

simplify81.0ms (2%)

Algorithm
egg-herbie
Rules
528×times-frac_binary64
436×div-sub_binary64
346×cancel-sign-sub-inv_binary64
327×associate-/l*_binary64
326×unswap-sqr_binary64
237×sub-neg_binary64
236×*-commutative_binary64
195×associate-*l/_binary64
158×sqr-pow_binary64
157×distribute-neg-in_binary64
156×associate-/r*_binary64
124×associate-*r/_binary64
109×log-prod_binary64
95×associate-/l/_binary64 associate-*l*_binary64
90×associate--r+_binary64
86×associate--l+_binary64 associate-+l+_binary64
82×cube-prod_binary64
75×associate-*r*_binary64
74×distribute-lft-out--_binary64
73×associate-/r/_binary64
72×distribute-rgt-neg-in_binary64
67×distribute-lft-neg-in_binary64
60×associate-+r+_binary64
56×distribute-rgt-in_binary64
53×pow-sqr_binary64
52×unpow3_binary64
49×neg-mul-1_binary64 unsub-neg_binary64
47×neg-sub0_binary64
43×associate-+l-_binary64
41×cube-mult_binary64
40×distribute-lft-in_binary64
36×log-div_binary64
34×log-pow_binary64
31×associate--r-_binary64
29×distribute-rgt-out_binary64
27×pow-plus_binary64
26×cube-div_binary64 associate--l-_binary64
25×swap-sqr_binary64
23×+-commutative_binary64
22×exp-prod_binary64
21×distribute-rgt-out--_binary64
20×associate-+r-_binary64
15×cube-unmult_binary64
14×+-rgt-identity_binary64
13×*-rgt-identity_binary64
12×*-lft-identity_binary64
10×distribute-lft-neg-out_binary64
sub0-neg_binary64 --rgt-identity_binary64
unpow2_binary64 count-2_binary64
distribute-rgt-neg-out_binary64
distribute-neg-out_binary64 distribute-lft-out_binary64
rem-sqrt-square_binary64 remove-double-neg_binary64
mul0-rgt_binary64 mul0-lft_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64
unpow1_binary64
unpow1/2_binary64 exp-diff_binary64 +-lft-identity_binary64
exp-sum_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-rec_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_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 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 /-rgt-identity_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 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64
Counts
27 → 22
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
047415
1118293
2406268
31753253
42599253
53619223
64507220
75166220

prune14.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New16622
Fresh000
Picked101
Done011
Total17724
Error
4.2b
Counts
24 → 7
Compiler

Compiled 189 to 142 computations (24.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (cbrt.f64 (pow.f64 (/.f64 x y) 2)))
24.2b
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
24.2b
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
24.2b
(cbrt.f64 (pow.f64 (/.f64 x y) 2))

rewrite534.0ms (13.4%)

Algorithm
rewrite-expression-head
Error
4.2b
Rules
186×cbrt-prod_binary64
124×add-sqr-sqrt_binary64
115×unpow-prod-down_binary64
75×times-frac_binary64
64×add-cube-cbrt_binary64 *-un-lft-identity_binary64
36×unswap-sqr_binary64
21×swap-sqr_binary64 associate-*l*_binary64 associate-*r*_binary64
19×unpow2_binary64 sqr-pow_binary64
11×pow1_binary64
pow1/3_binary64
div-inv_binary64
add-exp-log_binary64
add-log-exp_binary64 add-cbrt-cube_binary64
pow-prod-down_binary64 pow-prod-up_binary64 pow-sqr_binary64
pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
4 → 195
Calls

4 calls:

26.0ms
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (cbrt.f64 (pow.f64 (/.f64 x y) 2)))
4.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
4.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
4.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
Compiler

Compiled 6571 to 3936 computations (40.1% saved)

series242.0ms (6.1%)

Error
4.2b
Counts
4 → 24
Calls

4 calls:

55.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
53.0ms
(*.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (cbrt.f64 (pow.f64 (/.f64 x y) 2)))
50.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
50.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
Compiler

Compiled 2202 to 1821 computations (17.3% saved)

simplify292.0ms (7.3%)

Algorithm
egg-herbie
Rules
775×unswap-sqr_binary64
221×exp-prod_binary64
219×*-commutative_binary64
197×sqr-pow_binary64
185×exp-sum_binary64
149×log-prod_binary64
141×unsub-neg_binary64
118×associate-*l*_binary64
116×associate-*r*_binary64
108×associate-*l/_binary64
100×sub-neg_binary64
97×log-pow_binary64
86×associate-*r/_binary64
76×swap-sqr_binary64 associate-/l*_binary64
75×exp-diff_binary64
74×div-sub_binary64
73×log-div_binary64
53×neg-mul-1_binary64
50×rem-sqrt-square_binary64
49×neg-sub0_binary64
47×distribute-rgt-in_binary64
44×distribute-rgt-out_binary64
42×distribute-lft-in_binary64
40×exp-to-pow_binary64
39×associate-/r*_binary64
36×*-rgt-identity_binary64 *-lft-identity_binary64
34×cube-prod_binary64 times-frac_binary64 pow-sqr_binary64
32×cancel-sign-sub-inv_binary64
30×exp-neg_binary64
27×associate-+r-_binary64
24×+-commutative_binary64
23×unpow1/2_binary64
22×unpow2_binary64 pow-plus_binary64 unpow1_binary64
21×distribute-rgt-neg-out_binary64
19×associate-+r+_binary64
18×log-rec_binary64 associate-/l/_binary64
17×cube-unmult_binary64 distribute-lft-neg-out_binary64 associate-+l+_binary64
16×unpow1/3_binary64
14×distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 associate-/r/_binary64
13×associate-+l-_binary64
12×exp-lft-sqr_binary64 distribute-lft-out_binary64
10×distribute-neg-out_binary64 distribute-rgt-out--_binary64
cube-div_binary64 +-rgt-identity_binary64
/-rgt-identity_binary64
remove-double-neg_binary64 distribute-neg-in_binary64 associate--l+_binary64 associate--r+_binary64
sub0-neg_binary64
rem-exp-log_binary64 distribute-frac-neg_binary64 associate--r-_binary64 associate--l-_binary64
rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64
unpow3_binary64 prod-exp_binary64 --rgt-identity_binary64 cancel-sign-sub_binary64 count-2_binary64
log-E_binary64 1-exp_binary64 exp-1-e_binary64 cube-mult_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 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-0_binary64 rem-log-exp_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_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 difference-of-squares_binary64 distribute-neg-frac_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64
Counts
219 → 185
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02625841
14834547
210954199
322094090
447824090
549744090
649924090
749514090

prune176.0ms (4.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1832185
Fresh325
Picked101
Done011
Total1875192
Error
4.2b
Counts
192 → 5
Compiler

Compiled 3614 to 2098 computations (41.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f64 (/.f64 x y) 2)
0.3b
(pow.f64 (/.f64 x y) 2)
12.0b
(pow.f64 (pow.f64 (/.f64 x y) 2) 2/3)
24.2b
(cbrt.f64 (pow.f64 (/.f64 x y) 2))

rewrite181.0ms (4.5%)

Algorithm
rewrite-expression-head
Error
4.2b
Rules
70×unpow-prod-down_binary64
37×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
36×times-frac_binary64
18×cbrt-prod_binary64
14×add-exp-log_binary64
10×pow-exp_binary64
pow-unpow_binary64
pow1_binary64
sqr-pow_binary64
add-log-exp_binary64 add-cbrt-cube_binary64 div-inv_binary64 unpow2_binary64 pow-to-exp_binary64
pow-pow_binary64 div-exp_binary64
pow1/3_binary64
Counts
4 → 119
Calls

4 calls:

6.0ms
(pow.f64 (pow.f64 (/.f64 x y) 2) 2/3)
5.0ms
(pow.f64 (/.f64 x y) 2)
4.0ms
(pow.f64 (/.f64 x y) 2)
4.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
Compiler

Compiled 2933 to 1882 computations (35.8% saved)

series158.0ms (3.9%)

Error
4.2b
Counts
4 → 24
Calls

4 calls:

49.0ms
(cbrt.f64 (pow.f64 (/.f64 x y) 2))
47.0ms
(pow.f64 (pow.f64 (/.f64 x y) 2) 2/3)
23.0ms
(pow.f64 (/.f64 x y) 2)
20.0ms
(pow.f64 (/.f64 x y) 2)
Compiler

Compiled 1450 to 1285 computations (11.4% saved)

simplify132.0ms (3.3%)

Algorithm
egg-herbie
Rules
363×sqr-pow_binary64
358×associate-*l*_binary64
335×exp-prod_binary64
323×associate-*r*_binary64
197×log-pow_binary64
181×exp-sum_binary64
174×log-prod_binary64
173×unswap-sqr_binary64
126×cube-prod_binary64
124×unsub-neg_binary64
123×associate-*l/_binary64
105×associate-*r/_binary64
93×pow-sqr_binary64
88×*-commutative_binary64
87×associate-/l*_binary64
73×rem-sqrt-square_binary64
66×sub-neg_binary64
64×cube-unmult_binary64
57×distribute-rgt-in_binary64
52×log-div_binary64 pow-plus_binary64
51×exp-diff_binary64
47×distribute-lft-in_binary64
45×div-sub_binary64 associate-/r*_binary64
44×times-frac_binary64
43×exp-to-pow_binary64
38×neg-sub0_binary64
35×cube-div_binary64 neg-mul-1_binary64
32×unpow1/3_binary64
26×distribute-rgt-out_binary64
25×exp-neg_binary64
24×associate-/l/_binary64
23×unpow1/2_binary64 unpow1_binary64
22×unpow2_binary64
21×exp-lft-sqr_binary64 distribute-rgt-neg-out_binary64 associate-+r-_binary64
20×associate-+r+_binary64
19×*-rgt-identity_binary64
18×distribute-lft-neg-out_binary64 associate-/r/_binary64 associate-+l+_binary64
16×cancel-sign-sub-inv_binary64 +-commutative_binary64
14×*-lft-identity_binary64
12×prod-exp_binary64
10×cube-mult_binary64 /-rgt-identity_binary64 associate-+l-_binary64
unpow3_binary64 swap-sqr_binary64
distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
log-rec_binary64
rem-exp-log_binary64 +-rgt-identity_binary64 distribute-lft-out_binary64
distribute-neg-out_binary64 distribute-rgt-out--_binary64
pow-base-1_binary64 remove-double-neg_binary64 distribute-neg-in_binary64
sub0-neg_binary64 associate--l+_binary64 associate--r+_binary64
rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 distribute-frac-neg_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64
log-E_binary64 rec-exp_binary64 1-exp_binary64 exp-1-e_binary64 --rgt-identity_binary64 cancel-sign-sub_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 pow-base-0_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_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 difference-of-squares_binary64 distribute-neg-frac_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64
Counts
143 → 120
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02032548
14441918
28681665
330551563
449561563
550161563

prune79.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1164120
Fresh213
Picked101
Done011
Total1196125
Error
4.2b
Counts
125 → 6
Compiler

Compiled 1490 to 915 computations (38.6% saved)

regimes365.0ms (9.1%)

Accuracy

Total 4.1b remaining (91.8%)

Threshold costs 0b (0%)

Compiler

Compiled 2709 to 2123 computations (21.6% saved)

bsearch3.0ms (0.1%)

Compiler

Compiled 15 to 9 computations (40% saved)

simplify7.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
1-exp_binary64 neg-mul-1_binary64 neg-sub0_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 sqr-abs_binary64 sqr-neg_binary64 unsub-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-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02680
13680
23980
34180
44280
54180

end1.0ms (0%)

Compiler

Compiled 53 to 27 computations (49.1% saved)

sample993.0ms (24.8%)

Algorithm
intervals
Results
311.0ms8000×body128valid
156.0ms8000×pre128true
Compiler

Compiled 224 to 162 computations (27.7% saved)

Profiling

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