Details

Time bar (total: 2.4s)

analyze404.0ms (16.8%)

Algorithm
search
egg-herbie
Rules
1067×sqr-pow_binary64
651×pow-sqr_binary64
454×associate-*l*_binary64
434×unswap-sqr_binary64
278×*-commutative_binary64
265×cube-prod_binary64
245×associate-*r*_binary64
201×unpow3_binary64
198×cube-mult_binary64
52×pow-plus_binary64
21×rem-sqrt-square_binary64
cube-unmult_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_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 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 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-div_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 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-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 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 swap-sqr_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 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 +-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1129
2229
3419
4889
52199
66879
710839
810839
912279
1013959
1116259
1219369
1323219
1427759
1533089
1635299
1735999
1836099
1936119
2036119
2141889
2248379
2347569
011
111
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0.1%14
Compiler

Compiled 7 to 7 computations (0% saved)

sample19.0ms (0.8%)

Algorithm
intervals
Results
9.0ms256×body128valid
Compiler

Compiled 13 to 14 computations (-7.7% saved)

simplify168.0ms (7%)

Algorithm
egg-herbie
Rules
1067×sqr-pow_binary64
651×pow-sqr_binary64
454×associate-*l*_binary64
434×unswap-sqr_binary64
278×*-commutative_binary64
265×cube-prod_binary64
245×associate-*r*_binary64
201×unpow3_binary64
198×cube-mult_binary64
52×pow-plus_binary64
21×rem-sqrt-square_binary64
cube-unmult_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_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 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 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-div_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 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-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 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 swap-sqr_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 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 +-commutative_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
1129
2229
3419
4889
52199
66879
710839
810839
912279
1013959
1116259
1219369
1323219
1427759
1533089
1635299
1735999
1836099
1936119
2036119
2141889
2248379
2347569

prune4.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
27.9b
Counts
2 → 1
Compiler

Compiled 12 to 11 computations (8.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 2 (pow.f64 x 2))
26.9b
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

rewrite69.0ms (2.9%)

Algorithm
rewrite-expression-head
Error
27.8b
Rules
11×add-sqr-sqrt_binary64
associate-*r*_binary64
add-exp-log_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
add-cbrt-cube_binary64 unpow-prod-down_binary64 unswap-sqr_binary64
pow1_binary64 prod-exp_binary64 associate-*l*_binary64
add-log-exp_binary64 unpow2_binary64 sqr-pow_binary64
pow1/2_binary64 sqrt-pow1_binary64 sqrt-prod_binary64 pow-to-exp_binary64 pow-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
2 → 37
Calls

2 calls:

6.0ms
(*.f64 2 (pow.f64 x 2))
4.0ms
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
Compiler

Compiled 420 to 357 computations (15% saved)

series31.0ms (1.3%)

Error
0.2b
Counts
2 → 6
Calls

2 calls:

19.0ms
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
7.0ms
(*.f64 2 (pow.f64 x 2))
Compiler

Compiled 80 to 78 computations (2.5% saved)

simplify64.0ms (2.6%)

Algorithm
egg-herbie
Rules
371×*-commutative_binary64
349×sqr-pow_binary64
257×unswap-sqr_binary64
248×times-frac_binary64
237×log-prod_binary64
231×associate-*l*_binary64
220×exp-prod_binary64
212×cube-prod_binary64
193×associate-/l*_binary64
184×associate-*r*_binary64
169×associate-/l/_binary64
161×pow-sqr_binary64
160×associate-/r*_binary64
126×associate-+l+_binary64
111×distribute-rgt-in_binary64
82×distribute-lft-in_binary64 associate-+r+_binary64
70×distribute-rgt-out_binary64
67×associate-/r/_binary64
63×unpow3_binary64
56×swap-sqr_binary64
55×distribute-rgt-neg-in_binary64
54×cube-mult_binary64
50×distribute-lft-neg-in_binary64
37×associate-*r/_binary64
33×log-pow_binary64 pow-plus_binary64
30×neg-sub0_binary64
27×neg-mul-1_binary64
25×rem-sqrt-square_binary64
20×sub-neg_binary64
18×distribute-lft-out_binary64
17×cancel-sign-sub-inv_binary64
14×cube-unmult_binary64 *-rgt-identity_binary64 count-2_binary64
11×*-lft-identity_binary64 associate-*l/_binary64
+-commutative_binary64
unpow2_binary64 unpow1_binary64 exp-lft-sqr_binary64 unsub-neg_binary64
mul-1-neg_binary64
unpow1/2_binary64
/-rgt-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-lft-neg-out_binary64
prod-exp_binary64 rem-square-sqrt_binary64 distribute-rgt-neg-out_binary64
1-exp_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 sub0-neg_binary64 --rgt-identity_binary64 associate-+l-_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 log-div_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-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-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-div_binary64 cube-neg_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 +-lft-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 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64
Counts
43 → 35
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
064421
1106376
2241366
3819360
41606360
53727360
64987360

prune26.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New31435
Fresh000
Picked011
Done000
Total31536
Error
0.2b
Counts
36 → 5
Compiler

Compiled 297 to 204 computations (31.3% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.4b
(*.f64 (sqrt.f64 2) (fabs.f64 x))

rewrite22.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
add-sqr-sqrt_binary64
associate-*l*_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64 sqrt-prod_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 associate-*r*_binary64
unswap-sqr_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
1 → 22
Calls

1 calls:

5.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
Compiler

Compiled 201 to 140 computations (30.3% saved)

series10.0ms (0.4%)

Error
0.2b
Counts
1 → 3
Calls

1 calls:

9.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
Compiler

Compiled 35 to 35 computations (0% saved)

simplify85.0ms (3.5%)

Algorithm
egg-herbie
Rules
411×log-div_binary64
359×unswap-sqr_binary64
274×associate-*l*_binary64
263×log-prod_binary64
258×associate-*l/_binary64
193×associate-/l/_binary64
192×associate-+l+_binary64
188×cube-div_binary64
164×associate-*r/_binary64
159×*-commutative_binary64
153×associate-*r*_binary64
147×associate-+l-_binary64
139×associate-/l*_binary64
126×exp-prod_binary64 sqr-pow_binary64
121×cube-prod_binary64
107×associate-/r/_binary64
99×unpow3_binary64
98×associate-+r-_binary64
72×associate-+r+_binary64
60×associate-/r*_binary64 associate--l+_binary64
54×swap-sqr_binary64
45×pow-sqr_binary64
38×log-pow_binary64
34×log-rec_binary64
29×unsub-neg_binary64 distribute-lft-out_binary64
28×pow-plus_binary64
25×*-lft-identity_binary64
22×times-frac_binary64 distribute-rgt-out_binary64
21×exp-sqrt_binary64 cube-unmult_binary64 rem-sqrt-square_binary64
20×*-rgt-identity_binary64
18×distribute-rgt-in_binary64
16×cube-mult_binary64
14×prod-exp_binary64
13×exp-lft-sqr_binary64
12×distribute-lft-in_binary64
11×+-commutative_binary64
distribute-rgt1-in_binary64 associate--l-_binary64
unpow2_binary64 sub-neg_binary64
remove-double-div_binary64
distribute-lft1-in_binary64
unpow1/2_binary64
neg-mul-1_binary64 neg-sub0_binary64 /-rgt-identity_binary64 distribute-neg-out_binary64 count-2_binary64
unpow1_binary64 1-exp_binary64 exp-1-e_binary64 sqr-abs_binary64 rem-square-sqrt_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 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 div-exp_binary64 rec-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_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-neg_binary64 div-sub_binary64 mul-1-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_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 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--r+_binary64
Counts
25 → 8
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
036282
167270
2167270
3279270
4409270
5640270
6967270
72319270
84358270
94925270
104863270

prune12.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New628
Fresh123
Picked011
Done011
Total7613
Error
0.0b
Counts
13 → 6
Compiler

Compiled 102 to 88 computations (13.7% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.3b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))

rewrite68.0ms (2.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
16×pow1_binary64 add-exp-log_binary64
12×add-sqr-sqrt_binary64
10×associate-*r*_binary64
pow-prod-down_binary64 prod-exp_binary64 add-cbrt-cube_binary64 cbrt-unprod_binary64
cbrt-prod_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
associate-*l*_binary64 sqrt-prod_binary64
unswap-sqr_binary64
add-log-exp_binary64 *-commutative_binary64
Counts
2 → 48
Calls

2 calls:

11.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
6.0ms
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
Compiler

Compiled 880 to 739 computations (16% saved)

series31.0ms (1.3%)

Error
0.0b
Counts
2 → 6
Calls

2 calls:

19.0ms
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
8.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
Compiler

Compiled 155 to 151 computations (2.6% saved)

simplify96.0ms (4%)

Algorithm
egg-herbie
Rules
428×associate-/l*_binary64
418×associate-/l/_binary64
406×associate-/r/_binary64
364×distribute-rgt-in_binary64
351×distribute-lft-in_binary64
332×*-commutative_binary64
263×sqr-pow_binary64
244×unswap-sqr_binary64
208×log-div_binary64
125×associate-*l*_binary64
114×distribute-lft-out_binary64
112×associate-*r*_binary64
106×distribute-rgt-out_binary64
104×pow-sqr_binary64
98×log-prod_binary64 times-frac_binary64
97×exp-prod_binary64
91×associate-+l+_binary64
71×+-commutative_binary64
63×associate-+r+_binary64
62×cube-prod_binary64
56×count-2_binary64
44×associate-*r/_binary64
39×associate-/r*_binary64
37×rem-sqrt-square_binary64
30×swap-sqr_binary64
26×log-pow_binary64
20×distribute-rgt1-in_binary64
13×unpow3_binary64
12×pow-plus_binary64 cube-mult_binary64 *-rgt-identity_binary64 *-lft-identity_binary64
11×cube-div_binary64
cube-unmult_binary64
unpow1/2_binary64 distribute-lft1-in_binary64
associate-*l/_binary64
log-rec_binary64
unpow2_binary64 /-rgt-identity_binary64
unpow1/3_binary64 unpow1_binary64 exp-lft-sqr_binary64 exp-sqrt_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 sqr-abs_binary64 rem-square-sqrt_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 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-neg_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_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 difference-of-squares_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 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
54 → 31
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0751151
1155624
2480624
3805624
41536624
52897624
64962624
75097624

prune18.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New29231
Fresh123
Picked101
Done022
Total31637
Error
0.0b
Counts
37 → 6
Compiler

Compiled 282 to 232 computations (17.7% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.2b
(*.f64 (fabs.f64 x) (pow.f64 (sqrt.f64 2) 2/3))
0.3b
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (fabs.f64 x) (pow.f64 (sqrt.f64 2) 2/3)))

rewrite72.0ms (3%)

Algorithm
rewrite-expression-head
Error
0b
Rules
17×add-exp-log_binary64
16×add-sqr-sqrt_binary64
12×associate-*l*_binary64
11×associate-*r*_binary64
10×prod-exp_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
unpow-prod-down_binary64
add-cbrt-cube_binary64 sqrt-prod_binary64
cbrt-prod_binary64
pow1_binary64 cbrt-unprod_binary64 unswap-sqr_binary64
pow-to-exp_binary64 pow-exp_binary64 add-log-exp_binary64 *-commutative_binary64 sqr-pow_binary64
pow-prod-down_binary64
Counts
2 → 54
Calls

2 calls:

11.0ms
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (fabs.f64 x) (pow.f64 (sqrt.f64 2) 2/3)))
6.0ms
(*.f64 (fabs.f64 x) (pow.f64 (sqrt.f64 2) 2/3))
Compiler

Compiled 869 to 721 computations (17% saved)

series32.0ms (1.3%)

Error
0.0b
Counts
2 → 6
Calls

2 calls:

21.0ms
(*.f64 (fabs.f64 x) (pow.f64 (sqrt.f64 2) 2/3))
8.0ms
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (fabs.f64 x) (pow.f64 (sqrt.f64 2) 2/3)))
Compiler

Compiled 139 to 135 computations (2.9% saved)

simplify79.0ms (3.3%)

Algorithm
egg-herbie
Rules
912×unswap-sqr_binary64
654×associate-/l/_binary64
328×*-commutative_binary64
281×sqr-pow_binary64
176×times-frac_binary64
136×distribute-rgt-in_binary64
131×associate-/l*_binary64
125×distribute-lft-in_binary64
112×associate-*r*_binary64
107×pow-sqr_binary64
105×associate-*l*_binary64
96×exp-prod_binary64
91×log-prod_binary64
87×+-commutative_binary64
78×distribute-lft-out_binary64
72×associate-+l+_binary64
70×distribute-rgt-out_binary64 associate-/r/_binary64
61×associate-/r*_binary64
60×cube-prod_binary64
56×swap-sqr_binary64
54×associate-+r+_binary64
53×associate-*r/_binary64
31×rem-sqrt-square_binary64
30×count-2_binary64
29×*-rgt-identity_binary64
26×*-lft-identity_binary64
20×log-pow_binary64
18×associate-*l/_binary64
16×log-div_binary64 cube-div_binary64
13×cube-unmult_binary64 distribute-rgt1-in_binary64
12×pow-plus_binary64
unpow3_binary64
unpow1/2_binary64
cube-mult_binary64
unpow1/3_binary64 pow-base-1_binary64
unpow2_binary64 distribute-lft1-in_binary64
log-rec_binary64 unpow1_binary64 exp-lft-sqr_binary64 exp-sqrt_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 sqr-abs_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 exp-to-pow_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-neg_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_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 difference-of-squares_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 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
60 → 42
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
088999
1177902
2537752
3817752
41449752
53226752
64873752

prune27.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New40242
Fresh303
Picked011
Done022
Total43548
Error
0b
Counts
48 → 5
Compiler

Compiled 404 to 327 computations (19.1% saved)

regimes369.0ms (15.3%)

Accuracy

Total 0.4b remaining (97.5%)

Threshold costs 0.4b (97.5%)

Compiler

Compiled 3801 to 3435 computations (9.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_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 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-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 +-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01244
11544
21544

end2.0ms (0.1%)

Compiler

Compiled 25 to 25 computations (0% saved)

sample667.0ms (27.7%)

Algorithm
intervals
Results
278.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 98 to 102 computations (-4.1% saved)

Profiling

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