Details

Time bar (total: 3.0s)

analyze73.0ms (2.4%)

Algorithm
search
egg-herbie
Rules
90×cancel-sign-sub-inv_binary64
62×sub-neg_binary64
52×distribute-rgt-in_binary64
46×associate--r+_binary64
26×distribute-rgt-neg-in_binary64
24×neg-mul-1_binary64 associate-+l-_binary64
22×unsub-neg_binary64 associate--l-_binary64 associate--l+_binary64 +-commutative_binary64
20×div-sub_binary64 *-commutative_binary64
18×distribute-lft-neg-in_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-+l+_binary64
16×sub0-neg_binary64 distribute-rgt-out--_binary64 associate-+r+_binary64
14×associate-*r*_binary64
12×neg-sub0_binary64 associate--r-_binary64 associate-+r-_binary64
10×distribute-neg-in_binary64 distribute-rgt-neg-out_binary64
distribute-neg-frac_binary64 distribute-neg-out_binary64 distribute-lft-neg-out_binary64
+-rgt-identity_binary64 +-lft-identity_binary64
*-lft-identity_binary64 remove-double-neg_binary64 associate-*l*_binary64
distribute-frac-neg_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 associate-/l/_binary64 associate-/r/_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 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 --rgt-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 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-rgt1-in_binary64 distribute-rgt-out_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 count-2_binary64 associate-*l/_binary64 associate-*r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01020
12020
24020
37220
413320
522220
636020
742020
846420
947220
1041220
022
122
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
50%50%0.1%4
50%50%0.1%5
74.9%25%0.1%6
74.9%25%0.1%7
87.4%12.5%0.1%8
87.4%12.5%0.1%9
93.7%6.2%0.1%10
93.7%6.2%0.1%11
96.8%3.1%0.1%12
96.8%3.1%0.1%13
98.3%1.6%0.1%14
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample14.0ms (0.5%)

Algorithm
intervals
Results
6.0ms242×body128valid
0.0msbody2048valid
0.0msbody512valid
0.0msbody1024valid
0.0msbody256valid
Compiler

Compiled 15 to 15 computations (0% saved)

simplify21.0ms (0.7%)

Algorithm
egg-herbie
Rules
90×cancel-sign-sub-inv_binary64
49×sub-neg_binary64
40×distribute-rgt-in_binary64
29×distribute-rgt-neg-in_binary64
25×associate--r+_binary64
23×unsub-neg_binary64
21×div-sub_binary64
19×neg-mul-1_binary64 associate--r-_binary64
18×associate-/r*_binary64
17×distribute-lft-neg-out_binary64
16×associate-/l*_binary64 associate-+l-_binary64
15×distribute-neg-in_binary64 *-commutative_binary64 +-commutative_binary64
12×neg-sub0_binary64 sub0-neg_binary64 distribute-rgt-neg-out_binary64 associate-+l+_binary64
10×distribute-neg-frac_binary64 distribute-lft-neg-in_binary64 associate--l+_binary64
associate--l-_binary64
associate-+r-_binary64 associate-+r+_binary64
*-lft-identity_binary64
+-lft-identity_binary64 distribute-rgt-out--_binary64 distribute-lft-in_binary64 associate-/r/_binary64
distribute-neg-out_binary64
--rgt-identity_binary64 +-rgt-identity_binary64
*-rgt-identity_binary64 remove-double-neg_binary64 distribute-lft-out--_binary64 associate-/l/_binary64 associate-*r*_binary64
1-exp_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_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-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 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 mul-1-neg_binary64 /-rgt-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 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-lft1-in_binary64 distribute-rgt-out_binary64 distribute-lft-out_binary64 count-2_binary64 associate-*l/_binary64 associate-*r/_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
11310
22410
34210
47510
513410
620610
727610
833010
936510
1037010
1131010

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.1b
Counts
1 → 1
Compiler

Compiled 7 to 6 computations (14.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 x (/.f64 (-.f64 x y) 2))

rewrite19.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
add-log-exp_binary64 *-un-lft-identity_binary64
sum-log_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 flip-+_binary64 distribute-lft-out_binary64 div-sub_binary64 associate-+r-_binary64 +-commutative_binary64
Counts
1 → 13
Calls

1 calls:

9.0ms
(+.f64 x (/.f64 (-.f64 x y) 2))
Compiler

Compiled 187 to 102 computations (45.5% saved)

series27.0ms (0.9%)

Error
0.1b
Counts
1 → 12
Calls

1 calls:

23.0ms
(+.f64 x (/.f64 (-.f64 x y) 2))
Compiler

Compiled 115 to 119 computations (-3.5% saved)

simplify68.0ms (2.3%)

Algorithm
egg-herbie
Rules
585×div-sub_binary64
455×distribute-rgt-in_binary64
436×neg-mul-1_binary64
427×distribute-lft-in_binary64
379×unsub-neg_binary64
274×times-frac_binary64
245×distribute-rgt-neg-out_binary64
236×distribute-rgt-out_binary64
206×distribute-lft-neg-out_binary64
197×cancel-sign-sub-inv_binary64
133×sub-neg_binary64
132×distribute-neg-in_binary64
130×associate-+l+_binary64
123×associate-+r+_binary64
119×associate-*l/_binary64
107×associate-*l*_binary64
101×associate-*r/_binary64
100×associate-*r*_binary64
72×neg-sub0_binary64
59×associate-/l*_binary64
58×distribute-rgt-neg-in_binary64
49×distribute-lft-neg-in_binary64
46×*-commutative_binary64
45×exp-sum_binary64
44×distribute-frac-neg_binary64 +-commutative_binary64
38×distribute-neg-frac_binary64
36×exp-prod_binary64
34×distribute-neg-out_binary64
30×exp-diff_binary64 associate-+l-_binary64
28×associate-+r-_binary64
26×unswap-sqr_binary64
25×distribute-rgt-out--_binary64
22×sqr-pow_binary64
21×remove-double-neg_binary64 associate-/r/_binary64 associate--r+_binary64
19×associate-/l/_binary64
14×cube-prod_binary64 +-rgt-identity_binary64
12×mul0-rgt_binary64 mul0-lft_binary64
11×sub0-neg_binary64
10×cube-unmult_binary64 associate-/r*_binary64 associate--r-_binary64
associate--l+_binary64
div0_binary64
unpow3_binary64 prod-exp_binary64
exp-sqrt_binary64
pow-plus_binary64 cube-neg_binary64 sqr-neg_binary64 --rgt-identity_binary64 swap-sqr_binary64 associate--l-_binary64
div-exp_binary64 exp-neg_binary64 cube-mult_binary64
cube-div_binary64 rem-sqrt-square_binary64 difference-of-squares_binary64
rec-exp_binary64 1-exp_binary64 exp-1-e_binary64 fabs-div_binary64 fabs-mul_binary64 mul-1-neg_binary64 *-lft-identity_binary64 pow-sqr_binary64 distribute-rgt1-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 unpow2_binary64 unpow1/2_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 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 +-lft-identity_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 cancel-sign-sub_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64
Counts
25 → 10
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037306
1104285
2230282
3668282
42467282
54066282
65191282

prune7.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New6410
Fresh000
Picked011
Done000
Total6511
Error
0.0b
Counts
11 → 5
Compiler

Compiled 143 to 90 computations (37.1% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(+.f64 (*.f64 -1/2 y) (*.f64 3/2 x))

rewrite18.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
add-log-exp_binary64
sum-log_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 *-un-lft-identity_binary64 flip-+_binary64 +-commutative_binary64
Counts
1 → 11
Calls

1 calls:

4.0ms
(+.f64 (*.f64 -1/2 y) (*.f64 3/2 x))
Compiler

Compiled 178 to 138 computations (22.5% saved)

series22.0ms (0.7%)

Error
0.0b
Counts
1 → 12
Calls

1 calls:

20.0ms
(+.f64 (*.f64 -1/2 y) (*.f64 3/2 x))
Compiler

Compiled 115 to 119 computations (-3.5% saved)

simplify77.0ms (2.6%)

Algorithm
egg-herbie
Rules
425×neg-sub0_binary64
404×neg-mul-1_binary64
364×distribute-rgt-out_binary64
344×distribute-rgt-neg-in_binary64
336×times-frac_binary64
334×distribute-rgt-neg-out_binary64
325×distribute-lft-neg-out_binary64
303×distribute-rgt-in_binary64
271×distribute-lft-in_binary64
261×*-commutative_binary64
241×distribute-lft-neg-in_binary64
222×associate-*l*_binary64
175×associate-*r*_binary64
160×cancel-sign-sub-inv_binary64
136×distribute-neg-in_binary64
106×unswap-sqr_binary64
87×sub-neg_binary64
85×remove-double-neg_binary64
82×associate-+l+_binary64
79×associate-+r+_binary64
72×distribute-rgt-out--_binary64
69×unsub-neg_binary64 distribute-lft-out_binary64
68×sqr-pow_binary64
53×exp-prod_binary64
45×cube-prod_binary64
31×mul0-rgt_binary64 mul0-lft_binary64
30×distribute-neg-out_binary64
26×cancel-sign-sub_binary64 +-commutative_binary64
17×exp-sum_binary64
16×exp-diff_binary64 associate-+l-_binary64
15×div-sub_binary64 pow-sqr_binary64
13×associate-+r-_binary64
11×sub0-neg_binary64 swap-sqr_binary64
unpow3_binary64 cube-unmult_binary64 cube-neg_binary64
+-rgt-identity_binary64
sqr-neg_binary64 difference-of-squares_binary64
cube-mult_binary64 distribute-frac-neg_binary64
pow-plus_binary64 exp-neg_binary64 distribute-lft-out--_binary64 associate-*r/_binary64 associate--r-_binary64 associate--r+_binary64
associate-/l/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate--l-_binary64 associate--l+_binary64
unpow1/2_binary64 *-lft-identity_binary64 distribute-rgt1-in_binary64 associate-/r/_binary64 associate-*l/_binary64
log-prod_binary64 prod-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-sqrt-square_binary64 mul-1-neg_binary64 *-rgt-identity_binary64 --rgt-identity_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 pow-base-0_binary64 unpow1/3_binary64 unpow2_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 div-exp_binary64 rec-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_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-square-sqrt_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 distribute-neg-frac_binary64 count-2_binary64
Counts
23 → 11
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
032283
1118259
2341259
31086259
42664259
54129259
65003259

prune10.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New9211
Fresh213
Picked011
Done011
Total11516
Error
0.0b
Counts
16 → 5
Compiler

Compiled 186 to 141 computations (24.2% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y))) (cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y))))
0.6b
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
0.6b
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
0.6b
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))

rewrite135.0ms (4.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
25×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
18×cbrt-div_binary64
15×add-cube-cbrt_binary64 *-un-lft-identity_binary64
11×pow1_binary64
pow1/3_binary64 flip3--_binary64 flip--_binary64
add-exp-log_binary64 swap-sqr_binary64 associate-*l*_binary64 associate-*r*_binary64
add-log-exp_binary64 add-cbrt-cube_binary64 frac-times_binary64 unswap-sqr_binary64
pow-prod-down_binary64 pow-prod-up_binary64 pow-sqr_binary64 associate-*l/_binary64 associate-*r/_binary64
pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
4 → 87
Calls

4 calls:

11.0ms
(*.f64 (cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y))) (cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y))))
4.0ms
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
3.0ms
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
3.0ms
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
Compiler

Compiled 3219 to 2525 computations (21.6% saved)

series311.0ms (10.4%)

Error
0.0b
Counts
4 → 58
Calls

4 calls:

66.0ms
(*.f64 (cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y))) (cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y))))
55.0ms
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
55.0ms
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
55.0ms
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
Compiler

Compiled 6168 to 5313 computations (13.9% saved)

simplify127.0ms (4.3%)

Algorithm
egg-herbie
Rules
705×times-frac_binary64
535×associate-/l*_binary64
230×distribute-rgt-neg-in_binary64
219×distribute-lft-neg-in_binary64
213×cancel-sign-sub-inv_binary64
171×associate-*r*_binary64
141×associate-/r/_binary64
118×associate-*l*_binary64
113×distribute-neg-frac_binary64 *-commutative_binary64
105×sub-neg_binary64
104×unswap-sqr_binary64
87×distribute-rgt-in_binary64
85×sqr-pow_binary64
81×neg-mul-1_binary64 neg-sub0_binary64
68×distribute-lft-in_binary64
46×+-commutative_binary64
36×exp-sum_binary64 associate-/r*_binary64 associate-*r/_binary64
32×distribute-neg-in_binary64
28×exp-prod_binary64 distribute-lft-neg-out_binary64
24×unsub-neg_binary64 associate-*l/_binary64
22×associate--r+_binary64
21×distribute-rgt-out_binary64
17×unpow1/3_binary64
15×distribute-rgt-neg-out_binary64
14×log-prod_binary64
13×cube-prod_binary64
12×pow-sqr_binary64
*-rgt-identity_binary64
exp-diff_binary64 div-sub_binary64 *-lft-identity_binary64
fabs-mul_binary64
swap-sqr_binary64 associate-+l+_binary64 associate-+r+_binary64
log-div_binary64 unpow3_binary64 cube-unmult_binary64 cube-mult_binary64 remove-double-neg_binary64 distribute-lft-out_binary64 associate-/l/_binary64 associate--r-_binary64
log-pow_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 unpow1_binary64 rem-sqrt-square_binary64 difference-of-squares_binary64 associate--l+_binary64
log-rec_binary64 rem-3cbrt-lft_binary64 count-2_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 fabs-sqr_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-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-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_binary64 /-rgt-identity_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 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 associate--l-_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
145 → 132
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02384912
16144707
218724413
352624413

prune158.0ms (5.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1302132
Fresh022
Picked011
Done112
Total1316137
Error
0.0b
Counts
137 → 6
Compiler

Compiled 4603 to 3590 computations (22% saved)

localize23.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
0.6b
(cbrt.f64 (+.f64 (*.f64 -1/2 y) (*.f64 3/2 x)))
0.6b
(cbrt.f64 (+.f64 (*.f64 -1/2 y) (*.f64 3/2 x)))
1.1b
(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (*.f64 -1/2 y) (*.f64 3/2 x)))) 6)

rewrite124.0ms (4.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
18×cbrt-prod_binary64
11×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
unpow-prod-down_binary64
cbrt-div_binary64
pow1_binary64 add-exp-log_binary64
pow1/3_binary64 add-log-exp_binary64 add-cbrt-cube_binary64
pow-unpow_binary64
pow-pow_binary64 flip3-+_binary64 flip-+_binary64
pow-to-exp_binary64 pow-exp_binary64 sqr-pow_binary64 flip3--_binary64 flip--_binary64
Counts
4 → 63
Calls

4 calls:

6.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (*.f64 -1/2 y) (*.f64 3/2 x)))) 6)
4.0ms
(cbrt.f64 (+.f64 (*.f64 -1/2 y) (*.f64 3/2 x)))
3.0ms
(cbrt.f64 (+.f64 (*.f64 -1/2 y) (*.f64 3/2 x)))
3.0ms
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
Compiler

Compiled 3137 to 2535 computations (19.2% saved)

series414.0ms (13.9%)

Error
0.0b
Counts
4 → 56
Calls

4 calls:

123.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 (*.f64 -1/2 y) (*.f64 3/2 x)))) 6)
65.0ms
(cbrt.f64 (-.f64 (*.f64 3/2 x) (*.f64 1/2 y)))
64.0ms
(cbrt.f64 (+.f64 (*.f64 -1/2 y) (*.f64 3/2 x)))
60.0ms
(cbrt.f64 (+.f64 (*.f64 -1/2 y) (*.f64 3/2 x)))
Compiler

Compiled 8096 to 6937 computations (14.3% saved)

simplify146.0ms (4.9%)

Algorithm
egg-herbie
Rules
791×times-frac_binary64
297×cancel-sign-sub-inv_binary64
247×unswap-sqr_binary64
194×associate-*r*_binary64
154×sqr-pow_binary64
136×associate-*l*_binary64
110×*-commutative_binary64
107×sub-neg_binary64
99×log-prod_binary64
95×distribute-neg-frac_binary64
81×neg-mul-1_binary64 neg-sub0_binary64
56×associate-/l*_binary64
46×+-commutative_binary64
45×exp-prod_binary64
44×distribute-rgt-neg-in_binary64
43×swap-sqr_binary64
38×distribute-lft-neg-in_binary64
37×associate-/r*_binary64
34×distribute-neg-in_binary64
32×associate-*r/_binary64
31×cube-prod_binary64
29×log-pow_binary64 distribute-rgt-neg-out_binary64
28×exp-sum_binary64
25×pow-sqr_binary64
24×unsub-neg_binary64
22×associate-*l/_binary64 associate--r+_binary64
19×unpow3_binary64 cube-mult_binary64
13×unpow1/3_binary64
12×associate-/r/_binary64
11×distribute-rgt-in_binary64 distribute-lft-in_binary64
rem-cube-cbrt_binary64
fabs-mul_binary64 rem-sqrt-square_binary64 associate-+l+_binary64 associate-+r+_binary64
pow-plus_binary64 difference-of-squares_binary64
distribute-rgt-out_binary64
log-div_binary64 unpow1/2_binary64 unpow1_binary64 prod-exp_binary64 exp-diff_binary64 cube-unmult_binary64 div-sub_binary64 associate--r-_binary64 associate--l+_binary64
unpow2_binary64 distribute-lft-neg-out_binary64 distribute-rgt-out--_binary64
log-rec_binary64 rem-3cbrt-lft_binary64 fabs-sqr_binary64 remove-double-neg_binary64
1-exp_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 rem-square-sqrt_binary64 distribute-neg-out_binary64 associate-+l-_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 pow-base-0_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-div_binary64 rem-3cbrt-rft_binary64 fabs-div_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 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 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate-/l/_binary64 associate--l-_binary64
Counts
119 → 105
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02543810
16743677
221203527
349443527
450013527

prune157.0ms (5.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1023105
Fresh123
Picked011
Done022
Total1038111
Error
0b
Counts
111 → 8
Compiler

Compiled 5145 to 4116 computations (20% saved)

regimes310.0ms (10.4%)

Accuracy

Total 0.1b remaining (58.2%)

Threshold costs 0.1b (58.2%)

Compiler

Compiled 4983 to 4163 computations (16.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64 *-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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_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
0710
11010
21510
31710
41810
51810

end1.0ms (0%)

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample696.0ms (23.3%)

Algorithm
intervals
Results
177.0ms7411×body128valid
15.0ms209×body1024valid
14.0ms153×body2048valid
8.0ms140×body512valid
3.0ms87×body256valid
0.0msbody128invalid
Compiler

Compiled 286 to 241 computations (15.7% saved)

Profiling

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