Details

Time bar (total: 1.8s)

analyze84.0ms (4.6%)

Algorithm
search
egg-herbie
Rules
+-commutative_binary64
count-2_binary64 associate-+l+_binary64 associate-+r+_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 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 1-exp_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 sqr-neg_binary64 rem-sqrt-square_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 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-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 associate-/l/_binary64 associate-/r/_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
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0920
11720
22220
32420
42420
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
0%99.9%0.1%4
25%74.9%0.1%5
25%56.2%18.8%6
37.5%40.6%22%7
46.8%29.7%23.5%8
54.6%21.1%24.3%9
60.1%15.2%24.7%10
64.4%10.7%24.9%11
67.3%7.7%25%12
69.6%5.4%25%13
71.1%3.9%25%14
Compiler

Compiled 8 to 6 computations (25% saved)

sample13.0ms (0.7%)

Algorithm
intervals
Results
5.0ms256×body128valid
Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify9.0ms (0.5%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
count-2_binary64 associate-+l+_binary64 associate-+r+_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 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 1-exp_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 sqr-neg_binary64 rem-sqrt-square_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 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-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 associate-/l/_binary64 associate-/r/_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
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
11010
21310
31410
41410

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
0.0b
Counts
2 → 1
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite31.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
add-log-exp_binary64
sum-log_binary64 *-un-lft-identity_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 flip3-+_binary64 flip-+_binary64 +-commutative_binary64
distribute-lft-out_binary64 associate-+l+_binary64
Counts
2 → 25
Calls

2 calls:

6.0ms
(+.f64 (+.f64 (*.f64 x x) y) y)
4.0ms
(+.f64 (*.f64 x x) y)
Compiler

Compiled 354 to 86 computations (75.7% saved)

series47.0ms (2.6%)

Error
0.0b
Counts
2 → 24
Calls

2 calls:

21.0ms
(+.f64 (+.f64 (*.f64 x x) y) y)
17.0ms
(+.f64 (*.f64 x x) y)
Compiler

Compiled 252 to 232 computations (7.9% saved)

simplify83.0ms (4.5%)

Algorithm
egg-herbie
Rules
569×unswap-sqr_binary64
481×associate-*l*_binary64
470×sub-neg_binary64
318×associate-*r*_binary64
260×times-frac_binary64
181×distribute-rgt-in_binary64
170×associate-+l-_binary64
158×+-commutative_binary64
156×distribute-lft-in_binary64
145×associate-+r-_binary64
144×associate--r+_binary64
129×distribute-neg-in_binary64
122×exp-sum_binary64 cancel-sign-sub-inv_binary64
110×associate--l+_binary64
101×exp-prod_binary64 unsub-neg_binary64
96×distribute-rgt-out_binary64
89×exp-diff_binary64
88×*-commutative_binary64
80×distribute-rgt-neg-out_binary64
78×associate-+l+_binary64
69×cube-prod_binary64
62×associate-+r+_binary64
57×cancel-sign-sub_binary64
50×sqr-pow_binary64
48×sub0-neg_binary64
45×neg-mul-1_binary64
40×neg-sub0_binary64
35×distribute-lft-out_binary64
34×distribute-rgt-neg-in_binary64
31×distribute-lft-neg-in_binary64
27×pow-plus_binary64 associate--r-_binary64
25×+-rgt-identity_binary64
24×cube-unmult_binary64 associate--l-_binary64
23×unpow3_binary64
18×distribute-rgt-out--_binary64
13×sqr-neg_binary64 distribute-neg-out_binary64
12×pow-sqr_binary64 swap-sqr_binary64
10×cube-mult_binary64 distribute-lft-neg-out_binary64
difference-of-squares_binary64
+-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64
cube-neg_binary64
remove-double-neg_binary64
+-inverses_binary64
--rgt-identity_binary64 distribute-rgt1-in_binary64 distribute-lft-out--_binary64
prod-exp_binary64 distribute-lft1-in_binary64
unpow1/2_binary64 unpow1_binary64 *-lft-identity_binary64 count-2_binary64 associate-/l/_binary64 associate-/l*_binary64 associate-*r/_binary64
unpow2_binary64 exp-neg_binary64 1-exp_binary64 rem-sqrt-square_binary64 mul-1-neg_binary64 associate-/r/_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 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 div-exp_binary64 rec-exp_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 div-sub_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 div0_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 associate-*l/_binary64
Counts
49 → 39
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
051514
1142471
2343457
31068457
42859457
54571457
65173457

prune14.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New36339
Fresh000
Picked101
Done000
Total37340
Error
0b
Counts
40 → 3
Compiler

Compiled 278 to 90 computations (67.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite14.0ms (0.8%)

Algorithm
rewrite-expression-head
Error
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 associate-+l+_binary64 +-commutative_binary64
Counts
1 → 13
Calls

1 calls:

7.0ms
(+.f64 (+.f64 y y) (*.f64 x x))
Compiler

Compiled 196 to 46 computations (76.5% saved)

series27.0ms (1.5%)

Error
0b
Counts
1 → 12
Calls

1 calls:

24.0ms
(+.f64 (+.f64 y y) (*.f64 x x))
Compiler

Compiled 122 to 124 computations (-1.6% saved)

simplify57.0ms (3.1%)

Algorithm
egg-herbie
Rules
721×distribute-rgt-in_binary64
667×distribute-lft-in_binary64
459×associate-+l+_binary64
414×associate-+r+_binary64
272×unswap-sqr_binary64
172×cancel-sign-sub-inv_binary64
145×unsub-neg_binary64
140×sub-neg_binary64
135×distribute-rgt-out_binary64
132×associate-*l*_binary64
121×associate-*r*_binary64
71×distribute-rgt-neg-in_binary64
61×distribute-lft-neg-in_binary64
53×distribute-lft-out_binary64
52×*-commutative_binary64
51×sqr-pow_binary64
49×neg-mul-1_binary64
47×neg-sub0_binary64
37×associate-+l-_binary64
34×associate--r+_binary64
30×associate-+r-_binary64
23×distribute-lft-neg-out_binary64 associate--l+_binary64
22×distribute-neg-in_binary64
21×distribute-rgt-out--_binary64 +-commutative_binary64
20×count-2_binary64
17×sub0-neg_binary64 +-rgt-identity_binary64
16×exp-prod_binary64
13×mul0-rgt_binary64 mul0-lft_binary64 pow-sqr_binary64
11×cube-unmult_binary64 cube-prod_binary64 distribute-rgt-neg-out_binary64
10×difference-of-squares_binary64
unpow3_binary64
pow-plus_binary64 distribute-lft-out--_binary64
exp-sum_binary64
prod-exp_binary64 cube-mult_binary64
unpow1/2_binary64 unpow1_binary64 +-lft-identity_binary64 swap-sqr_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate-/l*_binary64 associate-*r/_binary64 associate--r-_binary64
unpow2_binary64 1-exp_binary64 rem-sqrt-square_binary64 times-frac_binary64 remove-double-neg_binary64 associate-/r/_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 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 div-exp_binary64 rec-exp_binary64 exp-diff_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 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 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_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 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 associate-*l/_binary64 associate--l-_binary64
Counts
25 → 22
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036311
1105275
2332272
31094272
44557272
55120272

prune7.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New22022
Fresh022
Picked011
Done000
Total22325
Error
0b
Counts
25 → 3
Compiler

Compiled 160 to 52 computations (67.5% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 y y) (*.f64 x x))
0.0b
(sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x)))
0.0b
(sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x)))
0.2b
(*.f64 (sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x))) (sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x))))

rewrite101.0ms (5.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
30×add-sqr-sqrt_binary64
24×sqrt-prod_binary64
21×pow1_binary64
16×sqrt-div_binary64
14×add-cube-cbrt_binary64 *-un-lft-identity_binary64
10×pow1/2_binary64 sqrt-pow1_binary64
add-log-exp_binary64 flip3-+_binary64 flip-+_binary64
swap-sqr_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 associate-*l*_binary64 associate-*r*_binary64
pow-prod-up_binary64
rem-sqrt-square_binary64 frac-times_binary64 unswap-sqr_binary64
pow-prod-down_binary64 pow-sqr_binary64 sum-log_binary64
associate-*l/_binary64 associate-*r/_binary64
pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 sqrt-unprod_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 *-commutative_binary64 associate-+l+_binary64 +-commutative_binary64
Counts
4 → 101
Calls

4 calls:

20.0ms
(*.f64 (sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x))) (sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x))))
7.0ms
(+.f64 (+.f64 y y) (*.f64 x x))
6.0ms
(sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x)))
6.0ms
(sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x)))
Compiler

Compiled 2427 to 323 computations (86.7% saved)

series125.0ms (6.8%)

Error
0b
Counts
4 → 56
Calls

4 calls:

30.0ms
(sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x)))
28.0ms
(sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x)))
27.0ms
(+.f64 (+.f64 y y) (*.f64 x x))
22.0ms
(*.f64 (sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x))) (sqrt.f64 (+.f64 (+.f64 y y) (*.f64 x x))))
Compiler

Compiled 1692 to 1130 computations (33.2% saved)

simplify178.0ms (9.7%)

Algorithm
egg-herbie
Rules
530×associate-*l*_binary64
508×cancel-sign-sub-inv_binary64
486×unswap-sqr_binary64
454×associate-*r*_binary64
258×distribute-rgt-in_binary64
237×distribute-lft-in_binary64
135×*-commutative_binary64
113×exp-prod_binary64
110×sub-neg_binary64
76×log-prod_binary64
72×sqr-pow_binary64
69×associate-+l+_binary64
66×cube-prod_binary64 associate-/l*_binary64
61×times-frac_binary64
54×swap-sqr_binary64
48×neg-sub0_binary64 associate-/r*_binary64
47×associate-+r+_binary64
46×neg-mul-1_binary64 +-commutative_binary64
42×unpow3_binary64
40×pow-plus_binary64
39×distribute-rgt-neg-in_binary64
34×distribute-lft-neg-in_binary64
33×associate-*l/_binary64
29×unsub-neg_binary64 associate-*r/_binary64
24×rem-sqrt-square_binary64 associate-+l-_binary64
23×cube-unmult_binary64 associate--r+_binary64
22×*-rgt-identity_binary64 *-lft-identity_binary64 difference-of-squares_binary64
21×associate--l+_binary64 associate-+r-_binary64
20×div-sub_binary64
19×distribute-rgt-out_binary64
18×+-rgt-identity_binary64
17×pow-sqr_binary64
15×log-pow_binary64
14×distribute-neg-frac_binary64 distribute-neg-in_binary64
13×exp-sum_binary64
11×sub0-neg_binary64 count-2_binary64
10×cube-mult_binary64
rem-square-sqrt_binary64
distribute-rgt-out--_binary64 associate-/r/_binary64
distribute-lft-neg-out_binary64
unpow2_binary64 unpow1/2_binary64
distribute-lft-out_binary64
unpow1_binary64 prod-exp_binary64
distribute-lft-out--_binary64 associate--l-_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 sqr-neg_binary64 mul-1-neg_binary64 distribute-rgt-neg-out_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-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 exp-diff_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-cube-cbrt_binary64 sqr-abs_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate--r-_binary64
Counts
157 → 130
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01202600
12572385
28052323
331442260
447742260
549522260
649422260

prune43.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1300130
Fresh011
Picked011
Done011
Total1303133
Error
0b
Counts
133 → 3
Compiler

Compiled 1592 to 392 computations (75.4% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (+.f64 y y) (*.f64 x x))
0.1b
(pow.f64 (+.f64 (+.f64 y y) (*.f64 x x)) 3)
38.0b
(cbrt.f64 (pow.f64 (+.f64 (+.f64 y y) (*.f64 x x)) 3))

rewrite57.0ms (3.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
12×cbrt-prod_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
unpow-prod-down_binary64 cube-prod_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 cube-div_binary64
flip3-+_binary64 flip-+_binary64 pow-unpow_binary64 sum-log_binary64
cbrt-div_binary64 unpow3_binary64 cube-mult_binary64 sqr-pow_binary64
pow1/3_binary64 rem-cbrt-cube_binary64 pow-pow_binary64 pow-to-exp_binary64 pow-exp_binary64 rem-cube-cbrt_binary64 associate-+l+_binary64 +-commutative_binary64
Counts
3 → 61
Calls

3 calls:

9.0ms
(pow.f64 (+.f64 (+.f64 y y) (*.f64 x x)) 3)
8.0ms
(cbrt.f64 (pow.f64 (+.f64 (+.f64 y y) (*.f64 x x)) 3))
7.0ms
(+.f64 (+.f64 y y) (*.f64 x x))
Compiler

Compiled 1040 to 339 computations (67.4% saved)

series101.0ms (5.5%)

Error
0b
Counts
3 → 48
Calls

3 calls:

39.0ms
(pow.f64 (+.f64 (+.f64 y y) (*.f64 x x)) 3)
25.0ms
(+.f64 (+.f64 y y) (*.f64 x x))
24.0ms
(cbrt.f64 (pow.f64 (+.f64 (+.f64 y y) (*.f64 x x)) 3))
Compiler

Compiled 870 to 800 computations (8% saved)

simplify125.0ms (6.8%)

Algorithm
egg-herbie
Rules
487×distribute-rgt-in_binary64
465×distribute-lft-in_binary64
413×unswap-sqr_binary64
282×exp-prod_binary64
255×*-commutative_binary64
222×exp-sum_binary64
204×log-prod_binary64
198×sqr-pow_binary64
127×swap-sqr_binary64
125×cube-prod_binary64
84×associate-+l+_binary64
78×associate-*l*_binary64
77×associate-*r*_binary64
70×associate-+r+_binary64
49×pow-sqr_binary64
48×distribute-rgt-out_binary64
46×sub-neg_binary64
43×cancel-sign-sub-inv_binary64
40×log-pow_binary64
34×unpow3_binary64 +-commutative_binary64
29×neg-mul-1_binary64 neg-sub0_binary64
28×distribute-lft-out_binary64
26×unsub-neg_binary64
24×pow-plus_binary64
23×cube-mult_binary64 distribute-rgt-neg-in_binary64
21×difference-of-squares_binary64
18×distribute-lft-neg-in_binary64
16×cube-unmult_binary64
15×rem-sqrt-square_binary64
12×count-2_binary64
10×distribute-lft-neg-out_binary64
associate-+r-_binary64
rem-cbrt-cube_binary64 associate--r+_binary64
+-rgt-identity_binary64 associate--l+_binary64 associate-+l-_binary64
distribute-rgt-out--_binary64
distribute-rgt-neg-out_binary64
unpow1_binary64 *-rgt-identity_binary64 *-lft-identity_binary64
unpow1/2_binary64 exp-lft-sqr_binary64 prod-exp_binary64 sub0-neg_binary64 distribute-neg-in_binary64 associate-/l/_binary64 associate-*r/_binary64
unpow2_binary64 sqr-neg_binary64 distribute-lft-out--_binary64 associate-/l*_binary64
1-exp_binary64 rem-3cbrt-lft_binary64 rem-cube-cbrt_binary64 rem-square-sqrt_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-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 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 sqr-abs_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-/r*_binary64 associate-*l/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
109 → 93
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01051935
12511797
28611731
333271731
449241731
549261731

prune24.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New93093
Fresh000
Picked011
Done022
Total93396
Error
0b
Counts
96 → 3
Compiler

Compiled 652 to 263 computations (59.7% saved)

regimes171.0ms (9.3%)

Accuracy

Total 0.0b remaining (34.4%)

Threshold costs 0.0b (34.4%)

Compiler

Compiled 1355 to 923 computations (31.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

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
0610
1710
2710

end1.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample490.0ms (26.8%)

Algorithm
intervals
Results
168.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 59 to 47 computations (20.3% saved)

Profiling

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