Details

Time bar (total: 3.3s)

analyze280.0ms (8.5%)

Algorithm
search
egg-herbie
Rules
43×distribute-rgt-in_binary64
39×distribute-lft-in_binary64
25×*-commutative_binary64
16×associate-+l+_binary64
15×+-commutative_binary64
13×associate-+r+_binary64
distribute-rgt-out_binary64
swap-b-c swap-b-d
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-lft-out--_binary64 distribute-lft-out_binary64 count-2_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 swap-c-d
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02570
17370
211370
314770
413570
513370
044
144
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
0%0%100%2
0%0%100%3
0%0%100%4
0%0%100%5
0%0%100%6
0%0%100%7
0%0%100%8
0%0%100%9
0%0%100%10
0%0%100%11
0%0%100%12
0%0%100%13
0%0%100%14
Symmetry

(sort b c d)

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample44.0ms (1.3%)

Algorithm
intervals
Results
10.0ms256×pre128true
6.0ms256×body128valid
0.0mspre128false
Compiler

Compiled 31 to 31 computations (0% saved)

simplify9.0ms (0.3%)

Algorithm
egg-herbie
Rules
10×distribute-rgt-in_binary64 distribute-lft-in_binary64
*-commutative_binary64
associate-+l+_binary64 associate-+r+_binary64
+-commutative_binary64
distribute-rgt-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-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-lft-out--_binary64 distribute-lft-out_binary64 count-2_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 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11910
23710
35010
44610
54310

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.0b
Counts
1 → 1
Compiler

Compiled 7 to 7 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(*.f64 a (+.f64 (+.f64 b c) d))

rewrite31.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64 associate-*r*_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 associate-*l*_binary64 distribute-lft-out_binary64
associate-*r/_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 flip3-+_binary64 flip-+_binary64 *-commutative_binary64
Counts
1 → 24
Calls

1 calls:

13.0ms
(*.f64 a (+.f64 (+.f64 b c) d))
Compiler

Compiled 300 to 75 computations (75% saved)

series43.0ms (1.3%)

Error
0.0b
Counts
1 → 21
Calls

1 calls:

35.0ms
(*.f64 a (+.f64 (+.f64 b c) d))
Compiler

Compiled 315 to 269 computations (14.6% saved)

simplify90.0ms (2.7%)

Algorithm
egg-herbie
Rules
676×distribute-rgt-in_binary64
674×distribute-lft-in_binary64
342×associate-*l*_binary64
318×unswap-sqr_binary64
291×rem-sqrt-square_binary64
272×associate-*r*_binary64
240×+-commutative_binary64
198×distribute-rgt-out_binary64
156×sqr-pow_binary64
116×distribute-neg-in_binary64
110×distribute-lft-out_binary64
103×sub-neg_binary64
98×*-commutative_binary64
90×cancel-sign-sub-inv_binary64
78×distribute-rgt-neg-in_binary64
61×associate-+l+_binary64
54×associate-+r+_binary64
53×pow-sqr_binary64
52×exp-prod_binary64
48×associate-/l*_binary64
46×neg-mul-1_binary64
44×associate--r+_binary64
43×neg-sub0_binary64 distribute-lft-neg-in_binary64
40×unsub-neg_binary64 *-rgt-identity_binary64
39×*-lft-identity_binary64
38×associate-/l/_binary64
34×distribute-lft-neg-out_binary64
33×associate--l+_binary64
31×associate-*r/_binary64
29×exp-sum_binary64
24×associate-/r/_binary64
23×associate-+l-_binary64
18×distribute-rgt-neg-out_binary64
17×distribute-rgt-out--_binary64
16×swap-sqr_binary64
15×unpow1/2_binary64 associate-/r*_binary64
14×sub0-neg_binary64
13×associate-+r-_binary64
11×log-prod_binary64 cube-unmult_binary64
10×+-rgt-identity_binary64
unpow3_binary64 associate--r-_binary64
log-div_binary64 cube-div_binary64 cube-prod_binary64 difference-of-squares_binary64
pow-plus_binary64 distribute-lft-out--_binary64
--rgt-identity_binary64
exp-sqrt_binary64 cube-mult_binary64
exp-diff_binary64 1-exp_binary64 exp-1-e_binary64 remove-double-neg_binary64 count-2_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_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 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-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 mul-1-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-*l/_binary64 associate--l-_binary64
Counts
45 → 29
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
058498
1160456
2599456
32228456
43008456
53581456
64784456
75029456

prune16.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New26329
Fresh000
Picked011
Done000
Total26430
Error
0b
Counts
30 → 4
Compiler

Compiled 237 to 74 computations (68.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 a (+.f64 b c)) (*.f64 a d))
0.0b
(*.f64 a (+.f64 b c))

rewrite40.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow1_binary64 add-exp-log_binary64 add-log-exp_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 associate-*r*_binary64
associate-*l*_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64 flip3-+_binary64 associate-*r/_binary64 flip-+_binary64 distribute-lft-out_binary64 associate-+l+_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64 sum-log_binary64 +-commutative_binary64
Counts
2 → 37
Calls

2 calls:

6.0ms
(+.f64 (*.f64 a (+.f64 b c)) (*.f64 a d))
6.0ms
(*.f64 a (+.f64 b c))
Compiler

Compiled 557 to 135 computations (75.8% saved)

series77.0ms (2.3%)

Error
0b
Counts
2 → 36
Calls

2 calls:

43.0ms
(+.f64 (*.f64 a (+.f64 b c)) (*.f64 a d))
25.0ms
(*.f64 a (+.f64 b c))
Compiler

Compiled 589 to 473 computations (19.7% saved)

simplify74.0ms (2.2%)

Algorithm
egg-herbie
Rules
572×sub-neg_binary64
503×distribute-rgt-in_binary64
474×distribute-lft-in_binary64
219×*-commutative_binary64
210×cancel-sign-sub-inv_binary64
198×unswap-sqr_binary64
166×associate--l+_binary64
163×associate--r+_binary64
139×distribute-rgt-out_binary64
121×sqr-pow_binary64
115×unsub-neg_binary64
110×associate-+l+_binary64
107×associate-+r+_binary64
106×associate-*l*_binary64
104×distribute-rgt-neg-in_binary64
103×neg-mul-1_binary64
99×neg-sub0_binary64
89×associate-*r*_binary64
88×distribute-neg-in_binary64
84×distribute-lft-out_binary64
82×associate-+l-_binary64
74×distribute-lft-neg-in_binary64
57×associate-+r-_binary64
54×exp-prod_binary64 distribute-rgt-out--_binary64
41×*-lft-identity_binary64
39×*-rgt-identity_binary64
37×sub0-neg_binary64
36×+-commutative_binary64
34×exp-sum_binary64
31×+-rgt-identity_binary64
29×pow-sqr_binary64
28×distribute-lft-neg-out_binary64
25×cube-prod_binary64
23×swap-sqr_binary64
21×distribute-lft-out--_binary64
17×log-prod_binary64
13×distribute-rgt-neg-out_binary64
12×associate--r-_binary64
10×difference-of-squares_binary64
unpow3_binary64
unpow1/2_binary64 cube-mult_binary64
associate-/l*_binary64
rem-sqrt-square_binary64 +-lft-identity_binary64 associate-/l/_binary64 associate-*r/_binary64
prod-exp_binary64 1-exp_binary64 exp-1-e_binary64 cube-unmult_binary64 remove-double-neg_binary64 count-2_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_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 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-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 mul-1-neg_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 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-/r*_binary64 associate-*l/_binary64 associate--l-_binary64
Counts
73 → 41
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
077714
1227687
2800684
32616681
43813681
54951681

prune17.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New41041
Fresh022
Picked011
Done011
Total41445
Error
0b
Counts
45 → 4
Compiler

Compiled 274 to 86 computations (68.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 a (+.f64 d (+.f64 b c)))
0.1b
(sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c))))
0.1b
(sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c))))
0.5b
(*.f64 (sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c)))) (sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c)))))

rewrite109.0ms (3.3%)

Algorithm
rewrite-expression-head
Error
0b
Rules
61×pow1_binary64
32×sqrt-pow1_binary64
23×pow-prod-down_binary64
20×associate-*r/_binary64
16×sqrt-div_binary64
15×*-un-lft-identity_binary64
14×add-sqr-sqrt_binary64
12×pow1/2_binary64
10×pow-prod-up_binary64 add-cube-cbrt_binary64
flip3-+_binary64 flip-+_binary64 associate-*r*_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
associate-*l*_binary64
pow-sqr_binary64 sqrt-prod_binary64
add-log-exp_binary64 frac-times_binary64 swap-sqr_binary64
distribute-lft-out_binary64
prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 associate-*l/_binary64 *-commutative_binary64
pow2_binary64 pow-plus_binary64 sqrt-unprod_binary64 rem-square-sqrt_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64
Counts
4 → 107
Calls

4 calls:

17.0ms
(*.f64 (sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c)))) (sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c)))))
8.0ms
(*.f64 a (+.f64 d (+.f64 b c)))
7.0ms
(sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c))))
6.0ms
(sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c))))
Compiler

Compiled 2268 to 347 computations (84.7% saved)

series224.0ms (6.8%)

Error
0b
Counts
4 → 74
Calls

4 calls:

55.0ms
(sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c))))
54.0ms
(*.f64 (sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c)))) (sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c)))))
54.0ms
(sqrt.f64 (*.f64 a (+.f64 d (+.f64 b c))))
40.0ms
(*.f64 a (+.f64 d (+.f64 b c)))
Compiler

Compiled 3423 to 2261 computations (33.9% saved)

simplify141.0ms (4.3%)

Algorithm
egg-herbie
Rules
801×distribute-rgt-in_binary64
770×distribute-lft-in_binary64
162×associate-*l*_binary64
153×associate-*r*_binary64
150×exp-prod_binary64
149×unswap-sqr_binary64
80×times-frac_binary64
77×*-commutative_binary64
68×log-prod_binary64
66×cancel-sign-sub-inv_binary64
47×associate-/l*_binary64
44×exp-sum_binary64 cube-prod_binary64
41×sqr-pow_binary64
37×distribute-rgt-neg-in_binary64
35×distribute-lft-neg-in_binary64
30×associate-/r*_binary64
29×sub-neg_binary64
24×*-lft-identity_binary64
23×*-rgt-identity_binary64
22×associate-*l/_binary64
19×rem-sqrt-square_binary64 +-commutative_binary64
18×neg-mul-1_binary64 neg-sub0_binary64
16×distribute-neg-in_binary64 distribute-rgt-out_binary64 associate-*r/_binary64
15×unpow3_binary64
14×swap-sqr_binary64
13×pow-plus_binary64
12×associate-/r/_binary64
11×log-pow_binary64 distribute-lft-out_binary64
cube-unmult_binary64 rem-square-sqrt_binary64 distribute-lft-neg-out_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l+_binary64
cube-mult_binary64 unsub-neg_binary64
unpow1/2_binary64 distribute-rgt-neg-out_binary64 associate-+r+_binary64
pow-sqr_binary64 distribute-rgt-out--_binary64
unpow2_binary64 unpow1_binary64 /-rgt-identity_binary64 count-2_binary64 associate-/l/_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 difference-of-squares_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 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 prod-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-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_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 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 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64
Counts
181 → 102
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01462559
13442391
213072340
347742324
449692324
549932324

prune32.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1020102
Fresh011
Picked011
Done022
Total1024106
Error
0b
Counts
106 → 4
Compiler

Compiled 991 to 251 computations (74.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt.f64 (+.f64 (+.f64 b c) d))
0.0b
(sqrt.f64 (+.f64 d (+.f64 b c)))
0.2b
(*.f64 a (sqrt.f64 (+.f64 d (+.f64 b c))))
0.3b
(*.f64 (*.f64 a (sqrt.f64 (+.f64 d (+.f64 b c)))) (sqrt.f64 (+.f64 (+.f64 b c) d)))

rewrite90.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
31×*-un-lft-identity_binary64
21×sqrt-prod_binary64
18×sqrt-div_binary64
17×add-sqr-sqrt_binary64
16×associate-*r*_binary64
13×pow1_binary64
12×distribute-lft-out_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64
10×associate-*r/_binary64
flip3-+_binary64 flip-+_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 frac-times_binary64 associate-*l*_binary64
associate-*l/_binary64 *-commutative_binary64 unswap-sqr_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64
Counts
4 → 91
Calls

4 calls:

17.0ms
(*.f64 (*.f64 a (sqrt.f64 (+.f64 d (+.f64 b c)))) (sqrt.f64 (+.f64 (+.f64 b c) d)))
9.0ms
(*.f64 a (sqrt.f64 (+.f64 d (+.f64 b c))))
6.0ms
(sqrt.f64 (+.f64 (+.f64 b c) d))
5.0ms
(sqrt.f64 (+.f64 d (+.f64 b c)))
Compiler

Compiled 1946 to 324 computations (83.4% saved)

series155.0ms (4.7%)

Error
0b
Counts
4 → 60
Calls

4 calls:

45.0ms
(*.f64 a (sqrt.f64 (+.f64 d (+.f64 b c))))
38.0ms
(*.f64 (*.f64 a (sqrt.f64 (+.f64 d (+.f64 b c)))) (sqrt.f64 (+.f64 (+.f64 b c) d)))
28.0ms
(sqrt.f64 (+.f64 (+.f64 b c) d))
27.0ms
(sqrt.f64 (+.f64 d (+.f64 b c)))
Compiler

Compiled 2236 to 1574 computations (29.6% saved)

simplify134.0ms (4.1%)

Algorithm
egg-herbie
Rules
737×distribute-rgt-in_binary64
713×distribute-lft-in_binary64
668×sub-neg_binary64
319×*-commutative_binary64
208×associate-*l*_binary64
180×associate--r+_binary64
156×associate-*r*_binary64
149×cancel-sign-sub-inv_binary64
140×associate--l+_binary64
138×associate-+l-_binary64
125×associate-+r-_binary64
91×unsub-neg_binary64
90×associate-+l+_binary64
88×neg-mul-1_binary64
82×neg-sub0_binary64
80×distribute-rgt-neg-in_binary64
71×distribute-lft-neg-in_binary64
63×sqr-pow_binary64 associate-+r+_binary64
62×exp-prod_binary64
56×*-lft-identity_binary64
53×unswap-sqr_binary64
50×+-commutative_binary64
48×distribute-neg-in_binary64
46×*-rgt-identity_binary64
34×swap-sqr_binary64
32×exp-sum_binary64
23×distribute-rgt-out--_binary64
22×distribute-lft-neg-out_binary64
18×log-prod_binary64 distribute-rgt-neg-out_binary64
17×associate-/r*_binary64
15×distribute-rgt-out_binary64
14×cube-prod_binary64 +-rgt-identity_binary64
13×rem-sqrt-square_binary64 associate--r-_binary64
11×pow-sqr_binary64
10×associate--l-_binary64
unpow1/2_binary64 associate-/l*_binary64
cube-unmult_binary64 sub0-neg_binary64
associate-/l/_binary64
rem-square-sqrt_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
unpow3_binary64 cube-mult_binary64
unpow2_binary64 pow-plus_binary64 distribute-lft-out_binary64 count-2_binary64 associate-*r/_binary64
unpow1_binary64 exp-diff_binary64 1-exp_binary64 exp-1-e_binary64 sqr-neg_binary64 div-sub_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 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-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 times-frac_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-*l/_binary64
Counts
151 → 78
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01622289
13772165
211732122
335382119
448042119
555522119

prune30.0ms (0.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New78078
Fresh000
Picked011
Done033
Total78482
Error
0b
Counts
82 → 4
Compiler

Compiled 1055 to 263 computations (75.1% saved)

regimes591.0ms (18%)

Accuracy

Total 0.0b remaining (72.6%)

Threshold costs 0.0b (72.6%)

Compiler

Compiled 4290 to 3221 computations (24.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_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 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
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11313
21313

end14.0ms (0.4%)

Remove

(sort b c d)

Compiler

Compiled 27 to 24 computations (11.1% saved)

sample1.0s (30.8%)

Algorithm
intervals
Results
318.0ms8000×pre128true
195.0ms8000×body128valid
Compiler

Compiled 93 to 90 computations (3.2% saved)

Profiling

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