Details

Time bar (total: 3.9s)

analyze168.0ms (4.3%)

Algorithm
search
egg-herbie
Rules
770×unswap-sqr_binary64
633×associate-*l*_binary64
432×sub-neg_binary64
416×associate-+l+_binary64
342×associate-+r+_binary64
284×unsub-neg_binary64
255×+-commutative_binary64
241×cancel-sign-sub-inv_binary64
211×distribute-rgt-neg-in_binary64
196×associate--l+_binary64
188×distribute-rgt-in_binary64
181×*-commutative_binary64
178×distribute-lft-neg-in_binary64
163×associate-+l-_binary64
151×neg-sub0_binary64
150×distribute-lft-in_binary64
147×neg-mul-1_binary64
114×distribute-lft-out_binary64
113×distribute-neg-in_binary64
108×associate--r+_binary64
105×associate-*r*_binary64
69×distribute-rgt-out_binary64
52×associate--r-_binary64 associate-+r-_binary64
33×distribute-lft-neg-out_binary64
30×sqr-pow_binary64
22×cube-prod_binary64
19×pow-plus_binary64
18×remove-double-neg_binary64
14×difference-of-sqr--1_binary64
12×cube-unmult_binary64 associate--l-_binary64
11×*-rgt-identity_binary64
10×rem-sqrt-square_binary64 *-lft-identity_binary64
unpow3_binary64 mul-1-neg_binary64
unpow2_binary64 difference-of-sqr-1_binary64
distribute-rgt-neg-out_binary64
sqr-neg_binary64 sub0-neg_binary64 pow-sqr_binary64
unpow1_binary64 cube-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64
unpow1/2_binary64 1-exp_binary64 cube-mult_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 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_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-squares_binary64 swap-sqr_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-rgt-out--_binary64 distribute-lft-out--_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01850
13950
26750
318150
449450
5145850
6337750
7499450
8481550
9509250
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%50%25.1%6
25%31.2%43.8%7
25%21.9%53.2%8
25%14%61%9
28.1%10.9%61%10
31.6%7.4%61%11
33.4%5.7%61%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 18 to 13 computations (27.8% saved)

sample19.0ms (0.5%)

Algorithm
intervals
Results
10.0ms256×body128valid
Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify42.0ms (1.1%)

Algorithm
egg-herbie
Rules
785×distribute-rgt-neg-in_binary64
770×unswap-sqr_binary64
631×associate-*l*_binary64
289×sub-neg_binary64
232×associate-+l+_binary64
216×cancel-sign-sub-inv_binary64
209×distribute-neg-in_binary64
200×associate-+r+_binary64
176×distribute-rgt-in_binary64
175×distribute-lft-neg-in_binary64
162×+-commutative_binary64
161×*-commutative_binary64
150×distribute-lft-in_binary64
115×associate--l+_binary64
104×associate-*r*_binary64
99×neg-sub0_binary64
98×neg-mul-1_binary64
96×associate-+l-_binary64
69×associate--r+_binary64
66×distribute-lft-out_binary64
65×unsub-neg_binary64
51×distribute-rgt-out_binary64
40×distribute-lft-neg-out_binary64
34×associate--r-_binary64
31×distribute-rgt-neg-out_binary64
29×sqr-pow_binary64
28×associate-+r-_binary64
19×cancel-sign-sub_binary64
17×remove-double-neg_binary64 swap-sqr_binary64
14×difference-of-sqr--1_binary64
13×pow-plus_binary64
12×associate--l-_binary64
11×*-rgt-identity_binary64
10×*-lft-identity_binary64
cube-unmult_binary64
cube-prod_binary64 mul-1-neg_binary64
difference-of-sqr-1_binary64
distribute-neg-out_binary64
pow-sqr_binary64
unpow2_binary64 sub0-neg_binary64
unpow3_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 rem-sqrt-square_binary64 --rgt-identity_binary64 +-rgt-identity_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 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-mult_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 /-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-squares_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01325
12925
25025
313825
437425
5111525
6283325
7512625

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
0.2b
Counts
2 → 1
Compiler

Compiled 34 to 24 computations (29.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) 1)
0.0b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b)))
0.0b
(*.f64 4 (*.f64 b b))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

rewrite130.0ms (3.3%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
13×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64 add-log-exp_binary64
10×pow1_binary64 add-exp-log_binary64
add-cbrt-cube_binary64
add-cube-cbrt_binary64
unpow-prod-down_binary64 pow-unpow_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64 cancel-sign-sub-inv_binary64
sum-log_binary64 diff-log_binary64 difference-of-squares_binary64
pow-pow_binary64 pow-to-exp_binary64 pow-exp_binary64 unpow2_binary64 sqr-pow_binary64 unswap-sqr_binary64 associate-*r*_binary64 *-commutative_binary64 flip3-+_binary64 flip-+_binary64 +-commutative_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 difference-of-sqr-1_binary64 distribute-lft-out--_binary64 associate--l+_binary64
Counts
4 → 68
Calls

4 calls:

10.0ms
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) 1)
8.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b)))
5.0ms
(*.f64 4 (*.f64 b b))
5.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
Compiler

Compiled 1729 to 796 computations (54% saved)

series246.0ms (6.3%)

Error
0.0b
Counts
4 → 57
Calls

4 calls:

81.0ms
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b))) 1)
77.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (*.f64 b b)))
50.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
8.0ms
(*.f64 4 (*.f64 b b))
Compiler

Compiled 1825 to 1572 computations (13.9% saved)

simplify104.0ms (2.7%)

Algorithm
egg-herbie
Rules
804×unswap-sqr_binary64
478×associate-*l*_binary64
402×associate-*r*_binary64
271×distribute-rgt-in_binary64
255×distribute-lft-in_binary64
153×*-commutative_binary64
144×associate-+l+_binary64
133×associate-+r+_binary64
102×+-commutative_binary64
90×exp-prod_binary64
88×sub-neg_binary64 sqr-pow_binary64
72×log-prod_binary64
67×cancel-sign-sub-inv_binary64
65×cube-prod_binary64 associate--l+_binary64
52×distribute-rgt-neg-in_binary64
50×exp-sum_binary64 distribute-rgt-out_binary64
43×distribute-lft-neg-in_binary64
36×neg-sub0_binary64
30×neg-mul-1_binary64 unsub-neg_binary64
23×*-rgt-identity_binary64 *-lft-identity_binary64 pow-sqr_binary64
17×pow-plus_binary64 distribute-lft-out_binary64
16×cube-unmult_binary64
15×rem-sqrt-square_binary64 difference-of-sqr-1_binary64
13×log-pow_binary64
12×mul-1-neg_binary64 distribute-rgt-out--_binary64
10×distribute-lft-neg-out_binary64 associate-+l-_binary64
difference-of-sqr--1_binary64 swap-sqr_binary64
unpow3_binary64 associate--r+_binary64
unpow2_binary64 unpow1/2_binary64
unpow1_binary64 distribute-neg-in_binary64 associate-+r-_binary64
div-exp_binary64 cube-mult_binary64 +-rgt-identity_binary64 associate-/l*_binary64
sub0-neg_binary64 distribute-rgt1-in_binary64 distribute-lft-out--_binary64 associate-/l/_binary64 associate-*r/_binary64
prod-exp_binary64 exp-diff_binary64 difference-of-squares_binary64 distribute-rgt-neg-out_binary64 distribute-lft1-in_binary64 associate-/r/_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_binary64 count-2_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 rec-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 sqr-abs_binary64 sqr-neg_binary64 times-frac_binary64 div-sub_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 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 associate-*l/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
125 → 87
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01432623
13112418
28602379
331272379
449932379

prune64.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New84387
Fresh000
Picked101
Done000
Total85388
Error
0.0b
Counts
88 → 3
Compiler

Compiled 1134 to 548 computations (51.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 a a) (*.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (*.f64 b b)))
0.0b
(*.f64 4 (*.f64 b b))
0.0b
(*.f64 2 (*.f64 (*.f64 a a) (*.f64 b b)))
2.9b
(*.f64 (*.f64 a a) (*.f64 b b))

rewrite167.0ms (4.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
55×pow1_binary64
39×add-exp-log_binary64 add-cbrt-cube_binary64
30×pow-prod-down_binary64
24×prod-exp_binary64 cbrt-unprod_binary64
13×add-log-exp_binary64
add-sqr-sqrt_binary64 associate-*l*_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64 sum-log_binary64
pow-prod-up_binary64 pow-plus_binary64
associate-*r*_binary64 *-commutative_binary64
pow2_binary64 pow-sqr_binary64 unswap-sqr_binary64
flip3-+_binary64 flip-+_binary64 associate-+l+_binary64 +-commutative_binary64
Counts
4 → 89
Calls

4 calls:

22.0ms
(+.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 a a) (*.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (*.f64 b b)))
12.0ms
(*.f64 2 (*.f64 (*.f64 a a) (*.f64 b b)))
8.0ms
(*.f64 (*.f64 a a) (*.f64 b b))
7.0ms
(*.f64 4 (*.f64 b b))
Compiler

Compiled 2526 to 1303 computations (48.4% saved)

series147.0ms (3.7%)

Error
0.0b
Counts
4 → 33
Calls

4 calls:

78.0ms
(+.f64 (+.f64 (*.f64 2 (*.f64 (*.f64 a a) (*.f64 b b))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (*.f64 4 (*.f64 b b)))
25.0ms
(*.f64 2 (*.f64 (*.f64 a a) (*.f64 b b)))
23.0ms
(*.f64 (*.f64 a a) (*.f64 b b))
10.0ms
(*.f64 4 (*.f64 b b))
Compiler

Compiled 1378 to 1174 computations (14.8% saved)

simplify125.0ms (3.2%)

Algorithm
egg-herbie
Rules
659×distribute-rgt-in_binary64
636×distribute-lft-in_binary64
244×associate-+l+_binary64
195×associate-*r*_binary64
190×associate-+r+_binary64
184×associate-*l*_binary64
116×exp-prod_binary64
101×cancel-sign-sub-inv_binary64
95×unswap-sqr_binary64
92×*-commutative_binary64
66×log-prod_binary64
61×distribute-rgt-neg-in_binary64
53×distribute-lft-neg-in_binary64 distribute-rgt-out_binary64
46×sqr-pow_binary64 associate--r+_binary64
39×+-commutative_binary64
37×associate--l+_binary64
27×swap-sqr_binary64
23×cube-prod_binary64
21×sub-neg_binary64
20×distribute-neg-in_binary64
19×distribute-rgt-out--_binary64
18×unpow3_binary64 distribute-lft-out_binary64
16×neg-mul-1_binary64 neg-sub0_binary64
13×prod-exp_binary64
12×associate-+r-_binary64
10×exp-sum_binary64
pow-plus_binary64 distribute-lft-neg-out_binary64
unsub-neg_binary64 associate-/l*_binary64
associate-+l-_binary64
log-pow_binary64
exp-lft-sqr_binary64 cube-unmult_binary64 pow-sqr_binary64
distribute-lft-out--_binary64
unpow2_binary64 unpow1_binary64 cube-mult_binary64
unpow1/2_binary64 count-2_binary64
1-exp_binary64 rem-sqrt-square_binary64 difference-of-squares_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-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 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 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-/r/_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
122 → 82
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01382222
13111893
212531790
349131790
449881790
549801790

prune56.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New82082
Fresh022
Picked011
Done000
Total82385
Error
0.0b
Counts
85 → 3
Compiler

Compiled 1064 to 626 computations (41.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 4 (*.f64 b b)) -1)
0.0b
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (+.f64 (*.f64 4 (*.f64 b b)) -1))
0.0b
(*.f64 4 (*.f64 b b))
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)

rewrite106.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
11×add-log-exp_binary64
10×pow1_binary64 add-exp-log_binary64
*-un-lft-identity_binary64 add-cbrt-cube_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
sum-log_binary64
unpow-prod-down_binary64 pow-unpow_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64
flip3-+_binary64 flip-+_binary64 +-commutative_binary64
pow-pow_binary64 pow-to-exp_binary64 pow-exp_binary64 unpow2_binary64 sqr-pow_binary64 unswap-sqr_binary64 associate-*r*_binary64 *-commutative_binary64 distribute-lft-out_binary64 associate-+r+_binary64
Counts
4 → 62
Calls

4 calls:

15.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (+.f64 (*.f64 4 (*.f64 b b)) -1))
6.0ms
(+.f64 (*.f64 4 (*.f64 b b)) -1)
5.0ms
(*.f64 4 (*.f64 b b))
5.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
Compiler

Compiled 1505 to 712 computations (52.7% saved)

series183.0ms (4.7%)

Error
0.0b
Counts
4 → 45
Calls

4 calls:

82.0ms
(+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (+.f64 (*.f64 4 (*.f64 b b)) -1))
50.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
13.0ms
(+.f64 (*.f64 4 (*.f64 b b)) -1)
8.0ms
(*.f64 4 (*.f64 b b))
Compiler

Compiled 1541 to 1284 computations (16.7% saved)

simplify94.0ms (2.4%)

Algorithm
egg-herbie
Rules
821×unswap-sqr_binary64
415×associate-*l*_binary64
339×associate-*r*_binary64
336×distribute-rgt-in_binary64
293×distribute-lft-in_binary64
166×unsub-neg_binary64
155×*-commutative_binary64
153×sub-neg_binary64
130×associate-+r+_binary64
129×associate-+l+_binary64
110×cancel-sign-sub-inv_binary64
100×exp-prod_binary64
92×+-commutative_binary64
84×sqr-pow_binary64
82×log-prod_binary64
78×associate--l+_binary64
75×cube-prod_binary64
50×neg-sub0_binary64
46×neg-mul-1_binary64 distribute-rgt-neg-in_binary64
44×distribute-lft-neg-in_binary64
40×associate--r+_binary64
34×distribute-rgt-out_binary64
32×exp-sum_binary64
23×distribute-lft-out_binary64
22×pow-sqr_binary64
21×associate-+l-_binary64 associate-+r-_binary64
18×distribute-neg-in_binary64
17×pow-plus_binary64
16×cube-unmult_binary64 rem-sqrt-square_binary64
15×difference-of-sqr-1_binary64
14×+-rgt-identity_binary64
13×log-pow_binary64
11×sub0-neg_binary64
10×mul-1-neg_binary64 distribute-rgt-out--_binary64
exp-diff_binary64
unpow3_binary64 difference-of-sqr--1_binary64 distribute-lft-neg-out_binary64
unpow2_binary64 swap-sqr_binary64
unpow1/2_binary64 unpow1_binary64
prod-exp_binary64 cube-mult_binary64 *-rgt-identity_binary64 remove-double-neg_binary64 difference-of-squares_binary64
sqr-neg_binary64 --rgt-identity_binary64 associate--r-_binary64
cube-neg_binary64 *-lft-identity_binary64 distribute-rgt-neg-out_binary64 distribute-lft-out--_binary64 associate-/l/_binary64 associate-/l*_binary64 associate-*r/_binary64 associate--l-_binary64
cancel-sign-sub_binary64 distribute-rgt1-in_binary64
1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-square-sqrt_binary64 distribute-neg-out_binary64 count-2_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 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 times-frac_binary64 div-sub_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 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-lft1-in_binary64 associate-/r*_binary64 associate-*l/_binary64
Counts
107 → 68
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01351926
13141778
28501760
331541760
453411760

prune43.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New67168
Fresh011
Picked101
Done011
Total68371
Error
0.0b
Counts
71 → 3
Compiler

Compiled 863 to 425 computations (50.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 4 (*.f64 b b))
0.1b
(pow.f64 (+.f64 (*.f64 4 (*.f64 b b)) -1) 3)
0.3b
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
4.4b
(cbrt.f64 (pow.f64 (+.f64 (*.f64 4 (*.f64 b b)) -1) 3))

rewrite133.0ms (3.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
14×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64 *-un-lft-identity_binary64
12×cbrt-prod_binary64
11×pow1_binary64 add-exp-log_binary64
10×add-cbrt-cube_binary64
unpow-prod-down_binary64
cube-prod_binary64 pow-unpow_binary64
add-log-exp_binary64 cube-div_binary64
sqr-pow_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64
flip3-+_binary64 cbrt-div_binary64 flip-+_binary64 unpow3_binary64 cube-mult_binary64 pow-pow_binary64 pow-to-exp_binary64 pow-exp_binary64
pow1/3_binary64 rem-cbrt-cube_binary64 unpow2_binary64 rem-cube-cbrt_binary64 unswap-sqr_binary64 associate-*r*_binary64 *-commutative_binary64
Counts
4 → 85
Calls

4 calls:

10.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 4 (*.f64 b b)) -1) 3))
8.0ms
(pow.f64 (+.f64 (*.f64 4 (*.f64 b b)) -1) 3)
6.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
5.0ms
(*.f64 4 (*.f64 b b))
Compiler

Compiled 2097 to 1173 computations (44.1% saved)

series121.0ms (3.1%)

Error
0.0b
Counts
4 → 39
Calls

4 calls:

53.0ms
(pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2)
21.0ms
(pow.f64 (+.f64 (*.f64 4 (*.f64 b b)) -1) 3)
13.0ms
(cbrt.f64 (pow.f64 (+.f64 (*.f64 4 (*.f64 b b)) -1) 3))
9.0ms
(*.f64 4 (*.f64 b b))
Compiler

Compiled 1478 to 1183 computations (20% saved)

simplify125.0ms (3.2%)

Algorithm
egg-herbie
Rules
496×exp-prod_binary64
311×log-prod_binary64
299×unswap-sqr_binary64
283×cancel-sign-sub-inv_binary64
267×distribute-rgt-in_binary64
257×*-commutative_binary64
244×distribute-lft-in_binary64
213×sqr-pow_binary64
155×cube-prod_binary64
138×distribute-rgt-neg-in_binary64
124×swap-sqr_binary64
119×distribute-lft-neg-in_binary64
112×unpow3_binary64
94×exp-sum_binary64
91×associate-*r*_binary64
90×sub-neg_binary64
88×associate-*l*_binary64
77×distribute-lft-neg-out_binary64
65×log-pow_binary64
64×distribute-rgt-neg-out_binary64 distribute-rgt-out_binary64
62×pow-sqr_binary64
49×pow-plus_binary64
42×distribute-neg-in_binary64
38×+-commutative_binary64
35×neg-sub0_binary64
32×unsub-neg_binary64
28×rem-sqrt-square_binary64 mul-1-neg_binary64
25×cube-mult_binary64
24×neg-mul-1_binary64
23×cube-unmult_binary64
20×associate-+l+_binary64
18×distribute-rgt-out--_binary64 associate-+r+_binary64
16×distribute-lft-out_binary64 associate--l+_binary64 associate-+l-_binary64
15×*-rgt-identity_binary64
13×*-lft-identity_binary64
11×unpow2_binary64
10×associate-+r-_binary64
unpow1_binary64 exp-diff_binary64 rem-cbrt-cube_binary64 distribute-lft-out--_binary64
unpow1/2_binary64 sub0-neg_binary64 associate--r+_binary64
associate-/l/_binary64 associate-*r/_binary64
+-rgt-identity_binary64
count-2_binary64 associate-/l*_binary64
difference-of-sqr-1_binary64
sqr-neg_binary64 rem-square-sqrt_binary64 div-sub_binary64 remove-double-neg_binary64 distribute-neg-out_binary64 associate-/r/_binary64
exp-neg_binary64 1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cube-cbrt_binary64 --rgt-identity_binary64 difference-of-sqr--1_binary64 distribute-rgt1-in_binary64 associate--r-_binary64 associate--l-_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 sqr-abs_binary64 times-frac_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-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-lft1-in_binary64 associate-/r*_binary64 associate-*l/_binary64
Counts
124 → 93
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01562006
13301837
29121825
327361822
446461819
550711819

prune65.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New93093
Fresh011
Picked011
Done011
Total93396
Error
0.0b
Counts
96 → 3
Compiler

Compiled 1254 to 687 computations (45.2% saved)

regimes1.0s (26%)

Accuracy

Total 0.0b remaining (35%)

Threshold costs 0.0b (35%)

Compiler

Compiled 16928 to 12042 computations (28.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
1-exp_binary64 sub-neg_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_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
01737
12837
22937
32737

end1.0ms (0%)

Compiler

Compiled 25 to 18 computations (28% saved)

sample713.0ms (18.2%)

Algorithm
intervals
Results
340.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 111 to 90 computations (18.9% saved)

Profiling

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