Details

Time bar (total: 10.3s)

analyze896.0ms (8.7%)

Algorithm
search
egg-herbie
Rules
55×associate-/l*_binary64
32×associate-/r/_binary64
31×associate-/r*_binary64
30×associate-*r/_binary64
23×*-commutative_binary64
20×times-frac_binary64 associate-*l/_binary64
18×associate-/l/_binary64
swap-a1-a2 swap-b1-b2
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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 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 count-2_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 +-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02270
16170
214670
322370
422870
522870
044
144
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
18.7%81.1%0.2%9
21.8%78%0.2%10
25%74.9%0.2%11
34.7%64.9%0.4%12
47.2%51.9%0.9%13
49%49.2%1.8%14
Symmetry

(sort a1 a2)

(sort b1 b2)

Compiler

Compiled 8 to 8 computations (0% saved)

sample40.0ms (0.4%)

Algorithm
intervals
Results
7.0ms256×body128valid
2.0ms64×body128invalid
Compiler

Compiled 15 to 19 computations (-26.7% saved)

simplify10.0ms (0.1%)

Algorithm
egg-herbie
Rules
14×associate-/l*_binary64
associate-/r/_binary64 associate-*r/_binary64
*-commutative_binary64
associate-/r*_binary64
times-frac_binary64 associate-/l/_binary64 associate-*l/_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 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 count-2_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 +-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11710
23810
36310
46910
56810
66810

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
10.6b
Counts
1 → 1
Compiler

Compiled 7 to 7 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

10.3b
(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

rewrite31.0ms (0.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
13×add-exp-log_binary64 add-cbrt-cube_binary64
prod-exp_binary64 div-exp_binary64 cbrt-undiv_binary64 cbrt-unprod_binary64
pow1_binary64 add-log-exp_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 frac-2neg_binary64 times-frac_binary64 *-un-lft-identity_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64 associate-/r*_binary64
Counts
1 → 21
Calls

1 calls:

5.0ms
(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))
Compiler

Compiled 291 to 77 computations (73.5% saved)

series47.0ms (0.5%)

Error
10.6b
Counts
1 → 12
Calls

1 calls:

46.0ms
(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))
Compiler

Compiled 175 to 175 computations (0% saved)

simplify88.0ms (0.9%)

Algorithm
egg-herbie
Rules
579×associate-/r*_binary64
393×associate-*l*_binary64
381×associate-*l/_binary64
297×associate-*r/_binary64
271×associate-*r*_binary64
251×div-sub_binary64
204×associate-/l/_binary64
181×times-frac_binary64
141×sub-neg_binary64
132×distribute-rgt-in_binary64
126×*-commutative_binary64
113×associate-/r/_binary64
98×sqr-pow_binary64
97×associate--r+_binary64
89×associate--l+_binary64
87×associate-/l*_binary64
73×distribute-lft-in_binary64
65×unswap-sqr_binary64
55×+-commutative_binary64
47×associate-+l-_binary64 associate-+l+_binary64
42×associate-+r+_binary64
40×distribute-neg-in_binary64
35×neg-mul-1_binary64
34×log-div_binary64 cube-div_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64
31×neg-sub0_binary64 associate--r-_binary64
24×log-prod_binary64
23×unsub-neg_binary64
21×cube-prod_binary64
17×unpow3_binary64 cube-mult_binary64
15×sub0-neg_binary64 pow-sqr_binary64
14×associate-+r-_binary64
12×distribute-lft-neg-in_binary64
11×remove-double-neg_binary64 +-rgt-identity_binary64
10×--rgt-identity_binary64
associate--l-_binary64
exp-prod_binary64 cube-unmult_binary64
distribute-rgt-neg-in_binary64
mul0-rgt_binary64 mul0-lft_binary64 distribute-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-lft-out--_binary64
exp-diff_binary64 *-lft-identity_binary64 +-lft-identity_binary64
exp-sum_binary64 1-exp_binary64 distribute-rgt-neg-out_binary64 distribute-lft-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 pow-base-0_binary64 unpow1/3_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 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 /-rgt-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 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 count-2_binary64
Counts
33 → 11
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
054475
1155370
2779370
33457370
43762370
54079370
64763370
75076370

prune7.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New8311
Fresh000
Picked011
Done000
Total8412
Error
0.1b
Counts
12 → 4
Compiler

Compiled 57 to 42 computations (26.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

4.6b
(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
6.0b
(/.f64 b1 (/.f64 a2 b2))

rewrite319.0ms (3.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
471×times-frac_binary64
229×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
57×associate-/r*_binary64
22×div-inv_binary64
16×add-exp-log_binary64 add-cbrt-cube_binary64
div-exp_binary64 cbrt-undiv_binary64
associate-/r/_binary64 associate-/l*_binary64
pow1_binary64 add-log-exp_binary64 frac-2neg_binary64 clear-num_binary64
Counts
2 → 266
Calls

2 calls:

12.0ms
(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
5.0ms
(/.f64 b1 (/.f64 a2 b2))
Compiler

Compiled 5185 to 1256 computations (75.8% saved)

series68.0ms (0.7%)

Error
0.1b
Counts
2 → 21
Calls

2 calls:

43.0ms
(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
23.0ms
(/.f64 b1 (/.f64 a2 b2))
Compiler

Compiled 308 to 303 computations (1.6% saved)

simplify313.0ms (3%)

Algorithm
egg-herbie
Rules
563×associate-/r/_binary64
414×associate-/l/_binary64
381×associate-*l/_binary64
332×associate-*r/_binary64
323×*-commutative_binary64
297×sub-neg_binary64
242×associate-/r*_binary64
168×associate-/l*_binary64
164×div-sub_binary64
111×associate-*r*_binary64
101×*-rgt-identity_binary64
98×times-frac_binary64
97×sqr-pow_binary64
74×associate--r+_binary64
73×unsub-neg_binary64
71×associate-+l-_binary64
68×neg-mul-1_binary64 associate--l-_binary64
63×associate--r-_binary64
59×associate-+r-_binary64
57×associate--l+_binary64
55×neg-sub0_binary64
54×log-div_binary64 associate-*l*_binary64
49×cube-prod_binary64
47×log-prod_binary64
43×associate-+r+_binary64
41×cube-div_binary64
39×associate-+l+_binary64
38×swap-sqr_binary64
35×exp-prod_binary64 cancel-sign-sub-inv_binary64
28×distribute-rgt-in_binary64
26×unswap-sqr_binary64
23×distribute-neg-in_binary64 distribute-lft-neg-in_binary64 +-commutative_binary64
22×distribute-rgt-neg-in_binary64
21×*-lft-identity_binary64
20×sub0-neg_binary64 remove-double-div_binary64
17×unpow3_binary64 cube-mult_binary64 distribute-neg-frac_binary64
15×/-rgt-identity_binary64
13×--rgt-identity_binary64 pow-sqr_binary64
11×+-rgt-identity_binary64
log-rec_binary64 unpow1/2_binary64 distribute-lft-in_binary64
cube-unmult_binary64
div0_binary64
remove-double-neg_binary64
distribute-lft-neg-out_binary64
exp-diff_binary64 exp-sum_binary64
+-lft-identity_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64
1-exp_binary64 exp-1-e_binary64 rem-sqrt-square_binary64 mul0-rgt_binary64 mul0-lft_binary64 +-inverses_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 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 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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_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
Counts
287 → 219
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04486523
19866310
237046307
336376307
445386307
546646307
649776307

prune175.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2136219
Fresh112
Picked011
Done011
Total2149223
Error
0b
Counts
223 → 9
Compiler

Compiled 3070 to 631 computations (79.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 b1)
2.1b
(/.f64 a1 (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2)))
2.3b
(/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))
4.8b
(*.f64 (/.f64 (*.f64 (cbrt.f64 a2) (cbrt.f64 a2)) (*.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))

rewrite1.6s (15.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
2803×times-frac_binary64
1338×add-sqr-sqrt_binary64
1280×add-cube-cbrt_binary64 *-un-lft-identity_binary64
985×cbrt-prod_binary64
416×associate-*r*_binary64
159×associate-/r*_binary64
120×add-exp-log_binary64
67×add-cbrt-cube_binary64
60×div-inv_binary64
55×div-exp_binary64 cbrt-undiv_binary64
36×prod-exp_binary64 cbrt-unprod_binary64
16×unswap-sqr_binary64
10×associate-/r/_binary64
associate-/l*_binary64
pow1_binary64
associate-*l*_binary64
add-log-exp_binary64
frac-2neg_binary64 clear-num_binary64
pow-prod-down_binary64 frac-times_binary64 associate-*l/_binary64 associate-*r/_binary64 *-commutative_binary64 pow1/3_binary64
Counts
4 → 1243
Calls

4 calls:

126.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 a2) (cbrt.f64 a2)) (*.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
29.0ms
(/.f64 a1 (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2)))
9.0ms
(/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))
1.0ms
(cbrt.f64 b1)
Compiler

Compiled 46708 to 6949 computations (85.1% saved)

series281.0ms (2.7%)

Error
0b
Counts
4 → 36
Calls

4 calls:

112.0ms
(/.f64 a1 (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2)))
76.0ms
(/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))
60.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 a2) (cbrt.f64 a2)) (*.f64 (cbrt.f64 b1) (cbrt.f64 b1))) (/.f64 a1 (/.f64 (cbrt.f64 b1) (/.f64 (cbrt.f64 a2) b2))))
18.0ms
(cbrt.f64 b1)
Compiler

Compiled 1774 to 1256 computations (29.2% saved)

simplify1.2s (12.1%)

Algorithm
egg-herbie
Rules
844×associate-/r/_binary64
475×*-commutative_binary64
437×associate-*r/_binary64
425×associate-*l/_binary64
171×associate-/l*_binary64
40×exp-prod_binary64
38×unswap-sqr_binary64
36×log-prod_binary64
32×sub-neg_binary64
31×log-div_binary64
30×associate-/r*_binary64
22×remove-double-div_binary64
21×unpow1/3_binary64 exp-sum_binary64
20×associate-*l*_binary64
19×sqr-pow_binary64
18×neg-sub0_binary64
16×associate-*r*_binary64 associate-+l-_binary64
15×neg-mul-1_binary64 /-rgt-identity_binary64
13×cube-unmult_binary64 times-frac_binary64
12×unpow3_binary64 cube-div_binary64
10×cube-prod_binary64
log-pow_binary64
exp-diff_binary64 mul-1-neg_binary64 swap-sqr_binary64 associate-/l/_binary64
log-rec_binary64 exp-to-pow_binary64 +-commutative_binary64
cancel-sign-sub-inv_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 associate-+r-_binary64
pow-plus_binary64
rem-3cbrt-lft_binary64 rem-sqrt-square_binary64 *-rgt-identity_binary64 remove-double-neg_binary64 distribute-neg-frac_binary64 count-2_binary64 associate--r-_binary64
1-exp_binary64 exp-1-e_binary64 rem-exp-log_binary64 cube-mult_binary64 rem-3cbrt-rft_binary64 rem-cube-cbrt_binary64 fabs-div_binary64 fabs-mul_binary64 div-sub_binary64 *-lft-identity_binary64 *-inverses_binary64 lft-mult-inverse_binary64 pow-sqr_binary64 associate--l+_binary64 associate--r+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow2_binary64 unpow1/2_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 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 cube-neg_binary64 rem-cbrt-cube_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 unsub-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 +-inverses_binary64 rgt-mult-inverse_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_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 associate--l-_binary64 associate-+l+_binary64 associate-+r+_binary64
Counts
1279 → 1041
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0158148202
1472743151
2487643013
3495343002
4498543002

prune735.0ms (7.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New104101041
Fresh066
Picked011
Done022
Total104191050
Error
0b
Counts
1050 → 9
Compiler

Compiled 31162 to 5726 computations (81.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b
(cbrt.f64 a1)
0.6b
(cbrt.f64 a1)
3.2b
(/.f64 (cbrt.f64 a1) (*.f64 b1 b2))
6.9b
(*.f64 (*.f64 a2 (*.f64 (cbrt.f64 a1) (cbrt.f64 a1))) (/.f64 (cbrt.f64 a1) (*.f64 b1 b2)))

rewrite93.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
45×add-exp-log_binary64
31×add-cbrt-cube_binary64
22×prod-exp_binary64 cbrt-unprod_binary64
15×cbrt-prod_binary64
13×pow1_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
12×times-frac_binary64
10×associate-*r*_binary64
div-exp_binary64 cbrt-undiv_binary64
pow-prod-down_binary64 associate-/l*_binary64
add-log-exp_binary64
div-inv_binary64 pow1/3_binary64
associate-*r/_binary64 associate-*l*_binary64 *-commutative_binary64 frac-2neg_binary64 clear-num_binary64 associate-/r*_binary64
Counts
4 → 90
Calls

4 calls:

12.0ms
(*.f64 (*.f64 a2 (*.f64 (cbrt.f64 a1) (cbrt.f64 a1))) (/.f64 (cbrt.f64 a1) (*.f64 b1 b2)))
4.0ms
(/.f64 (cbrt.f64 a1) (*.f64 b1 b2))
1.0ms
(cbrt.f64 a1)
1.0ms
(cbrt.f64 a1)
Compiler

Compiled 1827 to 299 computations (83.6% saved)

series148.0ms (1.4%)

Error
0b
Counts
4 → 27
Calls

4 calls:

61.0ms
(/.f64 (cbrt.f64 a1) (*.f64 b1 b2))
48.0ms
(*.f64 (*.f64 a2 (*.f64 (cbrt.f64 a1) (cbrt.f64 a1))) (/.f64 (cbrt.f64 a1) (*.f64 b1 b2)))
17.0ms
(cbrt.f64 a1)
15.0ms
(cbrt.f64 a1)
Compiler

Compiled 822 to 667 computations (18.9% saved)

simplify86.0ms (0.8%)

Algorithm
egg-herbie
Rules
823×associate-*l/_binary64
559×*-commutative_binary64
448×associate-/r*_binary64
310×associate-*l*_binary64
215×log-div_binary64
210×log-prod_binary64
206×associate-*r*_binary64
184×cube-div_binary64
173×cube-prod_binary64
145×exp-prod_binary64
132×associate-/l/_binary64
93×associate-/r/_binary64
80×times-frac_binary64
77×associate-*r/_binary64
69×associate-/l*_binary64
65×unswap-sqr_binary64
56×associate-+l+_binary64
44×swap-sqr_binary64
40×associate-+r+_binary64
36×distribute-rgt-neg-in_binary64
33×unpow3_binary64 distribute-lft-neg-in_binary64
32×cube-mult_binary64
31×sqr-pow_binary64
27×sub-neg_binary64
22×+-commutative_binary64
21×*-lft-identity_binary64 associate-+r-_binary64
20×distribute-neg-frac_binary64 associate--l+_binary64
17×neg-sub0_binary64 associate--r+_binary64
16×associate-+l-_binary64
14×cancel-sign-sub-inv_binary64
13×*-rgt-identity_binary64
12×neg-mul-1_binary64
11×cube-unmult_binary64
distribute-frac-neg_binary64
pow-plus_binary64 mul-1-neg_binary64
log-pow_binary64
log-rec_binary64 div-sub_binary64
rem-sqrt-square_binary64 distribute-rgt-in_binary64
unpow1/3_binary64 pow-sqr_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64
exp-diff_binary64 unsub-neg_binary64 distribute-neg-in_binary64 distribute-lft-in_binary64 count-2_binary64
unpow1/2_binary64 exp-sum_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-lft_binary64 rem-cube-cbrt_binary64 fabs-mul_binary64 fabs-sqr_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 distribute-rgt-out_binary64 distribute-lft-out_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 pow-base-0_binary64 unpow2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 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-cbrt-cube_binary64 fabs-div_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64
Counts
117 → 74
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01331569
13311220
214501212
341241212
450141212

prune26.0ms (0.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New74074
Fresh055
Picked011
Done033
Total74983
Error
0b
Counts
83 → 9
Compiler

Compiled 598 to 190 computations (68.2% saved)

regimes2.7s (25.8%)

Accuracy

Total 2.9b remaining (99%)

Threshold costs 0b (0%)

Compiler

Compiled 26882 to 19453 computations (27.6% saved)

bsearch7.0ms (0.1%)

Compiler

Compiled 7 to 7 computations (0% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same 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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_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
036123
141123
240123

end33.0ms (0.3%)

Compiler

Compiled 390 to 170 computations (56.4% saved)

sample1.3s (12.6%)

Algorithm
intervals
Results
246.0ms8000×body128valid
56.0ms1795×body128invalid
Compiler

Compiled 188 to 146 computations (22.3% saved)

Profiling

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