Details

Time bar (total: 4.6s)

analyze895.0ms (19.3%)

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)

sample35.0ms (0.8%)

Algorithm
intervals
Results
7.0ms256×body128valid
2.0ms65×body128invalid
Compiler

Compiled 15 to 19 computations (-26.7% saved)

simplify15.0ms (0.3%)

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
14.1b
Counts
1 → 1
Compiler

Compiled 7 to 7 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

13.8b
(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

rewrite30.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
0.1b
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:

6.0ms
(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))
Compiler

Compiled 291 to 77 computations (73.5% saved)

series45.0ms (1%)

Error
14.1b
Counts
1 → 12
Calls

1 calls:

44.0ms
(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))
Compiler

Compiled 175 to 175 computations (0% saved)

simplify86.0ms (1.8%)

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 (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New9211
Fresh000
Picked011
Done000
Total9312
Error
0.1b
Counts
12 → 3
Compiler

Compiled 47 to 32 computations (31.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

5.4b
(*.f64 a2 (/.f64 a1 b1))
6.9b
(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)

rewrite68.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
17×add-sqr-sqrt_binary64
16×add-exp-log_binary64 add-cbrt-cube_binary64
13×times-frac_binary64 associate-*r*_binary64
12×add-cube-cbrt_binary64 *-un-lft-identity_binary64
div-exp_binary64 cbrt-undiv_binary64
pow1_binary64 prod-exp_binary64 cbrt-unprod_binary64
associate-/r*_binary64 associate-*l*_binary64
add-log-exp_binary64 div-inv_binary64 associate-*r/_binary64 unswap-sqr_binary64
frac-2neg_binary64 clear-num_binary64 associate-/l/_binary64 associate-/l*_binary64 pow-prod-down_binary64 *-commutative_binary64
Counts
2 → 56
Calls

2 calls:

10.0ms
(*.f64 a2 (/.f64 a1 b1))
6.0ms
(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
Compiler

Compiled 736 to 212 computations (71.2% saved)

series71.0ms (1.5%)

Error
0.1b
Counts
2 → 21
Calls

2 calls:

43.0ms
(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
26.0ms
(*.f64 a2 (/.f64 a1 b1))
Compiler

Compiled 308 to 303 computations (1.6% saved)

simplify105.0ms (2.3%)

Algorithm
egg-herbie
Rules
919×times-frac_binary64
527×associate-/l/_binary64
421×associate-*l*_binary64
340×associate-*r*_binary64
297×associate-/r/_binary64
290×associate-/r*_binary64
178×sub-neg_binary64
136×sqr-pow_binary64 *-commutative_binary64
114×associate-/l*_binary64
113×log-div_binary64
112×log-prod_binary64
109×cube-prod_binary64
104×cube-div_binary64
84×associate--l+_binary64
79×associate-*r/_binary64
74×associate-*l/_binary64
73×unsub-neg_binary64
67×*-lft-identity_binary64 associate--l-_binary64
59×neg-mul-1_binary64 neg-sub0_binary64
57×*-rgt-identity_binary64
53×exp-prod_binary64
49×swap-sqr_binary64
46×/-rgt-identity_binary64
36×unpow3_binary64
32×cube-mult_binary64
23×associate--r-_binary64
21×unswap-sqr_binary64
19×log-rec_binary64
18×pow-sqr_binary64 distribute-neg-in_binary64
17×div-sub_binary64 cancel-sign-sub-inv_binary64
15×distribute-rgt-neg-in_binary64 associate-+l+_binary64
14×distribute-neg-frac_binary64 associate-+l-_binary64
13×rem-sqrt-square_binary64
12×distribute-lft-neg-in_binary64 associate-+r-_binary64 associate-+r+_binary64
10×remove-double-neg_binary64
cube-unmult_binary64 distribute-neg-out_binary64
--rgt-identity_binary64 div0_binary64 +-commutative_binary64
unpow1/2_binary64 +-rgt-identity_binary64 +-lft-identity_binary64
mul0-rgt_binary64 mul0-lft_binary64 remove-double-div_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64
fabs-mul_binary64 +-inverses_binary64 distribute-frac-neg_binary64
1-exp_binary64 exp-1-e_binary64 fabs-sqr_binary64 distribute-lft-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-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-diff_binary64 exp-neg_binary64 exp-sum_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-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 sub0-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-rgt-neg-out_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
77 → 39
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0108929
1263800
21046800
34062800
44579800
54958800
64967800

prune26.0ms (0.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New34539
Fresh011
Picked011
Done011
Total34842
Error
0.0b
Counts
42 → 8
Compiler

Compiled 362 to 152 computations (58% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

5.8b
(/.f64 a1 (*.f64 b1 b2))
6.6b
(*.f64 a2 (/.f64 a1 (*.f64 b1 b2)))

rewrite54.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
16×add-exp-log_binary64 add-cbrt-cube_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64 associate-*r*_binary64
times-frac_binary64
prod-exp_binary64 cbrt-unprod_binary64
pow1_binary64 div-exp_binary64 cbrt-undiv_binary64
associate-*l*_binary64 associate-/l*_binary64
add-log-exp_binary64 div-inv_binary64
pow-prod-down_binary64 unswap-sqr_binary64 associate-*r/_binary64 *-commutative_binary64 frac-2neg_binary64 clear-num_binary64 associate-/r*_binary64
Counts
2 → 48
Calls

2 calls:

7.0ms
(*.f64 a2 (/.f64 a1 (*.f64 b1 b2)))
4.0ms
(/.f64 a1 (*.f64 b1 b2))
Compiler

Compiled 602 to 154 computations (74.4% saved)

series71.0ms (1.5%)

Error
0.0b
Counts
2 → 21
Calls

2 calls:

44.0ms
(*.f64 a2 (/.f64 a1 (*.f64 b1 b2)))
25.0ms
(/.f64 a1 (*.f64 b1 b2))
Compiler

Compiled 308 to 303 computations (1.6% saved)

simplify101.0ms (2.2%)

Algorithm
egg-herbie
Rules
772×times-frac_binary64
466×associate-*l*_binary64
433×associate-*l/_binary64
425×associate-*r/_binary64
383×associate-*r*_binary64
372×associate-/l*_binary64
352×associate-/r*_binary64
124×associate-+l+_binary64
109×sqr-pow_binary64
95×associate-/l/_binary64
85×log-div_binary64
82×log-prod_binary64
76×associate-/r/_binary64 associate-+l-_binary64
73×sub-neg_binary64
72×cube-div_binary64
71×cube-prod_binary64
56×exp-prod_binary64
52×associate-+r-_binary64
50×swap-sqr_binary64 associate--l+_binary64
48×unswap-sqr_binary64
44×*-commutative_binary64
42×*-lft-identity_binary64
29×unpow3_binary64
27×associate--r+_binary64
26×cube-mult_binary64 *-rgt-identity_binary64
24×rem-sqrt-square_binary64
23×neg-mul-1_binary64 distribute-neg-in_binary64 associate--l-_binary64
22×neg-sub0_binary64 unsub-neg_binary64 +-commutative_binary64
17×distribute-rgt-in_binary64 associate-+r+_binary64
15×pow-sqr_binary64
14×associate--r-_binary64
11×/-rgt-identity_binary64
10×log-rec_binary64
div-sub_binary64
+-rgt-identity_binary64 cancel-sign-sub-inv_binary64
cube-unmult_binary64
distribute-neg-out_binary64
unpow1/2_binary64 distribute-neg-frac_binary64 distribute-lft-neg-in_binary64 distribute-lft-in_binary64
remove-double-neg_binary64 distribute-rgt-neg-in_binary64
fabs-mul_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-rgt-out_binary64
1-exp_binary64 exp-1-e_binary64 fabs-sqr_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-diff_binary64 exp-neg_binary64 exp-sum_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-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 sub0-neg_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-frac-neg_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64
Counts
69 → 28
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
080831
1192702
2739702
33815702
44206702
54960702
64969702

prune16.0ms (0.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New26228
Fresh055
Picked011
Done022
Total261036
Error
0b
Counts
36 → 10
Compiler

Compiled 261 to 120 computations (54% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

8.9b
(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))

rewrite52.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
27×add-sqr-sqrt_binary64
22×times-frac_binary64
15×add-cube-cbrt_binary64 *-un-lft-identity_binary64
13×add-exp-log_binary64 add-cbrt-cube_binary64 associate-*l*_binary64 associate-*r*_binary64
div-exp_binary64 prod-exp_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 unswap-sqr_binary64
pow1_binary64
div-inv_binary64
pow-prod-down_binary64 add-log-exp_binary64 frac-times_binary64 associate-*l/_binary64 associate-*r/_binary64 *-commutative_binary64
Counts
1 → 50
Calls

1 calls:

11.0ms
(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
Compiler

Compiled 726 to 192 computations (73.6% saved)

series47.0ms (1%)

Error
0b
Counts
1 → 12
Calls

1 calls:

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

Compiled 175 to 175 computations (0% saved)

simplify141.0ms (3%)

Algorithm
egg-herbie
Rules
669×associate-*l/_binary64
565×associate-*r/_binary64
498×associate-*l*_binary64
468×associate-/l*_binary64
386×associate-*r*_binary64
219×associate-/l/_binary64
201×times-frac_binary64
184×sqr-pow_binary64
158×*-commutative_binary64
156×sub-neg_binary64
138×associate-/r/_binary64
137×unsub-neg_binary64
120×associate-/r*_binary64
85×associate--r-_binary64
84×log-div_binary64
81×cube-div_binary64
69×distribute-neg-in_binary64
67×fabs-mul_binary64
65×log-prod_binary64
63×associate-+l+_binary64
61×distribute-rgt-in_binary64
59×*-lft-identity_binary64
58×cube-prod_binary64 unswap-sqr_binary64
54×*-rgt-identity_binary64
52×associate-+r+_binary64
48×associate--l-_binary64
47×cancel-sign-sub-inv_binary64
46×associate-+l-_binary64
45×neg-mul-1_binary64 swap-sqr_binary64
41×pow-sqr_binary64
38×neg-sub0_binary64
37×exp-prod_binary64 /-rgt-identity_binary64
34×associate--r+_binary64
29×rem-sqrt-square_binary64 associate-+r-_binary64
28×unpow3_binary64
27×cube-mult_binary64 associate--l+_binary64
24×distribute-lft-in_binary64
23×+-commutative_binary64
17×fabs-sqr_binary64
15×log-rec_binary64
13×+-rgt-identity_binary64
10×remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 distribute-neg-out_binary64
unpow1/2_binary64
cube-unmult_binary64 remove-double-div_binary64
distribute-rgt-neg-in_binary64
distribute-lft-neg-in_binary64
distribute-lft-neg-out_binary64
+-lft-identity_binary64 distribute-lft-out_binary64
distribute-rgt-neg-out_binary64 distribute-lft-out--_binary64
1-exp_binary64 exp-1-e_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_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-diff_binary64 exp-neg_binary64 exp-sum_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-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 div-sub_binary64 mul-1-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_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-neg-frac_binary64 distribute-frac-neg_binary64
Counts
62 → 38
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0111911
1306803
2959803
33793803
44205803
54706803
64935803
74969803
85019803

prune24.0ms (0.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New37138
Fresh246
Picked011
Done123
Total40848
Error
0b
Counts
48 → 8
Compiler

Compiled 392 to 109 computations (72.2% saved)

regimes1.4s (29.3%)

Accuracy

Total 5.2b remaining (99.3%)

Threshold costs 0b (0%)

Compiler

Compiled 5232 to 4180 computations (20.1% saved)

bsearch2.0ms (0%)

Compiler

Compiled 3 to 5 computations (-66.7% saved)

simplify8.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 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
032105
136105
236105

end36.0ms (0.8%)

Compiler

Compiled 360 to 150 computations (58.3% saved)

sample1.3s (28.4%)

Algorithm
intervals
Results
242.0ms8000×body128valid
54.0ms1910×body128invalid
Compiler

Compiled 156 to 126 computations (19.2% saved)

Profiling

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