Details

Time bar (total: 4.7s)

analyze377.0ms (8%)

Algorithm
search
egg-herbie
Rules
544×neg-sub0_binary64
540×neg-mul-1_binary64
514×distribute-rgt-in_binary64
504×div-sub_binary64
476×distribute-lft-in_binary64
258×sub-neg_binary64
216×distribute-neg-in_binary64
196×distribute-neg-out_binary64
178×times-frac_binary64 associate-*r*_binary64
162×distribute-neg-frac_binary64 associate-*l*_binary64
150×associate-/l*_binary64
148×distribute-frac-neg_binary64 associate-*l/_binary64
134×unsub-neg_binary64 associate-*r/_binary64
114×distribute-rgt-neg-out_binary64
104×associate-/r/_binary64
98×distribute-lft-neg-out_binary64
86×associate-/r*_binary64
84×associate-+r+_binary64
82×associate-+l+_binary64
76×*-commutative_binary64
58×associate-+l-_binary64
56×cancel-sign-sub-inv_binary64
50×*-rgt-identity_binary64 remove-double-neg_binary64 +-commutative_binary64
44×distribute-rgt-out_binary64
42×*-lft-identity_binary64
40×mul0-rgt_binary64
36×sub0-neg_binary64
34×mul0-lft_binary64 associate-+r-_binary64
32×distribute-lft-neg-in_binary64 associate-/l/_binary64
30×associate--r+_binary64
28×distribute-rgt-neg-in_binary64
20×+-rgt-identity_binary64
16×div0_binary64
14×associate--l-_binary64 associate--l+_binary64
12×mul-1-neg_binary64
10×/-rgt-identity_binary64
sqr-neg_binary64 associate--r-_binary64
--rgt-identity_binary64 swap-sqr_binary64
distribute-rgt1-in_binary64 distribute-lft1-in_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 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 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 +-lft-identity_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 cancel-sign-sub_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01532
14132
213332
335732
4115732
5328932
6434232
7487232
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
37.5%62.4%0.1%6
50%46.8%3.2%7
56.2%37.5%6.3%8
62.4%25.8%11.8%9
65.6%20.3%14.1%10
68.7%13.5%17.9%11
70.2%10.5%19.2%12
71.8%6.9%21.3%13
72.6%5.4%22%14
Compiler

Compiled 12 to 11 computations (8.3% saved)

sample17.0ms (0.4%)

Algorithm
intervals
Results
8.0ms256×body128valid
0.0ms14×body128invalid
Compiler

Compiled 23 to 23 computations (0% saved)

simplify78.0ms (1.7%)

Algorithm
egg-herbie
Rules
785×div-sub_binary64
608×unsub-neg_binary64
520×sub-neg_binary64
408×distribute-neg-frac_binary64
350×neg-mul-1_binary64
349×neg-sub0_binary64
342×associate-/l*_binary64
273×associate-*l/_binary64
269×times-frac_binary64
261×distribute-rgt-in_binary64
259×distribute-rgt-neg-out_binary64
243×distribute-lft-in_binary64
228×distribute-rgt-neg-in_binary64
194×distribute-lft-neg-out_binary64
191×cancel-sign-sub-inv_binary64
172×distribute-neg-in_binary64 associate-*r/_binary64
124×distribute-neg-out_binary64
116×associate-/r*_binary64
111×associate-/l/_binary64
109×associate-/r/_binary64
91×distribute-frac-neg_binary64
89×associate-*r*_binary64
81×associate-*l*_binary64
79×remove-double-neg_binary64
68×distribute-lft-neg-in_binary64
55×distribute-rgt-out--_binary64 distribute-rgt-out_binary64
46×associate-+r+_binary64
45×associate-+l+_binary64
42×*-commutative_binary64
40×*-rgt-identity_binary64
34×*-lft-identity_binary64
29×associate-+l-_binary64
25×mul0-rgt_binary64 +-commutative_binary64
20×sub0-neg_binary64
19×mul0-lft_binary64 associate--r+_binary64
17×associate-+r-_binary64
14×cancel-sign-sub_binary64 distribute-lft-out_binary64
12×distribute-rgt1-in_binary64
11×div0_binary64
10×/-rgt-identity_binary64 +-rgt-identity_binary64
mul-1-neg_binary64
associate--l-_binary64 associate--l+_binary64
distribute-lft1-in_binary64
remove-double-div_binary64
sqr-neg_binary64 associate--r-_binary64
--rgt-identity_binary64 swap-sqr_binary64 distribute-lft-out--_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 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 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 +-lft-identity_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 count-2_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01016
12416
27116
318616
459716
5167416
6307616
7425916
8495716

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
3.6b
Counts
2 → 1
Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 (-.f64 1 x) (-.f64 3 x))
3.4b
(/.f64 (*.f64 (-.f64 1 x) (-.f64 3 x)) (*.f64 y 3))

rewrite116.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
16×add-exp-log_binary64 add-cbrt-cube_binary64
13×add-sqr-sqrt_binary64
12×flip3--_binary64 flip--_binary64
11×*-un-lft-identity_binary64
frac-times_binary64 associate-/l/_binary64
add-cube-cbrt_binary64 cancel-sign-sub-inv_binary64 associate-*l*_binary64
prod-exp_binary64 cbrt-unprod_binary64 associate-*r*_binary64
pow1_binary64 div-exp_binary64 cbrt-undiv_binary64 associate-*l/_binary64 associate-*r/_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64
difference-of-squares_binary64
add-log-exp_binary64 sub-neg_binary64 distribute-lft-out--_binary64
frac-2neg_binary64 times-frac_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64 associate-/r*_binary64 pow-prod-down_binary64 unswap-sqr_binary64 *-commutative_binary64
Counts
2 → 68
Calls

2 calls:

14.0ms
(*.f64 (-.f64 1 x) (-.f64 3 x))
12.0ms
(/.f64 (*.f64 (-.f64 1 x) (-.f64 3 x)) (*.f64 y 3))
Compiler

Compiled 1398 to 1024 computations (26.8% saved)

series68.0ms (1.5%)

Error
3.2b
Counts
2 → 21
Calls

2 calls:

37.0ms
(/.f64 (*.f64 (-.f64 1 x) (-.f64 3 x)) (*.f64 y 3))
17.0ms
(*.f64 (-.f64 1 x) (-.f64 3 x))
Compiler

Compiled 493 to 423 computations (14.2% saved)

simplify89.0ms (1.9%)

Algorithm
egg-herbie
Rules
602×associate-/r*_binary64
408×associate-*l/_binary64
319×associate-*r/_binary64
194×associate-/l/_binary64
166×times-frac_binary64
149×associate-*l*_binary64
147×associate-/r/_binary64
133×distribute-rgt-in_binary64
127×associate-*r*_binary64
126×distribute-lft-in_binary64
119×exp-prod_binary64
114×associate-+l+_binary64
110×*-commutative_binary64
100×associate-/l*_binary64
78×log-div_binary64
62×sub-neg_binary64
60×log-prod_binary64
53×distribute-rgt-neg-out_binary64
49×div-sub_binary64 distribute-lft-neg-out_binary64
45×distribute-rgt-neg-in_binary64
44×cancel-sign-sub-inv_binary64
36×+-commutative_binary64
32×neg-sub0_binary64
29×neg-mul-1_binary64 distribute-lft-neg-in_binary64
28×exp-diff_binary64
26×associate-+l-_binary64
24×swap-sqr_binary64
22×*-lft-identity_binary64
21×associate--l+_binary64
20×distribute-neg-in_binary64
18×cube-prod_binary64 sqr-pow_binary64
17×*-rgt-identity_binary64 associate--r+_binary64
15×distribute-lft-out_binary64 associate-+r-_binary64
14×unsub-neg_binary64 distribute-rgt-out_binary64
13×unpow3_binary64
exp-sum_binary64
exp-cbrt_binary64 cube-div_binary64 distribute-neg-frac_binary64
cube-unmult_binary64
associate-+r+_binary64
distribute-rgt1-in_binary64
/-rgt-identity_binary64 distribute-rgt-out--_binary64
log-rec_binary64 mul-1-neg_binary64
unpow1/2_binary64 pow-plus_binary64 unswap-sqr_binary64 distribute-lft-out--_binary64 associate--r-_binary64
unpow2_binary64 unpow1_binary64 exp-lft-cube_binary64 1-exp_binary64 exp-1-e_binary64 cube-mult_binary64 rem-3cbrt-lft_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 remove-double-neg_binary64 pow-sqr_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 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_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 rem-cube-cbrt_binary64 sqr-abs_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-frac-neg_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--l-_binary64
Counts
89 → 75
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01661589
14791363
219291315
347341315
449431315

prune61.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New71475
Fresh000
Picked011
Done000
Total71576
Error
0.0b
Counts
76 → 5
Compiler

Compiled 908 to 660 computations (27.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (-.f64 3 x) 3)
0.1b
(/.f64 y (/.f64 (-.f64 3 x) 3))
0.1b
(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))

rewrite641.0ms (13.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
1218×times-frac_binary64
808×add-sqr-sqrt_binary64 *-un-lft-identity_binary64
461×add-cube-cbrt_binary64
205×difference-of-squares_binary64
142×distribute-lft-out--_binary64
84×associate-/r*_binary64
35×div-inv_binary64
19×add-exp-log_binary64 add-cbrt-cube_binary64
14×associate-/l*_binary64
10×div-exp_binary64 cbrt-undiv_binary64
associate-/r/_binary64
associate-/l/_binary64
pow1_binary64 add-log-exp_binary64 frac-2neg_binary64 clear-num_binary64
div-sub_binary64 flip3--_binary64 flip--_binary64
Counts
3 → 592
Calls

3 calls:

26.0ms
(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
10.0ms
(/.f64 (-.f64 3 x) 3)
8.0ms
(/.f64 y (/.f64 (-.f64 3 x) 3))
Compiler

Compiled 12544 to 9075 computations (27.7% saved)

series94.0ms (2%)

Error
0.0b
Counts
3 → 33
Calls

3 calls:

39.0ms
(/.f64 (-.f64 1 x) (/.f64 y (/.f64 (-.f64 3 x) 3)))
26.0ms
(/.f64 y (/.f64 (-.f64 3 x) 3))
9.0ms
(/.f64 (-.f64 3 x) 3)
Compiler

Compiled 900 to 730 computations (18.9% saved)

simplify387.0ms (8.2%)

Algorithm
egg-herbie
Rules
554×associate-/l/_binary64
532×associate-/r*_binary64
489×associate-/r/_binary64
395×associate-/l*_binary64
278×div-sub_binary64
254×times-frac_binary64
183×sub-neg_binary64
90×distribute-rgt-in_binary64
89×distribute-lft-in_binary64
29×*-commutative_binary64
22×neg-sub0_binary64
21×neg-mul-1_binary64 cancel-sign-sub-inv_binary64 +-commutative_binary64
20×distribute-neg-in_binary64
17×remove-double-div_binary64
16×associate-*r/_binary64
15×distribute-rgt-neg-in_binary64
14×/-rgt-identity_binary64
11×distribute-lft-neg-in_binary64
10×distribute-neg-frac_binary64
log-div_binary64 associate-+r+_binary64
cube-unmult_binary64 swap-sqr_binary64 associate-*l*_binary64
sqr-pow_binary64 associate-*l/_binary64
log-prod_binary64 exp-diff_binary64 unswap-sqr_binary64 distribute-rgt1-in_binary64
exp-prod_binary64 unsub-neg_binary64 distribute-rgt-out_binary64 associate-*r*_binary64
cube-prod_binary64 mul-1-neg_binary64 *-lft-identity_binary64 associate--r-_binary64 associate--l+_binary64
log-rec_binary64 unpow3_binary64 unpow2_binary64 unpow1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sum_binary64 1-exp_binary64 cube-mult_binary64 *-rgt-identity_binary64 *-inverses_binary64 distribute-rgt-out--_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 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_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-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-sqrt-square_binary64 rem-square-sqrt_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 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 pow-sqr_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-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64 associate--l-_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64
Counts
625 → 481
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
073320662
1198720379
2511220379

prune282.0ms (6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New4792481
Fresh123
Picked011
Done011
Total4806486
Error
0b
Counts
486 → 6
Compiler

Compiled 6824 to 4807 computations (29.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b
(*.f64 (-.f64 3 x) (/.f64 (-.f64 1 x) (/.f64 y 1/3)))
0.3b
(/.f64 (-.f64 1 x) (/.f64 y 1/3))
0.4b
(/.f64 y 1/3)

rewrite277.0ms (5.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
285×times-frac_binary64
223×add-sqr-sqrt_binary64
214×*-un-lft-identity_binary64
131×add-cube-cbrt_binary64
83×associate-*r*_binary64
55×difference-of-squares_binary64
28×distribute-lft-out--_binary64
19×add-exp-log_binary64 add-cbrt-cube_binary64
16×div-inv_binary64 associate-/r*_binary64
associate-/l*_binary64
div-exp_binary64 cbrt-undiv_binary64
pow1_binary64 associate-*l*_binary64
add-log-exp_binary64 flip3--_binary64 flip--_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64
frac-2neg_binary64 clear-num_binary64 associate-/l/_binary64 associate-/r/_binary64 frac-times_binary64 associate-*l/_binary64
div-sub_binary64 pow-prod-down_binary64 associate-*r/_binary64 *-commutative_binary64
Counts
3 → 253
Calls

3 calls:

33.0ms
(*.f64 (-.f64 3 x) (/.f64 (-.f64 1 x) (/.f64 y 1/3)))
9.0ms
(/.f64 (-.f64 1 x) (/.f64 y 1/3))
3.0ms
(/.f64 y 1/3)
Compiler

Compiled 5013 to 3639 computations (27.4% saved)

series81.0ms (1.7%)

Error
0b
Counts
3 → 24
Calls

3 calls:

36.0ms
(*.f64 (-.f64 3 x) (/.f64 (-.f64 1 x) (/.f64 y 1/3)))
23.0ms
(/.f64 (-.f64 1 x) (/.f64 y 1/3))
6.0ms
(/.f64 y 1/3)
Compiler

Compiled 648 to 547 computations (15.6% saved)

simplify174.0ms (3.7%)

Algorithm
egg-herbie
Rules
857×distribute-rgt-in_binary64
282×associate-/r/_binary64
215×associate-*l*_binary64
208×associate-/l*_binary64
199×div-sub_binary64
197×*-commutative_binary64
181×associate-*r/_binary64
169×associate-*r*_binary64
162×associate-*l/_binary64
152×associate-/l/_binary64
126×distribute-lft-neg-out_binary64
125×distribute-rgt-neg-out_binary64
107×distribute-lft-in_binary64
106×cancel-sign-sub-inv_binary64
102×sub-neg_binary64
76×*-rgt-identity_binary64
73×distribute-rgt-neg-in_binary64
70×distribute-neg-frac_binary64
61×*-lft-identity_binary64
59×distribute-lft-neg-in_binary64
58×neg-sub0_binary64
54×neg-mul-1_binary64
49×times-frac_binary64
47×associate-/r*_binary64
40×exp-prod_binary64
35×+-commutative_binary64
29×log-prod_binary64
28×/-rgt-identity_binary64
22×log-div_binary64
20×sqr-pow_binary64
19×cube-prod_binary64
17×swap-sqr_binary64
16×cube-div_binary64 distribute-rgt-out--_binary64
13×distribute-neg-in_binary64
10×exp-sum_binary64
unswap-sqr_binary64 distribute-rgt-out_binary64 associate-+l+_binary64
exp-diff_binary64 cube-unmult_binary64
mul-1-neg_binary64 distribute-frac-neg_binary64 associate--r+_binary64 associate-+r+_binary64
distribute-rgt1-in_binary64 associate--l+_binary64
unsub-neg_binary64 remove-double-div_binary64 associate--r-_binary64
remove-double-neg_binary64 associate-+r-_binary64
unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 exp-1-e_binary64 cube-mult_binary64 cube-neg_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 pow-sqr_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 log-pow_binary64 log-rec_binary64 pow-base-0_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64 count-2_binary64 associate--l-_binary64
Counts
277 → 194
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03275584
18505345
234435337
360215337

prune118.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1931194
Fresh123
Picked101
Done022
Total1955200
Error
0b
Counts
200 → 5
Compiler

Compiled 2553 to 1799 computations (29.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b
(*.f64 (-.f64 3 x) (/.f64 (-.f64 1 x) (*.f64 y 3)))
0.3b
(/.f64 (-.f64 1 x) (*.f64 y 3))

rewrite86.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
20×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64
16×add-exp-log_binary64 add-cbrt-cube_binary64
12×times-frac_binary64
10×associate-*r*_binary64
add-cube-cbrt_binary64 difference-of-squares_binary64
associate-/l*_binary64
prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64
pow1_binary64 div-exp_binary64 cbrt-undiv_binary64 distribute-lft-out--_binary64
flip3--_binary64 flip--_binary64
add-log-exp_binary64 div-inv_binary64 associate-/l/_binary64 frac-times_binary64 associate-*l/_binary64
frac-2neg_binary64 div-sub_binary64 clear-num_binary64 associate-/r*_binary64 pow-prod-down_binary64 unswap-sqr_binary64 associate-*r/_binary64 *-commutative_binary64
Counts
2 → 66
Calls

2 calls:

13.0ms
(*.f64 (-.f64 3 x) (/.f64 (-.f64 1 x) (*.f64 y 3)))
7.0ms
(/.f64 (-.f64 1 x) (*.f64 y 3))
Compiler

Compiled 1158 to 867 computations (25.1% saved)

series68.0ms (1.4%)

Error
0b
Counts
2 → 21
Calls

2 calls:

38.0ms
(*.f64 (-.f64 3 x) (/.f64 (-.f64 1 x) (*.f64 y 3)))
22.0ms
(/.f64 (-.f64 1 x) (*.f64 y 3))
Compiler

Compiled 571 to 479 computations (16.1% saved)

simplify93.0ms (2%)

Algorithm
egg-herbie
Rules
916×times-frac_binary64
479×distribute-rgt-in_binary64
460×distribute-lft-in_binary64
110×associate-*l*_binary64
84×exp-prod_binary64
83×*-commutative_binary64
76×associate-*r*_binary64
71×log-prod_binary64
67×associate-/l*_binary64
65×exp-sum_binary64
64×div-sub_binary64
63×associate-*r/_binary64
62×sub-neg_binary64
57×distribute-lft-neg-out_binary64
54×distribute-rgt-neg-out_binary64
50×associate-/r*_binary64
44×cancel-sign-sub-inv_binary64
42×associate-*l/_binary64
37×log-div_binary64
36×distribute-rgt-neg-in_binary64
34×+-commutative_binary64
28×neg-sub0_binary64
27×*-lft-identity_binary64
24×neg-mul-1_binary64 distribute-lft-neg-in_binary64
20×cube-prod_binary64
19×*-rgt-identity_binary64 distribute-neg-frac_binary64
18×exp-diff_binary64 sqr-pow_binary64
17×unpow3_binary64
16×swap-sqr_binary64 distribute-rgt-out_binary64
12×cube-div_binary64 distribute-neg-in_binary64
10×exp-cbrt_binary64 exp-neg_binary64
associate-/r/_binary64
associate--r+_binary64
cube-unmult_binary64 distribute-lft-out_binary64 associate-+l+_binary64
mul-1-neg_binary64 distribute-rgt-out--_binary64
unsub-neg_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 associate--l+_binary64 associate-+r+_binary64
/-rgt-identity_binary64 unswap-sqr_binary64 associate-+r-_binary64
log-rec_binary64 unpow1/2_binary64 associate-+l-_binary64
unpow2_binary64 pow-plus_binary64 unpow1_binary64 exp-lft-cube_binary64 1-exp_binary64 exp-1-e_binary64 cube-mult_binary64 cube-neg_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 remove-double-neg_binary64 pow-sqr_binary64 distribute-lft-out--_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 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-sqr_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 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_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-lft1-in_binary64 count-2_binary64 associate-/l/_binary64 associate--l-_binary64
Counts
87 → 69
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01511514
14001315
214271309
347131309
449881309

prune40.0ms (0.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New69069
Fresh022
Picked011
Done022
Total69574
Error
0b
Counts
74 → 5
Compiler

Compiled 760 to 550 computations (27.6% saved)

regimes892.0ms (19%)

Accuracy

Total 0.1b remaining (85.4%)

Threshold costs 0.1b (85.4%)

Compiler

Compiled 11906 to 10240 computations (14% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
sub-neg_binary64 +-commutative_binary64
1-exp_binary64 neg-mul-1_binary64 neg-sub0_binary64 *-commutative_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_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
01016
11516
22016
32216
42316
52216

end1.0ms (0%)

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample630.0ms (13.4%)

Algorithm
intervals
Results
259.0ms8000×body128valid
9.0ms313×body128invalid
Compiler

Compiled 96 to 95 computations (1% saved)

Profiling

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