Details

Time bar (total: 2.6s)

analyze285.0ms (10.8%)

Algorithm
search
egg-herbie
Rules
948×div-sub_binary64
542×sub-neg_binary64
535×associate-/l*_binary64
531×distribute-rgt-in_binary64
459×unsub-neg_binary64
417×associate-/l/_binary64
390×distribute-lft-in_binary64
360×times-frac_binary64
331×cancel-sign-sub-inv_binary64
297×associate-/r*_binary64
189×associate-/r/_binary64
167×distribute-neg-in_binary64
150×distribute-rgt-neg-in_binary64
137×*-commutative_binary64
129×neg-mul-1_binary64
127×distribute-neg-frac_binary64
110×distribute-frac-neg_binary64
109×distribute-lft-neg-in_binary64
108×neg-sub0_binary64
100×associate--r-_binary64
74×associate-*l/_binary64
72×associate--l-_binary64 associate-+r-_binary64
63×distribute-rgt-neg-out_binary64
61×distribute-lft-neg-out_binary64
59×+-commutative_binary64
46×associate--r+_binary64
44×associate-*r*_binary64
38×associate-*r/_binary64
37×associate-+l-_binary64
32×associate-*l*_binary64
28×mul0-rgt_binary64
27×remove-double-neg_binary64 mul0-lft_binary64
26×div0_binary64
23×*-lft-identity_binary64
20×+-rgt-identity_binary64 associate--l+_binary64
17×sub0-neg_binary64
16×--rgt-identity_binary64
14×mul-1-neg_binary64
12×/-rgt-identity_binary64 *-rgt-identity_binary64
associate-+l+_binary64
associate-+r+_binary64
remove-double-div_binary64 distribute-neg-out_binary64
+-lft-identity_binary64
distribute-lft-out--_binary64
*-inverses_binary64
1-exp_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 +-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 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64 count-2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01226
12526
24626
38926
416926
526926
680426
7120026
8195626
9180726
10189426
11207026
12209026
13191826
14265026
15217026
16217626
17218226
18219426
19218826
20218826
21218826
22228426
23233226
24214226
022
122
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
25%74.9%0.1%3
25%74.9%0.1%4
56.2%43.7%0.1%5
65.6%34.3%0.1%6
79.6%20.3%0.1%7
83.5%16.4%0.1%8
90.1%9.8%0.1%9
91.9%8%0.1%10
95.1%4.8%0.1%11
96%4%0.1%12
97.5%2.4%0.1%13
97.9%2%0.1%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample16.0ms (0.6%)

Algorithm
intervals
Results
7.0ms256×body128valid
Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify229.0ms (8.7%)

Algorithm
egg-herbie
Rules
700×div-sub_binary64
434×sub-neg_binary64
412×distribute-rgt-in_binary64
366×associate-/l*_binary64
361×associate-/l/_binary64
333×distribute-lft-in_binary64
313×associate-/r/_binary64
250×times-frac_binary64 unsub-neg_binary64
233×associate-/r*_binary64
232×cancel-sign-sub-inv_binary64
129×*-commutative_binary64
117×neg-mul-1_binary64
110×distribute-frac-neg_binary64 distribute-rgt-neg-in_binary64
99×distribute-neg-frac_binary64
93×associate--r+_binary64
83×distribute-lft-neg-in_binary64 associate--l-_binary64
82×distribute-neg-in_binary64
75×neg-sub0_binary64
73×distribute-lft-neg-out_binary64
72×distribute-rgt-neg-out_binary64
54×associate-*l/_binary64
51×associate--r-_binary64
50×associate-+l-_binary64
40×associate--l+_binary64
32×distribute-rgt-out--_binary64 +-commutative_binary64
29×sub0-neg_binary64
28×mul0-rgt_binary64 associate-+r-_binary64
26×div0_binary64
23×mul0-lft_binary64
19×*-lft-identity_binary64
18×distribute-neg-out_binary64
16×mul-1-neg_binary64
15×+-rgt-identity_binary64
14×associate-*r*_binary64
12×/-rgt-identity_binary64 associate-*l*_binary64 associate-+l+_binary64
11×associate-+r+_binary64
associate-*r/_binary64
remove-double-neg_binary64 remove-double-div_binary64
*-rgt-identity_binary64 --rgt-identity_binary64
distribute-rgt1-in_binary64
*-inverses_binary64 distribute-lft-out--_binary64
+-lft-identity_binary64 lft-mult-inverse_binary64
1-exp_binary64 distribute-rgt-out_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 +-inverses_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 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64 count-2_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11813
23513
37113
413513
522113
656913
792913
8176013
9196213
10227013
11222813
12228213
13229613
14219813
15218813
16218813
17218813
18218813
19228413
20233213
21214213

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Compiled 9 to 7 computations (22.2% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))

rewrite57.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
58×*-un-lft-identity_binary64
40×add-sqr-sqrt_binary64
30×times-frac_binary64
19×distribute-lft-out--_binary64
14×add-cube-cbrt_binary64
13×difference-of-squares_binary64
distribute-lft-out_binary64 associate-/r*_binary64
associate-/l*_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
flip3--_binary64 associate-/l/_binary64 flip--_binary64 associate-/r/_binary64
pow1_binary64 div-exp_binary64 add-log-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 div-sub_binary64 clear-num_binary64 div-inv_binary64
Counts
1 → 58
Calls

1 calls:

10.0ms
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
Compiler

Compiled 826 to 347 computations (58% saved)

series72.0ms (2.7%)

Error
0.0b
Counts
1 → 20
Calls

1 calls:

53.0ms
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 x y)))
Compiler

Compiled 1158 to 923 computations (20.3% saved)

simplify106.0ms (4%)

Algorithm
egg-herbie
Rules
338×times-frac_binary64
327×div-sub_binary64
318×associate-/l*_binary64
270×distribute-rgt-in_binary64
228×distribute-lft-in_binary64 associate-/r*_binary64
178×sub-neg_binary64
169×cancel-sign-sub-inv_binary64
137×associate-*l/_binary64
132×associate-*l*_binary64
129×associate-/r/_binary64
123×associate-*r*_binary64
115×associate-*r/_binary64
104×associate-/l/_binary64
87×distribute-neg-in_binary64
80×+-commutative_binary64
61×neg-sub0_binary64
60×neg-mul-1_binary64
52×associate--r+_binary64
50×distribute-neg-frac_binary64
47×associate--l+_binary64
43×associate-+l+_binary64
38×associate-+r+_binary64
36×unsub-neg_binary64
34×sqr-pow_binary64 unswap-sqr_binary64 distribute-rgt-neg-in_binary64 *-commutative_binary64
31×distribute-lft-neg-in_binary64
22×distribute-rgt-out_binary64
21×distribute-lft-neg-out_binary64
20×cube-prod_binary64
15×distribute-rgt-neg-out_binary64
14×cube-unmult_binary64
11×cube-div_binary64
10×distribute-rgt1-in_binary64
unpow3_binary64
*-rgt-identity_binary64
/-rgt-identity_binary64 distribute-rgt-out--_binary64
pow-plus_binary64
cube-mult_binary64
log-div_binary64 log-prod_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64 rem-sqrt-square_binary64
sqr-neg_binary64 difference-of-squares_binary64 distribute-lft-out_binary64 associate--r-_binary64
exp-diff_binary64 cube-neg_binary64 remove-double-neg_binary64 distribute-lft1-in_binary64
exp-prod_binary64 exp-sum_binary64 1-exp_binary64 mul-1-neg_binary64 *-lft-identity_binary64 sub0-neg_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same 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 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-1-e_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 --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 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 swap-sqr_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-lft-out--_binary64 count-2_binary64 associate--l-_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
78 → 71
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01872043
15081987
214831918
347691918
453991918

prune45.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New68371
Fresh000
Picked011
Done000
Total68472
Error
0b
Counts
72 → 4
Compiler

Compiled 1078 to 538 computations (50.1% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x)))
0.0b
(exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))))
2.5b
(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x)))))

rewrite138.0ms (5.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
159×*-un-lft-identity_binary64
111×add-sqr-sqrt_binary64
90×times-frac_binary64
72×exp-prod_binary64
51×distribute-lft-out--_binary64
41×add-cube-cbrt_binary64
37×log-pow_binary64
35×difference-of-squares_binary64
16×distribute-lft-out_binary64
associate-/r/_binary64 associate-/r*_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 associate-/l*_binary64
pow1_binary64 flip3--_binary64 flip--_binary64 add-log-exp_binary64
div-inv_binary64 div-sub_binary64 log-prod_binary64
exp-diff_binary64 associate-/l/_binary64
log-div_binary64 rem-log-exp_binary64 rem-exp-log_binary64 div-exp_binary64 cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64
Counts
3 → 152
Calls

3 calls:

13.0ms
(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x)))))
12.0ms
(exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))))
10.0ms
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x)))
Compiler

Compiled 2436 to 1139 computations (53.2% saved)

series274.0ms (10.4%)

Error
0b
Counts
3 → 62
Calls

3 calls:

86.0ms
(exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x))))
80.0ms
(log.f64 (exp.f64 (/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x)))))
55.0ms
(/.f64 (-.f64 x y) (-.f64 2 (+.f64 y x)))
Compiler

Compiled 4365 to 3491 computations (20% saved)

simplify170.0ms (6.4%)

Algorithm
egg-herbie
Rules
541×cancel-sign-sub-inv_binary64
387×sub-neg_binary64
213×times-frac_binary64
198×+-commutative_binary64
192×associate-/l*_binary64
158×associate--l+_binary64
146×associate-/r*_binary64
141×associate-+l+_binary64
132×associate-+r+_binary64
119×associate--r+_binary64 *-commutative_binary64
112×associate-*r*_binary64
107×neg-sub0_binary64
106×neg-mul-1_binary64
93×unsub-neg_binary64
80×div-sub_binary64
70×associate-*l*_binary64
69×associate-*r/_binary64
63×unswap-sqr_binary64 associate-*l/_binary64
51×distribute-neg-in_binary64
46×sqr-pow_binary64
41×associate-/r/_binary64
35×distribute-rgt-in_binary64
33×distribute-lft-in_binary64
30×rem-log-exp_binary64
27×associate-/l/_binary64
15×exp-prod_binary64
13×distribute-neg-frac_binary64 distribute-rgt-neg-in_binary64
12×distribute-lft-neg-in_binary64
exp-diff_binary64 cube-unmult_binary64
*-rgt-identity_binary64
log-div_binary64 exp-sum_binary64 /-rgt-identity_binary64
log-prod_binary64
unpow3_binary64 cube-mult_binary64 distribute-rgt-out_binary64
log-pow_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64 cube-div_binary64 cube-prod_binary64
prod-exp_binary64 difference-of-squares_binary64 distribute-rgt-out--_binary64 distribute-lft-out_binary64 associate--r-_binary64
rem-sqrt-square_binary64 remove-double-neg_binary64 pow-sqr_binary64 swap-sqr_binary64 count-2_binary64
log-rec_binary64 exp-neg_binary64 e-exp-1_binary64 1-exp_binary64 rem-exp-log_binary64 mul-1-neg_binary64 *-lft-identity_binary64 sub0-neg_binary64 distribute-lft-neg-out_binary64 distribute-lft-out--_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 unpow1/3_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 exp-1-e_binary64 exp-0_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate--l-_binary64
Counts
214 → 141
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04285755
110835593
237305569
350555569

prune82.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1410141
Fresh022
Picked011
Done011
Total1414145
Error
0b
Counts
145 → 4
Compiler

Compiled 2376 to 1314 computations (44.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(*.f64 2 (/.f64 x y))
0.0b
(-.f64 (+.f64 1 (/.f64 2 y)) (*.f64 2 (/.f64 x y)))

rewrite59.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
15×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×add-cube-cbrt_binary64 *-un-lft-identity_binary64 times-frac_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64
associate-*r/_binary64 associate-*l*_binary64
diff-log_binary64 frac-sub_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64
sum-log_binary64 flip3-+_binary64 flip-+_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 cancel-sign-sub-inv_binary64 associate--l+_binary64 pow-prod-down_binary64 div-exp_binary64 cbrt-undiv_binary64 div-inv_binary64 *-commutative_binary64
Counts
2 → 48
Calls

2 calls:

9.0ms
(-.f64 (+.f64 1 (/.f64 2 y)) (*.f64 2 (/.f64 x y)))
7.0ms
(*.f64 2 (/.f64 x y))
Compiler

Compiled 924 to 608 computations (34.2% saved)

series55.0ms (2.1%)

Error
0b
Counts
2 → 18
Calls

2 calls:

34.0ms
(-.f64 (+.f64 1 (/.f64 2 y)) (*.f64 2 (/.f64 x y)))
16.0ms
(*.f64 2 (/.f64 x y))
Compiler

Compiled 371 to 337 computations (9.2% saved)

simplify88.0ms (3.3%)

Algorithm
egg-herbie
Rules
346×cancel-sign-sub-inv_binary64
331×neg-sub0_binary64
329×neg-mul-1_binary64
323×associate-*l*_binary64
272×distribute-rgt-in_binary64
269×distribute-rgt-neg-in_binary64
264×associate-*r*_binary64
259×distribute-lft-in_binary64
231×distribute-lft-neg-in_binary64 associate-*r/_binary64
215×associate-*l/_binary64
178×distribute-neg-frac_binary64
146×associate-/l*_binary64
139×distribute-lft-neg-out_binary64
136×*-commutative_binary64
130×distribute-rgt-neg-out_binary64
122×div-sub_binary64
111×unsub-neg_binary64
94×sub-neg_binary64
71×prod-exp_binary64
69×times-frac_binary64
63×associate-+l+_binary64
62×distribute-neg-in_binary64
58×exp-prod_binary64
57×associate-/l/_binary64
54×associate-/r*_binary64
50×sqr-pow_binary64
49×cube-prod_binary64
47×+-commutative_binary64
46×associate-+r+_binary64
44×exp-sum_binary64 associate-/r/_binary64
43×div-exp_binary64
29×*-lft-identity_binary64
28×*-rgt-identity_binary64
27×log-prod_binary64
24×distribute-rgt-out_binary64
22×swap-sqr_binary64
20×exp-diff_binary64
17×associate--l+_binary64 associate-+l-_binary64
16×unswap-sqr_binary64 associate--r+_binary64
14×unpow3_binary64 cube-div_binary64 associate-+r-_binary64
12×+-rgt-identity_binary64
11×log-div_binary64
10×cube-unmult_binary64 sub0-neg_binary64 distribute-lft-out_binary64
exp-lft-sqr_binary64 difference-of-squares_binary64
cube-mult_binary64 sqr-neg_binary64 distribute-rgt-out--_binary64
cube-neg_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64
mul0-rgt_binary64 mul0-lft_binary64 distribute-rgt1-in_binary64
unpow1/2_binary64 rec-exp_binary64 rem-sqrt-square_binary64 mul-1-neg_binary64 pow-sqr_binary64 distribute-neg-out_binary64
pow-plus_binary64 unpow1_binary64
exp-neg_binary64 distribute-lft-out--_binary64
1-exp_binary64 exp-1-e_binary64 div0_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr-1_binary64 associate--r-_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_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 --rgt-identity_binary64 +-lft-identity_binary64 *-inverses_binary64 +-inverses_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--l-_binary64
Counts
66 → 37
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0127893
1313863
2942851
33194833
44324833
55142833

prune24.0ms (0.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New37037
Fresh011
Picked011
Done022
Total37441
Error
0b
Counts
41 → 4
Compiler

Compiled 411 to 303 computations (26.3% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b
(*.f64 2 (/.f64 y x))

rewrite35.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0b
Rules
14×add-sqr-sqrt_binary64
13×associate-*r*_binary64
10×times-frac_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
pow1_binary64 associate-*l*_binary64
prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64
pow-prod-down_binary64 div-exp_binary64 add-log-exp_binary64 cbrt-undiv_binary64 associate-*r/_binary64 div-inv_binary64 *-commutative_binary64
Counts
1 → 32
Calls

1 calls:

8.0ms
(*.f64 2 (/.f64 y x))
Compiler

Compiled 539 to 336 computations (37.7% saved)

series18.0ms (0.7%)

Error
0b
Counts
1 → 6
Calls

1 calls:

16.0ms
(*.f64 2 (/.f64 y x))
Compiler

Compiled 143 to 130 computations (9.1% saved)

simplify110.0ms (4.2%)

Algorithm
egg-herbie
Rules
873×times-frac_binary64
762×distribute-rgt-out_binary64
407×associate-/l*_binary64
338×associate-*l/_binary64
306×*-commutative_binary64
293×associate-+l+_binary64
280×associate-*r/_binary64
258×associate-/l/_binary64
252×+-commutative_binary64
249×associate-+r+_binary64
243×associate-*l*_binary64
235×unswap-sqr_binary64
177×sqr-pow_binary64
147×associate-*r*_binary64
130×distribute-rgt-in_binary64
126×associate-/r/_binary64
120×associate-/r*_binary64
92×pow-sqr_binary64
53×count-2_binary64
51×distribute-rgt1-in_binary64
45×sub-neg_binary64 cancel-sign-sub-inv_binary64
43×distribute-lft1-in_binary64
37×distribute-lft-in_binary64
26×cube-prod_binary64
24×associate--r+_binary64
20×unsub-neg_binary64
18×neg-mul-1_binary64 associate--r-_binary64
17×unpow3_binary64 associate--l+_binary64
15×*-lft-identity_binary64 distribute-neg-in_binary64 associate-+l-_binary64
14×*-rgt-identity_binary64 distribute-rgt-neg-in_binary64
13×neg-sub0_binary64
12×cube-unmult_binary64
11×distribute-lft-neg-out_binary64
10×cube-mult_binary64 sub0-neg_binary64
swap-sqr_binary64
associate-+r-_binary64
log-div_binary64
/-rgt-identity_binary64 distribute-rgt-neg-out_binary64
pow-plus_binary64 cube-div_binary64 +-rgt-identity_binary64
exp-prod_binary64 distribute-lft-neg-in_binary64 associate--l-_binary64
log-prod_binary64 unpow2_binary64 unpow1_binary64 remove-double-neg_binary64 +-lft-identity_binary64
unpow1/2_binary64 --rgt-identity_binary64 remove-double-div_binary64
exp-lft-sqr_binary64 prod-exp_binary64 1-exp_binary64 rem-sqrt-square_binary64 distribute-rgt-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 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_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 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 distribute-neg-out_binary64 distribute-lft-out_binary64
Counts
38 → 15
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
070405
1154369
2388369
3847369
41882369
52019369
62502369
73298369
84203369
94479369
104974369

prune8.0ms (0.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New15015
Fresh000
Picked011
Done033
Total15419
Error
0b
Counts
19 → 4
Compiler

Compiled 161 to 112 computations (30.4% saved)

regimes168.0ms (6.3%)

Accuracy

Total 0.0b remaining (27.1%)

Threshold costs 0.0b (27.1%)

Compiler

Compiled 1667 to 1316 computations (21.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64 *-commutative_binary64
unsub-neg_binary64 distribute-neg-in_binary64
distribute-neg-frac_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 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-frac-neg_binary64 distribute-neg-out_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
0922
11422
22722
33722
44322
54522
64522

end1.0ms (0%)

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample573.0ms (21.7%)

Algorithm
intervals
Results
231.0ms8000×body128valid
Compiler

Compiled 85 to 75 computations (11.8% saved)

Profiling

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