Details

Time bar (total: 3.1s)

analyze69.0ms (2.2%)

Algorithm
search
egg-herbie
Rules
581×associate-/r*_binary64
516×cancel-sign-sub-inv_binary64
510×distribute-rgt-in_binary64
489×distribute-lft-in_binary64
415×associate-/r/_binary64
333×associate-*l*_binary64
267×associate-*r*_binary64
258×div-sub_binary64
232×times-frac_binary64
184×associate-/l*_binary64
153×swap-sqr_binary64
130×*-commutative_binary64
82×sub-neg_binary64
78×unsub-neg_binary64
67×*-rgt-identity_binary64
63×associate-/l/_binary64
42×neg-sub0_binary64
34×neg-mul-1_binary64
32×associate-*l/_binary64 associate-+l+_binary64
31×*-lft-identity_binary64
29×associate-*r/_binary64
28×associate-+r+_binary64
22×/-rgt-identity_binary64
21×cube-div_binary64 cube-prod_binary64
20×distribute-rgt-out_binary64
16×distribute-rgt-neg-in_binary64
13×mul-1-neg_binary64
12×sqr-pow_binary64
10×unswap-sqr_binary64 distribute-lft-neg-in_binary64
distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64
remove-double-div_binary64 distribute-neg-frac_binary64
distribute-lft-out_binary64
unpow3_binary64 distribute-rgt-out--_binary64 +-commutative_binary64
pow-plus_binary64 cube-mult_binary64
cube-unmult_binary64 *-inverses_binary64 pow-sqr_binary64
unpow2_binary64 unpow1_binary64 1-exp_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr-1_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 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow1/2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-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 difference-of-sqr--1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01131
13928
217719
390413
4232013
5406913
6504713
011
111
Search
TrueOtherFalseIter
0%50%50%0
0%50%50%1
0%50%50%2
0%50%50%3
37.5%12.5%50%4
43.7%6.2%50%5
46.9%3.1%50%6
48.4%1.6%50%7
49.2%0.8%50%8
49.6%0.4%50%9
49.8%0.2%50%10
49.9%0.1%50%11
49.9%0%50%12
50%0%50%13
50%0%50%14
Compiler

Compiled 29 to 20 computations (31% saved)

sample32.0ms (1%)

Algorithm
intervals
Results
18.0ms256×body128valid
3.0ms256×pre128true
Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify51.0ms (1.6%)

Algorithm
egg-herbie
Rules
581×associate-/r*_binary64
516×cancel-sign-sub-inv_binary64
510×distribute-rgt-in_binary64
489×distribute-lft-in_binary64
415×associate-/r/_binary64
333×associate-*l*_binary64
267×associate-*r*_binary64
258×div-sub_binary64
232×times-frac_binary64
184×associate-/l*_binary64
153×swap-sqr_binary64
130×*-commutative_binary64
82×sub-neg_binary64
78×unsub-neg_binary64
67×*-rgt-identity_binary64
63×associate-/l/_binary64
42×neg-sub0_binary64
34×neg-mul-1_binary64
32×associate-*l/_binary64 associate-+l+_binary64
31×*-lft-identity_binary64
29×associate-*r/_binary64
28×associate-+r+_binary64
22×/-rgt-identity_binary64
21×cube-div_binary64 cube-prod_binary64
20×distribute-rgt-out_binary64
16×distribute-rgt-neg-in_binary64
13×mul-1-neg_binary64
12×sqr-pow_binary64
10×unswap-sqr_binary64 distribute-lft-neg-in_binary64
distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64
remove-double-div_binary64 distribute-neg-frac_binary64
distribute-lft-out_binary64
unpow3_binary64 distribute-rgt-out--_binary64 +-commutative_binary64
pow-plus_binary64 cube-mult_binary64
cube-unmult_binary64 *-inverses_binary64 pow-sqr_binary64
unpow2_binary64 unpow1_binary64 1-exp_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 difference-of-sqr-1_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 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow1/2_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-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 difference-of-sqr--1_binary64 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64
Counts
1 → 1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01131
13928
217719
390413
4232013
5406913
6504713

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.4b
Counts
2 → 2
Compiler

Compiled 43 to 33 computations (23.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.6b
(/.f64 1 (*.f64 i i))

rewrite114.0ms (3.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
37×add-sqr-sqrt_binary64
35×times-frac_binary64
33×*-un-lft-identity_binary64
17×add-cube-cbrt_binary64
15×add-exp-log_binary64
12×difference-of-squares_binary64
10×pow1_binary64
add-cbrt-cube_binary64 associate-/r*_binary64
distribute-lft-out--_binary64
pow-flip_binary64 div-inv_binary64 associate-/l*_binary64
div-exp_binary64
prod-exp_binary64 cbrt-undiv_binary64
1-exp_binary64 rec-exp_binary64 add-log-exp_binary64 frac-2neg_binary64 clear-num_binary64 associate-/r/_binary64
inv-pow_binary64 pow2_binary64 pow-prod-down_binary64 pow-prod-up_binary64 pow-plus_binary64 pow-sqr_binary64 cbrt-unprod_binary64 flip3--_binary64 flip--_binary64
Counts
2 → 81
Calls

2 calls:

7.0ms
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms
(/.f64 1 (*.f64 i i))
Compiler

Compiled 1182 to 881 computations (25.5% saved)

series31.0ms (1%)

Error
0.0b
Counts
2 → 15
Calls

2 calls:

15.0ms
(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
6.0ms
(/.f64 1 (*.f64 i i))
Compiler

Compiled 325 to 299 computations (8% saved)

simplify104.0ms (3.3%)

Algorithm
egg-herbie
Rules
480×associate-/l*_binary64
434×cancel-sign-sub-inv_binary64
311×associate-/r/_binary64
297×div-sub_binary64
273×associate-/l/_binary64
154×distribute-rgt-in_binary64
143×distribute-rgt-neg-in_binary64
131×distribute-rgt-out_binary64
128×distribute-lft-neg-in_binary64
121×unswap-sqr_binary64
118×distribute-lft-in_binary64
112×distribute-lft-out_binary64
111×associate-*l*_binary64
106×sub-neg_binary64
96×distribute-neg-frac_binary64
94×associate-/r*_binary64
91×associate-*l/_binary64
84×associate-*r*_binary64
70×associate-*r/_binary64
67×*-commutative_binary64
65×times-frac_binary64
59×distribute-neg-in_binary64
53×+-commutative_binary64
52×associate-+r+_binary64
49×associate-+l+_binary64
47×neg-sub0_binary64
45×neg-mul-1_binary64
43×log-div_binary64
42×log-prod_binary64
40×unsub-neg_binary64 distribute-rgt-out--_binary64
39×cube-div_binary64
37×distribute-lft-out--_binary64
36×distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64
32×associate--r+_binary64
31×cube-prod_binary64 sqr-pow_binary64
28×exp-prod_binary64
26×associate-+r-_binary64
20×associate-+l-_binary64
15×pow-plus_binary64
14×sub0-neg_binary64 distribute-frac-neg_binary64
13×*-rgt-identity_binary64 swap-sqr_binary64
11×unpow3_binary64
10×cube-unmult_binary64 +-rgt-identity_binary64
/-rgt-identity_binary64
log-pow_binary64 log-rec_binary64
exp-sum_binary64 sqr-neg_binary64 distribute-rgt1-in_binary64 count-2_binary64 associate--l+_binary64
exp-diff_binary64 cube-mult_binary64 rem-sqrt-square_binary64 *-lft-identity_binary64 remove-double-neg_binary64 +-lft-identity_binary64 div0_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-lft1-in_binary64
unpow2_binary64 unpow1/2_binary64 cube-neg_binary64 --rgt-identity_binary64 pow-sqr_binary64 associate--r-_binary64 associate--l-_binary64
unpow1_binary64 1-exp_binary64 exp-1-e_binary64 mul-1-neg_binary64 mul0-rgt_binary64 mul0-lft_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 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 *-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
Counts
96 → 71
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01601474
13111381
27021341
317061341
445651341
550261341

prune59.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New69271
Fresh011
Picked101
Done000
Total70373
Error
0b
Counts
73 → 3
Compiler

Compiled 580 to 448 computations (22.8% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 1 (pow.f64 i 6))
0.5b
(/.f64 1/4 (-.f64 4 (cbrt.f64 (/.f64 1 (pow.f64 i 6)))))
19.1b
(cbrt.f64 (/.f64 1 (pow.f64 i 6)))

rewrite215.0ms (6.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
118×add-sqr-sqrt_binary64
102×times-frac_binary64
70×*-un-lft-identity_binary64
53×cbrt-prod_binary64
50×add-cube-cbrt_binary64
32×difference-of-squares_binary64
29×unpow-prod-down_binary64
19×associate-/r*_binary64
15×sqr-pow_binary64
14×add-exp-log_binary64
add-cbrt-cube_binary64 div-exp_binary64
associate-/l*_binary64
distribute-lft-out--_binary64
pow1_binary64 add-log-exp_binary64 div-inv_binary64 pow-to-exp_binary64 1-exp_binary64 pow-exp_binary64 rec-exp_binary64
cbrt-undiv_binary64 frac-2neg_binary64 clear-num_binary64 associate-/r/_binary64
pow1/3_binary64 cbrt-div_binary64 flip3--_binary64 flip--_binary64 inv-pow_binary64 pow-flip_binary64
Counts
3 → 152
Calls

3 calls:

14.0ms
(/.f64 1/4 (-.f64 4 (cbrt.f64 (/.f64 1 (pow.f64 i 6)))))
7.0ms
(cbrt.f64 (/.f64 1 (pow.f64 i 6)))
5.0ms
(/.f64 1 (pow.f64 i 6))
Compiler

Compiled 2968 to 2654 computations (10.6% saved)

series43.0ms (1.4%)

Error
0b
Counts
3 → 18
Calls

3 calls:

16.0ms
(/.f64 1/4 (-.f64 4 (cbrt.f64 (/.f64 1 (pow.f64 i 6)))))
8.0ms
(/.f64 1 (pow.f64 i 6))
8.0ms
(cbrt.f64 (/.f64 1 (pow.f64 i 6)))
Compiler

Compiled 395 to 368 computations (6.8% saved)

simplify172.0ms (5.5%)

Algorithm
egg-herbie
Rules
427×times-frac_binary64
306×associate-*l*_binary64
302×log-prod_binary64
252×associate-/r*_binary64
239×distribute-rgt-neg-in_binary64
237×associate-*r*_binary64
230×distribute-lft-neg-in_binary64
137×cube-prod_binary64 associate-/l*_binary64
115×swap-sqr_binary64 *-commutative_binary64
110×sub-neg_binary64
109×unpow3_binary64
92×log-div_binary64
71×associate-/l/_binary64
68×distribute-neg-in_binary64 associate-*l/_binary64
65×associate-*r/_binary64
60×sqr-pow_binary64
57×distribute-rgt-out--_binary64 associate-+r+_binary64
56×+-commutative_binary64
53×neg-sub0_binary64
51×neg-mul-1_binary64 associate-+l+_binary64
47×distribute-rgt-in_binary64 associate-/r/_binary64
46×unswap-sqr_binary64
43×log-pow_binary64 distribute-neg-frac_binary64
40×distribute-rgt-neg-out_binary64
37×cube-div_binary64
36×unsub-neg_binary64 distribute-lft-neg-out_binary64
35×div-sub_binary64
34×cancel-sign-sub-inv_binary64
33×*-rgt-identity_binary64
32×associate--r+_binary64
29×distribute-lft-in_binary64
27×exp-prod_binary64
23×pow-plus_binary64
20×distribute-frac-neg_binary64
19×associate-+l-_binary64
18×cube-unmult_binary64 associate-+r-_binary64
16×sub0-neg_binary64
14×pow-sqr_binary64
13×+-rgt-identity_binary64
12×/-rgt-identity_binary64
*-lft-identity_binary64
log-rec_binary64 cube-mult_binary64 rem-sqrt-square_binary64 distribute-rgt-out_binary64
cancel-sign-sub_binary64
+-lft-identity_binary64
distribute-rgt1-in_binary64 distribute-lft-out_binary64 associate--l+_binary64
distribute-neg-out_binary64 distribute-lft1-in_binary64 count-2_binary64
mul-1-neg_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 exp-diff_binary64 1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 remove-double-neg_binary64 --rgt-identity_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 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 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 sqr-abs_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
Counts
170 → 125
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02353395
14113185
29253073
330133071
446843071
548783071

prune83.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1250125
Fresh022
Picked011
Done000
Total1253128
Error
0b
Counts
128 → 3
Compiler

Compiled 1189 to 1038 computations (12.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(-.f64 (*.f64 (*.f64 i i) -1/4) (pow.f64 i 4))

rewrite23.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
cancel-sign-sub-inv_binary64
add-log-exp_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64 unpow-prod-down_binary64
diff-log_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 sqr-pow_binary64
Counts
1 → 18
Calls

1 calls:

7.0ms
(-.f64 (*.f64 (*.f64 i i) -1/4) (pow.f64 i 4))
Compiler

Compiled 337 to 217 computations (35.6% saved)

series20.0ms (0.7%)

Error
0b
Counts
1 → 6
Calls

1 calls:

18.0ms
(-.f64 (*.f64 (*.f64 i i) -1/4) (pow.f64 i 4))
Compiler

Compiled 95 to 86 computations (9.5% saved)

simplify96.0ms (3.1%)

Algorithm
egg-herbie
Rules
420×associate-*l*_binary64
343×associate-*r*_binary64
305×distribute-rgt-neg-out_binary64
295×cancel-sign-sub-inv_binary64
283×distribute-lft-neg-out_binary64
258×unswap-sqr_binary64
257×distribute-rgt-out_binary64
255×exp-prod_binary64
215×cube-prod_binary64
153×log-prod_binary64
129×distribute-rgt-neg-in_binary64
126×unsub-neg_binary64
115×distribute-lft-neg-in_binary64
87×sqr-pow_binary64
79×distribute-rgt-out--_binary64
70×swap-sqr_binary64
69×distribute-neg-out_binary64
68×*-commutative_binary64
63×neg-sub0_binary64
57×exp-sum_binary64
50×distribute-rgt-in_binary64
49×distribute-lft-in_binary64
46×sub-neg_binary64
45×neg-mul-1_binary64
40×difference-of-squares_binary64
38×unpow3_binary64
31×pow-plus_binary64
27×log-pow_binary64
25×exp-diff_binary64
23×cube-unmult_binary64 cube-mult_binary64
20×+-commutative_binary64
19×distribute-lft-out_binary64
18×cancel-sign-sub_binary64
15×pow-sqr_binary64
13×mul0-rgt_binary64 mul0-lft_binary64 distribute-neg-in_binary64
cube-neg_binary64
sub0-neg_binary64 associate-+l-_binary64 associate-+r+_binary64
unpow2_binary64 exp-neg_binary64 sqr-neg_binary64 mul-1-neg_binary64 distribute-lft-out--_binary64 associate-+r-_binary64 associate-+l+_binary64
unpow1/2_binary64 unpow1_binary64 times-frac_binary64
rem-sqrt-square_binary64 +-rgt-identity_binary64
rem-square-sqrt_binary64 remove-double-neg_binary64 --rgt-identity_binary64
div-exp_binary64 1-exp_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 *-lft-identity_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 log-rec_binary64 log-div_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 prod-exp_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 div-sub_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 +-lft-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 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64
Counts
24 → 21
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
062350
1154311
2406305
31813305
44354305
54953305
64925305

prune10.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New21021
Fresh011
Picked011
Done011
Total21324
Error
0b
Counts
24 → 3
Compiler

Compiled 184 to 121 computations (34.2% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b
(*.f64 (*.f64 i i) (*.f64 i i))
13.1b
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
42.4b
(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

rewrite288.0ms (9.3%)

Algorithm
rewrite-expression-head
Error
0b
Rules
302×add-exp-log_binary64 add-cbrt-cube_binary64
168×prod-exp_binary64 cbrt-unprod_binary64
114×pow1_binary64
76×div-exp_binary64 cbrt-undiv_binary64
38×times-frac_binary64
36×pow-prod-up_binary64
23×pow-prod-down_binary64
22×add-sqr-sqrt_binary64 *-un-lft-identity_binary64 pow-sqr_binary64
18×pow-plus_binary64
16×add-cube-cbrt_binary64
13×pow2_binary64
12×difference-of-squares_binary64
div-inv_binary64
associate-/r*_binary64
associate-/l*_binary64 difference-of-sqr-1_binary64
add-log-exp_binary64
frac-2neg_binary64 clear-num_binary64 associate-/r/_binary64
associate-/l/_binary64 flip3--_binary64 flip--_binary64 unswap-sqr_binary64 swap-sqr_binary64 associate-*l*_binary64 associate-*r*_binary64 *-commutative_binary64
Counts
3 → 232
Calls

3 calls:

33.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
26.0ms
(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))
8.0ms
(*.f64 (*.f64 i i) (*.f64 i i))
Compiler

Compiled 8458 to 4631 computations (45.2% saved)

series44.0ms (1.4%)

Error
0b
Counts
3 → 18
Calls

3 calls:

18.0ms
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
9.0ms
(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))
8.0ms
(*.f64 (*.f64 i i) (*.f64 i i))
Compiler

Compiled 514 to 445 computations (13.4% saved)

simplify219.0ms (7.1%)

Algorithm
egg-herbie
Rules
585×times-frac_binary64
294×associate-/l*_binary64
258×log-div_binary64
236×associate-/r*_binary64
205×log-prod_binary64
178×associate-*r*_binary64
170×associate-/l/_binary64
139×distribute-rgt-in_binary64 associate-*l*_binary64
122×sub-neg_binary64 associate--r+_binary64
111×swap-sqr_binary64
106×associate--l+_binary64
97×distribute-lft-in_binary64
83×unswap-sqr_binary64
82×distribute-rgt-neg-in_binary64
79×distribute-lft-neg-in_binary64
74×cancel-sign-sub-inv_binary64
69×associate-/r/_binary64
65×unpow3_binary64
63×distribute-neg-in_binary64
60×*-commutative_binary64
59×associate--l-_binary64
56×associate-*l/_binary64
55×div-sub_binary64
51×distribute-neg-frac_binary64
50×cube-prod_binary64
44×associate-*r/_binary64
42×exp-prod_binary64
40×cube-div_binary64
39×distribute-rgt-out_binary64
36×neg-mul-1_binary64 neg-sub0_binary64
34×+-commutative_binary64
29×distribute-lft-out_binary64 associate-+l+_binary64
28×sqr-pow_binary64
26×associate-+r+_binary64
24×*-rgt-identity_binary64
22×unsub-neg_binary64
19×/-rgt-identity_binary64
14×distribute-rgt-out--_binary64
12×log-rec_binary64
11×log-pow_binary64
cube-unmult_binary64
distribute-frac-neg_binary64
exp-sqrt_binary64
pow-plus_binary64 *-lft-identity_binary64 count-2_binary64
pow-sqr_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate-+l-_binary64
*-inverses_binary64 difference-of-sqr-1_binary64 distribute-rgt-neg-out_binary64
cube-mult_binary64 sub0-neg_binary64 distribute-lft-neg-out_binary64 distribute-rgt1-in_binary64
rem-sqrt-square_binary64 mul-1-neg_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 div0_binary64 difference-of-squares_binary64 distribute-neg-out_binary64 distribute-lft1-in_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 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_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-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 remove-double-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 cancel-sign-sub_binary64 associate-+r-_binary64
Counts
250 → 229
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02817256
15253668
228183583
346543583
449523583
548693583

prune77.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2290229
Fresh000
Picked011
Done022
Total2293232
Error
0b
Counts
232 → 3
Compiler

Compiled 1529 to 1033 computations (32.4% saved)

regimes414.0ms (13.4%)

Accuracy

Total 0.1b remaining (94.9%)

Threshold costs 0.1b (94.9%)

Compiler

Compiled 4983 to 4407 computations (11.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64 *-commutative_binary64
1-exp_binary64 neg-mul-1_binary64 neg-sub0_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 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-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
01122
11722
22322
32522
42622
52422

end1.0ms (0%)

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample892.0ms (28.8%)

Algorithm
intervals
Results
437.0ms8000×body128valid
87.0ms8000×pre128true
Compiler

Compiled 91 to 75 computations (17.6% saved)

Profiling

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