Details

Time bar (total: 4.2s)

analyze686.0ms (16.2%)

Algorithm
search
egg-herbie
Rules
724×sub-neg_binary64
708×div-sub_binary64
646×associate-/l*_binary64
593×cancel-sign-sub-inv_binary64
423×distribute-neg-frac_binary64
403×distribute-frac-neg_binary64
349×unsub-neg_binary64
289×distribute-rgt-in_binary64
283×neg-mul-1_binary64
237×neg-sub0_binary64
179×cancel-sign-sub_binary64
165×associate--r+_binary64
123×+-commutative_binary64
112×distribute-lft-in_binary64
103×associate-+r-_binary64
102×distribute-neg-in_binary64
98×associate-/r*_binary64
85×associate--r-_binary64
80×distribute-rgt-neg-in_binary64 associate-+r+_binary64
79×+-lft-identity_binary64
77×distribute-lft-neg-out_binary64
74×distribute-lft-neg-in_binary64
69×associate--l+_binary64
64×associate-+l-_binary64
61×associate-/l/_binary64
60×associate-/r/_binary64
58×sub0-neg_binary64
55×remove-double-neg_binary64
54×times-frac_binary64
53×distribute-rgt-neg-out_binary64
51×*-commutative_binary64
43×/-rgt-identity_binary64
37×*-lft-identity_binary64
33×+-rgt-identity_binary64 associate-+l+_binary64
30×associate--l-_binary64
28×distribute-rgt-out--_binary64
24×associate-*l/_binary64
22×*-rgt-identity_binary64
20×distribute-lft-out_binary64
18×associate-*r/_binary64
15×--rgt-identity_binary64
13×mul0-rgt_binary64 mul0-lft_binary64
div0_binary64
remove-double-div_binary64
distribute-neg-out_binary64 distribute-lft-out--_binary64
1-exp_binary64 distribute-rgt-out_binary64 swap-x-y
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 mul-1-neg_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 swap-sqr_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate-*l*_binary64 associate-*r*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03091
18991
220791
332991
464591
5143491
6254191
7452091
8457791
9518991
044
144
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
49.1%50.7%0.2%9
49.5%50.3%0.2%10
49.7%50.1%0.2%11
50.2%49.6%0.2%12
60.5%39.3%0.2%13
60.6%37.9%1.4%14
Symmetry

(sort x y)

Compiler

Compiled 10 to 10 computations (0% saved)

sample34.0ms (0.8%)

Algorithm
intervals
Results
8.0ms256×body128valid
2.0ms72×body128invalid
Compiler

Compiled 19 to 23 computations (-21.1% saved)

simplify157.0ms (3.7%)

Algorithm
egg-herbie
Rules
465×distribute-rgt-in_binary64
442×div-sub_binary64
329×cancel-sign-sub-inv_binary64 associate-/l*_binary64
321×distribute-lft-in_binary64
320×unsub-neg_binary64
317×times-frac_binary64
194×sub-neg_binary64
168×associate-/r/_binary64
162×associate-/r*_binary64
158×associate-*l/_binary64
133×associate-/l/_binary64
128×distribute-neg-frac_binary64
101×distribute-rgt-neg-out_binary64
97×distribute-rgt-neg-in_binary64
92×neg-mul-1_binary64
91×distribute-neg-in_binary64
80×associate-*l*_binary64
72×neg-sub0_binary64 distribute-lft-neg-out_binary64
71×distribute-lft-neg-in_binary64 associate-*r*_binary64
70×associate-*r/_binary64
63×associate--r+_binary64
54×+-commutative_binary64
53×associate--r-_binary64
41×*-commutative_binary64
36×associate-+l-_binary64
33×+-lft-identity_binary64 associate-+l+_binary64
32×mul0-rgt_binary64 mul0-lft_binary64
30×*-lft-identity_binary64 cancel-sign-sub_binary64
26×associate--l+_binary64
25×associate--l-_binary64
24×remove-double-neg_binary64 associate-+r+_binary64
22×associate-+r-_binary64
21×sub0-neg_binary64
18×div0_binary64
17×*-rgt-identity_binary64
14×distribute-frac-neg_binary64
+-rgt-identity_binary64
/-rgt-identity_binary64
1-exp_binary64 --rgt-identity_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 mul-1-neg_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 count-2_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
12113
24513
36913
413113
524213
646413
783213
8134013
9185813
10182113
11181713
12181313
13181413
14181413
15220613
16187013
17187013
18187013
19174413

prune2.0ms (0%)

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 9 computations (0% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite34.0ms (0.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
13×*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 times-frac_binary64 associate-/l*_binary64
distribute-lft-out--_binary64
add-cube-cbrt_binary64
div-exp_binary64 cbrt-undiv_binary64 difference-of-squares_binary64 distribute-lft-out_binary64 associate-/l/_binary64
pow1_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 frac-2neg_binary64 div-sub_binary64 clear-num_binary64 div-inv_binary64 flip3--_binary64 flip--_binary64 associate-/r*_binary64
Counts
1 → 30
Calls

1 calls:

9.0ms
(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
Compiler

Compiled 450 to 176 computations (60.9% saved)

series70.0ms (1.7%)

Error
0.0b
Counts
1 → 21
Calls

1 calls:

59.0ms
(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
Compiler

Compiled 538 to 475 computations (11.7% saved)

simplify72.0ms (1.7%)

Algorithm
egg-herbie
Rules
523×associate-/r/_binary64
380×div-sub_binary64
286×distribute-rgt-in_binary64
271×distribute-lft-in_binary64
243×neg-mul-1_binary64
241×neg-sub0_binary64
200×associate-/l*_binary64
189×times-frac_binary64
165×associate-*l*_binary64
138×associate-/r*_binary64
128×*-commutative_binary64
120×associate-*r*_binary64
119×sub-neg_binary64
117×associate-*l/_binary64
100×associate-*r/_binary64
95×distribute-rgt-neg-out_binary64
89×distribute-lft-neg-out_binary64
80×associate-/l/_binary64
77×cancel-sign-sub-inv_binary64
70×associate-+l+_binary64
64×distribute-rgt-out_binary64
61×associate-+r+_binary64
48×distribute-neg-in_binary64 +-commutative_binary64
45×distribute-rgt-neg-in_binary64
41×unsub-neg_binary64
38×distribute-lft-out_binary64
28×distribute-lft-neg-in_binary64
27×distribute-frac-neg_binary64
18×distribute-neg-frac_binary64
15×associate--r+_binary64
14×distribute-rgt-out--_binary64 associate-+l-_binary64
13×+-rgt-identity_binary64 associate-+r-_binary64
11×exp-diff_binary64
10×sqr-pow_binary64 distribute-lft-out--_binary64 associate--l+_binary64
sub0-neg_binary64 swap-sqr_binary64
exp-sum_binary64
log-div_binary64 log-prod_binary64 cube-prod_binary64 associate--r-_binary64
exp-sqrt_binary64 cube-unmult_binary64 mul-1-neg_binary64
cube-div_binary64 sqr-neg_binary64 remove-double-neg_binary64
unpow3_binary64 exp-prod_binary64
exp-neg_binary64 1-exp_binary64 cube-mult_binary64 cube-neg_binary64 --rgt-identity_binary64 div0_binary64 distribute-neg-out_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 div-exp_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 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 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_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 difference-of-squares_binary64 unswap-sqr_binary64 cancel-sign-sub_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--l-_binary64
Counts
51 → 43
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0103918
1265797
2810756
32773720
44655720
55057720

prune23.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New40343
Fresh000
Picked011
Done000
Total40444
Error
0.0b
Counts
44 → 4
Compiler

Compiled 382 to 172 computations (55% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite63.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
17×*-un-lft-identity_binary64
11×times-frac_binary64
add-sqr-sqrt_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 cancel-sign-sub-inv_binary64
add-cube-cbrt_binary64
add-log-exp_binary64 div-inv_binary64 associate-/l*_binary64
distribute-lft-out--_binary64 distribute-lft-out_binary64
pow1_binary64 div-exp_binary64 cbrt-undiv_binary64 associate-/l/_binary64
diff-log_binary64 frac-sub_binary64 sub-div_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 difference-of-squares_binary64 distribute-rgt-out--_binary64 prod-exp_binary64 cbrt-unprod_binary64 frac-2neg_binary64 clear-num_binary64 flip3-+_binary64 flip-+_binary64 associate-/r*_binary64
Counts
2 → 50
Calls

2 calls:

12.0ms
(-.f64 (/.f64 (+.f64 y x) (*.f64 t 2)) (/.f64 z (*.f64 t 2)))
6.0ms
(/.f64 (+.f64 y x) (*.f64 t 2))
Compiler

Compiled 975 to 556 computations (43% saved)

series145.0ms (3.4%)

Error
0b
Counts
2 → 36
Calls

2 calls:

88.0ms
(-.f64 (/.f64 (+.f64 y x) (*.f64 t 2)) (/.f64 z (*.f64 t 2)))
36.0ms
(/.f64 (+.f64 y x) (*.f64 t 2))
Compiler

Compiled 1001 to 865 computations (13.6% saved)

simplify77.0ms (1.8%)

Algorithm
egg-herbie
Rules
387×associate-*l*_binary64
331×times-frac_binary64
324×cancel-sign-sub-inv_binary64
311×associate-*r*_binary64
310×associate-/l*_binary64
290×associate-*l/_binary64
242×associate-*r/_binary64
204×associate-/r*_binary64
175×*-commutative_binary64
150×sub-neg_binary64 distribute-rgt-in_binary64
136×distribute-lft-in_binary64
115×associate-/l/_binary64
92×exp-prod_binary64
84×neg-sub0_binary64
77×div-sub_binary64 unsub-neg_binary64
73×neg-mul-1_binary64
53×sqr-pow_binary64 swap-sqr_binary64
50×distribute-rgt-neg-in_binary64
43×associate-/r/_binary64
41×distribute-neg-frac_binary64
39×distribute-lft-neg-out_binary64
36×distribute-lft-neg-in_binary64
34×associate-+l+_binary64
33×exp-sum_binary64
32×cube-prod_binary64 +-commutative_binary64
29×associate-+r+_binary64
25×cube-div_binary64 associate-+l-_binary64 associate-+r-_binary64
24×distribute-rgt-out_binary64
23×distribute-rgt-neg-out_binary64
22×exp-diff_binary64
21×+-rgt-identity_binary64 distribute-lft-out_binary64
17×log-prod_binary64
16×mul0-rgt_binary64 mul0-lft_binary64 difference-of-squares_binary64 unswap-sqr_binary64
14×log-div_binary64 sub0-neg_binary64
13×distribute-neg-in_binary64 associate--l+_binary64
12×exp-sqrt_binary64
11×unpow3_binary64 distribute-rgt-out--_binary64
distribute-lft-out--_binary64
cube-unmult_binary64 associate--r+_binary64
cube-mult_binary64 mul-1-neg_binary64
*-rgt-identity_binary64 *-lft-identity_binary64
div0_binary64
distribute-frac-neg_binary64
rem-3cbrt-lft_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 /-rgt-identity_binary64 remove-double-neg_binary64 pow-sqr_binary64 associate--r-_binary64
pow-plus_binary64 div-exp_binary64 1-exp_binary64 cube-neg_binary64 rem-sqrt-square_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 unpow1/2_binary64 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 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-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 --rgt-identity_binary64 +-lft-identity_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-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--l-_binary64
Counts
86 → 70
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01441374
13901280
211071136
340511132
450621132

prune36.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New68270
Fresh112
Picked011
Done101
Total70474
Error
0b
Counts
74 → 4
Compiler

Compiled 658 to 333 computations (49.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 t (-.f64 (+.f64 x y) z))
0.3b
(/.f64 1/2 (/.f64 t (-.f64 (+.f64 x y) z)))

rewrite119.0ms (2.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
162×times-frac_binary64
158×*-un-lft-identity_binary64
110×add-sqr-sqrt_binary64
78×add-cube-cbrt_binary64
32×distribute-lft-out--_binary64
30×associate-/r*_binary64
16×difference-of-squares_binary64 distribute-lft-out_binary64
11×associate-/r/_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
div-inv_binary64 associate-/l*_binary64
flip3--_binary64 flip--_binary64
div-exp_binary64 cbrt-undiv_binary64
pow1_binary64 add-log-exp_binary64 frac-2neg_binary64 clear-num_binary64
Counts
2 → 155
Calls

2 calls:

13.0ms
(/.f64 1/2 (/.f64 t (-.f64 (+.f64 x y) z)))
7.0ms
(/.f64 t (-.f64 (+.f64 x y) z))
Compiler

Compiled 2666 to 818 computations (69.3% saved)

series166.0ms (3.9%)

Error
0b
Counts
2 → 49
Calls

2 calls:

80.0ms
(/.f64 t (-.f64 (+.f64 x y) z))
58.0ms
(/.f64 1/2 (/.f64 t (-.f64 (+.f64 x y) z)))
Compiler

Compiled 2074 to 1570 computations (24.3% saved)

simplify253.0ms (6%)

Algorithm
egg-herbie
Rules
648×distribute-rgt-in_binary64
212×associate-/r/_binary64
180×cancel-sign-sub-inv_binary64
151×*-commutative_binary64
149×associate-/l/_binary64
140×associate-/l*_binary64
139×associate-*l/_binary64
138×times-frac_binary64
118×sub-neg_binary64
98×distribute-neg-in_binary64
95×associate-/r*_binary64
88×distribute-lft-in_binary64 +-commutative_binary64
74×*-rgt-identity_binary64
70×associate-*r/_binary64
66×distribute-rgt-neg-in_binary64
63×associate-*r*_binary64
61×distribute-lft-neg-in_binary64
60×associate-+r+_binary64
55×neg-sub0_binary64
53×associate-+l+_binary64
52×neg-mul-1_binary64
50×distribute-neg-frac_binary64
48×unswap-sqr_binary64
41×distribute-lft-neg-out_binary64
40×associate-*l*_binary64
39×sqr-pow_binary64
38×associate--l+_binary64
36×exp-prod_binary64
34×distribute-rgt-neg-out_binary64
31×unsub-neg_binary64
28×log-prod_binary64
27×distribute-rgt-out_binary64
26×associate--r+_binary64
25×div-sub_binary64
21×distribute-rgt-out--_binary64
16×distribute-lft-out_binary64
15×log-div_binary64
14×unpow3_binary64
10×cube-prod_binary64
*-lft-identity_binary64 distribute-rgt1-in_binary64
difference-of-squares_binary64 distribute-lft-out--_binary64
/-rgt-identity_binary64
unpow1/2_binary64 swap-sqr_binary64
log-rec_binary64 unpow2_binary64 pow-plus_binary64 unpow1_binary64 exp-sum_binary64 cube-mult_binary64
cube-unmult_binary64 cube-div_binary64 mul-1-neg_binary64 remove-double-div_binary64
rem-sqrt-square_binary64 remove-double-neg_binary64 div0_binary64 associate--r-_binary64
exp-diff_binary64 1-exp_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 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-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-square-sqrt_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 pow-sqr_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 count-2_binary64 associate--l-_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
204 → 141
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03415162
18274988
230554777
349314776
449904776
549974776
649684776

prune64.0ms (1.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Compiled 1690 to 638 computations (62.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b
(/.f64 (*.f64 1/2 (-.f64 z y)) t)

rewrite23.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
add-exp-log_binary64 add-cbrt-cube_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 times-frac_binary64 *-un-lft-identity_binary64 associate-/r*_binary64
div-exp_binary64 cbrt-undiv_binary64 associate-*r/_binary64 associate-/l/_binary64
pow1_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 frac-2neg_binary64 clear-num_binary64 div-inv_binary64 flip3--_binary64 flip--_binary64 associate-/l*_binary64
Counts
1 → 23
Calls

1 calls:

7.0ms
(/.f64 (*.f64 1/2 (-.f64 z y)) t)
Compiler

Compiled 335 to 184 computations (45.1% saved)

series43.0ms (1%)

Error
0b
Counts
1 → 15
Calls

1 calls:

37.0ms
(/.f64 (*.f64 1/2 (-.f64 z y)) t)
Compiler

Compiled 294 to 297 computations (-1% saved)

simplify71.0ms (1.7%)

Algorithm
egg-herbie
Rules
440×div-sub_binary64
315×associate-/l*_binary64
313×associate-*l*_binary64
297×distribute-rgt-neg-out_binary64
252×times-frac_binary64
241×associate-*r*_binary64
231×associate-*l/_binary64
213×distribute-rgt-in_binary64
208×distribute-lft-in_binary64
195×associate-*r/_binary64
112×associate-/l/_binary64
107×distribute-frac-neg_binary64
85×associate-/r*_binary64
84×*-commutative_binary64
75×associate-/r/_binary64
70×sub-neg_binary64
64×cancel-sign-sub-inv_binary64
57×exp-sum_binary64
55×log-div_binary64
54×neg-sub0_binary64
52×cube-div_binary64
49×log-prod_binary64 swap-sqr_binary64
40×exp-prod_binary64
39×neg-mul-1_binary64 distribute-neg-frac_binary64
38×exp-diff_binary64
30×unsub-neg_binary64
27×cube-prod_binary64 sqr-pow_binary64
25×distribute-neg-in_binary64
21×+-commutative_binary64
17×unpow3_binary64 distribute-lft-neg-out_binary64
15×cube-mult_binary64 distribute-rgt-neg-in_binary64
13×distribute-lft-neg-in_binary64
12×*-rgt-identity_binary64
11×/-rgt-identity_binary64
10×associate-+r-_binary64
associate-+r+_binary64
+-rgt-identity_binary64 associate-+l+_binary64
sqr-neg_binary64 *-lft-identity_binary64
cube-unmult_binary64 remove-double-neg_binary64 associate-+l-_binary64
log-rec_binary64 unpow1/2_binary64 mul-1-neg_binary64 distribute-rgt-out_binary64 associate--l-_binary64 associate--l+_binary64
exp-neg_binary64 distribute-lft-out--_binary64
cube-neg_binary64 associate--r-_binary64 associate--r+_binary64
1-exp_binary64 sub0-neg_binary64 --rgt-identity_binary64 div0_binary64 pow-sqr_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 pow-base-0_binary64 unpow1/3_binary64 unpow2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 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-sqrt-square_binary64 rem-square-sqrt_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_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 unswap-sqr_binary64 cancel-sign-sub_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out_binary64 count-2_binary64
Counts
38 → 24
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
077477
1195414
2656413
32950413
44754413
54991413

prune8.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New24024
Fresh011
Picked011
Done022
Total24428
Error
0b
Counts
28 → 4
Compiler

Compiled 165 to 87 computations (47.3% saved)

regimes917.0ms (21.6%)

Accuracy

Total 0.0b remaining (84.7%)

Threshold costs 0.0b (84.7%)

Compiler

Compiled 8663 to 8038 computations (7.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64 *-commutative_binary64
neg-mul-1_binary64 neg-sub0_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 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
01116
11516
22016
32216
42316
52316

end7.0ms (0.2%)

Compiler

Compiled 33 to 30 computations (9.1% saved)

sample1.1s (26.8%)

Algorithm
intervals
Results
271.0ms8000×body128valid
94.0ms2749×body128invalid
Compiler

Compiled 75 to 83 computations (-10.7% saved)

Profiling

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