Details

Time bar (total: 4.8s)

analyze631.0ms (13.2%)

Algorithm
search
egg-herbie
Rules
11×*-commutative_binary64
10×+-commutative_binary64
distribute-lft-out_binary64 associate-+l+_binary64
distribute-rgt-out_binary64
swap-x-y swap-x-z
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 log-rec_binary64 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+r+_binary64 swap-y-z
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02772
13672
24072
33872
033
133
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
6.2%93.6%0.1%6
12.5%87.4%0.1%7
15.6%84.3%0.1%8
18.7%71.8%9.5%9
23.4%56%20.6%10
26.3%52.2%21.5%11
31%40.1%28.9%12
35.6%28.9%35.5%13
36.8%27.5%35.7%14
Symmetry

(sort x y z)

Compiler

Compiled 15 to 12 computations (20% saved)

sample47.0ms (1%)

Algorithm
intervals
Results
11.0ms256×body128valid
3.0ms81×body128nan
Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify11.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64 +-commutative_binary64
distribute-rgt-out_binary64
associate-+l+_binary64 associate-+r+_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 log-div_binary64 log-prod_binary64 pow-base-0_binary64 unpow1/3_binary64 unpow3_binary64 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 exp-prod_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01218
12218
23218
33818
43818
53818

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
20.7b
Counts
2 → 1
Compiler

Compiled 24 to 20 computations (16.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 x (+.f64 y z))
1.4b
(+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z))
19.6b
(sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z)))

rewrite96.0ms (2%)

Algorithm
rewrite-expression-head
Error
20.6b
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
pow1_binary64 add-cube-cbrt_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
associate-*r*_binary64
flip3-+_binary64 flip-+_binary64 sqrt-prod_binary64 associate-*l*_binary64
sqrt-div_binary64 distribute-rgt-in_binary64 associate-+l+_binary64 distribute-lft-in_binary64 associate-*r/_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 sum-log_binary64 +-commutative_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 distribute-lft-out_binary64 *-commutative_binary64
Counts
3 → 51
Calls

3 calls:

7.0ms
(+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z))
7.0ms
(*.f64 x (+.f64 y z))
7.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z)))
Compiler

Compiled 974 to 297 computations (69.5% saved)

series132.0ms (2.8%)

Error
20.2b
Counts
3 → 46
Calls

3 calls:

51.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z)))
36.0ms
(+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z))
28.0ms
(*.f64 x (+.f64 y z))
Compiler

Compiled 1589 to 1211 computations (23.8% saved)

simplify103.0ms (2.1%)

Algorithm
egg-herbie
Rules
521×distribute-rgt-in_binary64
512×cancel-sign-sub-inv_binary64
490×distribute-lft-in_binary64
301×*-commutative_binary64
224×sub-neg_binary64
202×times-frac_binary64
167×distribute-rgt-neg-in_binary64
157×distribute-rgt-out_binary64
143×unsub-neg_binary64
141×neg-mul-1_binary64
137×associate-+l+_binary64
136×neg-sub0_binary64
135×distribute-lft-neg-in_binary64
127×associate-+r+_binary64
125×associate-*l*_binary64
116×unswap-sqr_binary64
115×associate-*l/_binary64
112×associate-*r*_binary64
98×distribute-neg-in_binary64
67×associate--r+_binary64
64×sqr-pow_binary64 +-commutative_binary64
59×associate--l+_binary64
51×associate-/r*_binary64
42×associate-*r/_binary64
39×associate-/l*_binary64
38×exp-prod_binary64 distribute-rgt-out--_binary64
35×distribute-lft-out_binary64
34×*-lft-identity_binary64 distribute-lft-neg-out_binary64
32×*-rgt-identity_binary64
21×exp-sum_binary64
16×swap-sqr_binary64 associate-/l/_binary64
14×associate-+r-_binary64
13×log-prod_binary64 cube-prod_binary64 +-rgt-identity_binary64 associate-/r/_binary64 associate--r-_binary64
12×distribute-rgt-neg-out_binary64 associate-+l-_binary64
10×pow-sqr_binary64
unpow3_binary64 distribute-lft-out--_binary64
cube-unmult_binary64 rem-sqrt-square_binary64
unpow1/2_binary64 div-sub_binary64 sub0-neg_binary64
cube-mult_binary64 cube-div_binary64 difference-of-squares_binary64
log-pow_binary64 pow-plus_binary64 count-2_binary64
unpow2_binary64 /-rgt-identity_binary64 distribute-neg-frac_binary64 associate--l-_binary64
unpow1_binary64 prod-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-square-sqrt_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 div-exp_binary64 rec-exp_binary64 exp-diff_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_binary64 remove-double-neg_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-rgt1-in_binary64 distribute-lft1-in_binary64
Counts
97 → 75
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01501355
13681313
211131277
331851271
444771271
549651271

prune71.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New621375
Fresh000
Picked101
Done000
Total631376
Error
20.2b
Counts
76 → 13
Compiler

Compiled 1104 to 454 computations (58.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 x (+.f64 z y))
1.4b
(+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 1) (*.f64 y z))
19.6b
(sqrt.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 1) (*.f64 y z)))

rewrite98.0ms (2%)

Algorithm
rewrite-expression-head
Error
20.2b
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
pow1_binary64 add-cube-cbrt_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
associate-*r*_binary64
flip3-+_binary64 flip-+_binary64 sqrt-prod_binary64 associate-*l*_binary64
sqrt-div_binary64 associate-*r/_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 sum-log_binary64 +-commutative_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 distribute-lft-out_binary64 *-commutative_binary64
Counts
3 → 49
Calls

3 calls:

6.0ms
(*.f64 x (+.f64 z y))
5.0ms
(sqrt.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 1) (*.f64 y z)))
5.0ms
(+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 1) (*.f64 y z))
Compiler

Compiled 1080 to 487 computations (54.9% saved)

series140.0ms (2.9%)

Error
20.2b
Counts
3 → 46
Calls

3 calls:

52.0ms
(sqrt.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 1) (*.f64 y z)))
40.0ms
(+.f64 (pow.f64 (*.f64 x (+.f64 z y)) 1) (*.f64 y z))
29.0ms
(*.f64 x (+.f64 z y))
Compiler

Compiled 1645 to 1267 computations (23% saved)

simplify127.0ms (2.7%)

Algorithm
egg-herbie
Rules
543×distribute-rgt-in_binary64
537×cancel-sign-sub-inv_binary64
518×distribute-lft-in_binary64
322×*-commutative_binary64
212×sub-neg_binary64
192×unswap-sqr_binary64
188×distribute-rgt-neg-in_binary64
163×distribute-rgt-out_binary64
158×neg-mul-1_binary64
155×distribute-lft-neg-in_binary64
153×neg-sub0_binary64
148×unsub-neg_binary64
138×times-frac_binary64
137×associate-+l+_binary64
131×associate-*l*_binary64
127×associate-+r+_binary64
117×associate-*r*_binary64
102×distribute-neg-in_binary64
73×sqr-pow_binary64
67×associate--r+_binary64
62×+-commutative_binary64
59×associate--l+_binary64
42×exp-prod_binary64
40×pow-sqr_binary64 distribute-rgt-out--_binary64
35×*-lft-identity_binary64 distribute-lft-neg-out_binary64
34×*-rgt-identity_binary64
23×distribute-lft-out_binary64
22×exp-sum_binary64 associate-/r*_binary64
17×log-prod_binary64
16×swap-sqr_binary64
14×cube-prod_binary64 associate-+r-_binary64
13×+-rgt-identity_binary64
12×associate-+l-_binary64
11×distribute-rgt-neg-out_binary64
log-pow_binary64 unpow3_binary64 pow-plus_binary64
cube-unmult_binary64
rem-sqrt-square_binary64
unpow1/2_binary64 associate-/l*_binary64
sub0-neg_binary64 distribute-lft-out--_binary64
cube-mult_binary64 /-rgt-identity_binary64 difference-of-squares_binary64 associate-/r/_binary64
log-div_binary64 unpow2_binary64 unpow1_binary64 cube-div_binary64 remove-double-neg_binary64 distribute-neg-frac_binary64 count-2_binary64 associate--l-_binary64
prod-exp_binary64 1-exp_binary64 exp-1-e_binary64 rem-square-sqrt_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 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 exp-diff_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 mul-1-neg_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-rgt1-in_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64
Counts
95 → 65
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01491317
13671275
211531245
333311245
445121245
549981245
649081245

prune48.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New63265
Fresh21012
Picked101
Done000
Total661278
Error
20.2b
Counts
78 → 12
Compiler

Compiled 954 to 429 computations (55% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
1.4b
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
19.6b
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
19.6b
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))

rewrite105.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
20.2b
Rules
add-log-exp_binary64 add-sqr-sqrt_binary64
pow1_binary64 add-cube-cbrt_binary64 sqrt-prod_binary64 *-un-lft-identity_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 flip3-+_binary64 sqrt-div_binary64 flip-+_binary64 associate-+r+_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 sum-log_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 +-commutative_binary64
Counts
4 → 56
Calls

4 calls:

7.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
4.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
4.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
Compiler

Compiled 1914 to 333 computations (82.6% saved)

series226.0ms (4.7%)

Error
20.2b
Counts
4 → 60
Calls

4 calls:

54.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
54.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
44.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
43.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
Compiler

Compiled 3820 to 2544 computations (33.4% saved)

simplify98.0ms (2%)

Algorithm
egg-herbie
Rules
439×associate-*l*_binary64
418×distribute-rgt-in_binary64
412×distribute-rgt-out_binary64
395×distribute-lft-in_binary64
363×associate-*r*_binary64
241×distribute-lft-out_binary64
211×distribute-rgt-neg-in_binary64
191×distribute-lft-neg-in_binary64
163×sub-neg_binary64
148×*-commutative_binary64
137×cancel-sign-sub-inv_binary64
122×unswap-sqr_binary64
100×distribute-neg-in_binary64
90×associate-+l+_binary64
88×distribute-rgt-out--_binary64
70×associate-+r+_binary64
66×unsub-neg_binary64
61×distribute-lft-neg-out_binary64
59×associate--r+_binary64
55×associate--l+_binary64
53×neg-sub0_binary64 sqr-pow_binary64
50×+-commutative_binary64
47×neg-mul-1_binary64 distribute-lft-out--_binary64
39×distribute-rgt-neg-out_binary64
22×swap-sqr_binary64
21×exp-prod_binary64
17×associate-/r*_binary64
12×exp-sum_binary64
11×associate-+l-_binary64
10×associate-+r-_binary64
+-rgt-identity_binary64 pow-sqr_binary64
cube-prod_binary64
unpow3_binary64 cube-unmult_binary64
cube-mult_binary64
sub0-neg_binary64
pow-plus_binary64 prod-exp_binary64 rem-sqrt-square_binary64
difference-of-squares_binary64 associate-/l*_binary64 associate--l-_binary64
log-prod_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 rem-square-sqrt_binary64 count-2_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 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 div-exp_binary64 rec-exp_binary64 exp-diff_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_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-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64
Counts
116 → 78
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01082020
12651942
28141888
329911876
451031876

prune86.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New76278
Fresh01111
Picked101
Done000
Total771390
Error
20.2b
Counts
90 → 13
Compiler

Compiled 2030 to 551 computations (72.9% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.4b
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
1.6b
(+.f64 (*.f64 (+.f64 x z) y) (*.f64 x z))
19.6b
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
19.6b
(sqrt.f64 (+.f64 (*.f64 (+.f64 x z) y) (*.f64 x z)))

rewrite112.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
20.2b
Rules
add-log-exp_binary64 add-sqr-sqrt_binary64
pow1_binary64 add-cube-cbrt_binary64 sqrt-prod_binary64 *-un-lft-identity_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 flip3-+_binary64 sqrt-div_binary64 flip-+_binary64
pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 sum-log_binary64 +-commutative_binary64 associate-+r+_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64
Counts
4 → 54
Calls

4 calls:

7.0ms
(sqrt.f64 (+.f64 (*.f64 (+.f64 x z) y) (*.f64 x z)))
7.0ms
(+.f64 (*.f64 (+.f64 x z) y) (*.f64 x z))
5.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
Compiler

Compiled 1860 to 398 computations (78.6% saved)

series219.0ms (4.6%)

Error
20.2b
Counts
4 → 60
Calls

4 calls:

55.0ms
(sqrt.f64 (+.f64 (*.f64 (+.f64 x z) y) (*.f64 x z)))
52.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
44.0ms
(+.f64 (*.f64 (+.f64 x z) y) (*.f64 x z))
43.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
Compiler

Compiled 3820 to 2523 computations (34% saved)

simplify104.0ms (2.2%)

Algorithm
egg-herbie
Rules
720×associate-*l*_binary64
649×distribute-rgt-in_binary64
597×distribute-lft-in_binary64
565×associate-*r*_binary64
561×cancel-sign-sub-inv_binary64
216×unswap-sqr_binary64
96×distribute-rgt-neg-in_binary64
88×sub-neg_binary64
83×*-commutative_binary64
80×neg-sub0_binary64 distribute-lft-neg-in_binary64
74×sqr-pow_binary64
72×neg-mul-1_binary64
66×unsub-neg_binary64
63×distribute-rgt-out_binary64
48×distribute-neg-in_binary64
35×+-commutative_binary64
33×distribute-lft-out_binary64
24×distribute-rgt-out--_binary64
23×distribute-lft-neg-out_binary64
22×exp-prod_binary64
17×associate-/r*_binary64
15×pow-sqr_binary64
14×exp-sum_binary64 cube-prod_binary64 swap-sqr_binary64 associate-+l+_binary64
12×associate--l+_binary64 associate--r+_binary64
11×cube-unmult_binary64
10×unpow3_binary64
cube-mult_binary64
distribute-lft-out--_binary64 associate-+r+_binary64
distribute-rgt-neg-out_binary64
rem-sqrt-square_binary64
pow-plus_binary64
log-prod_binary64 prod-exp_binary64 rem-square-sqrt_binary64 difference-of-squares_binary64 associate-/l*_binary64 associate-+l-_binary64 associate-+r-_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 count-2_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 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 div-exp_binary64 rec-exp_binary64 exp-diff_binary64 exp-neg_binary64 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-div_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 times-frac_binary64 div-sub_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64 associate--l-_binary64
Counts
114 → 86
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01432012
13681934
211711874
343101874
454151874

prune74.0ms (1.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New85186
Fresh01212
Picked011
Done000
Total851499
Error
20.2b
Counts
99 → 14
Compiler

Compiled 1712 to 415 computations (75.8% saved)

regimes1.1s (22.5%)

Accuracy

Total 0.9b remaining (4.7%)

Threshold costs 0.9b (4.7%)

Compiler

Compiled 17263 to 11023 computations (36.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
unpow1_binary64 1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same 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 e-exp-1_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01318
12018
21918

end12.0ms (0.3%)

Remove

(sort x y z)

Compiler

Compiled 36 to 30 computations (16.7% saved)

sample1.1s (23.4%)

Algorithm
intervals
Results
347.0ms8000×body128valid
102.0ms2292×body128nan
Compiler

Compiled 429 to 287 computations (33.1% saved)

Profiling

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