Details

Time bar (total: 8.4s)

analyze646.0ms (7.7%)

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)

sample40.0ms (0.5%)

Algorithm
intervals
Results
11.0ms256×body128valid
2.0ms60×body128nan
Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify9.0ms (0.1%)

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%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
19.5b
Counts
2 → 1
Compiler

Compiled 24 to 20 computations (16.7% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 x (+.f64 y z))
0.8b
(+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z))
18.5b
(sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z)))

rewrite86.0ms (1%)

Algorithm
rewrite-expression-head
Error
19.4b
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))
6.0ms
(*.f64 x (+.f64 y z))
6.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z)))
Compiler

Compiled 974 to 297 computations (69.5% saved)

series140.0ms (1.7%)

Error
19.0b
Counts
3 → 47
Calls

3 calls:

54.0ms
(sqrt.f64 (+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z)))
39.0ms
(+.f64 (*.f64 x (+.f64 y z)) (*.f64 y z))
28.0ms
(*.f64 x (+.f64 y z))
Compiler

Compiled 1708 to 1292 computations (24.4% saved)

simplify86.0ms (1%)

Algorithm
egg-herbie
Rules
527×distribute-rgt-in_binary64
494×distribute-lft-in_binary64
360×associate-+l+_binary64
354×sub-neg_binary64
248×cancel-sign-sub-inv_binary64
218×associate--l+_binary64
151×associate-*l*_binary64
144×associate-*r*_binary64
120×associate--r+_binary64
110×*-commutative_binary64
82×unsub-neg_binary64
80×distribute-rgt-neg-in_binary64
78×times-frac_binary64
65×distribute-lft-neg-in_binary64 distribute-rgt-out_binary64
64×neg-mul-1_binary64 neg-sub0_binary64
60×associate-/r*_binary64
56×+-commutative_binary64
45×unswap-sqr_binary64
38×sqr-pow_binary64
35×exp-prod_binary64 associate-+r+_binary64
32×distribute-lft-out_binary64
20×distribute-neg-in_binary64 associate-+l-_binary64
18×associate-+r-_binary64
16×*-lft-identity_binary64
14×exp-sum_binary64 *-rgt-identity_binary64
13×cube-prod_binary64 distribute-rgt-out--_binary64
12×log-prod_binary64 distribute-lft-neg-out_binary64
unpow3_binary64
swap-sqr_binary64 associate-/l/_binary64 associate-/l*_binary64
cube-mult_binary64
distribute-lft-out--_binary64 associate-/r/_binary64 associate--l-_binary64
pow-plus_binary64 cube-unmult_binary64 rem-sqrt-square_binary64 pow-sqr_binary64
log-pow_binary64 unpow1/2_binary64 cube-div_binary64 /-rgt-identity_binary64 difference-of-squares_binary64 distribute-rgt-neg-out_binary64
unpow2_binary64 unpow1_binary64 prod-exp_binary64 1-exp_binary64 exp-1-e_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-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 div-sub_binary64 mul-1-neg_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--r-_binary64
Counts
98 → 76
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01831535
14471448
214391433
346781433
451171433

prune67.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New651176
Fresh000
Picked101
Done000
Total661177
Error
18.9b
Counts
77 → 11
Compiler

Compiled 1179 to 497 computations (57.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
1.2b
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
18.5b
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
18.5b
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))

rewrite92.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
18.9b
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:

6.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
4.0ms
(+.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))))
Compiler

Compiled 1914 to 333 computations (82.6% saved)

series236.0ms (2.8%)

Error
18.9b
Counts
4 → 64
Calls

4 calls:

59.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
56.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
44.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
44.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
Compiler

Compiled 4310 to 2848 computations (33.9% saved)

simplify108.0ms (1.3%)

Algorithm
egg-herbie
Rules
583×associate-*l*_binary64
496×associate-*r*_binary64
418×distribute-rgt-in_binary64
393×distribute-lft-in_binary64
329×sub-neg_binary64
316×associate-+l+_binary64
241×cancel-sign-sub-inv_binary64
214×associate--l+_binary64
112×associate--r+_binary64
82×unsub-neg_binary64
80×*-commutative_binary64
69×distribute-rgt-neg-in_binary64
64×neg-sub0_binary64
62×distribute-rgt-out_binary64
60×distribute-lft-neg-in_binary64
58×neg-mul-1_binary64
56×associate-/r*_binary64
52×+-commutative_binary64
44×distribute-neg-in_binary64
36×associate-+r+_binary64
35×sqr-pow_binary64
34×distribute-lft-out_binary64
25×unswap-sqr_binary64
21×exp-prod_binary64
19×associate-+l-_binary64
16×distribute-lft-neg-out_binary64
14×associate-+r-_binary64
13×distribute-rgt-out--_binary64
12×exp-sum_binary64
10×cube-unmult_binary64
cube-prod_binary64
unpow3_binary64 distribute-rgt-neg-out_binary64
cube-mult_binary64 associate-/l/_binary64
swap-sqr_binary64 distribute-lft-out--_binary64 associate--l-_binary64
pow-plus_binary64 prod-exp_binary64 rem-sqrt-square_binary64 pow-sqr_binary64 associate-/l*_binary64
log-prod_binary64 unpow2_binary64 unpow1/2_binary64 unpow1_binary64 1-exp_binary64 rem-square-sqrt_binary64 difference-of-squares_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-/r/_binary64 associate-*l/_binary64 associate-*r/_binary64 associate--r-_binary64
Counts
120 → 78
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01512448
13682274
211932256
347022256
450212256

prune81.0ms (1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New75378
Fresh01010
Picked011
Done000
Total751489
Error
18.9b
Counts
89 → 14
Compiler

Compiled 2328 to 708 computations (69.6% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
18.5b
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
19.1b
(cbrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))
19.1b
(cbrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))

rewrite99.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
18.9b
Rules
add-sqr-sqrt_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64 cbrt-prod_binary64
pow1_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 flip3-+_binary64 cbrt-div_binary64 flip-+_binary64
sqrt-prod_binary64
pow1/3_binary64 sqrt-div_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 → 54
Calls

4 calls:

4.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
4.0ms
(cbrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))
4.0ms
(cbrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))
3.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
Compiler

Compiled 2628 to 434 computations (83.5% saved)

series378.0ms (4.5%)

Error
18.9b
Counts
4 → 66
Calls

4 calls:

93.0ms
(cbrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))
93.0ms
(cbrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))
61.0ms
(sqrt.f64 (+.f64 (*.f64 y x) (*.f64 z (+.f64 y x))))
46.0ms
(+.f64 (*.f64 y x) (*.f64 z (+.f64 y x)))
Compiler

Compiled 8572 to 4997 computations (41.7% saved)

simplify109.0ms (1.3%)

Algorithm
egg-herbie
Rules
847×times-frac_binary64
556×cancel-sign-sub-inv_binary64
229×associate-*r*_binary64
213×unswap-sqr_binary64
189×associate-*l*_binary64
171×sub-neg_binary64
153×*-commutative_binary64
107×sqr-pow_binary64
98×+-commutative_binary64
74×distribute-rgt-in_binary64
68×associate-/r*_binary64
66×associate-+r+_binary64
63×distribute-lft-in_binary64
54×neg-mul-1_binary64 neg-sub0_binary64
53×associate-+l+_binary64
49×associate--r+_binary64
47×associate-/l*_binary64
40×exp-sum_binary64 associate--l+_binary64
30×unsub-neg_binary64
29×exp-prod_binary64
26×associate-*r/_binary64
20×associate-*l/_binary64
18×unpow1/3_binary64
17×distribute-neg-in_binary64 distribute-rgt-neg-in_binary64
14×log-prod_binary64 distribute-lft-neg-in_binary64
11×swap-sqr_binary64
10×pow-sqr_binary64
distribute-rgt-out_binary64
unpow3_binary64 cube-mult_binary64 cube-prod_binary64 distribute-lft-out_binary64
log-div_binary64 exp-diff_binary64 div-sub_binary64 associate--r-_binary64
log-pow_binary64 associate-/r/_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 cube-unmult_binary64
log-rec_binary64 remove-double-neg_binary64 distribute-lft-neg-out_binary64 distribute-rgt-out--_binary64
pow-plus_binary64 rem-sqrt-square_binary64 difference-of-squares_binary64 distribute-neg-frac_binary64 associate-+r-_binary64
prod-exp_binary64 1-exp_binary64 rem-3cbrt-lft_binary64 rem-square-sqrt_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 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-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-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_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-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 count-2_binary64 associate-/l/_binary64 associate--l-_binary64
Counts
120 → 103
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03073650
17903483
227473447
355653447

prune141.0ms (1.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New994103
Fresh21012
Picked101
Done011
Total10215117
Error
18.9b
Counts
117 → 15
Compiler

Compiled 4843 to 1349 computations (72.1% saved)

localize39.0ms (0.5%)

Local error

Found 4 expressions with local error:

19.1b
(cbrt.f64 (+.f64 (*.f64 z y) (*.f64 x (+.f64 z y))))
19.1b
(cbrt.f64 (+.f64 (*.f64 z y) (*.f64 x (+.f64 z y))))
19.1b
(cbrt.f64 (+.f64 (*.f64 z y) (*.f64 x (+.f64 z y))))
19.1b
(cbrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))

rewrite114.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
18.9b
Rules
12×cbrt-prod_binary64
add-cube-cbrt_binary64 cbrt-div_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow1/3_binary64 pow1_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 flip3-+_binary64 flip-+_binary64
Counts
4 → 52
Calls

4 calls:

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

Compiled 3888 to 556 computations (85.7% saved)

series538.0ms (6.4%)

Error
18.9b
Counts
4 → 68
Calls

4 calls:

101.0ms
(cbrt.f64 (+.f64 (*.f64 z y) (*.f64 x (+.f64 z y))))
101.0ms
(cbrt.f64 (+.f64 (*.f64 z y) (*.f64 x (+.f64 z y))))
100.0ms
(cbrt.f64 (+.f64 (*.f64 z y) (*.f64 x (+.f64 z y))))
97.0ms
(cbrt.f64 (+.f64 (*.f64 x y) (*.f64 z (+.f64 x y))))
Compiler

Compiled 15280 to 7726 computations (49.4% saved)

simplify163.0ms (1.9%)

Algorithm
egg-herbie
Rules
839×times-frac_binary64
435×cancel-sign-sub-inv_binary64
186×unswap-sqr_binary64
162×distribute-rgt-neg-in_binary64 associate-*r*_binary64
136×associate-*l*_binary64
128×sub-neg_binary64
100×sqr-pow_binary64
97×*-commutative_binary64
68×distribute-neg-in_binary64
60×+-commutative_binary64
53×associate-/r*_binary64
52×neg-mul-1_binary64 neg-sub0_binary64 distribute-rgt-in_binary64
47×associate-/l*_binary64
43×distribute-lft-in_binary64
36×distribute-lft-neg-out_binary64
34×distribute-neg-frac_binary64
30×exp-sum_binary64 associate-+r+_binary64
29×associate--r+_binary64
28×associate-+l+_binary64
26×unsub-neg_binary64 associate-*r/_binary64
23×associate--l+_binary64
22×distribute-lft-neg-in_binary64
20×associate-*l/_binary64
18×unpow1/3_binary64 distribute-rgt-neg-out_binary64
15×log-prod_binary64
12×exp-prod_binary64
11×cube-prod_binary64
unpow3_binary64 cube-mult_binary64
log-pow_binary64
swap-sqr_binary64
log-div_binary64 exp-diff_binary64 div-sub_binary64 pow-sqr_binary64 associate--r-_binary64
associate-/r/_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 distribute-rgt-out--_binary64 distribute-lft-out_binary64
log-rec_binary64 remove-double-neg_binary64 distribute-rgt-out_binary64
cube-unmult_binary64 rem-3cbrt-lft_binary64 difference-of-squares_binary64 associate-+l-_binary64 associate-+r-_binary64
1-exp_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-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-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 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_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-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-lft-out--_binary64 count-2_binary64 associate-/l/_binary64 associate--l-_binary64
Counts
120 → 105
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02044852
15964692
221514620
349934620
449754620

prune177.0ms (2.1%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1041105
Fresh01313
Picked011
Done011
Total10416120
Error
18.9b
Counts
120 → 16
Compiler

Compiled 8231 to 1738 computations (78.9% saved)

regimes1.5s (17.6%)

Accuracy

Total 0.9b remaining (4.6%)

Threshold costs 0.9b (4.6%)

Compiler

Compiled 22783 to 13639 computations (40.1% saved)

bsearch0.0ms (0%)

simplify5.0ms (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

end23.0ms (0.3%)

Compiler

Compiled 36 to 30 computations (16.7% saved)

sample3.5s (41.5%)

Algorithm
intervals
Results
655.0ms8000×body128valid
181.0ms2258×body128nan
Compiler

Compiled 576 to 363 computations (37% saved)

Profiling

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