Details

Time bar (total: 2.7s)

analyze578.0ms (21.6%)

Algorithm
search
egg-herbie
Rules
*-commutative_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64
+-commutative_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 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-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_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-+l+_binary64 associate-+r+_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01228
11628
23428
32828
42828
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
0%99.9%0.1%6
12.5%87.4%0.1%7
18.7%81.1%0.1%8
31.2%68.6%0.1%9
46.8%44.5%8.7%10
51.5%39%9.5%11
57.3%32.6%10.1%12
63.8%21.6%14.7%13
66.2%18.7%15.1%14
Symmetry

(sort x y)

Compiler

Compiled 6 to 6 computations (0% saved)

sample29.0ms (1.1%)

Algorithm
intervals
Results
6.0ms256×body128valid
0.0ms14×body128invalid
Compiler

Compiled 11 to 14 computations (-27.3% saved)

simplify10.0ms (0.4%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
distribute-rgt-in_binary64 distribute-lft-in_binary64
+-commutative_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-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_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-+l+_binary64 associate-+r+_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
187
2167
3147
4147

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Compiled 5 to 5 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b
(*.f64 (+.f64 x y) z)

rewrite25.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0b
Rules
add-sqr-sqrt_binary64 *-un-lft-identity_binary64
associate-*l*_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 associate-*r*_binary64
associate-*l/_binary64
pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 flip3-+_binary64 flip-+_binary64 distribute-lft-out_binary64 *-commutative_binary64
Counts
1 → 21
Calls

1 calls:

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

Compiled 214 to 67 computations (68.7% saved)

series44.0ms (1.7%)

Error
0.0b
Counts
1 → 15
Calls

1 calls:

40.0ms
(*.f64 (+.f64 x y) z)
Compiler

Compiled 150 to 134 computations (10.7% saved)

simplify76.0ms (2.9%)

Algorithm
egg-herbie
Rules
783×distribute-rgt-in_binary64
767×distribute-lft-in_binary64
612×associate-*l/_binary64
198×unswap-sqr_binary64
177×associate-*l*_binary64
170×distribute-rgt-out_binary64
144×*-commutative_binary64
136×sqr-pow_binary64
133×sub-neg_binary64
126×associate-*r*_binary64
124×cancel-sign-sub-inv_binary64
111×associate-/l/_binary64
104×unsub-neg_binary64
102×associate-+l+_binary64
92×associate-+r+_binary64
74×*-rgt-identity_binary64
73×distribute-lft-neg-out_binary64 associate-/r/_binary64
72×*-lft-identity_binary64 distribute-rgt-neg-in_binary64
71×associate-/l*_binary64
63×distribute-rgt-neg-out_binary64
59×distribute-rgt-out--_binary64
57×neg-mul-1_binary64
54×neg-sub0_binary64
48×pow-sqr_binary64
40×distribute-lft-neg-in_binary64 associate--r+_binary64
33×distribute-neg-in_binary64 associate-+r-_binary64
31×rem-sqrt-square_binary64
30×distribute-lft-out_binary64
27×associate-+l-_binary64
26×associate-/r*_binary64
25×exp-prod_binary64
22×distribute-neg-out_binary64
21×sub0-neg_binary64
18×associate-*r/_binary64
15×exp-sum_binary64 +-commutative_binary64
14×+-rgt-identity_binary64
12×log-prod_binary64
11×cube-unmult_binary64 cube-prod_binary64 swap-sqr_binary64
10×cancel-sign-sub_binary64
distribute-rgt1-in_binary64 associate--l+_binary64
log-div_binary64 cube-div_binary64 times-frac_binary64 distribute-neg-frac_binary64
unpow1/2_binary64
unpow3_binary64 pow-plus_binary64
remove-double-neg_binary64 mul0-rgt_binary64 mul0-lft_binary64 distribute-lft-out--_binary64
difference-of-squares_binary64
exp-sqrt_binary64 associate--r-_binary64
unpow2_binary64 cube-mult_binary64 --rgt-identity_binary64 +-inverses_binary64
exp-lft-sqr_binary64 exp-diff_binary64 1-exp_binary64 exp-1-e_binary64 div-sub_binary64 /-rgt-identity_binary64 +-lft-identity_binary64 distribute-lft1-in_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 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 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 mul-1-neg_binary64 div0_binary64 *-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 distribute-frac-neg_binary64 associate--l-_binary64
Counts
36 → 30
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
045361
1111295
2325295
3762295
42426295
52578295
63218295
75403295

prune14.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New27330
Fresh000
Picked011
Done000
Total27431
Error
0b
Counts
31 → 4
Compiler

Compiled 225 to 91 computations (59.6% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.5b
(cbrt.f64 z)
0.5b
(cbrt.f64 z)
0.5b
(cbrt.f64 z)

rewrite48.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
25×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
15×add-cube-cbrt_binary64 *-un-lft-identity_binary64
11×pow1_binary64
pow1/3_binary64
add-exp-log_binary64 swap-sqr_binary64 associate-*l*_binary64 associate-*r*_binary64
add-log-exp_binary64 add-cbrt-cube_binary64 unswap-sqr_binary64
pow-prod-down_binary64 pow-prod-up_binary64 pow-sqr_binary64
pow2_binary64 pow-plus_binary64 prod-exp_binary64 cbrt-unprod_binary64 *-commutative_binary64
Counts
4 → 73
Calls

4 calls:

6.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms
(cbrt.f64 z)
1.0ms
(cbrt.f64 z)
1.0ms
(cbrt.f64 z)
Compiler

Compiled 1147 to 279 computations (75.7% saved)

series80.0ms (3%)

Error
0b
Counts
4 → 12
Calls

4 calls:

22.0ms
(*.f64 (cbrt.f64 z) (cbrt.f64 z))
21.0ms
(cbrt.f64 z)
16.0ms
(cbrt.f64 z)
16.0ms
(cbrt.f64 z)
Compiler

Compiled 468 to 351 computations (25% saved)

simplify101.0ms (3.8%)

Algorithm
egg-herbie
Rules
586×log-prod_binary64
416×sqr-pow_binary64
335×associate-*l*_binary64
309×*-commutative_binary64
277×distribute-rgt-neg-in_binary64
257×distribute-lft-neg-in_binary64
227×associate-*r*_binary64
188×exp-prod_binary64
161×log-pow_binary64
149×cube-prod_binary64
128×pow-sqr_binary64
124×unswap-sqr_binary64
111×swap-sqr_binary64
104×associate-/l*_binary64
81×cancel-sign-sub-inv_binary64
75×associate-+l+_binary64
69×associate-+r+_binary64
61×distribute-rgt-in_binary64
60×distribute-lft-out_binary64
57×distribute-lft-in_binary64
54×neg-sub0_binary64
53×neg-mul-1_binary64
48×distribute-rgt-out_binary64
45×+-commutative_binary64
43×pow-plus_binary64 rem-sqrt-square_binary64
41×times-frac_binary64 sub-neg_binary64
37×associate-/r/_binary64
35×associate-*r/_binary64
32×unpow3_binary64
31×*-rgt-identity_binary64 *-lft-identity_binary64 associate-/l/_binary64
29×count-2_binary64
27×cube-mult_binary64
24×associate-/r*_binary64
17×log-div_binary64 cube-div_binary64 distribute-neg-frac_binary64
13×cube-unmult_binary64 distribute-rgt1-in_binary64
11×distribute-rgt-neg-out_binary64
10×unpow1/2_binary64
distribute-lft-neg-out_binary64 distribute-lft1-in_binary64
unpow2_binary64 associate-*l/_binary64
unpow1_binary64
unpow1/3_binary64
exp-sqrt_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 mul-1-neg_binary64
exp-lft-sqr_binary64 1-exp_binary64 exp-1-e_binary64 rem-3cbrt-rft_binary64 rem-square-sqrt_binary64 sub0-neg_binary64 --rgt-identity_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 log-rec_binary64 pow-base-0_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-cbrt_binary64 div-exp_binary64 rec-exp_binary64 prod-exp_binary64 exp-diff_binary64 exp-neg_binary64 exp-sum_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-neg_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 div-sub_binary64 unsub-neg_binary64 /-rgt-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 difference-of-squares_binary64 cancel-sign-sub_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-out--_binary64 distribute-lft-out--_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+r-_binary64
Counts
85 → 50
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
056718
197666
2308646
31135632
42034548
53257548
64939548
74873548

prune15.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New50050
Fresh022
Picked011
Done011
Total50454
Error
0b
Counts
54 → 4
Compiler

Compiled 429 to 182 computations (57.6% saved)

localize11.0ms (0.4%)

Local error

Found 3 expressions with local error:

2.6b
(-.f64 (*.f64 x x) (*.f64 y y))
8.2b
(*.f64 z (-.f64 (*.f64 x x) (*.f64 y y)))
17.9b
(/.f64 (*.f64 z (-.f64 (*.f64 x x) (*.f64 y y))) (-.f64 x y))

rewrite56.0ms (2.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
13×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
add-cube-cbrt_binary64
pow1_binary64 add-log-exp_binary64 times-frac_binary64 associate-/r*_binary64
difference-of-squares_binary64 flip3--_binary64 associate-*r/_binary64 flip--_binary64 associate-*r*_binary64
sub-neg_binary64 cancel-sign-sub-inv_binary64 associate-*l*_binary64
prod-exp_binary64 div-exp_binary64 cbrt-undiv_binary64 cbrt-unprod_binary64 distribute-lft-out--_binary64 associate-/l/_binary64 associate-/r/_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64
frac-2neg_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64 pow-prod-down_binary64 unswap-sqr_binary64 *-commutative_binary64 diff-log_binary64
Counts
3 → 67
Calls

3 calls:

10.0ms
(/.f64 (*.f64 z (-.f64 (*.f64 x x) (*.f64 y y))) (-.f64 x y))
7.0ms
(*.f64 z (-.f64 (*.f64 x x) (*.f64 y y)))
4.0ms
(-.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 1399 to 249 computations (82.2% saved)

series133.0ms (4.9%)

Error
0b
Counts
3 → 42
Calls

3 calls:

53.0ms
(/.f64 (*.f64 z (-.f64 (*.f64 x x) (*.f64 y y))) (-.f64 x y))
45.0ms
(*.f64 z (-.f64 (*.f64 x x) (*.f64 y y)))
25.0ms
(-.f64 (*.f64 x x) (*.f64 y y))
Compiler

Compiled 808 to 661 computations (18.2% saved)

simplify100.0ms (3.7%)

Algorithm
egg-herbie
Rules
801×times-frac_binary64
388×distribute-rgt-in_binary64
371×distribute-lft-in_binary64
316×associate-/l/_binary64
98×associate-*l*_binary64
95×div-sub_binary64
94×log-div_binary64
88×associate-*r*_binary64
87×associate-/l*_binary64
59×*-commutative_binary64
50×cancel-sign-sub-inv_binary64
44×sub-neg_binary64
43×distribute-rgt-neg-in_binary64
39×associate-*l/_binary64
38×unswap-sqr_binary64 distribute-lft-neg-in_binary64
35×sqr-pow_binary64
33×associate-/r*_binary64
26×neg-sub0_binary64
25×exp-prod_binary64 neg-mul-1_binary64 *-rgt-identity_binary64 distribute-lft-neg-out_binary64
22×distribute-neg-frac_binary64 distribute-rgt-neg-out_binary64 associate-*r/_binary64
20×cube-div_binary64
18×log-rec_binary64 associate-/r/_binary64 +-commutative_binary64
17×log-prod_binary64 cube-prod_binary64 *-lft-identity_binary64
13×/-rgt-identity_binary64 swap-sqr_binary64 distribute-neg-in_binary64
12×difference-of-squares_binary64 distribute-rgt-out_binary64
exp-sum_binary64
cube-unmult_binary64
pow-plus_binary64
exp-diff_binary64 pow-sqr_binary64
unpow3_binary64 cube-mult_binary64 unsub-neg_binary64
*-inverses_binary64 distribute-rgt-out--_binary64 associate-+l+_binary64
unpow2_binary64 unpow1/2_binary64 unpow1_binary64 rem-sqrt-square_binary64 mul-1-neg_binary64 remove-double-neg_binary64 +-rgt-identity_binary64 distribute-lft-out_binary64 associate--l+_binary64 associate-+r-_binary64 associate-+r+_binary64
div-exp_binary64 1-exp_binary64 exp-1-e_binary64 rgt-mult-inverse_binary64 associate--r-_binary64 associate--r+_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-pow_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 prod-exp_binary64 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 rem-square-sqrt_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 +-inverses_binary64 lft-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
109 → 83
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01251785
13191563
212291410
349651410
450341410

prune28.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New83083
Fresh011
Picked011
Done022
Total83487
Error
0b
Counts
87 → 4
Compiler

Compiled 677 to 221 computations (67.4% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

2.0b
(-.f64 (*.f64 y y) (*.f64 x y))
2.2b
(+.f64 (pow.f64 x 3) (pow.f64 y 3))
6.4b
(*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
33.9b
(/.f64 (*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (*.f64 x x) (-.f64 (*.f64 y y) (*.f64 x y))))

rewrite123.0ms (4.6%)

Algorithm
rewrite-expression-head
Error
0b
Rules
28×*-un-lft-identity_binary64
11×add-exp-log_binary64 add-cbrt-cube_binary64
10×add-sqr-sqrt_binary64 distribute-lft-out_binary64
associate-*r*_binary64
add-log-exp_binary64 add-cube-cbrt_binary64 unpow-prod-down_binary64 cube-prod_binary64
pow1_binary64
flip3-+_binary64 associate-*r/_binary64 flip-+_binary64
times-frac_binary64 associate-/r*_binary64 associate-*l*_binary64
prod-exp_binary64 div-exp_binary64 cbrt-undiv_binary64 cbrt-unprod_binary64 associate-/l/_binary64 associate-/r/_binary64 sum-cubes_binary64
frac-2neg_binary64 clear-num_binary64 div-inv_binary64 associate-/l*_binary64 pow-prod-down_binary64 unswap-sqr_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 *-commutative_binary64 sum-log_binary64 +-commutative_binary64 diff-log_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 cancel-sign-sub-inv_binary64 distribute-rgt-out--_binary64
Counts
4 → 83
Calls

4 calls:

20.0ms
(/.f64 (*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (*.f64 x x) (-.f64 (*.f64 y y) (*.f64 x y))))
16.0ms
(*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
14.0ms
(+.f64 (pow.f64 x 3) (pow.f64 y 3))
4.0ms
(-.f64 (*.f64 y y) (*.f64 x y))
Compiler

Compiled 2372 to 950 computations (59.9% saved)

series215.0ms (8%)

Error
0b
Counts
4 → 54
Calls

4 calls:

84.0ms
(/.f64 (*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (*.f64 x x) (-.f64 (*.f64 y y) (*.f64 x y))))
58.0ms
(*.f64 z (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
35.0ms
(+.f64 (pow.f64 x 3) (pow.f64 y 3))
28.0ms
(-.f64 (*.f64 y y) (*.f64 x y))
Compiler

Compiled 1674 to 1185 computations (29.2% saved)

simplify112.0ms (4.2%)

Algorithm
egg-herbie
Rules
699×distribute-rgt-in_binary64
506×times-frac_binary64
209×cancel-sign-sub-inv_binary64
180×div-sub_binary64
176×associate-*l*_binary64
160×associate-*r*_binary64
127×exp-prod_binary64
122×unswap-sqr_binary64
109×distribute-rgt-neg-in_binary64
93×distribute-lft-in_binary64
90×distribute-lft-neg-in_binary64
86×distribute-rgt-out_binary64
72×associate-/l*_binary64
70×*-commutative_binary64
61×sub-neg_binary64
59×cube-prod_binary64
55×sqr-pow_binary64
46×distribute-lft-out_binary64
38×associate-*l/_binary64
37×log-prod_binary64 distribute-lft-neg-out_binary64
30×log-div_binary64 difference-of-squares_binary64
29×neg-mul-1_binary64 neg-sub0_binary64
28×distribute-rgt-out--_binary64
27×*-rgt-identity_binary64
26×+-commutative_binary64
24×cube-div_binary64
23×unpow3_binary64 associate-*r/_binary64
22×associate-/l/_binary64
20×distribute-neg-in_binary64 distribute-rgt-neg-out_binary64
19×*-lft-identity_binary64 distribute-lft-out--_binary64 associate-/r*_binary64
17×exp-sum_binary64
14×pow-plus_binary64 cube-mult_binary64
12×/-rgt-identity_binary64 associate-/r/_binary64
11×cube-unmult_binary64
unsub-neg_binary64 swap-sqr_binary64
distribute-neg-frac_binary64
exp-diff_binary64 pow-sqr_binary64
associate-+l+_binary64
log-rec_binary64 associate--r+_binary64 associate-+r-_binary64
associate--l+_binary64
unpow1/2_binary64 +-rgt-identity_binary64
log-pow_binary64 unpow2_binary64 unpow1_binary64 rem-sqrt-square_binary64 associate--r-_binary64 associate-+l-_binary64 associate-+r+_binary64
div-exp_binary64 prod-exp_binary64 1-exp_binary64 exp-1-e_binary64 cube-neg_binary64 sqr-neg_binary64 remove-double-neg_binary64 cancel-sign-sub_binary64
not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 pow-base-0_binary64 unpow1/3_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow-1_binary64 exp-lft-cube_binary64 exp-lft-sqr_binary64 exp-cbrt_binary64 exp-sqrt_binary64 rec-exp_binary64 exp-neg_binary64 e-exp-1_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 rem-square-sqrt_binary64 mul-1-neg_binary64 sub0-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 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 count-2_binary64 associate--l-_binary64
Counts
137 → 108
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01452307
13982037
217842037
346092037
452162037

prune51.0ms (1.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1080108
Fresh000
Picked011
Done033
Total1084112
Error
0b
Counts
112 → 4
Compiler

Compiled 1654 to 686 computations (58.5% saved)

regimes222.0ms (8.3%)

Accuracy

Total 0.0b remaining (43.8%)

Threshold costs 0.0b (43.8%)

Compiler

Compiled 1758 to 1360 computations (22.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_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 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
0710
11010
21010

end9.0ms (0.3%)

Remove

(sort x y)

Compiler

Compiled 21 to 18 computations (14.3% saved)

sample564.0ms (21.1%)

Algorithm
intervals
Results
177.0ms8000×body128valid
11.0ms540×body128invalid
Compiler

Compiled 67 to 64 computations (4.5% saved)

Profiling

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