Details

Time bar (total: 8.4s)

analyze238.0ms (2.8%)

Algorithm
search
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%87.4%12.6%5
9.4%65.5%25.1%6
14%60.8%25.1%7
19.5%49.1%31.4%8
24.6%37.8%37.6%9
28.7%33.7%37.6%10
33.3%26%40.7%11
36.2%19.9%43.8%12
38.6%17.6%43.8%13
41.3%13.3%45.4%14
Compiler

Compiled 9 to 8 computations (11.1% saved)

sample54.0ms (0.6%)

Algorithm
intervals
Results
18.0ms256×body128valid
1.0ms27×body128nan
0.0msbody128invalid
Compiler

Compiled 17 to 18 computations (-5.9% saved)

simplify476.0ms (5.7%)

Algorithm
egg-herbie
Rules
442×div-sub_binary64_7926
425×exp-prod_binary64_7973
359×associate-+l-_binary64_7856
303×swap-sqr_binary64_7888
293×associate-/r*_binary64_7865
291×associate--l-_binary64_7859
279×unsub-neg_binary64_7915
240×associate--r-_binary64_7860
195×distribute-neg-in_binary64_7882
180×distribute-rgt-neg-in_binary64_7879
139×distribute-rgt-in_binary64_7871
137×distribute-lft-neg-in_binary64_7878 distribute-rgt1-in_binary64_7877
135×associate-/l*_binary64_7866
131×sub-neg_binary64_7914
129×associate-/r/_binary64_7867
120×exp-sum_binary64_7967
109×neg-mul-1_binary64_7917
105×neg-sub0_binary64_7916
101×cancel-sign-sub-inv_binary64_7887
99×distribute-rgt-neg-out_binary64_7881
86×*-commutative_binary64_7852
85×sqr-pow_binary64_7893
83×distribute-lft-in_binary64_7870
67×associate-*r*_binary64_7861
65×distribute-lft-neg-out_binary64_7880
64×associate--r+_binary64_7857
49×associate-+r+_binary64_7853
48×associate-+l+_binary64_7854
44×pow-plus_binary64_7984 associate--l+_binary64_7858
41×distribute-rgt-out_binary64_7874
39×pow-sqr_binary64_7894
38×+-commutative_binary64_7851
37×exp-diff_binary64_7969
34×distribute-neg-out_binary64_7883
32×remove-double-neg_binary64_7909
31×sqr-neg_binary64_7935
30×log-prod_binary64_8007 associate-*l*_binary64_7862
28×distribute-rgt-out--_binary64_7875
27×exp-neg_binary64_7968
22×distribute-lft1-in_binary64_7876
18×associate-+r-_binary64_7855
17×log-div_binary64_8008 sub0-neg_binary64_7908
16×mul0-lft_binary64_7903
15×mul0-rgt_binary64_7904 distribute-neg-frac_binary64_7885
11×exp-lft-sqr_binary64_7976 count-2_binary64_7869
10×--rgt-identity_binary64_7907 +-rgt-identity_binary64_7906
*-rgt-identity_binary64_7911 *-lft-identity_binary64_7910
distribute-frac-neg_binary64_7884
+-lft-identity_binary64_7905 distribute-lft-out_binary64_7872
cube-unmult_binary64_7958 +-inverses_binary64_7900 distribute-lft-out--_binary64_7873
cube-prod_binary64_7949
exp-to-pow_binary64_7983
log-pow_binary64_8010 1-exp_binary64_7965 cube-neg_binary64_7948 mul-1-neg_binary64_7913 div0_binary64_7902 difference-of-sqr--1_binary64_7892 difference-of-squares_binary64_7890 cancel-sign-sub_binary64_7886
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_8184 erf-erfc_binary64_8183 erf-odd_binary64_8182 if-if-and-not_binary64_8181 if-if-and_binary64_8180 if-if-or-not_binary64_8179 if-if-or_binary64_8178 if-not_binary64_8177 if-same_binary64_8176 if-false_binary64_8175 if-true_binary64_8174 not-gte_binary64_8173 not-lte_binary64_8172 not-gt_binary64_8171 not-lt_binary64_8170 gte-same_binary64_8169 lte-same_binary64_8168 gt-same_binary64_8167 lt-same_binary64_8166 sinh---cosh_binary64_8113 sinh-+-cosh_binary64_8112 sinh-cosh_binary64_8111 tanh-def-c_binary64_8110 tanh-def-b_binary64_8109 tanh-def-a_binary64_8108 cosh-def_binary64_8107 sinh-def_binary64_8106 tan-neg_binary64_8053 cos-neg_binary64_8052 sin-neg_binary64_8051 tan-0_binary64_8050 cos-0_binary64_8049 sin-0_binary64_8048 hang-m-tan_binary64_8047 hang-p-tan_binary64_8046 hang-m0-tan_binary64_8045 hang-p0-tan_binary64_8044 hang-0m-tan_binary64_8043 hang-0p-tan_binary64_8042 tan-+PI/2_binary64_8041 tan-+PI_binary64_8040 tan-PI_binary64_8039 tan-PI/3_binary64_8038 tan-PI/4_binary64_8037 tan-PI/6_binary64_8036 cos-+PI/2_binary64_8035 cos-+PI_binary64_8034 cos-PI_binary64_8033 cos-PI/2_binary64_8032 cos-PI/3_binary64_8031 cos-PI/4_binary64_8030 cos-PI/6_binary64_8029 sin-+PI/2_binary64_8028 sin-+PI_binary64_8027 sin-PI_binary64_8026 sin-PI/2_binary64_8025 sin-PI/3_binary64_8024 sin-PI/4_binary64_8023 sin-PI/6_binary64_8022 sub-1-sin_binary64_8021 sub-1-cos_binary64_8020 -1-add-sin_binary64_8019 -1-add-cos_binary64_8018 1-sub-sin_binary64_8017 1-sub-cos_binary64_8016 cos-sin-sum_binary64_8015 log-E_binary64_8011 log-rec_binary64_8009 pow-base-0_binary64_8005 unpow1/3_binary64_7988 unpow3_binary64_7987 unpow2_binary64_7986 unpow1/2_binary64_7985 pow-base-1_binary64_7981 unpow0_binary64_7980 unpow1_binary64_7979 unpow-1_binary64_7978 exp-lft-cube_binary64_7977 exp-cbrt_binary64_7975 exp-sqrt_binary64_7974 div-exp_binary64_7972 rec-exp_binary64_7971 prod-exp_binary64_7970 e-exp-1_binary64_7966 exp-1-e_binary64_7964 exp-0_binary64_7963 rem-log-exp_binary64_7962 rem-exp-log_binary64_7961 cube-mult_binary64_7951 cube-div_binary64_7950 rem-3cbrt-rft_binary64_7947 rem-3cbrt-lft_binary64_7946 rem-cbrt-cube_binary64_7945 rem-cube-cbrt_binary64_7944 sqr-abs_binary64_7936 rem-sqrt-square_binary64_7934 rem-square-sqrt_binary64_7933 times-frac_binary64_7927 /-rgt-identity_binary64_7912 *-inverses_binary64_7901 lft-mult-inverse_binary64_7899 rgt-mult-inverse_binary64_7898 remove-double-div_binary64_7897 difference-of-sqr-1_binary64_7891 unswap-sqr_binary64_7889 associate-/l/_binary64_7868 associate-*l/_binary64_7864 associate-*r/_binary64_7863
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0812
11412
22112
33612
48012
515912
628412
764312
8169012

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
18.9b
Counts
1 → 1
Compiler

Compiled 8 to 7 computations (12.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)
0.2b
(*.f64 x (log.f64 (/.f64 x y)))
18.4b
(log.f64 (/.f64 x y))

rewrite153.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
0.8b
Rules
65×log-prod_binary64_8007
45×times-frac_binary64_7927
43×add-sqr-sqrt_binary64_7943
41×add-cube-cbrt_binary64_7956 *-un-lft-identity_binary64_7921
26×distribute-rgt-in_binary64_7871 distribute-lft-in_binary64_7870 associate--l+_binary64_7858
add-exp-log_binary64_7959
pow1_binary64_7982
div-inv_binary64_7918 add-log-exp_binary64_7960 add-cbrt-cube_binary64_7957
associate-*r*_binary64_7861
associate-*l*_binary64_7862 cancel-sign-sub-inv_binary64_7887
log-pow_binary64_8010 rem-log-exp_binary64_7962
log-div_binary64_8008 div-exp_binary64_7972 pow-prod-down_binary64_7992 prod-exp_binary64_7970 cbrt-unprod_binary64_7954 unswap-sqr_binary64_7889 *-commutative_binary64_7852 diff-log_binary64_8013 flip3--_binary64_7925 sub-neg_binary64_7914 flip--_binary64_7896
Counts
3 → 109
Calls

3 calls:

9.0ms
(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)
7.0ms
(*.f64 x (log.f64 (/.f64 x y)))
4.0ms
(log.f64 (/.f64 x y))
Compiler

Compiled 1824 to 491 computations (73.1% saved)

series998.0ms (11.9%)

Error
0.1b
Counts
3 → 27
Calls

3 calls:

494.0ms
(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)
280.0ms
(*.f64 x (log.f64 (/.f64 x y)))
195.0ms
(log.f64 (/.f64 x y))
Compiler

Compiled 807 to 630 computations (21.9% saved)

simplify292.0ms (3.5%)

Algorithm
egg-herbie
Rules
660×distribute-rgt-neg-out_binary64_7881
489×unsub-neg_binary64_7915
385×distribute-rgt-in_binary64_7871
361×distribute-lft-in_binary64_7870
234×sub-neg_binary64_7914
221×distribute-neg-out_binary64_7883
153×neg-mul-1_binary64_7917
147×*-commutative_binary64_7852
146×neg-sub0_binary64_7916
110×div-sub_binary64_7926
107×associate-*l/_binary64_7864
103×associate-*l*_binary64_7862
102×exp-prod_binary64_7973
101×log-div_binary64_8008
93×associate-*r*_binary64_7861
86×associate-+l+_binary64_7854
82×+-commutative_binary64_7851
74×associate-+r+_binary64_7853
69×sqr-pow_binary64_7893
68×*-rgt-identity_binary64_7911
66×*-lft-identity_binary64_7910
65×distribute-lft-neg-out_binary64_7880
61×exp-sum_binary64_7967
58×distribute-neg-in_binary64_7882
57×log-prod_binary64_8007
56×associate-+l-_binary64_7856
55×cancel-sign-sub_binary64_7886
53×exp-diff_binary64_7969
44×distribute-frac-neg_binary64_7884
43×sub0-neg_binary64_7908 unswap-sqr_binary64_7889
38×times-frac_binary64_7927 associate--l-_binary64_7859
35×swap-sqr_binary64_7888 associate-+r-_binary64_7855
33×associate-/l*_binary64_7866
31×associate--l+_binary64_7858
29×cancel-sign-sub-inv_binary64_7887
28×difference-of-squares_binary64_7890
26×distribute-rgt-neg-in_binary64_7879
25×pow-sqr_binary64_7894 associate-/l/_binary64_7868
24×associate-/r*_binary64_7865
22×exp-to-pow_binary64_7983
20×log-rec_binary64_8009 +-rgt-identity_binary64_7906 distribute-rgt-out_binary64_7874
19×cube-prod_binary64_7949 mul0-rgt_binary64_7904
18×mul0-lft_binary64_7903
17×distribute-rgt-out--_binary64_7875 associate-/r/_binary64_7867
16×sqr-neg_binary64_7935 +-lft-identity_binary64_7905
15×exp-neg_binary64_7968 distribute-lft-neg-in_binary64_7878 associate-*r/_binary64_7863
14×distribute-lft-out_binary64_7872
13×associate--r+_binary64_7857
12×distribute-neg-frac_binary64_7885
10×/-rgt-identity_binary64_7912
unpow3_binary64_7987 cube-neg_binary64_7948
cube-div_binary64_7950 remove-double-neg_binary64_7909 associate--r-_binary64_7860
div-exp_binary64_7972 count-2_binary64_7869
log-pow_binary64_8010 cube-unmult_binary64_7958 rem-sqrt-square_binary64_7934 mul-1-neg_binary64_7913
rem-exp-log_binary64_7961 --rgt-identity_binary64_7907 div0_binary64_7902
cube-mult_binary64_7951 distribute-rgt1-in_binary64_7877 distribute-lft-out--_binary64_7873
pow-plus_binary64_7984 pow-base-1_binary64_7981 rec-exp_binary64_7971 prod-exp_binary64_7970 1-exp_binary64_7965 exp-1-e_binary64_7964 rem-log-exp_binary64_7962 rem-3cbrt-lft_binary64_7946 rem-square-sqrt_binary64_7933 +-inverses_binary64_7900
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_8184 erf-erfc_binary64_8183 erf-odd_binary64_8182 if-if-and-not_binary64_8181 if-if-and_binary64_8180 if-if-or-not_binary64_8179 if-if-or_binary64_8178 if-not_binary64_8177 if-same_binary64_8176 if-false_binary64_8175 if-true_binary64_8174 not-gte_binary64_8173 not-lte_binary64_8172 not-gt_binary64_8171 not-lt_binary64_8170 gte-same_binary64_8169 lte-same_binary64_8168 gt-same_binary64_8167 lt-same_binary64_8166 sinh---cosh_binary64_8113 sinh-+-cosh_binary64_8112 sinh-cosh_binary64_8111 tanh-def-c_binary64_8110 tanh-def-b_binary64_8109 tanh-def-a_binary64_8108 cosh-def_binary64_8107 sinh-def_binary64_8106 tan-neg_binary64_8053 cos-neg_binary64_8052 sin-neg_binary64_8051 tan-0_binary64_8050 cos-0_binary64_8049 sin-0_binary64_8048 hang-m-tan_binary64_8047 hang-p-tan_binary64_8046 hang-m0-tan_binary64_8045 hang-p0-tan_binary64_8044 hang-0m-tan_binary64_8043 hang-0p-tan_binary64_8042 tan-+PI/2_binary64_8041 tan-+PI_binary64_8040 tan-PI_binary64_8039 tan-PI/3_binary64_8038 tan-PI/4_binary64_8037 tan-PI/6_binary64_8036 cos-+PI/2_binary64_8035 cos-+PI_binary64_8034 cos-PI_binary64_8033 cos-PI/2_binary64_8032 cos-PI/3_binary64_8031 cos-PI/4_binary64_8030 cos-PI/6_binary64_8029 sin-+PI/2_binary64_8028 sin-+PI_binary64_8027 sin-PI_binary64_8026 sin-PI/2_binary64_8025 sin-PI/3_binary64_8024 sin-PI/4_binary64_8023 sin-PI/6_binary64_8022 sub-1-sin_binary64_8021 sub-1-cos_binary64_8020 -1-add-sin_binary64_8019 -1-add-cos_binary64_8018 1-sub-sin_binary64_8017 1-sub-cos_binary64_8016 cos-sin-sum_binary64_8015 log-E_binary64_8011 pow-base-0_binary64_8005 unpow1/3_binary64_7988 unpow2_binary64_7986 unpow1/2_binary64_7985 unpow0_binary64_7980 unpow1_binary64_7979 unpow-1_binary64_7978 exp-lft-cube_binary64_7977 exp-lft-sqr_binary64_7976 exp-cbrt_binary64_7975 exp-sqrt_binary64_7974 e-exp-1_binary64_7966 exp-0_binary64_7963 rem-3cbrt-rft_binary64_7947 rem-cbrt-cube_binary64_7945 rem-cube-cbrt_binary64_7944 sqr-abs_binary64_7936 *-inverses_binary64_7901 lft-mult-inverse_binary64_7899 rgt-mult-inverse_binary64_7898 remove-double-div_binary64_7897 difference-of-sqr--1_binary64_7892 difference-of-sqr-1_binary64_7891 distribute-lft1-in_binary64_7876
Counts
136 → 161
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02172057
13771984
210871940
332631940

prune182.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1547161
Fresh000
Picked101
Done000
Total1557162
Error
0.0b
Counts
162 → 7
Compiler

Compiled 2671 to 682 computations (74.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 y)
0.5b
(cbrt.f64 y)
0.6b
(cbrt.f64 x)
0.6b
(cbrt.f64 x)

rewrite63.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
12×cbrt-prod_binary64_7952
add-cube-cbrt_binary64_7956 add-sqr-sqrt_binary64_7943 *-un-lft-identity_binary64_7921
pow1/3_binary64_8003 pow1_binary64_7982 add-log-exp_binary64_7960 add-exp-log_binary64_7959 add-cbrt-cube_binary64_7957
Counts
4 → 44
Calls

4 calls:

1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
Compiler

Compiled 1108 to 380 computations (65.7% saved)

series505.0ms (6%)

Error
0.0b
Counts
4 → 12
Calls

4 calls:

127.0ms
(cbrt.f64 y)
124.0ms
(cbrt.f64 x)
124.0ms
(cbrt.f64 y)
112.0ms
(cbrt.f64 x)
Compiler

Compiled 852 to 590 computations (30.8% saved)

simplify85.0ms (1%)

Algorithm
egg-herbie
Rules
804×distribute-rgt-in_binary64_7871
792×distribute-lft-in_binary64_7870
484×unswap-sqr_binary64_7889
342×associate-*l*_binary64_7862
222×log-prod_binary64_8007
190×associate-*r*_binary64_7861
168×distribute-rgt-neg-in_binary64_7879 distribute-lft-neg-in_binary64_7878
140×distribute-rgt-out_binary64_7874
90×sqr-pow_binary64_7893
70×cancel-sign-sub-inv_binary64_7887
56×pow-sqr_binary64_7894
50×distribute-lft-out_binary64_7872
36×exp-prod_binary64_7973
34×log-pow_binary64_8010 distribute-rgt-neg-out_binary64_7881 distribute-lft-neg-out_binary64_7880
32×*-commutative_binary64_7852
26×neg-sub0_binary64_7916
24×cube-prod_binary64_7949 neg-mul-1_binary64_7917
14×distribute-rgt1-in_binary64_7877
13×cube-unmult_binary64_7958
12×sub-neg_binary64_7914
10×pow-plus_binary64_7984 rem-sqrt-square_binary64_7934
count-2_binary64_7869 associate-/l*_binary64_7866 associate-+r+_binary64_7853
unpow1/3_binary64_7988 associate-/l/_binary64_7868 associate-*l/_binary64_7864 associate-+l+_binary64_7854
associate-*r/_binary64_7863
unpow3_binary64_7987 rem-3cbrt-lft_binary64_7946 times-frac_binary64_7927 mul-1-neg_binary64_7913 associate-+r-_binary64_7855 +-commutative_binary64_7851
1-exp_binary64_7965 +-rgt-identity_binary64_7906 *-inverses_binary64_7901
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_8184 erf-erfc_binary64_8183 erf-odd_binary64_8182 if-if-and-not_binary64_8181 if-if-and_binary64_8180 if-if-or-not_binary64_8179 if-if-or_binary64_8178 if-not_binary64_8177 if-same_binary64_8176 if-false_binary64_8175 if-true_binary64_8174 not-gte_binary64_8173 not-lte_binary64_8172 not-gt_binary64_8171 not-lt_binary64_8170 gte-same_binary64_8169 lte-same_binary64_8168 gt-same_binary64_8167 lt-same_binary64_8166 sinh---cosh_binary64_8113 sinh-+-cosh_binary64_8112 sinh-cosh_binary64_8111 tanh-def-c_binary64_8110 tanh-def-b_binary64_8109 tanh-def-a_binary64_8108 cosh-def_binary64_8107 sinh-def_binary64_8106 tan-neg_binary64_8053 cos-neg_binary64_8052 sin-neg_binary64_8051 tan-0_binary64_8050 cos-0_binary64_8049 sin-0_binary64_8048 hang-m-tan_binary64_8047 hang-p-tan_binary64_8046 hang-m0-tan_binary64_8045 hang-p0-tan_binary64_8044 hang-0m-tan_binary64_8043 hang-0p-tan_binary64_8042 tan-+PI/2_binary64_8041 tan-+PI_binary64_8040 tan-PI_binary64_8039 tan-PI/3_binary64_8038 tan-PI/4_binary64_8037 tan-PI/6_binary64_8036 cos-+PI/2_binary64_8035 cos-+PI_binary64_8034 cos-PI_binary64_8033 cos-PI/2_binary64_8032 cos-PI/3_binary64_8031 cos-PI/4_binary64_8030 cos-PI/6_binary64_8029 sin-+PI/2_binary64_8028 sin-+PI_binary64_8027 sin-PI_binary64_8026 sin-PI/2_binary64_8025 sin-PI/3_binary64_8024 sin-PI/4_binary64_8023 sin-PI/6_binary64_8022 sub-1-sin_binary64_8021 sub-1-cos_binary64_8020 -1-add-sin_binary64_8019 -1-add-cos_binary64_8018 1-sub-sin_binary64_8017 1-sub-cos_binary64_8016 cos-sin-sum_binary64_8015 log-E_binary64_8011 log-rec_binary64_8009 log-div_binary64_8008 pow-base-0_binary64_8005 unpow2_binary64_7986 unpow1/2_binary64_7985 exp-to-pow_binary64_7983 pow-base-1_binary64_7981 unpow0_binary64_7980 unpow1_binary64_7979 unpow-1_binary64_7978 exp-lft-cube_binary64_7977 exp-lft-sqr_binary64_7976 exp-cbrt_binary64_7975 exp-sqrt_binary64_7974 div-exp_binary64_7972 rec-exp_binary64_7971 prod-exp_binary64_7970 exp-diff_binary64_7969 exp-neg_binary64_7968 exp-sum_binary64_7967 e-exp-1_binary64_7966 exp-1-e_binary64_7964 exp-0_binary64_7963 rem-log-exp_binary64_7962 rem-exp-log_binary64_7961 cube-mult_binary64_7951 cube-div_binary64_7950 cube-neg_binary64_7948 rem-3cbrt-rft_binary64_7947 rem-cbrt-cube_binary64_7945 rem-cube-cbrt_binary64_7944 sqr-abs_binary64_7936 sqr-neg_binary64_7935 rem-square-sqrt_binary64_7933 div-sub_binary64_7926 unsub-neg_binary64_7915 /-rgt-identity_binary64_7912 *-rgt-identity_binary64_7911 *-lft-identity_binary64_7910 remove-double-neg_binary64_7909 sub0-neg_binary64_7908 --rgt-identity_binary64_7907 +-lft-identity_binary64_7905 mul0-rgt_binary64_7904 mul0-lft_binary64_7903 div0_binary64_7902 +-inverses_binary64_7900 lft-mult-inverse_binary64_7899 rgt-mult-inverse_binary64_7898 remove-double-div_binary64_7897 difference-of-sqr--1_binary64_7892 difference-of-sqr-1_binary64_7891 difference-of-squares_binary64_7890 swap-sqr_binary64_7888 cancel-sign-sub_binary64_7886 distribute-neg-frac_binary64_7885 distribute-frac-neg_binary64_7884 distribute-neg-out_binary64_7883 distribute-neg-in_binary64_7882 distribute-lft1-in_binary64_7876 distribute-rgt-out--_binary64_7875 distribute-lft-out--_binary64_7873 associate-/r/_binary64_7867 associate-/r*_binary64_7865 associate--r-_binary64_7860 associate--l-_binary64_7859 associate--l+_binary64_7858 associate--r+_binary64_7857 associate-+l-_binary64_7856
Counts
56 → 24
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
038340
160336
2152336
3398336
41293336

prune38.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New24024
Fresh066
Picked011
Done000
Total24731
Error
0.0b
Counts
31 → 7
Compiler

Compiled 691 to 296 computations (57.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 y)
0.5b
(cbrt.f64 y)
0.6b
(cbrt.f64 x)
0.6b
(cbrt.f64 x)

rewrite63.0ms (0.8%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
12×cbrt-prod_binary64_7952
add-cube-cbrt_binary64_7956 add-sqr-sqrt_binary64_7943 *-un-lft-identity_binary64_7921
pow1/3_binary64_8003 pow1_binary64_7982 add-log-exp_binary64_7960 add-exp-log_binary64_7959 add-cbrt-cube_binary64_7957
Counts
4 → 44
Calls

4 calls:

1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 x)
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
Compiler

Compiled 1020 to 357 computations (65% saved)

series479.0ms (5.7%)

Error
0.0b
Counts
4 → 12
Calls

4 calls:

122.0ms
(cbrt.f64 x)
122.0ms
(cbrt.f64 x)
111.0ms
(cbrt.f64 y)
109.0ms
(cbrt.f64 y)
Compiler

Compiled 780 to 559 computations (28.3% saved)

simplify86.0ms (1%)

Algorithm
egg-herbie
Rules
804×distribute-rgt-in_binary64_7871
792×distribute-lft-in_binary64_7870
484×unswap-sqr_binary64_7889
342×associate-*l*_binary64_7862
222×log-prod_binary64_8007
190×associate-*r*_binary64_7861
168×distribute-rgt-neg-in_binary64_7879 distribute-lft-neg-in_binary64_7878
140×distribute-rgt-out_binary64_7874
90×sqr-pow_binary64_7893
70×cancel-sign-sub-inv_binary64_7887
56×pow-sqr_binary64_7894
50×distribute-lft-out_binary64_7872
36×exp-prod_binary64_7973
34×log-pow_binary64_8010 distribute-rgt-neg-out_binary64_7881 distribute-lft-neg-out_binary64_7880
32×*-commutative_binary64_7852
26×neg-sub0_binary64_7916
24×cube-prod_binary64_7949 neg-mul-1_binary64_7917
14×distribute-rgt1-in_binary64_7877
13×cube-unmult_binary64_7958
12×sub-neg_binary64_7914
10×pow-plus_binary64_7984 rem-sqrt-square_binary64_7934
count-2_binary64_7869 associate-/l*_binary64_7866 associate-+r+_binary64_7853
unpow1/3_binary64_7988 associate-/l/_binary64_7868 associate-*l/_binary64_7864 associate-+l+_binary64_7854
associate-*r/_binary64_7863
unpow3_binary64_7987 rem-3cbrt-lft_binary64_7946 times-frac_binary64_7927 mul-1-neg_binary64_7913 associate-+r-_binary64_7855 +-commutative_binary64_7851
1-exp_binary64_7965 +-rgt-identity_binary64_7906 *-inverses_binary64_7901
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_8184 erf-erfc_binary64_8183 erf-odd_binary64_8182 if-if-and-not_binary64_8181 if-if-and_binary64_8180 if-if-or-not_binary64_8179 if-if-or_binary64_8178 if-not_binary64_8177 if-same_binary64_8176 if-false_binary64_8175 if-true_binary64_8174 not-gte_binary64_8173 not-lte_binary64_8172 not-gt_binary64_8171 not-lt_binary64_8170 gte-same_binary64_8169 lte-same_binary64_8168 gt-same_binary64_8167 lt-same_binary64_8166 sinh---cosh_binary64_8113 sinh-+-cosh_binary64_8112 sinh-cosh_binary64_8111 tanh-def-c_binary64_8110 tanh-def-b_binary64_8109 tanh-def-a_binary64_8108 cosh-def_binary64_8107 sinh-def_binary64_8106 tan-neg_binary64_8053 cos-neg_binary64_8052 sin-neg_binary64_8051 tan-0_binary64_8050 cos-0_binary64_8049 sin-0_binary64_8048 hang-m-tan_binary64_8047 hang-p-tan_binary64_8046 hang-m0-tan_binary64_8045 hang-p0-tan_binary64_8044 hang-0m-tan_binary64_8043 hang-0p-tan_binary64_8042 tan-+PI/2_binary64_8041 tan-+PI_binary64_8040 tan-PI_binary64_8039 tan-PI/3_binary64_8038 tan-PI/4_binary64_8037 tan-PI/6_binary64_8036 cos-+PI/2_binary64_8035 cos-+PI_binary64_8034 cos-PI_binary64_8033 cos-PI/2_binary64_8032 cos-PI/3_binary64_8031 cos-PI/4_binary64_8030 cos-PI/6_binary64_8029 sin-+PI/2_binary64_8028 sin-+PI_binary64_8027 sin-PI_binary64_8026 sin-PI/2_binary64_8025 sin-PI/3_binary64_8024 sin-PI/4_binary64_8023 sin-PI/6_binary64_8022 sub-1-sin_binary64_8021 sub-1-cos_binary64_8020 -1-add-sin_binary64_8019 -1-add-cos_binary64_8018 1-sub-sin_binary64_8017 1-sub-cos_binary64_8016 cos-sin-sum_binary64_8015 log-E_binary64_8011 log-rec_binary64_8009 log-div_binary64_8008 pow-base-0_binary64_8005 unpow2_binary64_7986 unpow1/2_binary64_7985 exp-to-pow_binary64_7983 pow-base-1_binary64_7981 unpow0_binary64_7980 unpow1_binary64_7979 unpow-1_binary64_7978 exp-lft-cube_binary64_7977 exp-lft-sqr_binary64_7976 exp-cbrt_binary64_7975 exp-sqrt_binary64_7974 div-exp_binary64_7972 rec-exp_binary64_7971 prod-exp_binary64_7970 exp-diff_binary64_7969 exp-neg_binary64_7968 exp-sum_binary64_7967 e-exp-1_binary64_7966 exp-1-e_binary64_7964 exp-0_binary64_7963 rem-log-exp_binary64_7962 rem-exp-log_binary64_7961 cube-mult_binary64_7951 cube-div_binary64_7950 cube-neg_binary64_7948 rem-3cbrt-rft_binary64_7947 rem-cbrt-cube_binary64_7945 rem-cube-cbrt_binary64_7944 sqr-abs_binary64_7936 sqr-neg_binary64_7935 rem-square-sqrt_binary64_7933 div-sub_binary64_7926 unsub-neg_binary64_7915 /-rgt-identity_binary64_7912 *-rgt-identity_binary64_7911 *-lft-identity_binary64_7910 remove-double-neg_binary64_7909 sub0-neg_binary64_7908 --rgt-identity_binary64_7907 +-lft-identity_binary64_7905 mul0-rgt_binary64_7904 mul0-lft_binary64_7903 div0_binary64_7902 +-inverses_binary64_7900 lft-mult-inverse_binary64_7899 rgt-mult-inverse_binary64_7898 remove-double-div_binary64_7897 difference-of-sqr--1_binary64_7892 difference-of-sqr-1_binary64_7891 difference-of-squares_binary64_7890 swap-sqr_binary64_7888 cancel-sign-sub_binary64_7886 distribute-neg-frac_binary64_7885 distribute-frac-neg_binary64_7884 distribute-neg-out_binary64_7883 distribute-neg-in_binary64_7882 distribute-lft1-in_binary64_7876 distribute-rgt-out--_binary64_7875 distribute-lft-out--_binary64_7873 associate-/r/_binary64_7867 associate-/r*_binary64_7865 associate--r-_binary64_7860 associate--l-_binary64_7859 associate--l+_binary64_7858 associate--r+_binary64_7857 associate-+l-_binary64_7856
Counts
56 → 24
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
038340
160336
2152336
3398336
41293336

prune37.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New24024
Fresh055
Picked011
Done011
Total24731
Error
0.0b
Counts
31 → 7
Compiler

Compiled 624 to 277 computations (55.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 y)
0.5b
(cbrt.f64 y)
0.5b
(cbrt.f64 y)
5.7b
(log.f64 (/.f64 x (cbrt.f64 y)))

rewrite92.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
22×log-prod_binary64_8007
20×add-cube-cbrt_binary64_7956 add-sqr-sqrt_binary64_7943 *-un-lft-identity_binary64_7921
18×times-frac_binary64_7927 cbrt-prod_binary64_7952
add-exp-log_binary64_7959
pow1_binary64_7982
add-log-exp_binary64_7960 add-cbrt-cube_binary64_7957
pow1/3_binary64_8003
rem-log-exp_binary64_7962
log-pow_binary64_8010 log-div_binary64_8008 div-inv_binary64_7918 div-exp_binary64_7972
Counts
4 → 66
Calls

4 calls:

4.0ms
(log.f64 (/.f64 x (cbrt.f64 y)))
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
1.0ms
(cbrt.f64 y)
Compiler

Compiled 1528 to 460 computations (69.9% saved)

series852.0ms (10.2%)

Error
0.0b
Counts
4 → 15
Calls

4 calls:

461.0ms
(log.f64 (/.f64 x (cbrt.f64 y)))
139.0ms
(cbrt.f64 y)
121.0ms
(cbrt.f64 y)
113.0ms
(cbrt.f64 y)
Compiler

Compiled 927 to 657 computations (29.1% saved)

simplify312.0ms (3.7%)

Algorithm
egg-herbie
Rules
504×log-prod_binary64_8007
480×log-div_binary64_8008
345×times-frac_binary64_7927
336×associate-*l*_binary64_7862
260×sub-neg_binary64_7914
231×associate-*r*_binary64_7861
228×associate-/r*_binary64_7865
163×associate-/l*_binary64_7866
145×exp-sum_binary64_7967
141×exp-prod_binary64_7973
128×cancel-sign-sub-inv_binary64_7887
116×unsub-neg_binary64_7915
104×*-commutative_binary64_7852
95×associate-/l/_binary64_7868
91×associate-+l-_binary64_7856
85×associate-+r+_binary64_7853
83×log-rec_binary64_8009 distribute-rgt-in_binary64_7871
71×exp-to-pow_binary64_7983 associate-+l+_binary64_7854
69×neg-mul-1_binary64_7917
68×distribute-lft-in_binary64_7870
67×associate--l-_binary64_7859 associate--r+_binary64_7857
63×unswap-sqr_binary64_7889
62×+-commutative_binary64_7851
59×log-pow_binary64_8010
58×neg-sub0_binary64_7916 associate--l+_binary64_7858
53×distribute-lft-neg-in_binary64_7878
46×distribute-rgt-neg-in_binary64_7879
43×associate-*l/_binary64_7864 associate-*r/_binary64_7863
42×sqr-pow_binary64_7893
37×exp-diff_binary64_7969 cube-prod_binary64_7949
34×div-sub_binary64_7926
31×associate-+r-_binary64_7855
28×pow-sqr_binary64_7894
26×distribute-rgt-out--_binary64_7875
25×distribute-rgt-out_binary64_7874
20×associate-/r/_binary64_7867
19×cube-unmult_binary64_7958
18×sub0-neg_binary64_7908
15×distribute-lft-out_binary64_7872 count-2_binary64_7869 associate--r-_binary64_7860
14×*-rgt-identity_binary64_7911 distribute-rgt-neg-out_binary64_7881
13×pow-plus_binary64_7984 distribute-lft-neg-out_binary64_7880
12×rem-sqrt-square_binary64_7934
11×div-exp_binary64_7972 cube-div_binary64_7950 +-lft-identity_binary64_7905
10×distribute-neg-out_binary64_7883
distribute-lft-out--_binary64_7873
distribute-neg-in_binary64_7882
unpow1/3_binary64_7988 exp-sqrt_binary64_7974
prod-exp_binary64_7970 rem-exp-log_binary64_7961 sqr-neg_binary64_7935 /-rgt-identity_binary64_7912
distribute-rgt1-in_binary64_7877
unpow3_binary64_7987 rem-log-exp_binary64_7962 --rgt-identity_binary64_7907
cube-neg_binary64_7948 mul-1-neg_binary64_7913 remove-double-neg_binary64_7909 +-rgt-identity_binary64_7906 +-inverses_binary64_7900 swap-sqr_binary64_7888 distribute-neg-frac_binary64_7885
pow-base-1_binary64_7981 exp-lft-sqr_binary64_7976 rec-exp_binary64_7971 1-exp_binary64_7965 exp-1-e_binary64_7964 rem-3cbrt-lft_binary64_7946 rem-cbrt-cube_binary64_7945 *-lft-identity_binary64_7910
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_8184 erf-erfc_binary64_8183 erf-odd_binary64_8182 if-if-and-not_binary64_8181 if-if-and_binary64_8180 if-if-or-not_binary64_8179 if-if-or_binary64_8178 if-not_binary64_8177 if-same_binary64_8176 if-false_binary64_8175 if-true_binary64_8174 not-gte_binary64_8173 not-lte_binary64_8172 not-gt_binary64_8171 not-lt_binary64_8170 gte-same_binary64_8169 lte-same_binary64_8168 gt-same_binary64_8167 lt-same_binary64_8166 sinh---cosh_binary64_8113 sinh-+-cosh_binary64_8112 sinh-cosh_binary64_8111 tanh-def-c_binary64_8110 tanh-def-b_binary64_8109 tanh-def-a_binary64_8108 cosh-def_binary64_8107 sinh-def_binary64_8106 tan-neg_binary64_8053 cos-neg_binary64_8052 sin-neg_binary64_8051 tan-0_binary64_8050 cos-0_binary64_8049 sin-0_binary64_8048 hang-m-tan_binary64_8047 hang-p-tan_binary64_8046 hang-m0-tan_binary64_8045 hang-p0-tan_binary64_8044 hang-0m-tan_binary64_8043 hang-0p-tan_binary64_8042 tan-+PI/2_binary64_8041 tan-+PI_binary64_8040 tan-PI_binary64_8039 tan-PI/3_binary64_8038 tan-PI/4_binary64_8037 tan-PI/6_binary64_8036 cos-+PI/2_binary64_8035 cos-+PI_binary64_8034 cos-PI_binary64_8033 cos-PI/2_binary64_8032 cos-PI/3_binary64_8031 cos-PI/4_binary64_8030 cos-PI/6_binary64_8029 sin-+PI/2_binary64_8028 sin-+PI_binary64_8027 sin-PI_binary64_8026 sin-PI/2_binary64_8025 sin-PI/3_binary64_8024 sin-PI/4_binary64_8023 sin-PI/6_binary64_8022 sub-1-sin_binary64_8021 sub-1-cos_binary64_8020 -1-add-sin_binary64_8019 -1-add-cos_binary64_8018 1-sub-sin_binary64_8017 1-sub-cos_binary64_8016 cos-sin-sum_binary64_8015 log-E_binary64_8011 pow-base-0_binary64_8005 unpow2_binary64_7986 unpow1/2_binary64_7985 unpow0_binary64_7980 unpow1_binary64_7979 unpow-1_binary64_7978 exp-lft-cube_binary64_7977 exp-cbrt_binary64_7975 exp-neg_binary64_7968 e-exp-1_binary64_7966 exp-0_binary64_7963 cube-mult_binary64_7951 rem-3cbrt-rft_binary64_7947 rem-cube-cbrt_binary64_7944 sqr-abs_binary64_7936 rem-square-sqrt_binary64_7933 mul0-rgt_binary64_7904 mul0-lft_binary64_7903 div0_binary64_7902 *-inverses_binary64_7901 lft-mult-inverse_binary64_7899 rgt-mult-inverse_binary64_7898 remove-double-div_binary64_7897 difference-of-sqr--1_binary64_7892 difference-of-sqr-1_binary64_7891 difference-of-squares_binary64_7890 cancel-sign-sub_binary64_7886 distribute-frac-neg_binary64_7884 distribute-lft1-in_binary64_7876
Counts
81 → 86
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0118969
1222939
2496897
31152849
43612849

prune98.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New86086
Fresh044
Picked011
Done022
Total86793
Error
0.0b
Counts
93 → 7
Compiler

Compiled 2011 to 652 computations (67.6% saved)

regimes847.0ms (10.1%)

Accuracy

Total 0.2b remaining (98.1%)

Threshold costs 0.2b (98.1%)

Compiler

Compiled 7314 to 5054 computations (30.9% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64_7852
+-commutative_binary64_7851
sub-neg_binary64_7914
neg-mul-1_binary64_7917 neg-sub0_binary64_7916
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_8181 if-if-and_binary64_8180 if-if-or-not_binary64_8179 if-if-or_binary64_8178 if-not_binary64_8177 if-same_binary64_8176 if-false_binary64_8175 if-true_binary64_8174 tan-0_binary64_8050 cos-0_binary64_8049 sin-0_binary64_8048 unpow1_binary64_7979 e-exp-1_binary64_7966 1-exp_binary64_7965 exp-1-e_binary64_7964 exp-0_binary64_7963 sqr-abs_binary64_7936 sqr-neg_binary64_7935 unsub-neg_binary64_7915 mul-1-neg_binary64_7913 /-rgt-identity_binary64_7912 *-rgt-identity_binary64_7911 *-lft-identity_binary64_7910 remove-double-neg_binary64_7909 sub0-neg_binary64_7908 --rgt-identity_binary64_7907 +-rgt-identity_binary64_7906 +-lft-identity_binary64_7905 cancel-sign-sub-inv_binary64_7887 cancel-sign-sub_binary64_7886 distribute-neg-frac_binary64_7885 distribute-frac-neg_binary64_7884 distribute-neg-out_binary64_7883 distribute-neg-in_binary64_7882 distribute-rgt-neg-out_binary64_7881 distribute-lft-neg-out_binary64_7880 distribute-rgt-neg-in_binary64_7879 distribute-lft-neg-in_binary64_7878
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01434
12034
22534
32734
42834
Proof
(- f64 (+ f64 (* f64 h0 (* f64 2 (log f64 (/ f64 (cbrt f64 h0) (cbrt f64 h1))))) (=> (* f64 (log f64 (/ f64 (cbrt f64 h0) (cbrt f64 h1))) h0))) h2) *-commutative_binary64_7852 => (- f64 (+ f64 (* f64 h0 (* f64 2 (log f64 (/ f64 (cbrt f64 h0) (cbrt f64 h1))))) (* f64 h0 (log f64 (/ f64 (cbrt f64 h0) (cbrt f64 h1))))) h2)

end0.0ms (0%)

sample2.4s (28.4%)

Algorithm
intervals
Results
592.0ms8000×body128valid
30.0ms732×body128nan
1.0ms29×body128invalid
Compiler

Compiled 1468 to 1017 computations (30.7% saved)

Profiling

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