Details

Time bar (total: 11.6s)

analyze867.0ms (7.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
13.2%86.5%0.2%11
16.8%83%0.2%12
22.7%77.1%0.2%13
24.1%74.7%1.3%14
Compiler

Compiled 10 to 10 computations (0% saved)

sample33.0ms (0.3%)

Algorithm
intervals
Results
13.0ms256×body128valid
3.0ms87×body128invalid
Compiler

Compiled 19 to 24 computations (-26.3% saved)

simplify631.0ms (5.5%)

Algorithm
egg-herbie
Rules
540×div-sub_binary64_4857
470×exp-diff_binary64_4900
419×associate-/r*_binary64_4796
356×swap-sqr_binary64_4819
328×unsub-neg_binary64_4846
311×exp-prod_binary64_4904
248×associate-/r/_binary64_4798
215×distribute-rgt1-in_binary64_4808
214×distribute-rgt-in_binary64_4802
204×distribute-rgt-neg-out_binary64_4812
199×distribute-rgt-neg-in_binary64_4810
189×distribute-lft-neg-in_binary64_4809
179×*-commutative_binary64_4783
162×sub-neg_binary64_4845
140×distribute-neg-in_binary64_4813
129×pow-plus_binary64_4915
128×distribute-lft-in_binary64_4801
126×neg-mul-1_binary64_4848
121×neg-sub0_binary64_4847
118×cancel-sign-sub-inv_binary64_4818
115×distribute-lft-neg-out_binary64_4811
104×+-commutative_binary64_4782
97×associate-/l*_binary64_4797
83×associate-*r*_binary64_4792
65×distribute-neg-frac_binary64_4816 associate--r+_binary64_4788
63×distribute-neg-out_binary64_4814 associate-*l*_binary64_4793
55×remove-double-neg_binary64_4840
52×sqr-neg_binary64_4866
35×associate-+l-_binary64_4787
32×associate--r-_binary64_4791
29×associate-+l+_binary64_4785
28×associate--l+_binary64_4789
27×associate-+r+_binary64_4784
24×distribute-rgt-out_binary64_4805 associate-+r-_binary64_4786
22×sub0-neg_binary64_4839 associate--l-_binary64_4790
19×distribute-frac-neg_binary64_4815
18×exp-lft-sqr_binary64_4907 distribute-rgt-out--_binary64_4806
17×mul0-lft_binary64_4834
15×mul0-rgt_binary64_4835
14×associate-/l/_binary64_4799
13×div0_binary64_4833 distribute-lft1-in_binary64_4807
--rgt-identity_binary64_4838 associate-*l/_binary64_4795
exp-sum_binary64_4898
+-rgt-identity_binary64_4837 +-lft-identity_binary64_4836 unswap-sqr_binary64_4820 count-2_binary64_4800
/-rgt-identity_binary64_4843 pow-sqr_binary64_4825 sqr-pow_binary64_4824 distribute-lft-out--_binary64_4804 distribute-lft-out_binary64_4803
+-inverses_binary64_4831 associate-*r/_binary64_4794
cube-unmult_binary64_4889 cube-prod_binary64_4880 *-rgt-identity_binary64_4842
difference-of-squares_binary64_4821
unpow3_binary64_4918 pow-base-1_binary64_4912 1-exp_binary64_4896 difference-of-sqr--1_binary64_4823 difference-of-sqr-1_binary64_4822
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_5115 erf-erfc_binary64_5114 erf-odd_binary64_5113 if-if-and-not_binary64_5112 if-if-and_binary64_5111 if-if-or-not_binary64_5110 if-if-or_binary64_5109 if-not_binary64_5108 if-same_binary64_5107 if-false_binary64_5106 if-true_binary64_5105 not-gte_binary64_5104 not-lte_binary64_5103 not-gt_binary64_5102 not-lt_binary64_5101 gte-same_binary64_5100 lte-same_binary64_5099 gt-same_binary64_5098 lt-same_binary64_5097 sinh---cosh_binary64_5044 sinh-+-cosh_binary64_5043 sinh-cosh_binary64_5042 tanh-def-c_binary64_5041 tanh-def-b_binary64_5040 tanh-def-a_binary64_5039 cosh-def_binary64_5038 sinh-def_binary64_5037 tan-neg_binary64_4984 cos-neg_binary64_4983 sin-neg_binary64_4982 tan-0_binary64_4981 cos-0_binary64_4980 sin-0_binary64_4979 hang-m-tan_binary64_4978 hang-p-tan_binary64_4977 hang-m0-tan_binary64_4976 hang-p0-tan_binary64_4975 hang-0m-tan_binary64_4974 hang-0p-tan_binary64_4973 tan-+PI/2_binary64_4972 tan-+PI_binary64_4971 tan-PI_binary64_4970 tan-PI/3_binary64_4969 tan-PI/4_binary64_4968 tan-PI/6_binary64_4967 cos-+PI/2_binary64_4966 cos-+PI_binary64_4965 cos-PI_binary64_4964 cos-PI/2_binary64_4963 cos-PI/3_binary64_4962 cos-PI/4_binary64_4961 cos-PI/6_binary64_4960 sin-+PI/2_binary64_4959 sin-+PI_binary64_4958 sin-PI_binary64_4957 sin-PI/2_binary64_4956 sin-PI/3_binary64_4955 sin-PI/4_binary64_4954 sin-PI/6_binary64_4953 sub-1-sin_binary64_4952 sub-1-cos_binary64_4951 -1-add-sin_binary64_4950 -1-add-cos_binary64_4949 1-sub-sin_binary64_4948 1-sub-cos_binary64_4947 cos-sin-sum_binary64_4946 log-E_binary64_4942 log-pow_binary64_4941 log-rec_binary64_4940 log-div_binary64_4939 log-prod_binary64_4938 pow-base-0_binary64_4936 unpow1/3_binary64_4919 unpow2_binary64_4917 unpow1/2_binary64_4916 exp-to-pow_binary64_4914 unpow0_binary64_4911 unpow1_binary64_4910 unpow-1_binary64_4909 exp-lft-cube_binary64_4908 exp-cbrt_binary64_4906 exp-sqrt_binary64_4905 div-exp_binary64_4903 rec-exp_binary64_4902 prod-exp_binary64_4901 exp-neg_binary64_4899 e-exp-1_binary64_4897 exp-1-e_binary64_4895 exp-0_binary64_4894 rem-log-exp_binary64_4893 rem-exp-log_binary64_4892 cube-mult_binary64_4882 cube-div_binary64_4881 cube-neg_binary64_4879 rem-3cbrt-rft_binary64_4878 rem-3cbrt-lft_binary64_4877 rem-cbrt-cube_binary64_4876 rem-cube-cbrt_binary64_4875 sqr-abs_binary64_4867 rem-sqrt-square_binary64_4865 rem-square-sqrt_binary64_4864 times-frac_binary64_4858 mul-1-neg_binary64_4844 *-lft-identity_binary64_4841 *-inverses_binary64_4832 lft-mult-inverse_binary64_4830 rgt-mult-inverse_binary64_4829 remove-double-div_binary64_4828 cancel-sign-sub_binary64_4817
Counts
1 → 5
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11713
23913
39713
425213
548213
6102613
7224713
8445513

prune9.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New235
Fresh011
Picked000
Done000
Total246
Error
0.0b
Counts
6 → 4
Compiler

Compiled 81 to 57 computations (29.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b
(-.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))
6.3b
(*.f64 (/.f64 y a) (-.f64 z t))

rewrite90.0ms (0.8%)

Algorithm
rewrite-expression-head
Error
0b
Rules
21×add-sqr-sqrt_binary64_4874
16×*-un-lft-identity_binary64_4852
14×add-cube-cbrt_binary64_4887
13×cancel-sign-sub-inv_binary64_4818 associate-*l*_binary64_4793
10×times-frac_binary64_4858
distribute-rgt-in_binary64_4802 distribute-lft-in_binary64_4801 associate--r+_binary64_4788
add-exp-log_binary64_4890 add-cbrt-cube_binary64_4888
sub-neg_binary64_4845 associate-*r*_binary64_4792
pow1_binary64_4913 add-log-exp_binary64_4891
flip3--_binary64_4856 flip--_binary64_4827
prod-exp_binary64_4901 cbrt-unprod_binary64_4885 frac-times_binary64_4862 unswap-sqr_binary64_4820 associate-*r/_binary64_4794
pow-prod-down_binary64_4923 div-exp_binary64_4903 cbrt-undiv_binary64_4886 associate-*l/_binary64_4795 div-inv_binary64_4849 difference-of-squares_binary64_4821 distribute-lft-out--_binary64_4804 *-commutative_binary64_4783 diff-log_binary64_4944
Counts
2 → 66
Calls

2 calls:

16.0ms
(*.f64 (/.f64 y a) (-.f64 z t))
4.0ms
(-.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))
Compiler

Compiled 1148 to 292 computations (74.6% saved)

series843.0ms (7.3%)

Error
0.0b
Counts
2 → 48
Calls

2 calls:

506.0ms
(-.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))
310.0ms
(*.f64 (/.f64 y a) (-.f64 z t))
Compiler

Compiled 1261 to 792 computations (37.2% saved)

simplify435.0ms (3.8%)

Algorithm
egg-herbie
Rules
436×distribute-rgt-in_binary64_4802 distribute-lft-in_binary64_4801
392×associate-*l/_binary64_4795
316×associate-*r/_binary64_4794
259×associate-/l*_binary64_4797
220×exp-prod_binary64_4904
217×*-commutative_binary64_4783
123×exp-sum_binary64_4898
120×distribute-rgt-neg-in_binary64_4810
116×cancel-sign-sub-inv_binary64_4818
97×associate-*l*_binary64_4793
90×distribute-lft-neg-in_binary64_4809
86×associate-*r*_binary64_4792
78×distribute-lft-neg-out_binary64_4811
72×distribute-rgt-neg-out_binary64_4812
65×distribute-neg-frac_binary64_4816
60×associate-/r*_binary64_4796
57×cube-prod_binary64_4880
52×exp-diff_binary64_4900 times-frac_binary64_4858 sub-neg_binary64_4845
47×neg-sub0_binary64_4847
43×+-commutative_binary64_4782
40×neg-mul-1_binary64_4848
39×associate-/r/_binary64_4798
35×log-prod_binary64_4938 associate-+r+_binary64_4784
31×sqr-pow_binary64_4824 distribute-neg-in_binary64_4813 associate-+l+_binary64_4785
27×div-sub_binary64_4857
26×cube-div_binary64_4881
25×log-div_binary64_4939 associate-+r-_binary64_4786
20×associate-+l-_binary64_4787
16×*-rgt-identity_binary64_4842
15×*-lft-identity_binary64_4841 distribute-rgt-out_binary64_4805 associate-/l/_binary64_4799 associate--r+_binary64_4788
13×unpow3_binary64_4918 swap-sqr_binary64_4819
11×pow-sqr_binary64_4825 unswap-sqr_binary64_4820
10×exp-neg_binary64_4899
cube-mult_binary64_4882
unsub-neg_binary64_4846
mul-1-neg_binary64_4844 difference-of-squares_binary64_4821 cancel-sign-sub_binary64_4817
log-rec_binary64_4940 cube-unmult_binary64_4889 remove-double-neg_binary64_4840 associate--r-_binary64_4791
distribute-lft-out_binary64_4803
distribute-frac-neg_binary64_4815 associate--l+_binary64_4789
pow-base-1_binary64_4912 div-exp_binary64_4903 +-rgt-identity_binary64_4837 distribute-rgt-out--_binary64_4806
log-pow_binary64_4941 pow-plus_binary64_4915 prod-exp_binary64_4901 1-exp_binary64_4896 exp-1-e_binary64_4895 rem-log-exp_binary64_4893 rem-3cbrt-lft_binary64_4877 rem-sqrt-square_binary64_4865 rem-square-sqrt_binary64_4864 /-rgt-identity_binary64_4843
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_5115 erf-erfc_binary64_5114 erf-odd_binary64_5113 if-if-and-not_binary64_5112 if-if-and_binary64_5111 if-if-or-not_binary64_5110 if-if-or_binary64_5109 if-not_binary64_5108 if-same_binary64_5107 if-false_binary64_5106 if-true_binary64_5105 not-gte_binary64_5104 not-lte_binary64_5103 not-gt_binary64_5102 not-lt_binary64_5101 gte-same_binary64_5100 lte-same_binary64_5099 gt-same_binary64_5098 lt-same_binary64_5097 sinh---cosh_binary64_5044 sinh-+-cosh_binary64_5043 sinh-cosh_binary64_5042 tanh-def-c_binary64_5041 tanh-def-b_binary64_5040 tanh-def-a_binary64_5039 cosh-def_binary64_5038 sinh-def_binary64_5037 tan-neg_binary64_4984 cos-neg_binary64_4983 sin-neg_binary64_4982 tan-0_binary64_4981 cos-0_binary64_4980 sin-0_binary64_4979 hang-m-tan_binary64_4978 hang-p-tan_binary64_4977 hang-m0-tan_binary64_4976 hang-p0-tan_binary64_4975 hang-0m-tan_binary64_4974 hang-0p-tan_binary64_4973 tan-+PI/2_binary64_4972 tan-+PI_binary64_4971 tan-PI_binary64_4970 tan-PI/3_binary64_4969 tan-PI/4_binary64_4968 tan-PI/6_binary64_4967 cos-+PI/2_binary64_4966 cos-+PI_binary64_4965 cos-PI_binary64_4964 cos-PI/2_binary64_4963 cos-PI/3_binary64_4962 cos-PI/4_binary64_4961 cos-PI/6_binary64_4960 sin-+PI/2_binary64_4959 sin-+PI_binary64_4958 sin-PI_binary64_4957 sin-PI/2_binary64_4956 sin-PI/3_binary64_4955 sin-PI/4_binary64_4954 sin-PI/6_binary64_4953 sub-1-sin_binary64_4952 sub-1-cos_binary64_4951 -1-add-sin_binary64_4950 -1-add-cos_binary64_4949 1-sub-sin_binary64_4948 1-sub-cos_binary64_4947 cos-sin-sum_binary64_4946 log-E_binary64_4942 pow-base-0_binary64_4936 unpow1/3_binary64_4919 unpow2_binary64_4917 unpow1/2_binary64_4916 exp-to-pow_binary64_4914 unpow0_binary64_4911 unpow1_binary64_4910 unpow-1_binary64_4909 exp-lft-cube_binary64_4908 exp-lft-sqr_binary64_4907 exp-cbrt_binary64_4906 exp-sqrt_binary64_4905 rec-exp_binary64_4902 e-exp-1_binary64_4897 exp-0_binary64_4894 rem-exp-log_binary64_4892 cube-neg_binary64_4879 rem-3cbrt-rft_binary64_4878 rem-cbrt-cube_binary64_4876 rem-cube-cbrt_binary64_4875 sqr-abs_binary64_4867 sqr-neg_binary64_4866 sub0-neg_binary64_4839 --rgt-identity_binary64_4838 +-lft-identity_binary64_4836 mul0-rgt_binary64_4835 mul0-lft_binary64_4834 div0_binary64_4833 *-inverses_binary64_4832 +-inverses_binary64_4831 lft-mult-inverse_binary64_4830 rgt-mult-inverse_binary64_4829 remove-double-div_binary64_4828 difference-of-sqr--1_binary64_4823 difference-of-sqr-1_binary64_4822 distribute-neg-out_binary64_4814 distribute-rgt1-in_binary64_4808 distribute-lft1-in_binary64_4807 distribute-lft-out--_binary64_4804 count-2_binary64_4800 associate--l-_binary64_4790
Counts
114 → 290
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01601553
14281433
212641433
345161433

prune213.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2855290
Fresh123
Picked011
Done000
Total2868294
Error
0b
Counts
294 → 8
Compiler

Compiled 4491 to 611 computations (86.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b
(*.f64 (*.f64 (cbrt.f64 (/.f64 y a)) (cbrt.f64 (/.f64 y a))) (*.f64 (-.f64 z t) (cbrt.f64 (/.f64 y a))))
10.1b
(cbrt.f64 (/.f64 y a))
10.1b
(cbrt.f64 (/.f64 y a))
10.1b
(cbrt.f64 (/.f64 y a))

rewrite156.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0b
Rules
39×cbrt-div_binary64_4884 cbrt-prod_binary64_4883
29×frac-times_binary64_4862
27×times-frac_binary64_4858
25×add-cube-cbrt_binary64_4887 add-sqr-sqrt_binary64_4874 *-un-lft-identity_binary64_4852
17×associate-*l/_binary64_4795
16×pow1_binary64_4913 add-exp-log_binary64_4890
15×associate-*r/_binary64_4794
10×add-cbrt-cube_binary64_4888
pow-prod-down_binary64_4923 prod-exp_binary64_4901 cbrt-unprod_binary64_4885 flip3--_binary64_4856 flip--_binary64_4827
add-log-exp_binary64_4891
pow1/3_binary64_4934 div-inv_binary64_4849
associate-*l*_binary64_4793 associate-*r*_binary64_4792 *-commutative_binary64_4783
Counts
4 → 111
Calls

4 calls:

18.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 y a)) (cbrt.f64 (/.f64 y a))) (*.f64 (-.f64 z t) (cbrt.f64 (/.f64 y a))))
2.0ms
(cbrt.f64 (/.f64 y a))
2.0ms
(cbrt.f64 (/.f64 y a))
2.0ms
(cbrt.f64 (/.f64 y a))
Compiler

Compiled 3130 to 579 computations (81.5% saved)

series1.3s (11.4%)

Error
0b
Counts
4 → 36
Calls

4 calls:

391.0ms
(*.f64 (*.f64 (cbrt.f64 (/.f64 y a)) (cbrt.f64 (/.f64 y a))) (*.f64 (-.f64 z t) (cbrt.f64 (/.f64 y a))))
307.0ms
(cbrt.f64 (/.f64 y a))
298.0ms
(cbrt.f64 (/.f64 y a))
291.0ms
(cbrt.f64 (/.f64 y a))
Compiler

Compiled 2037 to 1369 computations (32.8% saved)

simplify311.0ms (2.7%)

Algorithm
egg-herbie
Rules
487×distribute-rgt-in_binary64_4802
484×distribute-lft-in_binary64_4801
424×associate-/l*_binary64_4797
396×times-frac_binary64_4858
203×associate-*l*_binary64_4793
183×associate-*r*_binary64_4792
85×*-commutative_binary64_4783
79×cancel-sign-sub-inv_binary64_4818
59×associate-/r/_binary64_4798
56×distribute-rgt-neg-in_binary64_4810
53×distribute-lft-neg-in_binary64_4809
40×associate-/l/_binary64_4799 associate-*l/_binary64_4795
39×associate-/r*_binary64_4796
35×sub-neg_binary64_4845
33×exp-prod_binary64_4904 sqr-pow_binary64_4824
30×distribute-lft-neg-out_binary64_4811
28×log-prod_binary64_4938
27×div-sub_binary64_4857
26×distribute-rgt-neg-out_binary64_4812
23×unswap-sqr_binary64_4820 associate-*r/_binary64_4794
22×log-div_binary64_4939 exp-sum_binary64_4898
21×neg-sub0_binary64_4847
19×neg-mul-1_binary64_4848
17×+-commutative_binary64_4782
16×distribute-frac-neg_binary64_4815
13×swap-sqr_binary64_4819
11×exp-diff_binary64_4900 mul-1-neg_binary64_4844 pow-sqr_binary64_4825 distribute-neg-frac_binary64_4816
cube-unmult_binary64_4889 unsub-neg_binary64_4846
cube-prod_binary64_4880
distribute-neg-in_binary64_4813 distribute-rgt-out_binary64_4805
*-rgt-identity_binary64_4842 distribute-neg-out_binary64_4814 associate-+l+_binary64_4785 associate-+r+_binary64_4784
log-rec_binary64_4940 cube-div_binary64_4881 distribute-rgt-out--_binary64_4806
log-pow_binary64_4941 /-rgt-identity_binary64_4843 remove-double-neg_binary64_4840
unpow1/3_binary64_4919 unpow3_binary64_4918 exp-to-pow_binary64_4914 cube-mult_binary64_4882 rem-3cbrt-lft_binary64_4877 difference-of-squares_binary64_4821 distribute-lft-out--_binary64_4804 associate-+l-_binary64_4787
exp-neg_binary64_4899 distribute-lft-out_binary64_4803 count-2_binary64_4800 associate--r-_binary64_4791 associate--l-_binary64_4790 associate-+r-_binary64_4786
pow-plus_binary64_4915 div-exp_binary64_4903 rec-exp_binary64_4902 1-exp_binary64_4896 rem-log-exp_binary64_4893 rem-3cbrt-rft_binary64_4878 rem-cube-cbrt_binary64_4875 *-lft-identity_binary64_4841 sub0-neg_binary64_4839 --rgt-identity_binary64_4838 +-rgt-identity_binary64_4837 distribute-rgt1-in_binary64_4808 distribute-lft1-in_binary64_4807
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_5115 erf-erfc_binary64_5114 erf-odd_binary64_5113 if-if-and-not_binary64_5112 if-if-and_binary64_5111 if-if-or-not_binary64_5110 if-if-or_binary64_5109 if-not_binary64_5108 if-same_binary64_5107 if-false_binary64_5106 if-true_binary64_5105 not-gte_binary64_5104 not-lte_binary64_5103 not-gt_binary64_5102 not-lt_binary64_5101 gte-same_binary64_5100 lte-same_binary64_5099 gt-same_binary64_5098 lt-same_binary64_5097 sinh---cosh_binary64_5044 sinh-+-cosh_binary64_5043 sinh-cosh_binary64_5042 tanh-def-c_binary64_5041 tanh-def-b_binary64_5040 tanh-def-a_binary64_5039 cosh-def_binary64_5038 sinh-def_binary64_5037 tan-neg_binary64_4984 cos-neg_binary64_4983 sin-neg_binary64_4982 tan-0_binary64_4981 cos-0_binary64_4980 sin-0_binary64_4979 hang-m-tan_binary64_4978 hang-p-tan_binary64_4977 hang-m0-tan_binary64_4976 hang-p0-tan_binary64_4975 hang-0m-tan_binary64_4974 hang-0p-tan_binary64_4973 tan-+PI/2_binary64_4972 tan-+PI_binary64_4971 tan-PI_binary64_4970 tan-PI/3_binary64_4969 tan-PI/4_binary64_4968 tan-PI/6_binary64_4967 cos-+PI/2_binary64_4966 cos-+PI_binary64_4965 cos-PI_binary64_4964 cos-PI/2_binary64_4963 cos-PI/3_binary64_4962 cos-PI/4_binary64_4961 cos-PI/6_binary64_4960 sin-+PI/2_binary64_4959 sin-+PI_binary64_4958 sin-PI_binary64_4957 sin-PI/2_binary64_4956 sin-PI/3_binary64_4955 sin-PI/4_binary64_4954 sin-PI/6_binary64_4953 sub-1-sin_binary64_4952 sub-1-cos_binary64_4951 -1-add-sin_binary64_4950 -1-add-cos_binary64_4949 1-sub-sin_binary64_4948 1-sub-cos_binary64_4947 cos-sin-sum_binary64_4946 log-E_binary64_4942 pow-base-0_binary64_4936 unpow2_binary64_4917 unpow1/2_binary64_4916 pow-base-1_binary64_4912 unpow0_binary64_4911 unpow1_binary64_4910 unpow-1_binary64_4909 exp-lft-cube_binary64_4908 exp-lft-sqr_binary64_4907 exp-cbrt_binary64_4906 exp-sqrt_binary64_4905 prod-exp_binary64_4901 e-exp-1_binary64_4897 exp-1-e_binary64_4895 exp-0_binary64_4894 rem-exp-log_binary64_4892 cube-neg_binary64_4879 rem-cbrt-cube_binary64_4876 sqr-abs_binary64_4867 sqr-neg_binary64_4866 rem-sqrt-square_binary64_4865 rem-square-sqrt_binary64_4864 +-lft-identity_binary64_4836 mul0-rgt_binary64_4835 mul0-lft_binary64_4834 div0_binary64_4833 *-inverses_binary64_4832 +-inverses_binary64_4831 lft-mult-inverse_binary64_4830 rgt-mult-inverse_binary64_4829 remove-double-div_binary64_4828 difference-of-sqr--1_binary64_4823 difference-of-sqr-1_binary64_4822 cancel-sign-sub_binary64_4817 associate--l+_binary64_4789 associate--r+_binary64_4788
Counts
147 → 246
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01942973
14762445
214592385

prune243.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2460246
Fresh066
Picked011
Done011
Total2468254
Error
0b
Counts
254 → 8
Compiler

Compiled 5935 to 1101 computations (81.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(*.f64 y (-.f64 z t))
0.0b
(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
6.0b
(/.f64 (*.f64 y (-.f64 z t)) a)

rewrite83.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
17×add-sqr-sqrt_binary64_4874
15×*-un-lft-identity_binary64_4852
13×cancel-sign-sub-inv_binary64_4818
11×add-cube-cbrt_binary64_4887
10×add-exp-log_binary64_4890 add-cbrt-cube_binary64_4888
times-frac_binary64_4858
pow1_binary64_4913 add-log-exp_binary64_4891 associate-*r*_binary64_4792
associate-*r/_binary64_4794 distribute-rgt-in_binary64_4802 distribute-lft-in_binary64_4801
flip3--_binary64_4856 flip--_binary64_4827 associate-/r*_binary64_4796 sub-neg_binary64_4845 associate-*l*_binary64_4793
prod-exp_binary64_4901 div-exp_binary64_4903 cbrt-undiv_binary64_4886 cbrt-unprod_binary64_4885 div-inv_binary64_4849 associate-/l/_binary64_4799 difference-of-squares_binary64_4821 distribute-lft-out--_binary64_4804
frac-2neg_binary64_4863 clear-num_binary64_4851 associate-/l*_binary64_4797 diff-log_binary64_4944 pow-prod-down_binary64_4923 unswap-sqr_binary64_4820 *-commutative_binary64_4783
Counts
3 → 73
Calls

3 calls:

7.0ms
(/.f64 (*.f64 y (-.f64 z t)) a)
7.0ms
(*.f64 y (-.f64 z t))
5.0ms
(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
Compiler

Compiled 1187 to 331 computations (72.1% saved)

series962.0ms (8.3%)

Error
0b
Counts
3 → 63
Calls

3 calls:

509.0ms
(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
282.0ms
(/.f64 (*.f64 y (-.f64 z t)) a)
137.0ms
(*.f64 y (-.f64 z t))
Compiler

Compiled 1636 to 1032 computations (36.9% saved)

simplify401.0ms (3.5%)

Algorithm
egg-herbie
Rules
699×times-frac_binary64_4858
503×distribute-lft-in_binary64_4801
502×distribute-rgt-in_binary64_4802
131×distribute-rgt-neg-in_binary64_4810
110×distribute-neg-frac_binary64_4816
102×associate-*l*_binary64_4793
99×distribute-lft-neg-in_binary64_4809
98×div-sub_binary64_4857 cancel-sign-sub-inv_binary64_4818
89×distribute-lft-neg-out_binary64_4811
86×associate-*r*_binary64_4792
84×exp-prod_binary64_4904
81×associate-/l*_binary64_4797
78×distribute-rgt-neg-out_binary64_4812
77×*-commutative_binary64_4783
70×sub-neg_binary64_4845
67×associate-*l/_binary64_4795
57×neg-sub0_binary64_4847
48×associate-*r/_binary64_4794
47×neg-mul-1_binary64_4848
35×distribute-neg-in_binary64_4813
32×sqr-pow_binary64_4824
30×+-commutative_binary64_4782
28×log-div_binary64_4939 *-rgt-identity_binary64_4842
27×cube-div_binary64_4881 cube-prod_binary64_4880
24×log-prod_binary64_4938 exp-sum_binary64_4898
23×*-lft-identity_binary64_4841
21×associate-/l/_binary64_4799
18×swap-sqr_binary64_4819
17×associate-/r*_binary64_4796
13×exp-diff_binary64_4900 associate-/r/_binary64_4798
12×/-rgt-identity_binary64_4843
11×pow-sqr_binary64_4825
10×unpow3_binary64_4918
cube-mult_binary64_4882 remove-double-neg_binary64_4840
mul-1-neg_binary64_4844 distribute-frac-neg_binary64_4815
unsub-neg_binary64_4846 difference-of-squares_binary64_4821 distribute-rgt-out_binary64_4805 associate-+l+_binary64_4785
cube-unmult_binary64_4889 unswap-sqr_binary64_4820 cancel-sign-sub_binary64_4817 associate-+r+_binary64_4784
log-rec_binary64_4940 associate--l+_binary64_4789 associate-+r-_binary64_4786
+-rgt-identity_binary64_4837 div0_binary64_4833 associate--r-_binary64_4791 associate--r+_binary64_4788
div-exp_binary64_4903 exp-neg_binary64_4899 rem-3cbrt-lft_binary64_4877 rem-sqrt-square_binary64_4865 rem-square-sqrt_binary64_4864 distribute-rgt-out--_binary64_4806
pow-base-1_binary64_4912 rec-exp_binary64_4902 prod-exp_binary64_4901 1-exp_binary64_4896 exp-1-e_binary64_4895 rem-log-exp_binary64_4893 associate-+l-_binary64_4787
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_5115 erf-erfc_binary64_5114 erf-odd_binary64_5113 if-if-and-not_binary64_5112 if-if-and_binary64_5111 if-if-or-not_binary64_5110 if-if-or_binary64_5109 if-not_binary64_5108 if-same_binary64_5107 if-false_binary64_5106 if-true_binary64_5105 not-gte_binary64_5104 not-lte_binary64_5103 not-gt_binary64_5102 not-lt_binary64_5101 gte-same_binary64_5100 lte-same_binary64_5099 gt-same_binary64_5098 lt-same_binary64_5097 sinh---cosh_binary64_5044 sinh-+-cosh_binary64_5043 sinh-cosh_binary64_5042 tanh-def-c_binary64_5041 tanh-def-b_binary64_5040 tanh-def-a_binary64_5039 cosh-def_binary64_5038 sinh-def_binary64_5037 tan-neg_binary64_4984 cos-neg_binary64_4983 sin-neg_binary64_4982 tan-0_binary64_4981 cos-0_binary64_4980 sin-0_binary64_4979 hang-m-tan_binary64_4978 hang-p-tan_binary64_4977 hang-m0-tan_binary64_4976 hang-p0-tan_binary64_4975 hang-0m-tan_binary64_4974 hang-0p-tan_binary64_4973 tan-+PI/2_binary64_4972 tan-+PI_binary64_4971 tan-PI_binary64_4970 tan-PI/3_binary64_4969 tan-PI/4_binary64_4968 tan-PI/6_binary64_4967 cos-+PI/2_binary64_4966 cos-+PI_binary64_4965 cos-PI_binary64_4964 cos-PI/2_binary64_4963 cos-PI/3_binary64_4962 cos-PI/4_binary64_4961 cos-PI/6_binary64_4960 sin-+PI/2_binary64_4959 sin-+PI_binary64_4958 sin-PI_binary64_4957 sin-PI/2_binary64_4956 sin-PI/3_binary64_4955 sin-PI/4_binary64_4954 sin-PI/6_binary64_4953 sub-1-sin_binary64_4952 sub-1-cos_binary64_4951 -1-add-sin_binary64_4950 -1-add-cos_binary64_4949 1-sub-sin_binary64_4948 1-sub-cos_binary64_4947 cos-sin-sum_binary64_4946 log-E_binary64_4942 log-pow_binary64_4941 pow-base-0_binary64_4936 unpow1/3_binary64_4919 unpow2_binary64_4917 unpow1/2_binary64_4916 pow-plus_binary64_4915 exp-to-pow_binary64_4914 unpow0_binary64_4911 unpow1_binary64_4910 unpow-1_binary64_4909 exp-lft-cube_binary64_4908 exp-lft-sqr_binary64_4907 exp-cbrt_binary64_4906 exp-sqrt_binary64_4905 e-exp-1_binary64_4897 exp-0_binary64_4894 rem-exp-log_binary64_4892 cube-neg_binary64_4879 rem-3cbrt-rft_binary64_4878 rem-cbrt-cube_binary64_4876 rem-cube-cbrt_binary64_4875 sqr-abs_binary64_4867 sqr-neg_binary64_4866 sub0-neg_binary64_4839 --rgt-identity_binary64_4838 +-lft-identity_binary64_4836 mul0-rgt_binary64_4835 mul0-lft_binary64_4834 *-inverses_binary64_4832 +-inverses_binary64_4831 lft-mult-inverse_binary64_4830 rgt-mult-inverse_binary64_4829 remove-double-div_binary64_4828 difference-of-sqr--1_binary64_4823 difference-of-sqr-1_binary64_4822 distribute-neg-out_binary64_4814 distribute-rgt1-in_binary64_4808 distribute-lft1-in_binary64_4807 distribute-lft-out--_binary64_4804 distribute-lft-out_binary64_4803 count-2_binary64_4800 associate--l-_binary64_4790
Counts
136 → 296
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01661662
14391503
214621503

prune203.0ms (1.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2960296
Fresh055
Picked011
Done022
Total2968304
Error
0b
Counts
304 → 8
Compiler

Compiled 4458 to 536 computations (88% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(/.f64 a (-.f64 z t))
0.0b
(-.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
7.3b
(/.f64 y (/.f64 a (-.f64 z t)))

rewrite263.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
0b
Rules
249×times-frac_binary64_4858
179×add-sqr-sqrt_binary64_4874
172×*-un-lft-identity_binary64_4852
120×add-cube-cbrt_binary64_4887
68×cancel-sign-sub-inv_binary64_4818
28×difference-of-squares_binary64_4821
26×distribute-lft-out--_binary64_4804 associate-/r*_binary64_4796
18×associate-/r/_binary64_4798
10×add-exp-log_binary64_4890 add-cbrt-cube_binary64_4888 div-inv_binary64_4849
flip3--_binary64_4856 flip--_binary64_4827
associate-/l*_binary64_4797
add-log-exp_binary64_4891
div-exp_binary64_4903 cbrt-undiv_binary64_4886
pow1_binary64_4913
frac-2neg_binary64_4863 clear-num_binary64_4851
diff-log_binary64_4944 sub-neg_binary64_4845
Counts
3 → 222
Calls

3 calls:

29.0ms
(-.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
10.0ms
(/.f64 y (/.f64 a (-.f64 z t)))
5.0ms
(/.f64 a (-.f64 z t))
Compiler

Compiled 4636 to 1117 computations (75.9% saved)

series1.0s (8.8%)

Error
0b
Counts
3 → 69
Calls

3 calls:

500.0ms
(-.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
324.0ms
(/.f64 y (/.f64 a (-.f64 z t)))
147.0ms
(/.f64 a (-.f64 z t))
Compiler

Compiled 2071 to 1353 computations (34.7% saved)

simplify463.0ms (4%)

Algorithm
egg-herbie
Rules
358×associate-*l/_binary64_4795
325×*-commutative_binary64_4783
277×associate-/l*_binary64_4797
265×associate-*r/_binary64_4794
262×associate-/r/_binary64_4798
236×associate-/l/_binary64_4799
212×associate-*r*_binary64_4792
179×associate-*l*_binary64_4793
140×neg-sub0_binary64_4847
135×neg-mul-1_binary64_4848
114×distribute-rgt-neg-in_binary64_4810
110×distribute-lft-neg-out_binary64_4811
86×sub-neg_binary64_4845 distribute-neg-frac_binary64_4816
82×times-frac_binary64_4858
78×distribute-rgt-in_binary64_4802
72×distribute-lft-in_binary64_4801
60×div-sub_binary64_4857
57×associate-/r*_binary64_4796
55×cancel-sign-sub-inv_binary64_4818
52×distribute-rgt-neg-out_binary64_4812 distribute-lft-neg-in_binary64_4809
46×+-commutative_binary64_4782
22×log-prod_binary64_4938
18×distribute-neg-in_binary64_4813
16×log-div_binary64_4939 sqr-pow_binary64_4824
13×associate-+l+_binary64_4785 associate-+r+_binary64_4784
associate--r+_binary64_4788
/-rgt-identity_binary64_4843
pow-sqr_binary64_4825 difference-of-squares_binary64_4821
unpow3_binary64_4918 mul-1-neg_binary64_4844
cube-unmult_binary64_4889 cube-mult_binary64_4882 associate-+r-_binary64_4786
cube-div_binary64_4881 unsub-neg_binary64_4846 remove-double-div_binary64_4828 unswap-sqr_binary64_4820 swap-sqr_binary64_4819
unpow2_binary64_4917 pow-plus_binary64_4915 div-exp_binary64_4903 cube-prod_binary64_4880 *-rgt-identity_binary64_4842 distribute-rgt-out--_binary64_4806 distribute-rgt-out_binary64_4805 associate--r-_binary64_4791 associate--l+_binary64_4789
log-pow_binary64_4941 log-rec_binary64_4940 exp-prod_binary64_4904 rec-exp_binary64_4902 prod-exp_binary64_4901 exp-sum_binary64_4898 1-exp_binary64_4896 rem-3cbrt-lft_binary64_4877 rem-square-sqrt_binary64_4864 *-lft-identity_binary64_4841 *-inverses_binary64_4832
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_5115 erf-erfc_binary64_5114 erf-odd_binary64_5113 if-if-and-not_binary64_5112 if-if-and_binary64_5111 if-if-or-not_binary64_5110 if-if-or_binary64_5109 if-not_binary64_5108 if-same_binary64_5107 if-false_binary64_5106 if-true_binary64_5105 not-gte_binary64_5104 not-lte_binary64_5103 not-gt_binary64_5102 not-lt_binary64_5101 gte-same_binary64_5100 lte-same_binary64_5099 gt-same_binary64_5098 lt-same_binary64_5097 sinh---cosh_binary64_5044 sinh-+-cosh_binary64_5043 sinh-cosh_binary64_5042 tanh-def-c_binary64_5041 tanh-def-b_binary64_5040 tanh-def-a_binary64_5039 cosh-def_binary64_5038 sinh-def_binary64_5037 tan-neg_binary64_4984 cos-neg_binary64_4983 sin-neg_binary64_4982 tan-0_binary64_4981 cos-0_binary64_4980 sin-0_binary64_4979 hang-m-tan_binary64_4978 hang-p-tan_binary64_4977 hang-m0-tan_binary64_4976 hang-p0-tan_binary64_4975 hang-0m-tan_binary64_4974 hang-0p-tan_binary64_4973 tan-+PI/2_binary64_4972 tan-+PI_binary64_4971 tan-PI_binary64_4970 tan-PI/3_binary64_4969 tan-PI/4_binary64_4968 tan-PI/6_binary64_4967 cos-+PI/2_binary64_4966 cos-+PI_binary64_4965 cos-PI_binary64_4964 cos-PI/2_binary64_4963 cos-PI/3_binary64_4962 cos-PI/4_binary64_4961 cos-PI/6_binary64_4960 sin-+PI/2_binary64_4959 sin-+PI_binary64_4958 sin-PI_binary64_4957 sin-PI/2_binary64_4956 sin-PI/3_binary64_4955 sin-PI/4_binary64_4954 sin-PI/6_binary64_4953 sub-1-sin_binary64_4952 sub-1-cos_binary64_4951 -1-add-sin_binary64_4950 -1-add-cos_binary64_4949 1-sub-sin_binary64_4948 1-sub-cos_binary64_4947 cos-sin-sum_binary64_4946 log-E_binary64_4942 pow-base-0_binary64_4936 unpow1/3_binary64_4919 unpow1/2_binary64_4916 exp-to-pow_binary64_4914 pow-base-1_binary64_4912 unpow0_binary64_4911 unpow1_binary64_4910 unpow-1_binary64_4909 exp-lft-cube_binary64_4908 exp-lft-sqr_binary64_4907 exp-cbrt_binary64_4906 exp-sqrt_binary64_4905 exp-diff_binary64_4900 exp-neg_binary64_4899 e-exp-1_binary64_4897 exp-1-e_binary64_4895 exp-0_binary64_4894 rem-log-exp_binary64_4893 rem-exp-log_binary64_4892 cube-neg_binary64_4879 rem-3cbrt-rft_binary64_4878 rem-cbrt-cube_binary64_4876 rem-cube-cbrt_binary64_4875 sqr-abs_binary64_4867 sqr-neg_binary64_4866 rem-sqrt-square_binary64_4865 remove-double-neg_binary64_4840 sub0-neg_binary64_4839 --rgt-identity_binary64_4838 +-rgt-identity_binary64_4837 +-lft-identity_binary64_4836 mul0-rgt_binary64_4835 mul0-lft_binary64_4834 div0_binary64_4833 +-inverses_binary64_4831 lft-mult-inverse_binary64_4830 rgt-mult-inverse_binary64_4829 difference-of-sqr--1_binary64_4823 difference-of-sqr-1_binary64_4822 cancel-sign-sub_binary64_4817 distribute-frac-neg_binary64_4815 distribute-neg-out_binary64_4814 distribute-rgt1-in_binary64_4808 distribute-lft1-in_binary64_4807 distribute-lft-out--_binary64_4804 distribute-lft-out_binary64_4803 count-2_binary64_4800 associate--l-_binary64_4790 associate-+l-_binary64_4787
Counts
291 → 733
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
04156342
112016132
249536132

prune655.0ms (5.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New7330733
Fresh044
Picked011
Done033
Total7338741
Error
0b
Counts
741 → 8
Compiler

Compiled 14882 to 2250 computations (84.9% saved)

regimes793.0ms (6.9%)

Accuracy

Total 0.9b remaining (99.9%)

Threshold costs 0.9b (99.9%)

Compiler

Compiled 6082 to 5525 computations (9.2% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm
egg-herbie
Rules
84×neg-mul-1_binary64_4848 neg-sub0_binary64_4847
56×unsub-neg_binary64_4846
53×distribute-neg-out_binary64_4814
36×distribute-rgt-neg-out_binary64_4812
31×distribute-rgt-neg-in_binary64_4810
25×distribute-lft-neg-out_binary64_4811
19×remove-double-neg_binary64_4840
17×distribute-lft-neg-in_binary64_4809
15×sub-neg_binary64_4845
12×*-commutative_binary64_4783 +-commutative_binary64_4782
+-rgt-identity_binary64_4837 +-lft-identity_binary64_4836 cancel-sign-sub-inv_binary64_4818
distribute-neg-in_binary64_4813
distribute-frac-neg_binary64_4815
distribute-neg-frac_binary64_4816
sqr-neg_binary64_4866 --rgt-identity_binary64_4838
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_5112 if-if-and_binary64_5111 if-if-or-not_binary64_5110 if-if-or_binary64_5109 if-not_binary64_5108 if-same_binary64_5107 if-false_binary64_5106 if-true_binary64_5105 tan-0_binary64_4981 cos-0_binary64_4980 sin-0_binary64_4979 unpow1_binary64_4910 e-exp-1_binary64_4897 1-exp_binary64_4896 exp-1-e_binary64_4895 exp-0_binary64_4894 sqr-abs_binary64_4867 mul-1-neg_binary64_4844 /-rgt-identity_binary64_4843 *-rgt-identity_binary64_4842 *-lft-identity_binary64_4841 sub0-neg_binary64_4839 cancel-sign-sub_binary64_4817
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01637
12537
24037
35937
47737
59837
611837
712037
819637
928437
1022937
Proof
(- f64 h0 (* f64 (/ f64 (* f64 (cbrt f64 h1) (cbrt f64 h1)) (* f64 (cbrt f64 h2) (cbrt f64 h2))) (* f64 (/ f64 (cbrt f64 h1) (cbrt f64 h2)) (- f64 h3 h4))))

end0.0ms (0%)

sample1.5s (13.2%)

Algorithm
intervals
Results
265.0ms8000×body128valid
95.0ms2618×body128invalid
Compiler

Compiled 734 to 645 computations (12.1% saved)

Profiling

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