Details

Time bar (total: 10.2s)

analyze330.0ms (3.2%)

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
25%74.9%0.1%5
43.7%56.2%0.1%6
43.7%46.8%9.5%7
46.8%42.1%11%8
46.8%36.7%16.5%9
48.4%34%17.7%10
48.4%31%20.6%11
49.2%29.6%21.3%12
49.2%28%22.8%13
49.6%27.3%23.1%14
Compiler

Compiled 8 to 7 computations (12.5% saved)

sample57.0ms (0.6%)

Algorithm
intervals
Results
13.0ms69×body1024invalid
9.0ms193×body128valid
8.0ms20×body1024valid
5.0ms33×body512invalid
3.0ms25×body512valid
2.0ms18×body256valid
1.0ms13×body256invalid
1.0ms22×body128invalid
Compiler

Compiled 15 to 15 computations (0% saved)

simplify380.0ms (3.7%)

Algorithm
egg-herbie
Rules
363×associate-/l/_binary64_8891
350×associate-/r*_binary64_8888
317×div-sub_binary64_8949
300×distribute-rgt-neg-in_binary64_8902
295×associate-*l/_binary64_8887
292×distribute-rgt-in_binary64_8894
229×exp-prod_binary64_8996
228×distribute-lft-in_binary64_8893
225×associate-/r/_binary64_8890
208×swap-sqr_binary64_8911
204×distribute-neg-frac_binary64_8908
153×distribute-lft-neg-in_binary64_8901
152×distribute-rgt-out_binary64_8897
151×cancel-sign-sub-inv_binary64_8910
142×unsub-neg_binary64_8938
129×*-commutative_binary64_8875
123×distribute-rgt-neg-out_binary64_8904
116×associate-/l*_binary64_8889
113×times-frac_binary64_8950
111×distribute-lft-neg-out_binary64_8903
97×distribute-frac-neg_binary64_8907
91×neg-sub0_binary64_8939
89×neg-mul-1_binary64_8940
83×sub-neg_binary64_8937
79×associate-*r*_binary64_8884
75×associate-*l*_binary64_8885
63×distribute-rgt1-in_binary64_8900
52×distribute-neg-in_binary64_8905
51×associate-*r/_binary64_8886
36×distribute-neg-out_binary64_8906
31×unswap-sqr_binary64_8912
30×sqr-pow_binary64_8916
28×mul0-rgt_binary64_8927
26×*-lft-identity_binary64_8933
24×mul0-lft_binary64_8926
20×*-rgt-identity_binary64_8934
16×pow-sqr_binary64_8917 distribute-lft-out_binary64_8895 +-commutative_binary64_8874
15×exp-sum_binary64_8990
13×div0_binary64_8925 associate-+l-_binary64_8879
12×associate--r+_binary64_8880
11×distribute-lft1-in_binary64_8899
/-rgt-identity_binary64_8935
sub0-neg_binary64_8931
pow-plus_binary64_9007 exp-diff_binary64_8992 distribute-rgt-out--_binary64_8898 associate-+r-_binary64_8878
+-rgt-identity_binary64_8929
associate-+r+_binary64_8876
cube-unmult_binary64_8981 --rgt-identity_binary64_8930 +-lft-identity_binary64_8928
exp-lft-sqr_binary64_8999 prod-exp_binary64_8993 exp-neg_binary64_8991 cube-prod_binary64_8972 mul-1-neg_binary64_8936
exp-sqrt_binary64_8997 remove-double-neg_binary64_8932 count-2_binary64_8892 associate--r-_binary64_8883 associate-+l+_binary64_8877
sinh-def_binary64_9129 div-exp_binary64_8995 1-exp_binary64_8988 exp-1-e_binary64_8987 cube-div_binary64_8973 sqr-neg_binary64_8958 rem-sqrt-square_binary64_8957 *-inverses_binary64_8924 rgt-mult-inverse_binary64_8921 cancel-sign-sub_binary64_8909
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_9207 erf-erfc_binary64_9206 erf-odd_binary64_9205 if-if-and-not_binary64_9204 if-if-and_binary64_9203 if-if-or-not_binary64_9202 if-if-or_binary64_9201 if-not_binary64_9200 if-same_binary64_9199 if-false_binary64_9198 if-true_binary64_9197 not-gte_binary64_9196 not-lte_binary64_9195 not-gt_binary64_9194 not-lt_binary64_9193 gte-same_binary64_9192 lte-same_binary64_9191 gt-same_binary64_9190 lt-same_binary64_9189 sinh---cosh_binary64_9136 sinh-+-cosh_binary64_9135 sinh-cosh_binary64_9134 tanh-def-c_binary64_9133 tanh-def-b_binary64_9132 tanh-def-a_binary64_9131 cosh-def_binary64_9130 tan-neg_binary64_9076 cos-neg_binary64_9075 sin-neg_binary64_9074 tan-0_binary64_9073 cos-0_binary64_9072 sin-0_binary64_9071 hang-m-tan_binary64_9070 hang-p-tan_binary64_9069 hang-m0-tan_binary64_9068 hang-p0-tan_binary64_9067 hang-0m-tan_binary64_9066 hang-0p-tan_binary64_9065 tan-+PI/2_binary64_9064 tan-+PI_binary64_9063 tan-PI_binary64_9062 tan-PI/3_binary64_9061 tan-PI/4_binary64_9060 tan-PI/6_binary64_9059 cos-+PI/2_binary64_9058 cos-+PI_binary64_9057 cos-PI_binary64_9056 cos-PI/2_binary64_9055 cos-PI/3_binary64_9054 cos-PI/4_binary64_9053 cos-PI/6_binary64_9052 sin-+PI/2_binary64_9051 sin-+PI_binary64_9050 sin-PI_binary64_9049 sin-PI/2_binary64_9048 sin-PI/3_binary64_9047 sin-PI/4_binary64_9046 sin-PI/6_binary64_9045 sub-1-sin_binary64_9044 sub-1-cos_binary64_9043 -1-add-sin_binary64_9042 -1-add-cos_binary64_9041 1-sub-sin_binary64_9040 1-sub-cos_binary64_9039 cos-sin-sum_binary64_9038 log-E_binary64_9034 log-pow_binary64_9033 log-rec_binary64_9032 log-div_binary64_9031 log-prod_binary64_9030 pow-base-0_binary64_9028 unpow1/3_binary64_9011 unpow3_binary64_9010 unpow2_binary64_9009 unpow1/2_binary64_9008 exp-to-pow_binary64_9006 pow-base-1_binary64_9004 unpow0_binary64_9003 unpow1_binary64_9002 unpow-1_binary64_9001 exp-lft-cube_binary64_9000 exp-cbrt_binary64_8998 rec-exp_binary64_8994 e-exp-1_binary64_8989 exp-0_binary64_8986 rem-log-exp_binary64_8985 rem-exp-log_binary64_8984 cube-mult_binary64_8974 cube-neg_binary64_8971 rem-3cbrt-rft_binary64_8970 rem-3cbrt-lft_binary64_8969 rem-cbrt-cube_binary64_8968 rem-cube-cbrt_binary64_8967 sqr-abs_binary64_8959 rem-square-sqrt_binary64_8956 +-inverses_binary64_8923 lft-mult-inverse_binary64_8922 remove-double-div_binary64_8920 difference-of-sqr--1_binary64_8915 difference-of-sqr-1_binary64_8914 difference-of-squares_binary64_8913 distribute-lft-out--_binary64_8896 associate--l-_binary64_8882 associate--l+_binary64_8881
Counts
1 → 3
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11611
23711
37611
416811
539011
6120111
7289111

prune9.0ms (0.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New033
Fresh011
Picked000
Done000
Total044
Error
0.3b
Counts
4 → 4
Compiler

Compiled 49 to 34 computations (30.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(sinh.f64 y)
0.1b
(/.f64 x (sin.f64 x))
0.3b
(/.f64 (sinh.f64 y) (/.f64 x (sin.f64 x)))

rewrite116.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0.3b
Rules
84×times-frac_binary64_8950
53×add-cube-cbrt_binary64_8979 add-sqr-sqrt_binary64_8966 *-un-lft-identity_binary64_8944
16×associate-/r*_binary64_8888
10×add-exp-log_binary64_8982 add-cbrt-cube_binary64_8980
div-inv_binary64_8941 associate-/l*_binary64_8889
div-exp_binary64_8995 cbrt-undiv_binary64_8978
pow1_binary64_9005 add-log-exp_binary64_8983
frac-2neg_binary64_8955 clear-num_binary64_8943 sinh-def_binary64_9129
associate-/l/_binary64_8891 associate-/r/_binary64_8890
Counts
3 → 106
Calls

3 calls:

7.0ms
(/.f64 (sinh.f64 y) (/.f64 x (sin.f64 x)))
3.0ms
(/.f64 x (sin.f64 x))
1.0ms
(sinh.f64 y)
Compiler

Compiled 1727 to 394 computations (77.2% saved)

series491.0ms (4.8%)

Error
0.2b
Counts
3 → 21
Calls

3 calls:

335.0ms
(/.f64 (sinh.f64 y) (/.f64 x (sin.f64 x)))
73.0ms
(sinh.f64 y)
58.0ms
(/.f64 x (sin.f64 x))
Compiler

Compiled 826 to 573 computations (30.6% saved)

simplify278.0ms (2.7%)

Algorithm
egg-herbie
Rules
564×associate-/r/_binary64_8890
470×div-sub_binary64_8949
448×associate-*l/_binary64_8887
375×associate-*l*_binary64_8885
341×associate-/r*_binary64_8888
316×*-commutative_binary64_8875
315×associate-*r/_binary64_8886
233×associate-*r*_binary64_8884
159×associate-/l/_binary64_8891
137×associate-/l*_binary64_8889
60×cancel-sign-sub-inv_binary64_8910
56×+-commutative_binary64_8874
53×associate-+l+_binary64_8877
44×log-div_binary64_9031
43×distribute-rgt-neg-in_binary64_8902
42×times-frac_binary64_8950
40×sub-neg_binary64_8937
39×exp-prod_binary64_8996 *-rgt-identity_binary64_8934
37×cube-div_binary64_8973 associate-+r+_binary64_8876
35×log-prod_binary64_9030
31×/-rgt-identity_binary64_8935 sqr-pow_binary64_8916
30×distribute-lft-neg-in_binary64_8901
29×neg-sub0_binary64_8939
28×div-exp_binary64_8995 neg-mul-1_binary64_8940
27×cube-prod_binary64_8972
25×prod-exp_binary64_8993
21×distribute-rgt-in_binary64_8894
20×unswap-sqr_binary64_8912
18×distribute-neg-frac_binary64_8908
17×exp-sqrt_binary64_8997 associate-+l-_binary64_8879
16×distribute-lft-in_binary64_8893
13×distribute-lft-neg-out_binary64_8903 associate-+r-_binary64_8878
12×pow-sqr_binary64_8917
11×exp-diff_binary64_8992 cube-unmult_binary64_8981
10×distribute-rgt-out_binary64_8897 associate--r+_binary64_8880
pow-plus_binary64_9007 *-lft-identity_binary64_8933
distribute-neg-in_binary64_8905 distribute-rgt-out--_binary64_8898 associate--l+_binary64_8881
unpow3_binary64_9010 rec-exp_binary64_8994 associate--l-_binary64_8882
log-pow_binary64_9033 exp-lft-sqr_binary64_8999 exp-sum_binary64_8990 cube-mult_binary64_8974 distribute-lft-out--_binary64_8896
unsub-neg_binary64_8938 swap-sqr_binary64_8911 associate--r-_binary64_8883
mul-1-neg_binary64_8936 remove-double-div_binary64_8920
sinh-def_binary64_9129 log-rec_binary64_9032 unpow2_binary64_9009 pow-base-1_binary64_9004 unpow1_binary64_9002 exp-neg_binary64_8991 1-exp_binary64_8988 exp-1-e_binary64_8987 rem-log-exp_binary64_8985 rem-sqrt-square_binary64_8957 remove-double-neg_binary64_8932 div0_binary64_8925 *-inverses_binary64_8924 distribute-rgt-neg-out_binary64_8904 distribute-rgt1-in_binary64_8900 distribute-lft-out_binary64_8895 count-2_binary64_8892
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_9207 erf-erfc_binary64_9206 erf-odd_binary64_9205 if-if-and-not_binary64_9204 if-if-and_binary64_9203 if-if-or-not_binary64_9202 if-if-or_binary64_9201 if-not_binary64_9200 if-same_binary64_9199 if-false_binary64_9198 if-true_binary64_9197 not-gte_binary64_9196 not-lte_binary64_9195 not-gt_binary64_9194 not-lt_binary64_9193 gte-same_binary64_9192 lte-same_binary64_9191 gt-same_binary64_9190 lt-same_binary64_9189 sinh---cosh_binary64_9136 sinh-+-cosh_binary64_9135 sinh-cosh_binary64_9134 tanh-def-c_binary64_9133 tanh-def-b_binary64_9132 tanh-def-a_binary64_9131 cosh-def_binary64_9130 tan-neg_binary64_9076 cos-neg_binary64_9075 sin-neg_binary64_9074 tan-0_binary64_9073 cos-0_binary64_9072 sin-0_binary64_9071 hang-m-tan_binary64_9070 hang-p-tan_binary64_9069 hang-m0-tan_binary64_9068 hang-p0-tan_binary64_9067 hang-0m-tan_binary64_9066 hang-0p-tan_binary64_9065 tan-+PI/2_binary64_9064 tan-+PI_binary64_9063 tan-PI_binary64_9062 tan-PI/3_binary64_9061 tan-PI/4_binary64_9060 tan-PI/6_binary64_9059 cos-+PI/2_binary64_9058 cos-+PI_binary64_9057 cos-PI_binary64_9056 cos-PI/2_binary64_9055 cos-PI/3_binary64_9054 cos-PI/4_binary64_9053 cos-PI/6_binary64_9052 sin-+PI/2_binary64_9051 sin-+PI_binary64_9050 sin-PI_binary64_9049 sin-PI/2_binary64_9048 sin-PI/3_binary64_9047 sin-PI/4_binary64_9046 sin-PI/6_binary64_9045 sub-1-sin_binary64_9044 sub-1-cos_binary64_9043 -1-add-sin_binary64_9042 -1-add-cos_binary64_9041 1-sub-sin_binary64_9040 1-sub-cos_binary64_9039 cos-sin-sum_binary64_9038 log-E_binary64_9034 pow-base-0_binary64_9028 unpow1/3_binary64_9011 unpow1/2_binary64_9008 exp-to-pow_binary64_9006 unpow0_binary64_9003 unpow-1_binary64_9001 exp-lft-cube_binary64_9000 exp-cbrt_binary64_8998 e-exp-1_binary64_8989 exp-0_binary64_8986 rem-exp-log_binary64_8984 cube-neg_binary64_8971 rem-3cbrt-rft_binary64_8970 rem-3cbrt-lft_binary64_8969 rem-cbrt-cube_binary64_8968 rem-cube-cbrt_binary64_8967 sqr-abs_binary64_8959 sqr-neg_binary64_8958 rem-square-sqrt_binary64_8956 sub0-neg_binary64_8931 --rgt-identity_binary64_8930 +-rgt-identity_binary64_8929 +-lft-identity_binary64_8928 mul0-rgt_binary64_8927 mul0-lft_binary64_8926 +-inverses_binary64_8923 lft-mult-inverse_binary64_8922 rgt-mult-inverse_binary64_8921 difference-of-sqr--1_binary64_8915 difference-of-sqr-1_binary64_8914 difference-of-squares_binary64_8913 cancel-sign-sub_binary64_8909 distribute-frac-neg_binary64_8907 distribute-neg-out_binary64_8906 distribute-lft1-in_binary64_8899
Counts
127 → 333
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02372531
15282411
217232396
343962396

prune535.0ms (5.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3312333
Fresh123
Picked011
Done000
Total3325337
Error
0.2b
Counts
337 → 5
Compiler

Compiled 6669 to 1196 computations (82.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b
(sinh.f64 y)
0.3b
(/.f64 (sinh.f64 y) x)
0.4b
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) x))

rewrite68.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
24×add-sqr-sqrt_binary64_8966
19×add-cube-cbrt_binary64_8979 *-un-lft-identity_binary64_8944 times-frac_binary64_8950
13×associate-*r*_binary64_8884
10×add-exp-log_binary64_8982 add-cbrt-cube_binary64_8980
pow1_binary64_9005
add-log-exp_binary64_8983 associate-*l*_binary64_8885 associate-/l*_binary64_8889 associate-/r*_binary64_8888
div-exp_binary64_8995 prod-exp_binary64_8993 cbrt-unprod_binary64_8977 cbrt-undiv_binary64_8978 unswap-sqr_binary64_8912 div-inv_binary64_8941 sinh-def_binary64_9129
pow-prod-down_binary64_9015 associate-*r/_binary64_8886 *-commutative_binary64_8875 frac-2neg_binary64_8955 clear-num_binary64_8943 associate-/l/_binary64_8891
Counts
3 → 68
Calls

3 calls:

8.0ms
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) x))
3.0ms
(/.f64 (sinh.f64 y) x)
1.0ms
(sinh.f64 y)
Compiler

Compiled 942 to 237 computations (74.8% saved)

series651.0ms (6.4%)

Error
0.2b
Counts
3 → 25
Calls

3 calls:

344.0ms
(*.f64 (sin.f64 x) (/.f64 (sinh.f64 y) x))
216.0ms
(/.f64 (sinh.f64 y) x)
66.0ms
(sinh.f64 y)
Compiler

Compiled 1062 to 731 computations (31.2% saved)

simplify245.0ms (2.4%)

Algorithm
egg-herbie
Rules
472×associate-/l*_binary64_8889
412×associate-*l/_binary64_8887
397×associate-*l*_binary64_8885
370×associate-*r/_binary64_8886
329×associate-*r*_binary64_8884
293×div-sub_binary64_8949
278×times-frac_binary64_8950
247×associate-/l/_binary64_8891
198×associate-/r/_binary64_8890
162×*-commutative_binary64_8875
144×associate-/r*_binary64_8888
74×associate-+l+_binary64_8877
65×log-div_binary64_9031 +-commutative_binary64_8874
59×cancel-sign-sub-inv_binary64_8910
57×cube-div_binary64_8973
51×associate-+r+_binary64_8876
49×distribute-rgt-neg-in_binary64_8902
46×log-prod_binary64_9030 exp-prod_binary64_8996
42×sub-neg_binary64_8937
34×distribute-lft-neg-in_binary64_8901
33×cube-prod_binary64_8972
31×neg-sub0_binary64_8939
30×distribute-neg-frac_binary64_8908 distribute-rgt-in_binary64_8894
29×sqr-pow_binary64_8916
28×neg-mul-1_binary64_8940
26×distribute-lft-in_binary64_8893
25×prod-exp_binary64_8993 *-rgt-identity_binary64_8934 *-lft-identity_binary64_8933
24×associate-+l-_binary64_8879
23×exp-sqrt_binary64_8997
18×div-exp_binary64_8995
17×unswap-sqr_binary64_8912
15×associate-+r-_binary64_8878
14×distribute-lft-neg-out_binary64_8903
12×/-rgt-identity_binary64_8935
10×log-rec_binary64_9032 exp-diff_binary64_8992 cube-unmult_binary64_8981 pow-sqr_binary64_8917 associate--r+_binary64_8880
associate--l+_binary64_8881
unpow3_binary64_9010 exp-sum_binary64_8990 distribute-neg-in_binary64_8905
pow-plus_binary64_9007 cube-mult_binary64_8974 distribute-rgt-out--_binary64_8898
rec-exp_binary64_8994 mul-1-neg_binary64_8936 distribute-lft-out--_binary64_8896
exp-lft-sqr_binary64_8999 swap-sqr_binary64_8911 associate--l-_binary64_8882
associate--r-_binary64_8883
log-pow_binary64_9033 unsub-neg_binary64_8938 distribute-rgt-out_binary64_8897
sinh-def_binary64_9129 unpow2_binary64_9009 unpow1_binary64_9002 exp-neg_binary64_8991 1-exp_binary64_8988 exp-1-e_binary64_8987 rem-log-exp_binary64_8985 rem-sqrt-square_binary64_8957 *-inverses_binary64_8924 distribute-rgt-neg-out_binary64_8904 distribute-rgt1-in_binary64_8900 distribute-lft-out_binary64_8895
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_9207 erf-erfc_binary64_9206 erf-odd_binary64_9205 if-if-and-not_binary64_9204 if-if-and_binary64_9203 if-if-or-not_binary64_9202 if-if-or_binary64_9201 if-not_binary64_9200 if-same_binary64_9199 if-false_binary64_9198 if-true_binary64_9197 not-gte_binary64_9196 not-lte_binary64_9195 not-gt_binary64_9194 not-lt_binary64_9193 gte-same_binary64_9192 lte-same_binary64_9191 gt-same_binary64_9190 lt-same_binary64_9189 sinh---cosh_binary64_9136 sinh-+-cosh_binary64_9135 sinh-cosh_binary64_9134 tanh-def-c_binary64_9133 tanh-def-b_binary64_9132 tanh-def-a_binary64_9131 cosh-def_binary64_9130 tan-neg_binary64_9076 cos-neg_binary64_9075 sin-neg_binary64_9074 tan-0_binary64_9073 cos-0_binary64_9072 sin-0_binary64_9071 hang-m-tan_binary64_9070 hang-p-tan_binary64_9069 hang-m0-tan_binary64_9068 hang-p0-tan_binary64_9067 hang-0m-tan_binary64_9066 hang-0p-tan_binary64_9065 tan-+PI/2_binary64_9064 tan-+PI_binary64_9063 tan-PI_binary64_9062 tan-PI/3_binary64_9061 tan-PI/4_binary64_9060 tan-PI/6_binary64_9059 cos-+PI/2_binary64_9058 cos-+PI_binary64_9057 cos-PI_binary64_9056 cos-PI/2_binary64_9055 cos-PI/3_binary64_9054 cos-PI/4_binary64_9053 cos-PI/6_binary64_9052 sin-+PI/2_binary64_9051 sin-+PI_binary64_9050 sin-PI_binary64_9049 sin-PI/2_binary64_9048 sin-PI/3_binary64_9047 sin-PI/4_binary64_9046 sin-PI/6_binary64_9045 sub-1-sin_binary64_9044 sub-1-cos_binary64_9043 -1-add-sin_binary64_9042 -1-add-cos_binary64_9041 1-sub-sin_binary64_9040 1-sub-cos_binary64_9039 cos-sin-sum_binary64_9038 log-E_binary64_9034 pow-base-0_binary64_9028 unpow1/3_binary64_9011 unpow1/2_binary64_9008 exp-to-pow_binary64_9006 pow-base-1_binary64_9004 unpow0_binary64_9003 unpow-1_binary64_9001 exp-lft-cube_binary64_9000 exp-cbrt_binary64_8998 e-exp-1_binary64_8989 exp-0_binary64_8986 rem-exp-log_binary64_8984 cube-neg_binary64_8971 rem-3cbrt-rft_binary64_8970 rem-3cbrt-lft_binary64_8969 rem-cbrt-cube_binary64_8968 rem-cube-cbrt_binary64_8967 sqr-abs_binary64_8959 sqr-neg_binary64_8958 rem-square-sqrt_binary64_8956 remove-double-neg_binary64_8932 sub0-neg_binary64_8931 --rgt-identity_binary64_8930 +-rgt-identity_binary64_8929 +-lft-identity_binary64_8928 mul0-rgt_binary64_8927 mul0-lft_binary64_8926 div0_binary64_8925 +-inverses_binary64_8923 lft-mult-inverse_binary64_8922 rgt-mult-inverse_binary64_8921 remove-double-div_binary64_8920 difference-of-sqr--1_binary64_8915 difference-of-sqr-1_binary64_8914 difference-of-squares_binary64_8913 cancel-sign-sub_binary64_8909 distribute-frac-neg_binary64_8907 distribute-neg-out_binary64_8906 distribute-lft1-in_binary64_8899 count-2_binary64_8892
Counts
93 → 105
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01791500
14211375
213441333
342761333

prune103.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1050105
Fresh033
Picked011
Done011
Total1055110
Error
0.2b
Counts
110 → 5
Compiler

Compiled 1899 to 712 computations (62.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (sin.f64 x) x)
0.1b
(/.f64 (sin.f64 x) x)
0.1b
(/.f64 (sin.f64 x) x)
0.1b
(/.f64 (sin.f64 x) x)

rewrite265.0ms (2.6%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
36×add-cube-cbrt_binary64_8979 add-sqr-sqrt_binary64_8966 times-frac_binary64_8950 *-un-lft-identity_binary64_8944
12×add-exp-log_binary64_8982 add-cbrt-cube_binary64_8980 associate-/l*_binary64_8889 associate-/r*_binary64_8888
pow1_binary64_9005 div-exp_binary64_8995 add-log-exp_binary64_8983 cbrt-undiv_binary64_8978 frac-2neg_binary64_8955 clear-num_binary64_8943 div-inv_binary64_8941
Counts
4 → 108
Calls

4 calls:

4.0ms
(/.f64 (sin.f64 x) x)
4.0ms
(/.f64 (sin.f64 x) x)
4.0ms
(/.f64 (sin.f64 x) x)
4.0ms
(/.f64 (sin.f64 x) x)
Compiler

Compiled 4912 to 2150 computations (56.2% saved)

series241.0ms (2.4%)

Error
0.2b
Counts
4 → 17
Calls

4 calls:

55.0ms
(/.f64 (sin.f64 x) x)
54.0ms
(/.f64 (sin.f64 x) x)
53.0ms
(/.f64 (sin.f64 x) x)
47.0ms
(/.f64 (sin.f64 x) x)
Compiler

Compiled 1854 to 1108 computations (40.2% saved)

simplify226.0ms (2.2%)

Algorithm
egg-herbie
Rules
490×distribute-rgt-in_binary64_8894
341×associate-/l*_binary64_8889
294×associate-/l/_binary64_8891
246×div-sub_binary64_8949
221×associate-*l*_binary64_8885
220×associate-/r/_binary64_8890
212×cancel-sign-sub-inv_binary64_8910
208×associate-/r*_binary64_8888
181×associate-*l/_binary64_8887
166×associate-*r*_binary64_8884
149×associate-*r/_binary64_8886
107×distribute-rgt-neg-in_binary64_8902
88×distribute-lft-neg-in_binary64_8901
81×unswap-sqr_binary64_8912
76×*-commutative_binary64_8875
72×sub-neg_binary64_8937
66×log-div_binary64_9031
65×times-frac_binary64_8950
59×log-prod_binary64_9030
57×cube-div_binary64_8973
54×distribute-rgt-out_binary64_8897
53×swap-sqr_binary64_8911
51×cube-prod_binary64_8972
48×sqr-pow_binary64_8916
45×distribute-neg-frac_binary64_8908
41×distribute-rgt-out--_binary64_8898
30×neg-mul-1_binary64_8940 neg-sub0_binary64_8939 *-lft-identity_binary64_8933
29×unsub-neg_binary64_8938 distribute-lft-out_binary64_8895
25×pow-sqr_binary64_8917
24×distribute-lft-neg-out_binary64_8903
23×exp-prod_binary64_8996
21×*-rgt-identity_binary64_8934
20×distribute-neg-in_binary64_8905
19×associate--l-_binary64_8882 associate-+l-_binary64_8879
16×sub0-neg_binary64_8931
15×/-rgt-identity_binary64_8935 distribute-rgt-neg-out_binary64_8904 +-commutative_binary64_8874
14×pow-plus_binary64_9007
11×log-rec_binary64_9032 cube-unmult_binary64_8981
10×distribute-neg-out_binary64_8906 distribute-lft-out--_binary64_8896 associate-+r-_binary64_8878
div-exp_binary64_8995 prod-exp_binary64_8993 +-lft-identity_binary64_8928 distribute-rgt1-in_binary64_8900
log-pow_binary64_9033
unpow3_binary64_9010 exp-sqrt_binary64_8997
exp-lft-sqr_binary64_8999 distribute-lft-in_binary64_8893
exp-diff_binary64_8992 cube-mult_binary64_8974 remove-double-div_binary64_8920 associate--r-_binary64_8883
exp-to-pow_binary64_9006 exp-sum_binary64_8990 distribute-frac-neg_binary64_8907
rec-exp_binary64_8994 rem-sqrt-square_binary64_8957 +-rgt-identity_binary64_8929 mul0-rgt_binary64_8927 mul0-lft_binary64_8926 associate--l+_binary64_8881 associate--r+_binary64_8880 associate-+l+_binary64_8877
--rgt-identity_binary64_8930 div0_binary64_8925 count-2_binary64_8892 associate-+r+_binary64_8876
unpow2_binary64_9009 pow-base-1_binary64_9004 unpow1_binary64_9002 1-exp_binary64_8988 rem-log-exp_binary64_8985 rem-exp-log_binary64_8984 sqr-neg_binary64_8958 *-inverses_binary64_8924 +-inverses_binary64_8923 rgt-mult-inverse_binary64_8921 distribute-lft1-in_binary64_8899
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_9207 erf-erfc_binary64_9206 erf-odd_binary64_9205 if-if-and-not_binary64_9204 if-if-and_binary64_9203 if-if-or-not_binary64_9202 if-if-or_binary64_9201 if-not_binary64_9200 if-same_binary64_9199 if-false_binary64_9198 if-true_binary64_9197 not-gte_binary64_9196 not-lte_binary64_9195 not-gt_binary64_9194 not-lt_binary64_9193 gte-same_binary64_9192 lte-same_binary64_9191 gt-same_binary64_9190 lt-same_binary64_9189 sinh---cosh_binary64_9136 sinh-+-cosh_binary64_9135 sinh-cosh_binary64_9134 tanh-def-c_binary64_9133 tanh-def-b_binary64_9132 tanh-def-a_binary64_9131 cosh-def_binary64_9130 sinh-def_binary64_9129 tan-neg_binary64_9076 cos-neg_binary64_9075 sin-neg_binary64_9074 tan-0_binary64_9073 cos-0_binary64_9072 sin-0_binary64_9071 hang-m-tan_binary64_9070 hang-p-tan_binary64_9069 hang-m0-tan_binary64_9068 hang-p0-tan_binary64_9067 hang-0m-tan_binary64_9066 hang-0p-tan_binary64_9065 tan-+PI/2_binary64_9064 tan-+PI_binary64_9063 tan-PI_binary64_9062 tan-PI/3_binary64_9061 tan-PI/4_binary64_9060 tan-PI/6_binary64_9059 cos-+PI/2_binary64_9058 cos-+PI_binary64_9057 cos-PI_binary64_9056 cos-PI/2_binary64_9055 cos-PI/3_binary64_9054 cos-PI/4_binary64_9053 cos-PI/6_binary64_9052 sin-+PI/2_binary64_9051 sin-+PI_binary64_9050 sin-PI_binary64_9049 sin-PI/2_binary64_9048 sin-PI/3_binary64_9047 sin-PI/4_binary64_9046 sin-PI/6_binary64_9045 sub-1-sin_binary64_9044 sub-1-cos_binary64_9043 -1-add-sin_binary64_9042 -1-add-cos_binary64_9041 1-sub-sin_binary64_9040 1-sub-cos_binary64_9039 cos-sin-sum_binary64_9038 log-E_binary64_9034 pow-base-0_binary64_9028 unpow1/3_binary64_9011 unpow1/2_binary64_9008 unpow0_binary64_9003 unpow-1_binary64_9001 exp-lft-cube_binary64_9000 exp-cbrt_binary64_8998 exp-neg_binary64_8991 e-exp-1_binary64_8989 exp-1-e_binary64_8987 exp-0_binary64_8986 cube-neg_binary64_8971 rem-3cbrt-rft_binary64_8970 rem-3cbrt-lft_binary64_8969 rem-cbrt-cube_binary64_8968 rem-cube-cbrt_binary64_8967 sqr-abs_binary64_8959 rem-square-sqrt_binary64_8956 mul-1-neg_binary64_8936 remove-double-neg_binary64_8932 lft-mult-inverse_binary64_8922 difference-of-sqr--1_binary64_8915 difference-of-sqr-1_binary64_8914 difference-of-squares_binary64_8913 cancel-sign-sub_binary64_8909
Counts
125 → 59
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0611515
11151411
22661411
35681411
427391411

prune132.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New58159
Fresh022
Picked101
Done022
Total59564
Error
0.2b
Counts
64 → 5
Compiler

Compiled 2843 to 1243 computations (56.3% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b
(/.f64 (sin.f64 x) (/.f64 x y))
1.6b
(/.f64 (*.f64 (sin.f64 x) (pow.f64 y 7)) x)
2.6b
(/.f64 x (pow.f64 y 5))
5.5b
(/.f64 x (pow.f64 y 3))

rewrite589.0ms (5.8%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
135×times-frac_binary64_8950
89×add-cube-cbrt_binary64_8979 add-sqr-sqrt_binary64_8966 *-un-lft-identity_binary64_8944
35×associate-/r*_binary64_8888
29×add-exp-log_binary64_8982
24×unpow-prod-down_binary64_9023
18×add-cbrt-cube_binary64_8980
13×div-exp_binary64_8995
12×cube-prod_binary64_8972
10×associate-/l*_binary64_8889
sqr-pow_binary64_8916 div-inv_binary64_8941
cbrt-undiv_binary64_8978
pow1_binary64_9005 add-log-exp_binary64_8983 frac-2neg_binary64_8955 unpow3_binary64_9010 cube-mult_binary64_8974 clear-num_binary64_8943
pow-to-exp_binary64_9013 pow-exp_binary64_9012 prod-exp_binary64_8993
cbrt-unprod_binary64_8977 associate-/r/_binary64_8890
Counts
4 → 203
Calls

4 calls:

7.0ms
(/.f64 (sin.f64 x) (/.f64 x y))
6.0ms
(/.f64 (*.f64 (sin.f64 x) (pow.f64 y 7)) x)
6.0ms
(/.f64 x (pow.f64 y 3))
5.0ms
(/.f64 x (pow.f64 y 5))
Compiler

Compiled 9650 to 5097 computations (47.2% saved)

series809.0ms (8%)

Error
0.2b
Counts
4 → 27
Calls

4 calls:

266.0ms
(/.f64 (*.f64 (sin.f64 x) (pow.f64 y 7)) x)
180.0ms
(/.f64 x (pow.f64 y 5))
166.0ms
(/.f64 (sin.f64 x) (/.f64 x y))
149.0ms
(/.f64 x (pow.f64 y 3))
Compiler

Compiled 3094 to 1968 computations (36.4% saved)

simplify394.0ms (3.9%)

Algorithm
egg-herbie
Rules
243×unswap-sqr_binary64_8912 associate-/l*_binary64_8889
240×log-prod_binary64_9030
236×sqr-pow_binary64_8916
212×associate-/l/_binary64_8891
210×associate-/r*_binary64_8888
183×times-frac_binary64_8950
174×associate-/r/_binary64_8890
165×cube-prod_binary64_8972
156×pow-sqr_binary64_8917
152×associate-*r*_binary64_8884
133×associate-*l/_binary64_8887
126×sub-neg_binary64_8937
116×log-div_binary64_9031
99×neg-mul-1_binary64_8940 associate-*l*_binary64_8885
96×distribute-rgt-neg-in_binary64_8902 *-commutative_binary64_8875
93×neg-sub0_binary64_8939
89×distribute-lft-neg-in_binary64_8901
85×cube-div_binary64_8973
79×associate-*r/_binary64_8886
78×cancel-sign-sub-inv_binary64_8910
71×log-pow_binary64_9033
62×*-rgt-identity_binary64_8934
55×pow-plus_binary64_9007
52×unpow3_binary64_9010
47×/-rgt-identity_binary64_8935
40×cube-mult_binary64_8974
35×exp-prod_binary64_8996
34×div-sub_binary64_8949 unsub-neg_binary64_8938 swap-sqr_binary64_8911
29×cube-unmult_binary64_8981
26×+-commutative_binary64_8874
25×distribute-rgt-in_binary64_8894
21×distribute-lft-in_binary64_8893
19×rem-sqrt-square_binary64_8957 *-lft-identity_binary64_8933
16×log-rec_binary64_9032 div-exp_binary64_8995 prod-exp_binary64_8993 associate--r+_binary64_8880 associate-+l-_binary64_8879
15×distribute-neg-frac_binary64_8908 associate-+l+_binary64_8877
14×pow-base-1_binary64_9004
13×distribute-rgt-out_binary64_8897
12×sub0-neg_binary64_8931
11×associate-+r-_binary64_8878 associate-+r+_binary64_8876
10×distribute-rgt-out--_binary64_8898
distribute-neg-in_binary64_8905 associate--l-_binary64_8882 associate--l+_binary64_8881
distribute-lft-neg-out_binary64_8903
div0_binary64_8925 count-2_binary64_8892
rec-exp_binary64_8994 +-rgt-identity_binary64_8929 +-lft-identity_binary64_8928 associate--r-_binary64_8883
remove-double-div_binary64_8920 distribute-frac-neg_binary64_8907 distribute-rgt1-in_binary64_8900
remove-double-neg_binary64_8932
unpow2_binary64_9009 unpow1_binary64_9002 exp-diff_binary64_8992 1-exp_binary64_8988 rem-log-exp_binary64_8985 rem-cbrt-cube_binary64_8968 rem-cube-cbrt_binary64_8967 rem-square-sqrt_binary64_8956 mul0-rgt_binary64_8927 mul0-lft_binary64_8926 *-inverses_binary64_8924 rgt-mult-inverse_binary64_8921
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_9207 erf-erfc_binary64_9206 erf-odd_binary64_9205 if-if-and-not_binary64_9204 if-if-and_binary64_9203 if-if-or-not_binary64_9202 if-if-or_binary64_9201 if-not_binary64_9200 if-same_binary64_9199 if-false_binary64_9198 if-true_binary64_9197 not-gte_binary64_9196 not-lte_binary64_9195 not-gt_binary64_9194 not-lt_binary64_9193 gte-same_binary64_9192 lte-same_binary64_9191 gt-same_binary64_9190 lt-same_binary64_9189 sinh---cosh_binary64_9136 sinh-+-cosh_binary64_9135 sinh-cosh_binary64_9134 tanh-def-c_binary64_9133 tanh-def-b_binary64_9132 tanh-def-a_binary64_9131 cosh-def_binary64_9130 sinh-def_binary64_9129 tan-neg_binary64_9076 cos-neg_binary64_9075 sin-neg_binary64_9074 tan-0_binary64_9073 cos-0_binary64_9072 sin-0_binary64_9071 hang-m-tan_binary64_9070 hang-p-tan_binary64_9069 hang-m0-tan_binary64_9068 hang-p0-tan_binary64_9067 hang-0m-tan_binary64_9066 hang-0p-tan_binary64_9065 tan-+PI/2_binary64_9064 tan-+PI_binary64_9063 tan-PI_binary64_9062 tan-PI/3_binary64_9061 tan-PI/4_binary64_9060 tan-PI/6_binary64_9059 cos-+PI/2_binary64_9058 cos-+PI_binary64_9057 cos-PI_binary64_9056 cos-PI/2_binary64_9055 cos-PI/3_binary64_9054 cos-PI/4_binary64_9053 cos-PI/6_binary64_9052 sin-+PI/2_binary64_9051 sin-+PI_binary64_9050 sin-PI_binary64_9049 sin-PI/2_binary64_9048 sin-PI/3_binary64_9047 sin-PI/4_binary64_9046 sin-PI/6_binary64_9045 sub-1-sin_binary64_9044 sub-1-cos_binary64_9043 -1-add-sin_binary64_9042 -1-add-cos_binary64_9041 1-sub-sin_binary64_9040 1-sub-cos_binary64_9039 cos-sin-sum_binary64_9038 log-E_binary64_9034 pow-base-0_binary64_9028 unpow1/3_binary64_9011 unpow1/2_binary64_9008 exp-to-pow_binary64_9006 unpow0_binary64_9003 unpow-1_binary64_9001 exp-lft-cube_binary64_9000 exp-lft-sqr_binary64_8999 exp-cbrt_binary64_8998 exp-sqrt_binary64_8997 exp-neg_binary64_8991 exp-sum_binary64_8990 e-exp-1_binary64_8989 exp-1-e_binary64_8987 exp-0_binary64_8986 rem-exp-log_binary64_8984 cube-neg_binary64_8971 rem-3cbrt-rft_binary64_8970 rem-3cbrt-lft_binary64_8969 sqr-abs_binary64_8959 sqr-neg_binary64_8958 mul-1-neg_binary64_8936 --rgt-identity_binary64_8930 +-inverses_binary64_8923 lft-mult-inverse_binary64_8922 difference-of-sqr--1_binary64_8915 difference-of-sqr-1_binary64_8914 difference-of-squares_binary64_8913 cancel-sign-sub_binary64_8909 distribute-neg-out_binary64_8906 distribute-rgt-neg-out_binary64_8904 distribute-lft1-in_binary64_8899 distribute-lft-out--_binary64_8896 distribute-lft-out_binary64_8895
Counts
230 → 441
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03443711
16803501
227473497
339433497

prune1.4s (14.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New4410441
Fresh022
Picked011
Done022
Total4415446
Error
0.2b
Counts
446 → 5
Compiler

Compiled 21506 to 10346 computations (51.9% saved)

regimes360.0ms (3.5%)

Accuracy

Total 0.1b remaining (82.9%)

Threshold costs 0.1b (82.9%)

Compiler

Compiled 3470 to 2402 computations (30.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
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_9204 if-if-and_binary64_9203 if-if-or-not_binary64_9202 if-if-or_binary64_9201 if-not_binary64_9200 if-same_binary64_9199 if-false_binary64_9198 if-true_binary64_9197 tan-0_binary64_9073 cos-0_binary64_9072 sin-0_binary64_9071 unpow1_binary64_9002 e-exp-1_binary64_8989 1-exp_binary64_8988 exp-1-e_binary64_8987 exp-0_binary64_8986 sqr-abs_binary64_8959 sqr-neg_binary64_8958 neg-mul-1_binary64_8940 neg-sub0_binary64_8939 unsub-neg_binary64_8938 sub-neg_binary64_8937 mul-1-neg_binary64_8936 /-rgt-identity_binary64_8935 *-rgt-identity_binary64_8934 *-lft-identity_binary64_8933 remove-double-neg_binary64_8932 sub0-neg_binary64_8931 --rgt-identity_binary64_8930 +-rgt-identity_binary64_8929 +-lft-identity_binary64_8928 cancel-sign-sub-inv_binary64_8910 cancel-sign-sub_binary64_8909 distribute-neg-frac_binary64_8908 distribute-frac-neg_binary64_8907 distribute-neg-out_binary64_8906 distribute-neg-in_binary64_8905 distribute-rgt-neg-out_binary64_8904 distribute-lft-neg-out_binary64_8903 distribute-rgt-neg-in_binary64_8902 distribute-lft-neg-in_binary64_8901 *-commutative_binary64_8875 +-commutative_binary64_8874
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
Proof
(/ f64 (sinh f64 h0) (/ f64 h1 (sin f64 h1)))

end0.0ms (0%)

sample2.4s (23.5%)

Algorithm
intervals
Results
365.0ms1958×body1024invalid
309.0ms6255×body128valid
151.0ms1059×body512invalid
150.0ms644×body1024valid
95.0ms664×body512valid
42.0ms442×body256invalid
41.0ms437×body256valid
40.0ms716×body128invalid
Compiler

Compiled 884 to 615 computations (30.4% saved)

Profiling

Loading profile data...