Details

analyze759.0ms (16.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	35.7%	19.8%	13
45.5%	34.4%	20.1%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample364.0ms (8%)

Algorithm

1×

intervals

Results

275.0ms	63×	body	2048	valid
46.0ms	77×	body	1024	valid
10.0ms	36×	body	512	valid
5.0ms	62×	body	128	valid
3.0ms	7×	body	512	invalid
3.0ms	17×	body	256	valid
3.0ms	4×	body	1024	invalid
2.0ms	16×	body	128	invalid
2.0ms	1×	body	4096	valid
1.0ms	1×	body	2048	invalid
1.0ms	3×	body	256	invalid
0.0ms	6×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify135.0ms (3%)

Algorithm

1×	egg-herbie

Rules

570×	`associate-/r/_binary64_3775`
510×	`associate-*l/_binary64_3772`
493×	`associate-/r*_binary64_3773`
443×	`associate-/l/_binary64_3776`
243×	`associate-l_binary64_3770`
236×	`associate-r_binary64_3769`
175×	`cancel-sign-sub-inv_binary64_3795`
139×	`associate-/l*_binary64_3774`
131×	`distribute-rgt-in_binary64_3779`
130×	`distribute-rgt-neg-in_binary64_3787`
123×	`distribute-lft-in_binary64_3778`
105×	`distribute-lft-neg-in_binary64_3786`
88×	`*-commutative_binary64_3760`
72×	`unswap-sqr_binary64_3797`
62×	`times-frac_binary64_3835`
55×	`div-sub_binary64_3834`
53×	`distribute-lft-neg-out_binary64_3788`
50×	`distribute-neg-frac_binary64_3793`
47×	`associate-*r/_binary64_3771`
46×	`distribute-rgt-out_binary64_3782`
43×	`sub-neg_binary64_3822`
42×	`distribute-rgt-neg-out_binary64_3789`
38×	`unsub-neg_binary64_3823`
35×	`neg-mul-1_binary64_3825` `neg-sub0_binary64_3824`
28×	`distribute-lft-out_binary64_3780`
26×	`*-rgt-identity_binary64_3819`
23×	`*-lft-identity_binary64_3818`
18×	`sqr-pow_binary64_3801`
17×	`distribute-neg-in_binary64_3790`
14×	`distribute-frac-neg_binary64_3792` `+-commutative_binary64_3759`
12×	`mul-1-neg_binary64_3821` `pow-sqr_binary64_3802`
11×	`associate-+r+_binary64_3761`
10×	`distribute-rgt-out--_binary64_3783`
7×	`associate-+r-_binary64_3763`
6×	`/-rgt-identity_binary64_3820` `associate-+l-_binary64_3764`
5×	`+-rgt-identity_binary64_3814` `mul0-rgt_binary64_3812` `difference-of-sqr-1_binary64_3799`
4×	`cube-unmult_binary64_3866` `sub0-neg_binary64_3816` `div0_binary64_3810`
3×	`+-lft-identity_binary64_3813` `associate--r+_binary64_3765`
2×	`pow-plus_binary64_3892` `cube-prod_binary64_3857` `mul0-lft_binary64_3811` `difference-of-sqr--1_binary64_3800` `distribute-lft-out--_binary64_3781` `associate-+l+_binary64_3762`
1×	`1-exp_binary64_3873` `remove-double-neg_binary64_3817` `--rgt-identity_binary64_3815` `*-inverses_binary64_3809` `count-2_binary64_3777`
0×	`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_4092` `erf-erfc_binary64_4091` `erf-odd_binary64_4090` `if-if-and-not_binary64_4089` `if-if-and_binary64_4088` `if-if-or-not_binary64_4087` `if-if-or_binary64_4086` `if-not_binary64_4085` `if-same_binary64_4084` `if-false_binary64_4083` `if-true_binary64_4082` `not-gte_binary64_4081` `not-lte_binary64_4080` `not-gt_binary64_4079` `not-lt_binary64_4078` `gte-same_binary64_4077` `lte-same_binary64_4076` `gt-same_binary64_4075` `lt-same_binary64_4074` `sinh---cosh_binary64_4021` `sinh-+-cosh_binary64_4020` `sinh-cosh_binary64_4019` `tanh-def-c_binary64_4018` `tanh-def-b_binary64_4017` `tanh-def-a_binary64_4016` `cosh-def_binary64_4015` `sinh-def_binary64_4014` `tan-neg_binary64_3961` `cos-neg_binary64_3960` `sin-neg_binary64_3959` `tan-0_binary64_3958` `cos-0_binary64_3957` `sin-0_binary64_3956` `hang-m-tan_binary64_3955` `hang-p-tan_binary64_3954` `hang-m0-tan_binary64_3953` `hang-p0-tan_binary64_3952` `hang-0m-tan_binary64_3951` `hang-0p-tan_binary64_3950` `tan-+PI/2_binary64_3949` `tan-+PI_binary64_3948` `tan-PI_binary64_3947` `tan-PI/3_binary64_3946` `tan-PI/4_binary64_3945` `tan-PI/6_binary64_3944` `cos-+PI/2_binary64_3943` `cos-+PI_binary64_3942` `cos-PI_binary64_3941` `cos-PI/2_binary64_3940` `cos-PI/3_binary64_3939` `cos-PI/4_binary64_3938` `cos-PI/6_binary64_3937` `sin-+PI/2_binary64_3936` `sin-+PI_binary64_3935` `sin-PI_binary64_3934` `sin-PI/2_binary64_3933` `sin-PI/3_binary64_3932` `sin-PI/4_binary64_3931` `sin-PI/6_binary64_3930` `sub-1-sin_binary64_3929` `sub-1-cos_binary64_3928` `-1-add-sin_binary64_3927` `-1-add-cos_binary64_3926` `1-sub-sin_binary64_3925` `1-sub-cos_binary64_3924` `cos-sin-sum_binary64_3923` `log-E_binary64_3919` `log-pow_binary64_3918` `log-rec_binary64_3917` `log-div_binary64_3916` `log-prod_binary64_3915` `pow-base-0_binary64_3913` `unpow1/3_binary64_3896` `unpow3_binary64_3895` `unpow2_binary64_3894` `unpow1/2_binary64_3893` `exp-to-pow_binary64_3891` `pow-base-1_binary64_3889` `unpow0_binary64_3888` `unpow1_binary64_3887` `unpow-1_binary64_3886` `exp-lft-cube_binary64_3885` `exp-lft-sqr_binary64_3884` `exp-cbrt_binary64_3883` `exp-sqrt_binary64_3882` `exp-prod_binary64_3881` `div-exp_binary64_3880` `rec-exp_binary64_3879` `prod-exp_binary64_3878` `exp-diff_binary64_3877` `exp-neg_binary64_3876` `exp-sum_binary64_3875` `e-exp-1_binary64_3874` `exp-1-e_binary64_3872` `exp-0_binary64_3871` `rem-log-exp_binary64_3870` `rem-exp-log_binary64_3869` `cube-mult_binary64_3859` `cube-div_binary64_3858` `cube-neg_binary64_3856` `rem-3cbrt-rft_binary64_3855` `rem-3cbrt-lft_binary64_3854` `rem-cbrt-cube_binary64_3853` `rem-cube-cbrt_binary64_3852` `sqr-abs_binary64_3844` `sqr-neg_binary64_3843` `rem-sqrt-square_binary64_3842` `rem-square-sqrt_binary64_3841` `+-inverses_binary64_3808` `lft-mult-inverse_binary64_3807` `rgt-mult-inverse_binary64_3806` `remove-double-div_binary64_3805` `difference-of-squares_binary64_3798` `swap-sqr_binary64_3796` `cancel-sign-sub_binary64_3794` `distribute-neg-out_binary64_3791` `distribute-rgt1-in_binary64_3785` `distribute-lft1-in_binary64_3784` `associate--r-_binary64_3768` `associate--l-_binary64_3767` `associate--l+_binary64_3766`

Counts

1 → 5

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	28	22
2	67	22
3	170	22
4	481	22
5	1858	22

prune12.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	3	2	5
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	3	6

Error

45.4b

Counts

6 → 3

Compiler

Compiled 120 to 81 computations (32.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.0b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
6.1b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
10.2b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite1.1s (24.2%)

Algorithm

1×	rewrite-expression-head

Error

45.4b

Rules

584×	`times-frac_binary64_3835`
486×	`add-sqr-sqrt_binary64_3851`
367×	`*-un-lft-identity_binary64_3829`
225×	`add-cube-cbrt_binary64_3864`
174×	`associate-r_binary64_3769`
168×	`difference-of-squares_binary64_3798`
88×	`unpow-prod-down_binary64_3908`
85×	`sqr-pow_binary64_3801`
84×	`difference-of-sqr-1_binary64_3799`
29×	`div-inv_binary64_3826`
28×	`distribute-lft-out--_binary64_3781`
19×	`add-exp-log_binary64_3867`
18×	`add-cbrt-cube_binary64_3865`
13×	`associate-/l_binary64_3774` `associate-/r_binary64_3773`
7×	`pow1_binary64_3890`
6×	`div-exp_binary64_3880` `add-log-exp_binary64_3868` `cbrt-undiv_binary64_3863`
3×	`pow-unpow_binary64_3906` `cancel-sign-sub-inv_binary64_3795` `prod-exp_binary64_3878` `cbrt-unprod_binary64_3862` `unswap-sqr_binary64_3797` `associate-l_binary64_3770`
2×	`flip3--_binary64_3833` `associate-/l/_binary64_3776` `flip--_binary64_3804` `associate-/r/_binary64_3775`
1×	`frac-2neg_binary64_3840` `div-sub_binary64_3834` `clear-num_binary64_3828` `distribute-lft-out_binary64_3780` `pow-pow_binary64_3901` `pow-to-exp_binary64_3898` `pow-exp_binary64_3897` `diff-log_binary64_3921` `sub-neg_binary64_3822` `pow-prod-down_binary64_3900` `associate-r/_binary64_3771` `-commutative_binary64_3760`

Counts

4 → 451

Calls

4 calls:

56.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
19.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
11.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 14661 to 7953 computations (45.8% saved)

series1.5s (33.3%)

Error

2.9b

Counts

4 → 56

Calls

4 calls:

532.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
467.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
247.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
128.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 6708 to 4799 computations (28.5% saved)

simplify657.0ms (14.4%)

Algorithm

1×	egg-herbie

Rules

524×	`associate-/r/_binary64_3775`
324×	`times-frac_binary64_3835`
309×	`*-commutative_binary64_3760`
269×	`associate-/l/_binary64_3776`
221×	`sub-neg_binary64_3822`
210×	`associate-*r/_binary64_3771`
190×	`+-commutative_binary64_3759`
150×	`div-sub_binary64_3834`
137×	`associate-+r+_binary64_3761`
130×	`cancel-sign-sub-inv_binary64_3795`
64×	`unswap-sqr_binary64_3797`
60×	`associate-/l*_binary64_3774`
55×	`sqr-pow_binary64_3801`
45×	`associate-r_binary64_3769`
44×	`neg-mul-1_binary64_3825` `neg-sub0_binary64_3824` `distribute-neg-in_binary64_3790`
39×	`distribute-rgt-in_binary64_3779`
37×	`distribute-lft-in_binary64_3778`
32×	`distribute-rgt-out_binary64_3782`
31×	`distribute-rgt-neg-in_binary64_3787`
29×	`associate--l+_binary64_3766`
23×	`pow-sqr_binary64_3802`
21×	`distribute-lft-neg-in_binary64_3786`
20×	`/-rgt-identity_binary64_3820`
18×	`associate--r+_binary64_3765`
15×	`associate-/r*_binary64_3773`
12×	`distribute-lft-out_binary64_3780`
11×	`exp-prod_binary64_3881`
10×	`log-prod_binary64_3915` `distribute-lft-neg-out_binary64_3788`
9×	`associate-l_binary64_3770`
8×	`log-div_binary64_3916` `swap-sqr_binary64_3796` `distribute-rgt-out--_binary64_3783`
7×	`distribute-neg-frac_binary64_3793`
6×	`unpow3_binary64_3895` `cube-mult_binary64_3859` `*-rgt-identity_binary64_3819`
5×	`cube-unmult_binary64_3866` `cube-prod_binary64_3857`
4×	`unpow2_binary64_3894` `pow-plus_binary64_3892` `pow-base-1_binary64_3889` `exp-diff_binary64_3877` `mul-1-neg_binary64_3821` `remove-double-div_binary64_3805` `difference-of-sqr-1_binary64_3799` `distribute-rgt1-in_binary64_3785` `distribute-lft-out--_binary64_3781` `associate-*l/_binary64_3772`
3×	`exp-sum_binary64_3875`
2×	`log-pow_binary64_3918` `log-rec_binary64_3917` `rem-sqrt-square_binary64_3842` `*-lft-identity_binary64_3818` `associate-+r-_binary64_3763`
1×	`unpow1_binary64_3887` `div-exp_binary64_3880` `1-exp_binary64_3873` `exp-1-e_binary64_3872` `rem-3cbrt-lft_binary64_3854` `rem-square-sqrt_binary64_3841` `remove-double-neg_binary64_3817` `*-inverses_binary64_3809` `difference-of-squares_binary64_3798` `distribute-neg-out_binary64_3791` `distribute-rgt-neg-out_binary64_3789` `distribute-lft1-in_binary64_3784` `associate--r-_binary64_3768`
0×	`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_4092` `erf-erfc_binary64_4091` `erf-odd_binary64_4090` `if-if-and-not_binary64_4089` `if-if-and_binary64_4088` `if-if-or-not_binary64_4087` `if-if-or_binary64_4086` `if-not_binary64_4085` `if-same_binary64_4084` `if-false_binary64_4083` `if-true_binary64_4082` `not-gte_binary64_4081` `not-lte_binary64_4080` `not-gt_binary64_4079` `not-lt_binary64_4078` `gte-same_binary64_4077` `lte-same_binary64_4076` `gt-same_binary64_4075` `lt-same_binary64_4074` `sinh---cosh_binary64_4021` `sinh-+-cosh_binary64_4020` `sinh-cosh_binary64_4019` `tanh-def-c_binary64_4018` `tanh-def-b_binary64_4017` `tanh-def-a_binary64_4016` `cosh-def_binary64_4015` `sinh-def_binary64_4014` `tan-neg_binary64_3961` `cos-neg_binary64_3960` `sin-neg_binary64_3959` `tan-0_binary64_3958` `cos-0_binary64_3957` `sin-0_binary64_3956` `hang-m-tan_binary64_3955` `hang-p-tan_binary64_3954` `hang-m0-tan_binary64_3953` `hang-p0-tan_binary64_3952` `hang-0m-tan_binary64_3951` `hang-0p-tan_binary64_3950` `tan-+PI/2_binary64_3949` `tan-+PI_binary64_3948` `tan-PI_binary64_3947` `tan-PI/3_binary64_3946` `tan-PI/4_binary64_3945` `tan-PI/6_binary64_3944` `cos-+PI/2_binary64_3943` `cos-+PI_binary64_3942` `cos-PI_binary64_3941` `cos-PI/2_binary64_3940` `cos-PI/3_binary64_3939` `cos-PI/4_binary64_3938` `cos-PI/6_binary64_3937` `sin-+PI/2_binary64_3936` `sin-+PI_binary64_3935` `sin-PI_binary64_3934` `sin-PI/2_binary64_3933` `sin-PI/3_binary64_3932` `sin-PI/4_binary64_3931` `sin-PI/6_binary64_3930` `sub-1-sin_binary64_3929` `sub-1-cos_binary64_3928` `-1-add-sin_binary64_3927` `-1-add-cos_binary64_3926` `1-sub-sin_binary64_3925` `1-sub-cos_binary64_3924` `cos-sin-sum_binary64_3923` `log-E_binary64_3919` `pow-base-0_binary64_3913` `unpow1/3_binary64_3896` `unpow1/2_binary64_3893` `exp-to-pow_binary64_3891` `unpow0_binary64_3888` `unpow-1_binary64_3886` `exp-lft-cube_binary64_3885` `exp-lft-sqr_binary64_3884` `exp-cbrt_binary64_3883` `exp-sqrt_binary64_3882` `rec-exp_binary64_3879` `prod-exp_binary64_3878` `exp-neg_binary64_3876` `e-exp-1_binary64_3874` `exp-0_binary64_3871` `rem-log-exp_binary64_3870` `rem-exp-log_binary64_3869` `cube-div_binary64_3858` `cube-neg_binary64_3856` `rem-3cbrt-rft_binary64_3855` `rem-cbrt-cube_binary64_3853` `rem-cube-cbrt_binary64_3852` `sqr-abs_binary64_3844` `sqr-neg_binary64_3843` `unsub-neg_binary64_3823` `sub0-neg_binary64_3816` `--rgt-identity_binary64_3815` `+-rgt-identity_binary64_3814` `+-lft-identity_binary64_3813` `mul0-rgt_binary64_3812` `mul0-lft_binary64_3811` `div0_binary64_3810` `+-inverses_binary64_3808` `lft-mult-inverse_binary64_3807` `rgt-mult-inverse_binary64_3806` `difference-of-sqr--1_binary64_3800` `cancel-sign-sub_binary64_3794` `distribute-frac-neg_binary64_3792` `count-2_binary64_3777` `associate--l-_binary64_3767` `associate-+l-_binary64_3764` `associate-+l+_binary64_3762`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1009	19287
1	2879	18817

Details

analyze759.0ms (16.7%)

sample364.0ms (8%)

simplify135.0ms (3%)

prune12.0ms (0.3%)

localize8.0ms (0.2%)

rewrite1.1s (24.2%)

series1.5s (33.3%)

simplify657.0ms (14.4%)

end0.0ms (0%)

Profiling