Details

analyze449.0ms (1.5%)

Algorithm

1×	search
2×	egg-herbie

Rules

570×	`neg-mul-1_binary64`
442×	`div-sub_binary64`
428×	`unswap-sqr_binary64`
418×	`associate-/l*_binary64`
306×	`associate-l_binary64`
304×	`distribute-rgt-in_binary64`
286×	`associate-/r*_binary64`
278×	`distribute-frac-neg_binary64`
228×	`associate-/l/_binary64`
210×	`associate-r_binary64`
205×	`*-commutative_binary64`
188×	`distribute-rgt-neg-out_binary64`
154×	`associate-/r/_binary64`
134×	`associate-*r/_binary64`
116×	`distribute-lft-neg-out_binary64`
106×	`associate-*l/_binary64`
70×	`sub-neg_binary64`
64×	`distribute-lft-in_binary64`
56×	`neg-sub0_binary64`
50×	`sqr-pow_binary64`
36×	`cube-prod_binary64`
30×	`*-lft-identity_binary64` `pow-sqr_binary64` `distribute-neg-frac_binary64`
24×	`+-commutative_binary64`
22×	`/-rgt-identity_binary64`
20×	`pow-plus_binary64`
18×	`distribute-lft-neg-in_binary64`
14×	`unsub-neg_binary64` `distribute-rgt-neg-in_binary64`
12×	`*-rgt-identity_binary64` `sub0-neg_binary64`
10×	`cube-unmult_binary64` `associate-+l-_binary64`
8×	`unpow3_binary64`
4×	`unpow2_binary64` `cube-mult_binary64` `--rgt-identity_binary64` `associate-+l+_binary64`
2×	`unpow1_binary64` `remove-double-div_binary64` `associate--r+_binary64` `associate-+r+_binary64`
1×	`1-exp_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate-+r-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	52	44
2	113	44
3	232	44
4	507	44
5	1156	44
6	2424	44
7	4691	44
8	4942	44
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

Compiler

Compiled 17 to 16 computations (5.9% saved)

sample74.0ms (0.2%)

Algorithm

1×

intervals

Results

20.0ms	44×	body	1024	nan
19.0ms	256×	body	128	valid
10.0ms	78×	body	128	overflowed
5.0ms	15×	body	512	nan
1.0ms	26×	body	128	nan
1.0ms	7×	body	256	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

788×	`neg-mul-1_binary64`
672×	`associate-/l*_binary64`
625×	`associate-/r*_binary64`
480×	`div-sub_binary64`
445×	`distribute-frac-neg_binary64`
288×	`distribute-rgt-neg-out_binary64`
267×	`associate-*r/_binary64`
257×	`associate-*l/_binary64`
235×	`distribute-lft-neg-out_binary64`
214×	`unswap-sqr_binary64`
164×	`*-commutative_binary64`
153×	`associate-l_binary64`
150×	`distribute-rgt-in_binary64`
125×	`distribute-lft-in_binary64`
115×	`associate-/l/_binary64`
105×	`associate-r_binary64`
77×	`associate-/r/_binary64`
76×	`sub-neg_binary64`
68×	`neg-sub0_binary64`
40×	`*-lft-identity_binary64`
38×	`sqr-pow_binary64`
27×	`cube-prod_binary64`
25×	`*-rgt-identity_binary64`
21×	`pow-sqr_binary64`
20×	`unsub-neg_binary64`
18×	`/-rgt-identity_binary64`
17×	`+-commutative_binary64`
15×	`pow-plus_binary64` `distribute-neg-frac_binary64`
12×	`associate-+l-_binary64`
9×	`unpow3_binary64` `distribute-lft-neg-in_binary64`
7×	`sub0-neg_binary64` `distribute-rgt-neg-in_binary64`
6×	`cube-unmult_binary64` `cube-mult_binary64`
4×	`unpow2_binary64`
3×	`--rgt-identity_binary64` `remove-double-div_binary64` `associate--r+_binary64` `associate-+l+_binary64`
2×	`unpow1_binary64`
1×	`unpow1/2_binary64` `1-exp_binary64` `associate-+r+_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate-+r-_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	65	22
3	128	22
4	277	22
5	623	22
6	1296	22
7	3024	22
8	4691	22
9	4933	22

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.3b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize14.0ms (0%)

Local error

Found 3 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

rewrite204.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

48×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
22×	`pow-unpow_binary64`
18×	`sqrt-prod_binary64`
14×	`pow1_binary64`
10×	`add-cbrt-cube_binary64`
9×	`prod-exp_binary64`
8×	`unpow-prod-down_binary64` `sqr-pow_binary64`
6×	`pow-exp_binary64` `associate-/r*_binary64` `pow-prod-down_binary64` `difference-of-squares_binary64`
5×	`div-exp_binary64` `associate-/l*_binary64`
3×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `distribute-lft-out--_binary64` `pow-pow_binary64`
2×	`pow-to-exp_binary64` `div-inv_binary64` `div-sub_binary64` `pow-sub_binary64`
1×	`cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64` `associate-l_binary64` `*-commutative_binary64`

Counts

3 → 115

Calls

3 calls:

9.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
6.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2465 to 1670 computations (32.3% saved)

series106.0ms (0.4%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

43.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
39.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
8.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1015 to 812 computations (20% saved)

simplify167.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

540×	`distribute-rgt-in_binary64`
536×	`distribute-lft-in_binary64`
199×	`associate-/l/_binary64`
169×	`associate-l_binary64`
149×	`exp-prod_binary64`
143×	`times-frac_binary64`
142×	`associate-r_binary64`
116×	`sqr-pow_binary64`
108×	`cancel-sign-sub-inv_binary64`
97×	`*-commutative_binary64`
82×	`associate-/r/_binary64`
78×	`log-pow_binary64`
74×	`log-prod_binary64`
56×	`associate-/l*_binary64`
53×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
43×	`pow-sqr_binary64`
37×	`unswap-sqr_binary64`
36×	`sub-neg_binary64`
32×	`exp-sum_binary64`
22×	`exp-to-pow_binary64`
20×	`-rgt-identity_binary64` `associate-/r_binary64`
18×	`log-div_binary64` `cube-prod_binary64` `distribute-lft-neg-out_binary64`
17×	`neg-mul-1_binary64` `neg-sub0_binary64`
16×	`swap-sqr_binary64` `distribute-rgt-neg-out_binary64`
15×	`unpow3_binary64`
14×	`-lft-identity_binary64` `associate-l/_binary64` `associate-*r/_binary64` `+-commutative_binary64`
13×	`distribute-lft-out--_binary64`
11×	`cube-unmult_binary64`
10×	`exp-diff_binary64` `/-rgt-identity_binary64`
9×	`unpow1/2_binary64` `associate--l+_binary64`
8×	`pow-plus_binary64` `div-sub_binary64` `unsub-neg_binary64`
6×	`distribute-neg-frac_binary64`
5×	`prod-exp_binary64` `distribute-rgt-out_binary64` `associate-+l+_binary64`
4×	`unpow1_binary64` `rem-sqrt-square_binary64` `distribute-neg-in_binary64` `distribute-rgt-out--_binary64` `associate--r+_binary64`
3×	`log-rec_binary64` `exp-lft-sqr_binary64` `cube-div_binary64` `distribute-lft-out_binary64`
2×	`unpow2_binary64` `cube-mult_binary64` `count-2_binary64` `associate--r-_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-square-sqrt_binary64` `remove-double-neg_binary64` `associate-+r+_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `associate--l-_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

133 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3711
1	512	3530
2	1621	3389
3	4700	3385
4	4972	3385
5	4969	3385

prune142.0ms (0.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	113	9	122
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	115	9	124

Error

0.0b

Counts

124 → 9

Compiler

Compiled 2136 to 1469 computations (31.2% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
0.3b	(.f64 n (.f64 2 PI.f64))
0.3b	(.f64 n (.f64 2 PI.f64))
0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))

rewrite670.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

284×	`times-frac_binary64`
126×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
111×	`sqrt-prod_binary64`
33×	`add-exp-log_binary64`
28×	`unpow-prod-down_binary64` `sqr-pow_binary64`
24×	`associate-/l*_binary64`
20×	`pow1_binary64`
19×	`add-cbrt-cube_binary64`
11×	`div-exp_binary64`
9×	`prod-exp_binary64` `pow-prod-down_binary64`
8×	`div-inv_binary64`
6×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64`
3×	`pow-exp_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64`
2×	`associate-r_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64` `pow1/2_binary64`

Counts

4 → 241

Calls

4 calls:

14.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
5.0ms	(.f64 n (.f64 2 PI.f64))
5.0ms	(.f64 n (.f64 2 PI.f64))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 7591 to 4927 computations (35.1% saved)

series76.0ms (0.3%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

40.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
11.0ms	(.f64 n (.f64 2 PI.f64))
9.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
8.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 842 to 698 computations (17.1% saved)

simplify332.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

850×	`associate-/l*_binary64`
386×	`associate-/l/_binary64`
276×	`associate-*l/_binary64`
261×	`associate-/r/_binary64`
224×	`associate-/r*_binary64`
217×	`associate-*r/_binary64`
141×	`associate-r_binary64`
138×	`exp-sum_binary64`
129×	`*-commutative_binary64`
126×	`distribute-rgt-in_binary64`
118×	`distribute-lft-in_binary64`
114×	`associate-l_binary64`
90×	`exp-prod_binary64`
83×	`times-frac_binary64`
41×	`log-prod_binary64` `sqr-pow_binary64`
40×	`*-rgt-identity_binary64`
32×	`log-div_binary64` `distribute-neg-in_binary64`
29×	`sub-neg_binary64` `/-rgt-identity_binary64` `unswap-sqr_binary64`
21×	`swap-sqr_binary64`
17×	`exp-to-pow_binary64` `neg-mul-1_binary64` `neg-sub0_binary64`
15×	`pow-sqr_binary64`
14×	`*-lft-identity_binary64`
12×	`cancel-sign-sub-inv_binary64`
11×	`cube-unmult_binary64`
10×	`unsub-neg_binary64` `distribute-neg-frac_binary64`
9×	`unpow3_binary64` `cube-prod_binary64` `+-commutative_binary64`
8×	`log-pow_binary64` `exp-neg_binary64` `distribute-lft-neg-out_binary64`
7×	`cube-div_binary64`
6×	`distribute-rgt-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
5×	`exp-diff_binary64`
4×	`rem-sqrt-square_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate-+l+_binary64`
3×	`unpow1/2_binary64` `exp-lft-sqr_binary64` `prod-exp_binary64` `div-sub_binary64`
2×	`log-rec_binary64` `pow-plus_binary64` `rem-square-sqrt_binary64` `distribute-rgt-out_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64`
1×	`unpow1_binary64` `1-exp_binary64` `remove-double-neg_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `associate-+l-_binary64` `associate-+r+_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-mult_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate--r+_binary64` `associate-+r-_binary64`

Counts

256 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	397	11834
1	856	11550
2	2336	11529
3	4747	11529
4	5070	11529

prune333.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	235	3	238
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	239	8	247

Error

Counts

247 → 8

Compiler

Compiled 5781 to 3730 computations (35.5% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
0.2b	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
0.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)))
0.3b	(.f64 n (.f64 2 PI.f64))

rewrite243.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

45×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
22×	`pow1_binary64`
19×	`add-cube-cbrt_binary64` `associate-l_binary64`
15×	`add-exp-log_binary64` `times-frac_binary64`
13×	`associate-r_binary64`
12×	`unpow-prod-down_binary64` `unswap-sqr_binary64`
11×	`add-cbrt-cube_binary64`
9×	`pow-prod-down_binary64`
8×	`unpow-prod-up_binary64`
6×	`prod-exp_binary64` `sqr-pow_binary64` `cancel-sign-sub-inv_binary64` `pow-unpow_binary64` `sqrt-pow1_binary64`
5×	`pow-pow_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64`
3×	`pow-sub_binary64`
2×	`*-commutative_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64` `sub-neg_binary64` `difference-of-squares_binary64` `pow1/2_binary64`
1×	`frac-times_binary64` `associate-l/_binary64` `associate-r/_binary64` `div-inv_binary64` `distribute-lft-out--_binary64` `sqrt-pow2_binary64`

Counts

4 → 116

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)))
8.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
7.0ms	(.f64 n (.f64 2 PI.f64))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 2456 to 1812 computations (26.2% saved)

series100.0ms (0.3%)

Error

Counts

4 → 21

Calls

4 calls:

37.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)))
34.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
9.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
8.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 1372 to 1078 computations (21.4% saved)

simplify192.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

535×	`times-frac_binary64`
248×	`sqr-pow_binary64`
242×	`associate-r_binary64`
235×	`exp-prod_binary64`
229×	`associate-l_binary64`
204×	`distribute-rgt-in_binary64`
201×	`distribute-lft-in_binary64`
200×	`exp-sum_binary64`
118×	`*-commutative_binary64`
93×	`pow-sqr_binary64`
88×	`log-prod_binary64` `cancel-sign-sub-inv_binary64`
84×	`neg-mul-1_binary64`
82×	`neg-sub0_binary64`
72×	`unsub-neg_binary64`
69×	`associate-/l*_binary64`
64×	`sub-neg_binary64` `*-lft-identity_binary64`
61×	`*-rgt-identity_binary64`
56×	`unswap-sqr_binary64`
55×	`distribute-rgt-neg-in_binary64`
50×	`distribute-lft-neg-in_binary64`
47×	`cube-prod_binary64`
45×	`associate-/r*_binary64`
40×	`div-sub_binary64`
37×	`log-pow_binary64` `associate-+l+_binary64`
34×	`exp-diff_binary64`
31×	`exp-to-pow_binary64` `swap-sqr_binary64`
29×	`associate-+r+_binary64` `+-commutative_binary64`
26×	`prod-exp_binary64`
25×	`unpow3_binary64`
23×	`associate-*r/_binary64`
18×	`associate-/r/_binary64`
17×	`associate-/l/_binary64` `associate-*l/_binary64`
16×	`cube-unmult_binary64`
15×	`unpow1/2_binary64` `distribute-lft-neg-out_binary64`
14×	`pow-plus_binary64`
12×	`associate--l+_binary64`
11×	`distribute-rgt-neg-out_binary64`
10×	`exp-neg_binary64` `associate-+l-_binary64`
9×	`mul0-rgt_binary64` `mul0-lft_binary64`
7×	`rem-exp-log_binary64` `cube-mult_binary64` `distribute-rgt-out_binary64` `associate-+r-_binary64`
6×	`unpow1_binary64` `rem-sqrt-square_binary64` `distribute-frac-neg_binary64` `distribute-neg-in_binary64` `distribute-rgt-out--_binary64` `associate--r+_binary64`
5×	`pow-base-1_binary64` `sub0-neg_binary64`
4×	`+-rgt-identity_binary64`
3×	`log-div_binary64` `exp-lft-sqr_binary64` `rem-square-sqrt_binary64` `/-rgt-identity_binary64` `distribute-neg-frac_binary64` `distribute-rgt1-in_binary64`
2×	`unpow2_binary64` `exp-sqrt_binary64` `mul-1-neg_binary64` `div0_binary64` `count-2_binary64`
1×	`log-E_binary64` `unpow-1_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64` `distribute-lft-out_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow0_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

137 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	3308
1	456	3193
2	1518	3145
3	3416	3133
4	4781	3133
5	4994	3133
6	4904	3133

prune163.0ms (0.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	116	8	124

Error

Counts

124 → 8

Compiler

Compiled 2079 to 1439 computations (30.8% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2))) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
0.2b	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2))) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
0.3b	(.f64 n (.f64 PI.f64 2))
0.3b	(.f64 n (.f64 PI.f64 2))

rewrite6.7s (22.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6356×	`times-frac_binary64`
4874×	`sqrt-prod_binary64`
2474×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
400×	`unpow-prod-down_binary64` `sqr-pow_binary64`
244×	`associate-/l*_binary64`
112×	`div-inv_binary64`
60×	`add-exp-log_binary64`
29×	`div-exp_binary64`
28×	`add-cbrt-cube_binary64`
18×	`associate-/r*_binary64`
14×	`pow1_binary64`
12×	`prod-exp_binary64`
9×	`cbrt-undiv_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64`
2×	`associate-r_binary64` `*-commutative_binary64` `pow-to-exp_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64`

Counts

4 → 2534

Calls

4 calls:

91.0ms	(/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2))) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
17.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2))) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
5.0ms	(.f64 n (.f64 PI.f64 2))
5.0ms	(.f64 n (.f64 PI.f64 2))

Compiler

Compiled 85611 to 48009 computations (43.9% saved)

series150.0ms (0.5%)

Error

Counts

4 → 21

Calls

4 calls:

71.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2))) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k)))
40.0ms	(/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 PI.f64 2))) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
11.0ms	(.f64 n (.f64 PI.f64 2))
9.0ms	(.f64 n (.f64 PI.f64 2))

Compiler

Compiled 1780 to 1356 computations (23.8% saved)

simplify4.1s (14%)

Algorithm

1×	egg-herbie

Rules

1332×	`associate-/l/_binary64`
290×	`associate-/r/_binary64`
201×	`associate-*l/_binary64`
198×	`associate-/l*_binary64`
166×	`times-frac_binary64`
148×	`/-rgt-identity_binary64` `associate-/r*_binary64`
69×	`sqr-pow_binary64`
63×	`*-commutative_binary64`
47×	`sub-neg_binary64`
32×	`distribute-rgt-in_binary64`
30×	`distribute-lft-in_binary64`
29×	`associate-r_binary64`
28×	`neg-mul-1_binary64` `neg-sub0_binary64`
26×	`exp-prod_binary64`
24×	`exp-sum_binary64`
21×	`log-prod_binary64`
20×	`associate-l_binary64`
19×	`log-div_binary64`
16×	`pow-sqr_binary64` `cancel-sign-sub-inv_binary64`
13×	`cube-unmult_binary64` `associate-*r/_binary64`
10×	`rem-sqrt-square_binary64` `unsub-neg_binary64` `*-lft-identity_binary64` `+-commutative_binary64`
9×	`cube-prod_binary64` `swap-sqr_binary64` `distribute-neg-in_binary64`
8×	`associate--l-_binary64`
7×	`rem-square-sqrt_binary64` `unswap-sqr_binary64` `distribute-neg-frac_binary64`
5×	`div-sub_binary64` `distribute-rgt-neg-in_binary64`
4×	`log-pow_binary64` `cube-div_binary64` `*-rgt-identity_binary64` `distribute-lft-neg-in_binary64`
3×	`unpow1/2_binary64` `associate-+r+_binary64`
2×	`unpow3_binary64` `exp-lft-sqr_binary64` `cube-mult_binary64` `associate--l+_binary64` `associate--r+_binary64`
1×	`log-rec_binary64` `unpow2_binary64` `exp-to-pow_binary64` `unpow1_binary64` `prod-exp_binary64` `1-exp_binary64` `sqr-abs_binary64` `remove-double-neg_binary64` `div0_binary64` `distribute-lft-neg-out_binary64` `count-2_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-plus_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `associate--r-_binary64` `associate-+l-_binary64` `associate-+r-_binary64` `associate-+l+_binary64`

Counts

2555 → 2534

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1814	187084
1	3818	183086
2	4758	182144
3	5017	182144

prune2.8s (9.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	2532	2	2534
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	2534	8	2542

Error

Counts

2542 → 8

Compiler

Compiled 46091 to 22724 computations (50.7% saved)

regimes9.9s (33.5%)

Accuracy

Total 0.4b remaining (92.3%)

Threshold costs 0.4b (92.3%)

Compiler

Compiled 150944 to 115223 computations (23.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`unpow1_binary64` `1-exp_binary64`
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` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	20	33
2	19	33

end1.0ms (0%)

Compiler: Compiled 20 to 17 computations (15% saved)

sample2.6s (8.8%)

Algorithm

1×

intervals

Results

628.0ms	8000×	body	128	valid
592.0ms	1307×	body	1024	nan
312.0ms	2313×	body	128	overflowed
208.0ms	666×	body	512	nan
63.0ms	344×	body	256	nan
54.0ms	976×	body	128	nan
21.0ms	228×	body	128	invalid

Compiler

Compiled 238 to 204 computations (14.3% saved)

Details

analyze449.0ms (1.5%)

sample74.0ms (0.2%)

simplify51.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0%)

rewrite204.0ms (0.7%)

series106.0ms (0.4%)

simplify167.0ms (0.6%)

prune142.0ms (0.5%)

localize10.0ms (0%)

rewrite670.0ms (2.3%)

series76.0ms (0.3%)

simplify332.0ms (1.1%)

prune333.0ms (1.1%)

localize11.0ms (0%)

rewrite243.0ms (0.8%)

series100.0ms (0.3%)

simplify192.0ms (0.6%)

prune163.0ms (0.6%)

localize13.0ms (0%)

rewrite6.7s (22.5%)

series150.0ms (0.5%)

simplify4.1s (14%)

prune2.8s (9.3%)

regimes9.9s (33.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end1.0ms (0%)

sample2.6s (8.8%)

Profiling