Details

analyze2.3s (10.7%)

Algorithm

1×	search
2×	egg-herbie

Rules

648×	`distribute-rgt-in_binary64`
636×	`distribute-lft-in_binary64`
356×	`cancel-sign-sub-inv_binary64`
251×	`distribute-rgt-neg-in_binary64`
235×	`distribute-lft-neg-in_binary64`
159×	`associate-l_binary64`
158×	`*-commutative_binary64`
132×	`sub-neg_binary64`
118×	`associate-r_binary64`
114×	`distribute-lft-neg-out_binary64`
112×	`neg-mul-1_binary64` `neg-sub0_binary64`
101×	`distribute-rgt-neg-out_binary64`
92×	`distribute-neg-in_binary64`
70×	`distribute-neg-frac_binary64`
55×	`+-commutative_binary64`
40×	`associate-*r/_binary64`
30×	`sqr-pow_binary64` `associate-*l/_binary64`
22×	`unsub-neg_binary64`
20×	`associate-/l*_binary64`
16×	`cancel-sign-sub_binary64` `distribute-neg-out_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate-+l-_binary64` `associate-+l+_binary64`
10×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `associate-/r/_binary64`
6×	`times-frac_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` `unpow3_binary64` `pow-plus_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-unmult_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_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` `div-sub_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` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `swap-sqr_binary64` `distribute-frac-neg_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-/l/_binary64` `associate-/r_binary64` `associate--r-_binary64` `associate--r+_binary64` `associate-+r-_binary64` `associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	170	672
1	563	672
2	2019	672
3	5820	672
0	6	6
1	6	6

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 29 to 24 computations (17.2% saved)

sample104.0ms (0.5%)

Algorithm

1×

intervals

Results

41.0ms	432×	body	128	nan
23.0ms	256×	body	128	valid
4.0ms	44×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify52.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

716×	`neg-mul-1_binary64` `neg-sub0_binary64`
377×	`distribute-rgt-neg-out_binary64`
358×	`cancel-sign-sub-inv_binary64`
354×	`distribute-lft-neg-out_binary64`
351×	`unsub-neg_binary64`
309×	`distribute-neg-frac_binary64`
281×	`distribute-rgt-in_binary64`
275×	`distribute-lft-in_binary64`
248×	`associate-*r/_binary64`
236×	`distribute-rgt-neg-in_binary64` `associate-*l/_binary64`
228×	`*-commutative_binary64`
125×	`distribute-neg-in_binary64`
106×	`div-sub_binary64`
95×	`associate-r_binary64`
88×	`associate-l_binary64`
87×	`sub-neg_binary64`
86×	`distribute-lft-neg-in_binary64`
85×	`distribute-neg-out_binary64`
61×	`times-frac_binary64`
43×	`associate-/l*_binary64`
35×	`remove-double-neg_binary64`
32×	`associate-+l+_binary64` `associate-+r+_binary64`
23×	`distribute-lft-out_binary64`
20×	`mul0-rgt_binary64` `mul0-lft_binary64` `associate--r+_binary64` `+-commutative_binary64`
16×	`associate-+l-_binary64`
12×	`distribute-rgt-out_binary64`
11×	`sub0-neg_binary64` `associate-+r-_binary64`
10×	`associate-/r/_binary64`
8×	`unswap-sqr_binary64`
7×	`sqr-pow_binary64` `associate--l+_binary64`
6×	`+-rgt-identity_binary64`
5×	`distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64`
4×	`*-lft-identity_binary64` `associate-/l/_binary64`
3×	`pow-plus_binary64` `cube-unmult_binary64` `--rgt-identity_binary64`
2×	`rem-sqrt-square_binary64` `-rgt-identity_binary64` `associate-/r_binary64`
1×	`unpow3_binary64` `unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `1-exp_binary64` `sqr-neg_binary64` `div0_binary64` `cancel-sign-sub_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-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `+-lft-identity_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `count-2_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	58	42
2	180	42
3	719	39
4	2459	39
5	3993	39
6	5178	39

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

29.2b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.3b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
10.5b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
17.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

rewrite357.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

21.4b

Rules

30×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
29×	`add-sqr-sqrt_binary64`
27×	`associate-l_binary64`
24×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
19×	`times-frac_binary64`
18×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
16×	`pow-prod-down_binary64`
14×	`prod-exp_binary64` `cbrt-unprod_binary64`
12×	`associate-*r/_binary64` `cancel-sign-sub-inv_binary64`
7×	`associate-r_binary64`
4×	`add-log-exp_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `frac-times_binary64` `sub-neg_binary64`
3×	`*-commutative_binary64` `div-exp_binary64` `cbrt-undiv_binary64`
2×	`sqrt-div_binary64` `flip3--_binary64` `flip--_binary64` `associate-*l/_binary64` `div-inv_binary64` `unswap-sqr_binary64`
1×	`pow1/2_binary64` `sqrt-prod_binary64`

Counts

4 → 131

Calls

4 calls:

15.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
9.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
6.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

Compiler

Compiled 4884 to 1897 computations (61.2% saved)

series1.3s (5.8%)

Error

16.9b

Counts

4 → 112

Calls

4 calls:

512.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
357.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
209.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
83.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 9559 to 7513 computations (21.4% saved)

simplify250.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

636×	`*-commutative_binary64`
242×	`associate-*l/_binary64`
232×	`associate-/l*_binary64`
220×	`distribute-rgt-in_binary64`
208×	`associate-*r/_binary64`
203×	`distribute-lft-in_binary64`
181×	`sub-neg_binary64`
138×	`neg-sub0_binary64`
125×	`associate-r_binary64`
122×	`neg-mul-1_binary64`
110×	`+-commutative_binary64`
100×	`cancel-sign-sub-inv_binary64`
96×	`times-frac_binary64`
83×	`associate-/r*_binary64`
73×	`sqr-pow_binary64`
71×	`distribute-rgt-neg-in_binary64`
68×	`div-sub_binary64`
67×	`exp-prod_binary64`
61×	`log-prod_binary64`
56×	`associate-l_binary64`
51×	`distribute-lft-neg-in_binary64`
48×	`cube-prod_binary64` `associate-/r/_binary64`
34×	`unpow3_binary64`
31×	`log-div_binary64` `unsub-neg_binary64`
29×	`distribute-neg-frac_binary64`
25×	`associate--r+_binary64` `associate-+l+_binary64`
24×	`exp-sum_binary64` `distribute-lft-neg-out_binary64`
22×	`associate--l+_binary64`
21×	`swap-sqr_binary64`
18×	`mul-1-neg_binary64`
17×	`cube-div_binary64`
15×	`distribute-neg-in_binary64`
14×	`distribute-rgt-neg-out_binary64`
13×	`associate-+r+_binary64`
11×	`cube-mult_binary64` `distribute-rgt-out--_binary64`
9×	`log-pow_binary64`
8×	`unswap-sqr_binary64`
7×	`cube-unmult_binary64`
6×	`*-rgt-identity_binary64` `associate-+l-_binary64`
5×	`*-lft-identity_binary64` `distribute-rgt-out_binary64` `associate-+r-_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `difference-of-squares_binary64`
3×	`distribute-lft-out_binary64`
2×	`exp-lft-sqr_binary64` `rem-square-sqrt_binary64` `distribute-lft-out--_binary64`
1×	`log-rec_binary64` `pow-plus_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `sqr-neg_binary64` `/-rgt-identity_binary64` `+-rgt-identity_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` `exp-to-pow_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` `prod-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `remove-double-neg_binary64` `sub0-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` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

243 → 224

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	534	8553
1	1629	8065
2	4296	7813
3	4959	7813
4	4974	7813

prune241.0ms (1.1%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	204	20	224
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	205	21	226

Error

13.0b

Counts

226 → 21

Compiler

Compiled 5063 to 2154 computations (57.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.1b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
6.5b	(/.f64 (.f64 l (-.f64 U U)) Om)
7.2b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
17.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

rewrite189.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

Rules

31×	`pow1_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`pow-prod-down_binary64`
12×	`associate-*r/_binary64`
10×	`add-sqr-sqrt_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
8×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
5×	`sqrt-pow1_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `associate-r_binary64`
3×	`flip3-+_binary64` `flip-+_binary64` `times-frac_binary64` `associate-/r*_binary64`
2×	`sqrt-div_binary64` `*-commutative_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-prod_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `flip3--_binary64` `flip--_binary64` `associate-/l*_binary64` `unswap-sqr_binary64`

Counts

4 → 89

Calls

4 calls:

8.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
7.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
6.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
5.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))

Compiler

Compiled 3349 to 1358 computations (59.5% saved)

series1.4s (6.4%)

Error

12.9b

Counts

4 → 121

Calls

4 calls:

515.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
373.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
357.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
60.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 10153 to 8070 computations (20.5% saved)

simplify235.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-r_binary64`
535×	`associate-l_binary64`
223×	`associate-/l*_binary64`
174×	`*-commutative_binary64`
162×	`distribute-rgt-in_binary64`
152×	`distribute-lft-in_binary64`
132×	`times-frac_binary64`
131×	`associate-*r/_binary64`
108×	`associate-*l/_binary64`
90×	`associate-/r*_binary64`
81×	`cancel-sign-sub-inv_binary64`
71×	`sub-neg_binary64`
61×	`exp-prod_binary64`
54×	`distribute-rgt-neg-in_binary64`
49×	`associate-/r/_binary64`
46×	`log-prod_binary64`
44×	`neg-sub0_binary64`
43×	`distribute-lft-neg-in_binary64`
36×	`neg-mul-1_binary64`
29×	`+-commutative_binary64`
22×	`distribute-neg-frac_binary64`
20×	`sqr-pow_binary64`
19×	`distribute-neg-in_binary64`
18×	`associate-/l/_binary64`
15×	`log-div_binary64` `exp-sum_binary64` `div-sub_binary64`
14×	`swap-sqr_binary64`
13×	`mul-1-neg_binary64`
11×	`associate--l+_binary64` `associate--r+_binary64`
9×	`unswap-sqr_binary64`
8×	`log-pow_binary64` `cube-unmult_binary64` `distribute-lft-neg-out_binary64`
7×	`unpow3_binary64` `distribute-rgt-out--_binary64`
6×	`cube-mult_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `cube-prod_binary64` `distribute-rgt-out_binary64`
3×	`pow-plus_binary64` `exp-lft-sqr_binary64` `distribute-lft-out_binary64` `associate-+r+_binary64`
2×	`exp-diff_binary64` `cube-div_binary64` `/-rgt-identity_binary64` `distribute-lft-out--_binary64` `associate-+l+_binary64`
1×	`log-rec_binary64` `prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `unsub-neg_binary64` `*-rgt-identity_binary64` `difference-of-squares_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` `exp-to-pow_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` `-lft-identity_binary64` `remove-double-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` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_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` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+l-_binary64`

Counts

210 → 151

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	422	8422
1	1199	7780
2	4815	7780
3	4999	7780
4	4974	7780

prune128.0ms (0.6%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	0	19	19
Picked	0	1	1
Done	0	1	1
Total	147	25	172

Error

12.6b

Counts

172 → 25

Compiler

Compiled 2986 to 1355 computations (54.6% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.5b	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
10.5b	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
17.5b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
17.5b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

rewrite196.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

12.6b

Rules

42×	`pow1_binary64`
24×	`pow-prod-down_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`prod-exp_binary64` `cbrt-unprod_binary64`
8×	`sqrt-pow1_binary64` `associate-*r/_binary64`
6×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
4×	`add-log-exp_binary64` `flip3-+_binary64` `sqrt-div_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `sqrt-prod_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

9.0ms	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
9.0ms	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
7.0ms	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
6.0ms	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

Compiler

Compiled 5256 to 2188 computations (58.4% saved)

series2.0s (9.2%)

Error

12.6b

Counts

4 → 128

Calls

4 calls:

541.0ms	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
540.0ms	(.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))
381.0ms	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
379.0ms	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

Compiler

Compiled 20960 to 15001 computations (28.4% saved)

simplify221.0ms (1%)

Algorithm

1×	egg-herbie

Rules

924×	`times-frac_binary64`
473×	`associate-r_binary64`
421×	`associate-l_binary64`
301×	`*-commutative_binary64`
125×	`associate-/l*_binary64`
122×	`distribute-rgt-in_binary64`
114×	`distribute-lft-in_binary64`
92×	`associate-*r/_binary64`
70×	`exp-prod_binary64`
65×	`associate-/r_binary64` `associate-l/_binary64`
61×	`cancel-sign-sub-inv_binary64` `+-commutative_binary64`
45×	`sub-neg_binary64`
39×	`distribute-rgt-neg-in_binary64`
38×	`log-prod_binary64`
32×	`cube-prod_binary64` `associate-/r/_binary64`
31×	`distribute-lft-neg-in_binary64`
29×	`neg-sub0_binary64`
25×	`neg-mul-1_binary64`
22×	`associate--r+_binary64`
21×	`associate--l+_binary64`
19×	`sqr-pow_binary64`
17×	`associate-+l+_binary64`
14×	`distribute-neg-frac_binary64` `distribute-neg-in_binary64`
12×	`exp-sum_binary64` `swap-sqr_binary64`
10×	`unswap-sqr_binary64`
9×	`unpow3_binary64` `cube-mult_binary64`
7×	`mul-1-neg_binary64` `associate-+r+_binary64`
6×	`distribute-lft-neg-out_binary64`
5×	`exp-lft-sqr_binary64` `cube-unmult_binary64` `div-sub_binary64` `distribute-rgt-out--_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `distribute-rgt-out_binary64`
3×	`cube-div_binary64` `distribute-lft-out_binary64`
2×	`log-pow_binary64` `*-rgt-identity_binary64` `distribute-lft-out--_binary64`
1×	`pow-plus_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `unsub-neg_binary64` `difference-of-squares_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` `log-rec_binary64` `log-div_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-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_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` `/-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-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` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_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` `count-2_binary64` `associate-/l/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

208 → 196

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	313	10464
1	905	9674
2	3527	9674
3	4993	9674

prune233.0ms (1.1%)

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	22	22
Picked	0	1	1
Done	0	2	2
Total	196	25	221

Error

12.6b

Counts

221 → 25

Compiler

Compiled 7864 to 3292 computations (58.1% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

17.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
19.2b	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
19.2b	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
19.2b	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

rewrite275.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

12.6b

Rules

68×	`associate-*r/_binary64`
60×	`cbrt-div_binary64`
30×	`flip3-+_binary64` `flip-+_binary64`
28×	`frac-times_binary64`
26×	`sqrt-div_binary64`
24×	`pow1_binary64`
15×	`sqrt-pow1_binary64`
14×	`associate-*l/_binary64`
12×	`pow1/3_binary64`
9×	`pow-prod-up_binary64`
6×	`pow-plus_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
3×	`cbrt-prod_binary64` `pow-sqr_binary64`
2×	`pow2_binary64`
1×	`pow1/2_binary64` `pow3_binary64` `sqrt-prod_binary64`

Counts

4 → 83

Calls

4 calls:

12.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))
7.0ms	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
6.0ms	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
6.0ms	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))

Compiler

Compiled 9954 to 3870 computations (61.1% saved)

series2.5s (11.7%)

Error

12.3b

Counts

4 → 104

Calls

4 calls:

738.0ms	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
577.0ms	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
567.0ms	(cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
455.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (.f64 l -2)))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (.f64 l -2))))))) (cbrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U U)) Om)) (*.f64 l -2))))))))

Compiler

Compiled 32666 to 22405 computations (31.4% saved)

simplify330.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

402×	`associate-r_binary64`
347×	`associate-l_binary64` `*-commutative_binary64`
250×	`associate-/l*_binary64`
249×	`times-frac_binary64`
150×	`associate-/r*_binary64`
124×	`associate-*r/_binary64`
90×	`cancel-sign-sub-inv_binary64`
89×	`associate-*l/_binary64`
86×	`log-prod_binary64`
84×	`distribute-rgt-in_binary64`
82×	`distribute-lft-in_binary64`
76×	`sub-neg_binary64`
59×	`distribute-rgt-neg-in_binary64`
53×	`neg-sub0_binary64`
51×	`sqr-pow_binary64`
50×	`distribute-lft-neg-in_binary64`
46×	`neg-mul-1_binary64`
43×	`associate-/r/_binary64`
39×	`log-div_binary64`
37×	`associate--l+_binary64`
34×	`exp-prod_binary64`
27×	`associate--r+_binary64`
24×	`+-commutative_binary64`
21×	`associate-+l+_binary64`
20×	`distribute-neg-frac_binary64`
19×	`unpow1/3_binary64`
18×	`distribute-neg-in_binary64`
15×	`exp-diff_binary64`
13×	`mul-1-neg_binary64`
11×	`unpow3_binary64`
9×	`distribute-lft-neg-out_binary64`
8×	`log-pow_binary64` `cube-mult_binary64`
6×	`cube-unmult_binary64` `div-sub_binary64` `distribute-rgt-neg-out_binary64`
5×	`log-rec_binary64` `unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `rem-3cbrt-lft_binary64` `distribute-rgt-out--_binary64`
4×	`exp-to-pow_binary64` `exp-sum_binary64` `rem-sqrt-square_binary64` `unswap-sqr_binary64` `associate--r-_binary64` `associate-+r+_binary64`
3×	`swap-sqr_binary64` `cancel-sign-sub_binary64` `associate-+l-_binary64` `associate-+r-_binary64`
2×	`cube-div_binary64` `cube-prod_binary64` `rem-cube-cbrt_binary64` `remove-double-neg_binary64` `associate--l-_binary64`
1×	`1-exp_binary64` `rem-square-sqrt_binary64` `unsub-neg_binary64` `*-rgt-identity_binary64` `difference-of-squares_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_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-E_binary64` `pow-base-0_binary64` `pow-plus_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_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-cbrt-cube_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `/-rgt-identity_binary64` `-lft-identity_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` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate-/l/_binary64`

Counts

187 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	535	15435
1	1361	15258
2	4808	15129
3	4971	15129

prune281.0ms (1.3%)

Pruning

26 alts after pruning (22 fresh and 4 done)

	Pruned	Kept	Total
New	171	4	175
Fresh	3	18	21
Picked	0	1	1
Done	0	3	3
Total	174	26	200

Error

11.6b

Counts

200 → 26

Compiler

Compiled 12244 to 4802 computations (60.8% saved)

regimes5.1s (23.5%)

Accuracy

Total 12.5b remaining (47.3%)

Threshold costs 0b (0%)

Compiler

Compiled 62438 to 45276 computations (27.5% saved)

bsearch14.0ms (0.1%)

Compiler: Compiled 27 to 22 computations (18.5% saved)

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

249×	`distribute-rgt-neg-in_binary64`
175×	`cancel-sign-sub-inv_binary64`
169×	`distribute-lft-neg-in_binary64`
147×	`neg-mul-1_binary64` `neg-sub0_binary64`
146×	`distribute-lft-neg-out_binary64`
126×	`distribute-rgt-neg-out_binary64`
118×	`distribute-neg-in_binary64`
83×	`*-commutative_binary64`
77×	`sub-neg_binary64`
65×	`+-commutative_binary64`
57×	`unsub-neg_binary64`
45×	`remove-double-neg_binary64`
11×	`distribute-neg-out_binary64`
8×	`distribute-frac-neg_binary64`
6×	`distribute-neg-frac_binary64`
1×	`1-exp_binary64` `sqr-neg_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` `unpow1_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	272
1	126	272
2	180	270
3	242	270
4	299	270
5	344	270
6	373	270
7	409	270
8	440	270
9	490	270
10	571	270
11	659	270
12	748	270
13	846	270
14	961	270
15	1065	270
16	1116	270
17	1132	270
18	1146	270
19	1163	270
20	1176	270
21	1187	270
22	1189	270
23	1181	270

end3.0ms (0%)

Compiler: Compiled 179 to 108 computations (39.7% saved)

sample3.8s (17.6%)

Algorithm

1×

intervals

Results

1.2s	13004×	body	128	nan
757.0ms	8000×	body	128	valid
110.0ms	1229×	body	128	invalid

Compiler

Compiled 1188 to 814 computations (31.5% saved)

Details

analyze2.3s (10.7%)

sample104.0ms (0.5%)

simplify52.0ms (0.2%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite357.0ms (1.6%)

series1.3s (5.8%)

simplify250.0ms (1.2%)

prune241.0ms (1.1%)

localize19.0ms (0.1%)

rewrite189.0ms (0.9%)

series1.4s (6.4%)

simplify235.0ms (1.1%)

prune128.0ms (0.6%)

localize25.0ms (0.1%)

rewrite196.0ms (0.9%)

series2.0s (9.2%)

simplify221.0ms (1%)

prune233.0ms (1.1%)

localize31.0ms (0.1%)

rewrite275.0ms (1.3%)

series2.5s (11.7%)

simplify330.0ms (1.5%)

prune281.0ms (1.3%)

regimes5.1s (23.5%)

bsearch14.0ms (0.1%)

simplify71.0ms (0.3%)

end3.0ms (0%)

sample3.8s (17.6%)

Profiling