Details

analyze208.0ms (1.5%)

Algorithm

1×	search
2×	egg-herbie

Rules

708×	`associate-+l+_binary64`
673×	`associate-+r+_binary64`
459×	`div-sub_binary64`
372×	`*-commutative_binary64`
272×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
210×	`sub-neg_binary64`
202×	`distribute-rgt-out_binary64` `associate-l_binary64`
194×	`times-frac_binary64`
190×	`associate-r_binary64`
183×	`unsub-neg_binary64`
164×	`+-commutative_binary64`
103×	`neg-mul-1_binary64`
92×	`distribute-lft-out_binary64`
91×	`associate-/r/_binary64`
89×	`neg-sub0_binary64`
88×	`associate-/l*_binary64`
68×	`cancel-sign-sub-inv_binary64`
56×	`associate-/r*_binary64`
45×	`associate-*l/_binary64`
39×	`associate-*r/_binary64`
35×	`associate--r+_binary64`
33×	`distribute-rgt-neg-out_binary64`
30×	`associate-/l/_binary64`
28×	`distribute-frac-neg_binary64`
27×	`distribute-lft-neg-out_binary64`
26×	`associate--r-_binary64`
25×	`associate-+l-_binary64`
24×	`distribute-lft-neg-in_binary64` `associate-+r-_binary64`
20×	`distribute-rgt-neg-in_binary64`
18×	`div0_binary64` `distribute-neg-in_binary64`
16×	`distribute-neg-frac_binary64`
6×	`sub0-neg_binary64` `swap-sqr_binary64`
4×	`distribute-neg-out_binary64`
3×	`mul-1-neg_binary64` `+-rgt-identity_binary64` `distribute-lft1-in_binary64`
2×	`sqr-neg_binary64` `associate--l+_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` `unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_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` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_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` `pow-sqr_binary64` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	172
1	100	172
2	349	172
3	1379	172
4	3193	172
5	4121	172
6	4980	172
7	4894	172
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	201×	body	128	valid
6.0ms	25×	body	1024	valid
6.0ms	256×	pre	128	true
4.0ms	22×	body	512	valid
1.0ms	3×	body	2048	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 68 to 50 computations (26.5% saved)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
576×	`sub-neg_binary64`
537×	`div-sub_binary64`
255×	`+-commutative_binary64`
194×	`associate-+l+_binary64`
187×	`*-commutative_binary64`
183×	`associate-+r+_binary64`
142×	`associate-/l*_binary64`
137×	`unsub-neg_binary64`
117×	`neg-mul-1_binary64`
115×	`associate-*l/_binary64`
111×	`neg-sub0_binary64`
104×	`distribute-rgt-out_binary64`
103×	`associate-l_binary64`
100×	`associate-r_binary64`
98×	`associate-*r/_binary64`
60×	`distribute-lft-out_binary64`
55×	`associate-+l-_binary64`
44×	`associate--r+_binary64`
42×	`associate-/r*_binary64`
33×	`cancel-sign-sub-inv_binary64` `distribute-frac-neg_binary64` `distribute-rgt-neg-out_binary64`
32×	`associate--l+_binary64`
28×	`associate-/l/_binary64` `associate-/r/_binary64`
27×	`distribute-lft-neg-out_binary64`
25×	`associate-+r-_binary64`
24×	`mul0-rgt_binary64`
23×	`mul0-lft_binary64`
21×	`distribute-rgt-neg-in_binary64`
20×	`distribute-lft-neg-in_binary64`
18×	`distribute-neg-out_binary64`
14×	`distribute-neg-in_binary64`
12×	`distribute-neg-frac_binary64`
10×	`-rgt-identity_binary64` `-lft-identity_binary64`
8×	`distribute-rgt-out--_binary64`
6×	`sub0-neg_binary64` `div0_binary64` `distribute-lft1-in_binary64`
5×	`distribute-rgt1-in_binary64`
4×	`associate--r-_binary64`
3×	`associate--l-_binary64`
2×	`mul-1-neg_binary64` `swap-sqr_binary64`
1×	`1-exp_binary64` `sqr-neg_binary64` `remove-double-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` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_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` `rem-sqrt-square_binary64` `rem-square-sqrt_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` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-lft-out--_binary64` `count-2_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	43
2	106	43
3	409	43
4	1505	43
5	2316	43
6	3123	43
7	4954	43
8	4973	43
9	5371	43

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

25.1b

Counts

2 → 1

Compiler

Compiled 58 to 40 computations (31% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))
0.1b	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
1.6b	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
20.4b	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))

rewrite502.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

13.8b

Rules

56×	`*-un-lft-identity_binary64`
54×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`flip3-+_binary64` `flip-+_binary64` `associate-/r/_binary64`
12×	`distribute-lft-out_binary64`
10×	`associate-/l*_binary64`
9×	`associate-/l/_binary64`
8×	`frac-times_binary64`
7×	`div-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-/r*_binary64`
6×	`pow1_binary64` `add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64`
5×	`associate-r_binary64`
4×	`associate-l/_binary64` `associate-r/_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-l_binary64`
3×	`prod-exp_binary64` `cbrt-unprod_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `sub-neg_binary64`
1×	`sum-log_binary64` `+-commutative_binary64` `pow-prod-down_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

4 → 148

Calls

4 calls:

31.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
20.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
14.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))
12.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

Compiler

Compiled 6163 to 3027 computations (50.9% saved)

series740.0ms (5.3%)

Error

0.5b

Counts

4 → 81

Calls

4 calls:

287.0ms	(+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
231.0ms	(/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
85.0ms	(/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))
33.0ms	(*.f64 (+.f64 alpha beta) (-.f64 beta alpha))

Compiler

Compiled 11007 to 8574 computations (22.1% saved)

simplify195.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

543×	`times-frac_binary64`
374×	`distribute-rgt-in_binary64`
354×	`distribute-lft-in_binary64`
168×	`+-commutative_binary64`
149×	`associate-/l/_binary64`
142×	`*-commutative_binary64`
127×	`sub-neg_binary64`
117×	`associate-+r+_binary64`
77×	`associate-*r/_binary64`
63×	`cancel-sign-sub-inv_binary64`
58×	`div-sub_binary64`
56×	`distribute-neg-in_binary64`
48×	`associate-/l*_binary64`
42×	`neg-sub0_binary64`
40×	`neg-mul-1_binary64`
39×	`sqr-pow_binary64`
35×	`associate-/r*_binary64`
33×	`distribute-rgt-out_binary64`
26×	`associate--l+_binary64`
25×	`distribute-rgt-neg-in_binary64`
21×	`associate--r+_binary64`
19×	`distribute-lft-out_binary64`
18×	`distribute-lft-neg-in_binary64`
15×	`associate-r_binary64`
14×	`distribute-neg-frac_binary64` `distribute-lft-neg-out_binary64`
12×	`distribute-rgt-neg-out_binary64`
11×	`/-rgt-identity_binary64` `associate-l_binary64`
10×	`log-div_binary64` `unpow3_binary64`
9×	`cube-div_binary64`
8×	`unpow2_binary64` `unpow1_binary64` `cube-mult_binary64` `*-rgt-identity_binary64` `swap-sqr_binary64`
7×	`*-lft-identity_binary64` `unswap-sqr_binary64`
6×	`exp-prod_binary64` `exp-sum_binary64` `cube-prod_binary64`
5×	`log-prod_binary64` `associate-/r/_binary64`
4×	`difference-of-squares_binary64` `distribute-rgt1-in_binary64`
3×	`cube-unmult_binary64` `mul-1-neg_binary64` `distribute-rgt-out--_binary64` `associate-*l/_binary64` `associate-+r-_binary64`
2×	`associate-+l+_binary64`
1×	`prod-exp_binary64` `exp-diff_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `unsub-neg_binary64` `difference-of-sqr-1_binary64` `associate--l-_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` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_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` `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-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_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` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--r-_binary64` `associate-+l-_binary64`

Counts

229 → 207

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	655	11335
1	2011	10975
2	4989	10975

prune218.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	203	4	207
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	204	4	208

Error

0.1b

Counts

208 → 4

Compiler

Compiled 7509 to 3999 computations (46.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
1.6b	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
5.3b	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)

rewrite504.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

321×	`times-frac_binary64`
290×	`*-un-lft-identity_binary64`
211×	`add-sqr-sqrt_binary64`
140×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`
44×	`distribute-lft-out_binary64`
31×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
26×	`associate-/l*_binary64`
24×	`associate-/r/_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
7×	`div-exp_binary64` `cbrt-undiv_binary64` `associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-l_binary64`
3×	`prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `div-sub_binary64` `associate-/l/_binary64`
2×	`frac-times_binary64` `associate-*l/_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`sum-log_binary64` `+-commutative_binary64` `pow-prod-down_binary64` `associate-r/_binary64` `-commutative_binary64` `flip3--_binary64` `flip--_binary64`

Counts

4 → 295

Calls

4 calls:

46.0ms	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
28.0ms	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
21.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 11513 to 6062 computations (47.3% saved)

series1.1s (7.7%)

Error

0.1b

Counts

4 → 94

Calls

4 calls:

327.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
287.0ms	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
238.0ms	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
76.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 16832 to 12861 computations (23.6% saved)

simplify572.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

391×	`distribute-rgt-in_binary64`
267×	`+-commutative_binary64`
260×	`*-commutative_binary64`
206×	`associate-*r/_binary64`
196×	`associate-+r+_binary64`
181×	`sub-neg_binary64`
128×	`div-sub_binary64`
84×	`distribute-neg-in_binary64`
82×	`associate-/r*_binary64`
81×	`associate-/l/_binary64`
80×	`cancel-sign-sub-inv_binary64`
71×	`associate-/l*_binary64`
46×	`times-frac_binary64` `neg-sub0_binary64` `distribute-rgt-out_binary64`
43×	`neg-mul-1_binary64` `sqr-pow_binary64`
36×	`associate--l+_binary64`
33×	`distribute-lft-out_binary64` `associate--r+_binary64`
23×	`cube-prod_binary64` `/-rgt-identity_binary64`
22×	`unswap-sqr_binary64`
20×	`unpow3_binary64` `distribute-lft-in_binary64`
18×	`distribute-rgt-neg-in_binary64`
17×	`log-prod_binary64`
16×	`associate-r_binary64`
13×	`log-div_binary64` `distribute-neg-frac_binary64` `associate-/r/_binary64`
12×	`exp-prod_binary64` `associate-l_binary64`
11×	`cube-mult_binary64` `cube-div_binary64`
10×	`distribute-lft-neg-in_binary64`
9×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64`
8×	`*-rgt-identity_binary64` `swap-sqr_binary64`
7×	`exp-sum_binary64` `*-lft-identity_binary64`
5×	`distribute-lft-neg-out_binary64` `associate-+r-_binary64`
4×	`cube-unmult_binary64` `distribute-rgt1-in_binary64`
3×	`exp-diff_binary64` `mul-1-neg_binary64`
2×	`log-pow_binary64` `unsub-neg_binary64` `difference-of-squares_binary64` `distribute-rgt-out--_binary64` `associate-*l/_binary64`
1×	`log-rec_binary64` `pow-plus_binary64` `prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `difference-of-sqr-1_binary64` `associate--l-_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-lft-sqr_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` `rem-sqrt-square_binary64` `rem-square-sqrt_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` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--r-_binary64` `associate-+l-_binary64` `associate-+l+_binary64`

Counts

389 → 356

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1012	22447
1	3218	21921
2	4931	21921
3	4992	21921
4	4976	21921

prune408.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	355	1	356
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	356	4	360

Error

0.1b

Counts

360 → 4

Compiler

Compiled 14517 to 7988 computations (45% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
0.1b	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
0.1b	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
1.6b	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

rewrite335.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

48×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
7×	`difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate-/l/_binary64` `associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `associate-/l*_binary64`
4×	`distribute-lft-out_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `associate-l/_binary64` `associate-l*_binary64`
3×	`div-inv_binary64`
2×	`unswap-sqr_binary64` `associate-*r/_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`sum-log_binary64` `+-commutative_binary64` `pow-prod-down_binary64` `*-commutative_binary64` `div-sub_binary64` `flip3--_binary64` `flip--_binary64`

Counts

4 → 129

Calls

4 calls:

24.0ms	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
22.0ms	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
17.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 5146 to 2609 computations (49.3% saved)

series796.0ms (5.7%)

Error

0.1b

Counts

4 → 88

Calls

4 calls:

284.0ms	(+.f64 (/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)
234.0ms	(/.f64 (.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))
88.0ms	(.f64 (+.f64 beta alpha) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
69.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 12382 to 9562 computations (22.8% saved)

simplify183.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

528×	`times-frac_binary64`
478×	`associate-/l*_binary64`
319×	`distribute-rgt-in_binary64`
309×	`distribute-lft-in_binary64`
186×	`+-commutative_binary64`
148×	`*-commutative_binary64`
145×	`sub-neg_binary64`
126×	`associate-+r+_binary64`
106×	`associate-*r/_binary64`
84×	`associate-/r/_binary64`
74×	`associate-/l/_binary64`
63×	`distribute-neg-in_binary64`
52×	`cancel-sign-sub-inv_binary64`
43×	`div-sub_binary64`
40×	`neg-sub0_binary64`
39×	`sqr-pow_binary64`
36×	`neg-mul-1_binary64`
35×	`distribute-rgt-out_binary64`
32×	`associate--l+_binary64`
29×	`associate-/r*_binary64`
26×	`associate--r+_binary64`
20×	`distribute-lft-out_binary64`
16×	`distribute-neg-frac_binary64`
14×	`distribute-rgt-neg-in_binary64`
10×	`unpow3_binary64` `associate-l_binary64`
9×	`log-div_binary64` `associate-r_binary64`
8×	`unpow2_binary64` `unpow1_binary64` `cube-mult_binary64` `cube-div_binary64` `/-rgt-identity_binary64` `swap-sqr_binary64` `distribute-lft-neg-in_binary64`
7×	`cube-prod_binary64`
6×	`exp-prod_binary64` `*-rgt-identity_binary64` `unswap-sqr_binary64`
5×	`log-prod_binary64`
4×	`mul-1-neg_binary64` `distribute-rgt1-in_binary64`
3×	`cube-unmult_binary64` `distribute-lft-neg-out_binary64` `associate-*l/_binary64` `associate-+r-_binary64`
2×	`exp-sum_binary64` `*-lft-identity_binary64` `difference-of-squares_binary64` `associate-+l+_binary64`
1×	`prod-exp_binary64` `exp-diff_binary64` `1-exp_binary64` `exp-1-e_binary64` `unsub-neg_binary64` `difference-of-sqr-1_binary64` `distribute-rgt-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` `log-pow_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_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` `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` `rem-sqrt-square_binary64` `rem-square-sqrt_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` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+l-_binary64`

Counts

217 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	654	10293
1	2000	9890
2	5193	9890

prune251.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	181	5	186

Error

0.1b

Counts

186 → 5

Compiler

Compiled 7129 to 4015 computations (43.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))
0.1b	(exp.f64 (log.f64 (+.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))))
1.6b	(+.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))
2.2b	(log.f64 (+.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))))

rewrite272.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

44×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`associate-r_binary64`
21×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`
9×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `log-prod_binary64`
6×	`flip3-+_binary64` `flip-+_binary64` `add-log-exp_binary64`
4×	`log-div_binary64` `exp-prod_binary64` `exp-sum_binary64` `associate-l_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`log-pow_binary64` `exp-diff_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `unswap-sqr_binary64` `associate-*l/_binary64` `associate-/r/_binary64`
1×	`rem-log-exp_binary64` `sum-log_binary64` `+-commutative_binary64` `rem-exp-log_binary64` `pow-prod-down_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

19.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))
14.0ms	(log.f64 (+.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))))
13.0ms	(exp.f64 (log.f64 (+.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))))
13.0ms	(+.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))

Compiler

Compiled 4152 to 2487 computations (40.1% saved)

series2.0s (14.4%)

Error

0.1b

Counts

4 → 93

Calls

4 calls:

1.0s	(log.f64 (+.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta))))))
400.0ms	(exp.f64 (log.f64 (+.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))))
291.0ms	(+.f64 1 (/.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta)))) (+.f64 2 (+.f64 alpha (+.f64 (*.f64 2 i) beta)))))
91.0ms	(.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 (.f64 2 i) beta))))

Compiler

Compiled 25503 to 19945 computations (21.8% saved)

simplify286.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

328×	`*-commutative_binary64`
298×	`+-commutative_binary64`
284×	`distribute-rgt-in_binary64`
275×	`distribute-lft-in_binary64`
235×	`associate-+r+_binary64`
202×	`associate-*r/_binary64`
130×	`sub-neg_binary64`
120×	`associate-/l*_binary64`
96×	`associate-/r*_binary64`
80×	`times-frac_binary64`
76×	`distribute-neg-in_binary64`
60×	`cancel-sign-sub-inv_binary64`
57×	`sqr-pow_binary64`
55×	`unswap-sqr_binary64`
53×	`distribute-rgt-out_binary64`
49×	`associate-r_binary64`
40×	`neg-sub0_binary64`
38×	`neg-mul-1_binary64`
30×	`distribute-lft-out_binary64`
28×	`associate--r+_binary64`
26×	`associate--l+_binary64`
17×	`rem-exp-log_binary64`
12×	`swap-sqr_binary64`
11×	`distribute-neg-frac_binary64` `distribute-rgt-neg-in_binary64` `associate-l_binary64`
10×	`unpow2_binary64` `unpow1_binary64`
9×	`unpow3_binary64`
8×	`cube-mult_binary64` `*-lft-identity_binary64`
7×	`exp-prod_binary64` `*-rgt-identity_binary64`
6×	`exp-sum_binary64` `distribute-lft-neg-in_binary64`
5×	`log-prod_binary64` `prod-exp_binary64` `cube-unmult_binary64` `cube-div_binary64` `div-sub_binary64`
4×	`log-div_binary64` `distribute-lft-neg-out_binary64`
3×	`cube-prod_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `difference-of-squares_binary64` `distribute-rgt1-in_binary64` `distribute-rgt-out--_binary64` `associate-+r-_binary64`
2×	`exp-diff_binary64` `unsub-neg_binary64` `associate-*l/_binary64`
1×	`log-rec_binary64` `pow-plus_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_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` `log-pow_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` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_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` `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-lft1-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+l-_binary64` `associate-+l+_binary64`

Counts

188 → 163

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1037	18105
1	3494	17414
2	5252	17414

prune340.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	162	6	168

Error

0.1b

Counts

168 → 6

Compiler

Compiled 10792 to 6865 computations (36.4% saved)

regimes3.3s (23.7%)

Accuracy

Total 1.3b remaining (95.2%)

Threshold costs 0b (0%)

Compiler

Compiled 47464 to 34399 computations (27.5% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 25 to 16 computations (36% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

33×	`+-commutative_binary64`
30×	`*-commutative_binary64`
22×	`sub-neg_binary64`
20×	`neg-mul-1_binary64` `neg-sub0_binary64`
12×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
10×	`unsub-neg_binary64` `distribute-neg-in_binary64`
5×	`distribute-neg-frac_binary64`
2×	`/-rgt-identity_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` `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` `sqr-neg_binary64` `mul-1-neg_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-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	185
1	79	185
2	90	185
3	111	185
4	138	185
5	167	185
6	202	185
7	232	185
8	248	185
9	255	185
10	257	185
11	252	185

end2.0ms (0%)

Compiler: Compiled 124 to 68 computations (45.2% saved)

sample1.5s (11%)

Algorithm

1×

intervals

Results

385.0ms	6414×	body	128	valid
185.0ms	8000×	pre	128	true
166.0ms	731×	body	1024	valid
89.0ms	512×	body	512	valid
37.0ms	299×	body	256	valid
13.0ms	44×	body	2048	valid

Compiler

Compiled 543 to 352 computations (35.2% saved)

Iter	Nodes	Cost
0	53	185
1	79	185
2	90	185
3	111	185
4	138	185
5	167	185
6	202	185
7	232	185
8	248	185
9	255	185
10	257	185
11	252	185

Iter	Nodes	Cost
0	53	185
1	79	185
2	90	185
3	111	185
4	138	185
5	167	185
6	202	185
7	232	185
8	248	185
9	255	185
10	257	185
11	252	185

Details

analyze208.0ms (1.5%)

sample40.0ms (0.3%)

simplify77.0ms (0.6%)

prune5.0ms (0%)

localize14.0ms (0.1%)

rewrite502.0ms (3.6%)

series740.0ms (5.3%)

simplify195.0ms (1.4%)

prune218.0ms (1.6%)

localize14.0ms (0.1%)

rewrite504.0ms (3.6%)

series1.1s (7.7%)

simplify572.0ms (4.1%)

prune408.0ms (2.9%)

localize18.0ms (0.1%)

rewrite335.0ms (2.4%)

series796.0ms (5.7%)

simplify183.0ms (1.3%)

prune251.0ms (1.8%)

localize18.0ms (0.1%)

rewrite272.0ms (1.9%)

series2.0s (14.4%)

simplify286.0ms (2.1%)

prune340.0ms (2.4%)

regimes3.3s (23.7%)

bsearch10.0ms (0.1%)

simplify14.0ms (0.1%)

end2.0ms (0%)

sample1.5s (11%)

Profiling

Iter	Nodes	Cost
0	53	185
1	79	185
2	90	185
3	111	185
4	138	185
5	167	185
6	202	185
7	232	185
8	248	185
9	255	185
10	257	185
11	252	185