Details

analyze111.0ms (0.9%)

Algorithm

1×	search
2×	egg-herbie

Rules

915×	`distribute-rgt-in_binary64`
897×	`distribute-lft-in_binary64`
556×	`associate-/l/_binary64`
241×	`times-frac_binary64`
214×	`associate-l_binary64`
202×	`associate-/l*_binary64`
175×	`associate-r_binary64`
94×	`associate-/r*_binary64`
69×	`associate--l+_binary64`
56×	`sub-neg_binary64`
48×	`associate-/r/_binary64`
39×	`div-sub_binary64`
38×	`*-commutative_binary64`
32×	`associate-+l+_binary64`
30×	`associate-*l/_binary64`
29×	`+-commutative_binary64`
27×	`associate-*r/_binary64`
24×	`swap-sqr_binary64`
12×	`mul-1-neg_binary64` `associate-+r+_binary64`
7×	`difference-of-sqr-1_binary64`
6×	`distribute-rgt-out_binary64` `distribute-lft-out_binary64`
3×	`cube-unmult_binary64` `-rgt-identity_binary64` `-lft-identity_binary64`
1×	`1-exp_binary64` `swap-alpha-beta`
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-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` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `/-rgt-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` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-squares_binary64` `unswap-sqr_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` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	316
1	180	316
2	812	316
3	4816	316
4	5646	316
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Symmetry

(sort alpha beta)

Compiler

Compiled 63 to 34 computations (46% saved)

sample45.0ms (0.4%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 116 to 64 computations (44.8% saved)

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-+l+_binary64`
492×	`associate-l_binary64`
422×	`associate-r_binary64`
369×	`times-frac_binary64`
336×	`associate-/l*_binary64`
252×	`distribute-rgt-in_binary64`
250×	`distribute-lft-in_binary64`
212×	`div-sub_binary64`
171×	`associate-/r*_binary64`
169×	`associate-/l/_binary64`
153×	`associate-*l/_binary64`
134×	`associate-*r/_binary64`
95×	`associate-/r/_binary64`
75×	`associate--l+_binary64`
58×	`*-commutative_binary64`
47×	`associate-+r+_binary64`
32×	`distribute-rgt-out_binary64`
28×	`+-commutative_binary64`
15×	`sub-neg_binary64` `distribute-lft-out_binary64`
8×	`swap-sqr_binary64`
4×	`mul-1-neg_binary64` `associate-+l-_binary64` `associate-+r-_binary64`
2×	`cube-unmult_binary64`
1×	`pow-plus_binary64` `1-exp_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_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` `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-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` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `/-rgt-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` `sqr-pow_binary64` `difference-of-squares_binary64` `unswap-sqr_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` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	79
1	65	79
2	280	79
3	1518	79
4	4862	79
5	5395	79

prune6.0ms (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

50.5b

Counts

2 → 1

Compiler

Compiled 106 to 54 computations (49.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
34.2b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
43.1b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite848.0ms (7.2%)

Algorithm

1×	rewrite-expression-head

Error

34.9b

Rules

86×	`times-frac_binary64`
66×	`flip3-+_binary64` `flip-+_binary64` `associate-/r/_binary64`
61×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64` `frac-times_binary64`
34×	`associate-*r/_binary64`
30×	`add-cube-cbrt_binary64`
28×	`difference-of-squares_binary64`
22×	`prod-exp_binary64` `cbrt-unprod_binary64` `associate-*l/_binary64`
19×	`div-exp_binary64` `cbrt-undiv_binary64`
16×	`pow1_binary64`
14×	`associate-/l*_binary64` `difference-of-sqr-1_binary64`
9×	`div-inv_binary64` `associate-/l/_binary64`
7×	`associate-/r*_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64` `pow-prod-down_binary64` `associate-l_binary64`
3×	`swap-sqr_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `flip--_binary64` `pow2_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `pow-sqr_binary64` `unswap-sqr_binary64`

Counts

4 → 228

Calls

4 calls:

38.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
24.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
18.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
13.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 17673 to 6571 computations (62.8% saved)

series2.6s (21.6%)

Error

9.2b

Counts

4 → 100

Calls

4 calls:

1.8s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
307.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))
138.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
73.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 31701 to 22040 computations (30.5% saved)

simplify398.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

406×	`*-commutative_binary64`
395×	`+-commutative_binary64`
329×	`associate-+r+_binary64`
259×	`associate-/l*_binary64`
200×	`associate-*r/_binary64`
179×	`associate-/r*_binary64`
156×	`times-frac_binary64`
117×	`associate-r_binary64`
59×	`associate-/l/_binary64`
47×	`sub-neg_binary64`
45×	`sqr-pow_binary64`
40×	`associate-l_binary64`
35×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
26×	`associate--l+_binary64`
20×	`associate--r+_binary64`
15×	`div-sub_binary64`
13×	`/-rgt-identity_binary64`
9×	`unpow3_binary64` `unpow2_binary64` `cube-mult_binary64`
8×	`cancel-sign-sub-inv_binary64`
6×	`distribute-lft-out_binary64`
4×	`cube-prod_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `swap-sqr_binary64` `associate-+l+_binary64`
3×	`log-prod_binary64` `difference-of-squares_binary64` `distribute-rgt-out--_binary64` `associate-/r/_binary64` `associate-+r-_binary64`
2×	`log-div_binary64` `exp-prod_binary64` `-rgt-identity_binary64` `difference-of-sqr-1_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `associate-l/_binary64` `associate--l-_binary64`
1×	`1-exp_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `unswap-sqr_binary64` `distribute-neg-frac_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` `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` `unpow1_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-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-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` `unsub-neg_binary64` `mul-1-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` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate-+l-_binary64`

Counts

328 → 309

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1430	36732
1	5011	36732

prune565.0ms (4.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	304	5	309
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	305	5	310

Error

12.3b

Counts

310 → 5

Compiler

Compiled 23018 to 10674 computations (53.6% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.4b	(/.f64 1/64 (*.f64 i i))
1.9b	(/.f64 (.f64 alpha alpha) (.f64 i i))
18.3b	(/.f64 (.f64 beta beta) (.f64 i i))

rewrite108.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

7.1b

Rules

32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`div-exp_binary64` `cbrt-undiv_binary64`
9×	`prod-exp_binary64` `cbrt-unprod_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `-un-lft-identity_binary64` `associate-/l_binary64`
3×	`pow1_binary64` `add-log-exp_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/r*_binary64`

Counts

3 → 63

Calls

3 calls:

6.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
6.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
4.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1945 to 675 computations (65.3% saved)

series62.0ms (0.5%)

Error

12.3b

Counts

3 → 15

Calls

3 calls:

25.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
23.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
9.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 825 to 608 computations (26.3% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

691×	`associate-/l*_binary64`
488×	`unswap-sqr_binary64`
465×	`associate-*l/_binary64`
360×	`associate-/r*_binary64`
318×	`associate-l_binary64`
300×	`associate-*r/_binary64`
246×	`associate-r_binary64`
229×	`associate-/l/_binary64`
201×	`times-frac_binary64`
164×	`associate-/r/_binary64`
144×	`sub-neg_binary64`
126×	`sqr-pow_binary64`
72×	`log-prod_binary64`
71×	`log-div_binary64`
59×	`cube-div_binary64` `*-commutative_binary64`
52×	`cube-prod_binary64`
44×	`unpow3_binary64`
36×	`cube-mult_binary64` `associate-+l+_binary64`
33×	`neg-mul-1_binary64`
30×	`neg-sub0_binary64` `swap-sqr_binary64`
29×	`cancel-sign-sub-inv_binary64` `+-commutative_binary64`
28×	`pow-plus_binary64`
27×	`associate--r+_binary64` `associate-+r+_binary64`
26×	`associate--l+_binary64` `associate-+l-_binary64`
23×	`pow-sqr_binary64`
20×	`unsub-neg_binary64`
17×	`distribute-lft-neg-in_binary64`
16×	`cube-unmult_binary64`
15×	`log-pow_binary64` `distribute-rgt-neg-in_binary64` `distribute-rgt-in_binary64`
14×	`distribute-lft-in_binary64`
13×	`+-rgt-identity_binary64` `associate-+r-_binary64`
12×	`exp-prod_binary64` `sub0-neg_binary64`
7×	`count-2_binary64`
6×	`mul0-rgt_binary64` `mul0-lft_binary64` `distribute-lft-out--_binary64`
5×	`rem-sqrt-square_binary64` `distribute-lft-out_binary64`
4×	`--rgt-identity_binary64` `distribute-neg-in_binary64` `distribute-rgt-out--_binary64`
3×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64`
1×	`1-exp_binary64` `remove-double-neg_binary64` `+-lft-identity_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` `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` `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-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-square-sqrt_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_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-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `associate--l-_binary64`

Counts

78 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	1090
1	247	801
2	854	742
3	3278	712
4	4137	712
5	5084	712

prune25.0ms (0.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Error

7.2b

Counts

57 → 5

Compiler

Compiled 620 to 292 computations (52.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 beta i) 6)
0.4b	(/.f64 1/64 (*.f64 i i))
1.9b	(/.f64 (.f64 alpha alpha) (.f64 i i))
16.9b	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))

rewrite152.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

26×	`unpow-prod-down_binary64`
24×	`add-exp-log_binary64`
22×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `*-un-lft-identity_binary64`
21×	`add-cbrt-cube_binary64`
17×	`cbrt-prod_binary64`
7×	`div-exp_binary64`
6×	`cbrt-undiv_binary64`
5×	`pow1_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `associate-/l*_binary64`
3×	`pow-unpow_binary64`
2×	`sqr-pow_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/r*_binary64` `pow-exp_binary64`
1×	`pow1/3_binary64` `pow-pow_binary64` `pow-to-exp_binary64`

Counts

4 → 95

Calls

4 calls:

6.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
5.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))
4.0ms	(/.f64 1/64 (*.f64 i i))
4.0ms	(pow.f64 (/.f64 beta i) 6)

Compiler

Compiled 2870 to 1404 computations (51.1% saved)

series93.0ms (0.8%)

Error

7.2b

Counts

4 → 21

Calls

4 calls:

29.0ms	(pow.f64 (/.f64 beta i) 6)
24.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
23.0ms	(cbrt.f64 (pow.f64 (/.f64 beta i) 6))
11.0ms	(/.f64 1/64 (*.f64 i i))

Compiler

Compiled 1143 to 903 computations (21% saved)

simplify103.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

656×	`times-frac_binary64`
438×	`associate-/l*_binary64`
391×	`associate-*l/_binary64`
380×	`associate-l_binary64`
373×	`log-prod_binary64`
327×	`associate-r_binary64`
291×	`associate-*r/_binary64`
274×	`associate-/r*_binary64`
163×	`log-div_binary64`
153×	`associate-/l/_binary64`
116×	`sqr-pow_binary64`
91×	`unswap-sqr_binary64`
89×	`associate-/r/_binary64`
54×	`cube-div_binary64`
48×	`swap-sqr_binary64`
40×	`log-pow_binary64`
31×	`unpow3_binary64`
30×	`cube-mult_binary64`
22×	`cube-prod_binary64`
21×	`sub-neg_binary64`
19×	`exp-prod_binary64`
14×	`pow-sqr_binary64`
12×	`cube-unmult_binary64`
11×	`*-commutative_binary64`
9×	`cancel-sign-sub-inv_binary64`
8×	`pow-plus_binary64`
7×	`distribute-rgt-in_binary64`
6×	`rem-sqrt-square_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
5×	`distribute-lft-in_binary64`
4×	`unpow1/2_binary64` `unpow1_binary64` `*-rgt-identity_binary64` `count-2_binary64` `+-commutative_binary64`
3×	`unpow2_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `/-rgt-identity_binary64` `associate--r+_binary64`
2×	`associate--l+_binary64`
1×	`1-exp_binary64` `rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `unsub-neg_binary64` `*-lft-identity_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_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` `log-rec_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` `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-neg_binary64` `rem-3cbrt-rft_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `div-sub_binary64` `mul-1-neg_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` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+l-_binary64` `associate-+r-_binary64` `associate-+l+_binary64` `associate-+r+_binary64`

Counts

116 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	1684
1	356	1391
2	978	1309
3	4305	1309
4	5069	1309

prune38.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	71	5	76

Error

7.2b

Counts

76 → 5

Compiler

Compiled 828 to 451 computations (45.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 i (+.f64 alpha (+.f64 beta i)))
0.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
32.5b	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
32.7b	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))

rewrite675.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

354×	`*-un-lft-identity_binary64`
335×	`times-frac_binary64`
216×	`add-sqr-sqrt_binary64`
155×	`associate-r_binary64`
121×	`add-cube-cbrt_binary64`
86×	`distribute-lft-out_binary64`
67×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
59×	`associate-l_binary64`
36×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
34×	`associate-/r/_binary64`
30×	`div-exp_binary64` `cbrt-undiv_binary64`
19×	`flip3-+_binary64` `flip-+_binary64`
18×	`difference-of-sqr-1_binary64`
17×	`div-inv_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
8×	`pow1_binary64` `associate-/r*_binary64`
7×	`unswap-sqr_binary64`
5×	`associate-*r/_binary64`
4×	`add-log-exp_binary64` `associate-/l/_binary64` `associate-/l*_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `pow-prod-down_binary64` `*-commutative_binary64`
1×	`frac-times_binary64` `associate-*l/_binary64` `flip3--_binary64` `flip--_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`

Counts

4 → 334

Calls

4 calls:

156.0ms	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
12.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
10.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
9.0ms	(*.f64 i (+.f64 alpha (+.f64 beta i)))

Compiler

Compiled 19369 to 9239 computations (52.3% saved)

series1.9s (15.8%)

Error

6.9b

Counts

4 → 89

Calls

4 calls:

1.4s	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (+.f64 1 (+.f64 alpha (+.f64 beta (.f64 2 i))))) (/.f64 (/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (.f64 2 i)))) (-.f64 (+.f64 alpha (+.f64 beta (.f64 2 i))) 1)))
121.0ms	(/.f64 (+.f64 (.f64 alpha beta) (.f64 i (+.f64 alpha (+.f64 beta i)))) (+.f64 alpha (+.f64 beta (*.f64 2 i))))
94.0ms	(/.f64 (.f64 i (+.f64 alpha (+.f64 beta i))) (+.f64 alpha (+.f64 beta (.f64 2 i))))
52.0ms	(*.f64 i (+.f64 alpha (+.f64 beta i)))

Compiler

Compiled 25349 to 17428 computations (31.2% saved)

simplify696.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

436×	`*-commutative_binary64`
295×	`+-commutative_binary64`
260×	`associate-*r/_binary64`
235×	`associate-+r+_binary64`
182×	`associate-/l*_binary64`
153×	`associate-/r*_binary64`
148×	`sub-neg_binary64`
130×	`times-frac_binary64`
107×	`associate-*l/_binary64`
103×	`associate-r_binary64`
59×	`associate-/l/_binary64`
46×	`sqr-pow_binary64`
39×	`neg-mul-1_binary64` `neg-sub0_binary64`
31×	`associate--l+_binary64`
27×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
26×	`associate--r+_binary64`
20×	`log-div_binary64`
18×	`log-prod_binary64` `associate-l_binary64`
17×	`exp-prod_binary64` `/-rgt-identity_binary64`
10×	`unpow3_binary64` `unpow2_binary64` `unpow1_binary64` `cube-unmult_binary64` `cube-mult_binary64` `div-sub_binary64` `-rgt-identity_binary64` `-lft-identity_binary64`
9×	`associate-+l-_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`associate-+r-_binary64`
4×	`cube-prod_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out_binary64`
3×	`exp-sum_binary64` `swap-sqr_binary64`
2×	`unsub-neg_binary64` `difference-of-squares_binary64` `distribute-neg-in_binary64` `associate--l-_binary64`
1×	`log-pow_binary64` `log-rec_binary64` `1-exp_binary64` `cube-div_binary64` `difference-of-sqr-1_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_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` `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` `prod-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-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `mul-1-neg_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` `unswap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate-/r/_binary64` `associate--r-_binary64` `associate-+l+_binary64`

Counts

423 → 401

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1327	38030
1	4710	36020
2	4978	36020
3	4980	36020

prune519.0ms (4.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	398	3	401
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	399	7	406

Error

6.9b

Counts

406 → 7

Compiler

Compiled 24956 to 13111 computations (47.5% saved)

regimes1.2s (10.5%)

Accuracy

Total 0.6b remaining (6.1%)

Threshold costs 0.6b (6.1%)

Compiler

Compiled 32803 to 18706 computations (43% saved)

bsearch32.0ms (0.3%)

Steps

Iters	Range		Point
6	6.356911603051417e+128	5.2271623552457846e+129	3.046160862116767e+129

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`*-commutative_binary64`
1×	`1-exp_binary64` `sub-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` `sqr-neg_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	89
1	42	89
2	43	89
3	41	89

end8.0ms (0.1%)

Remove: (sort alpha beta)
Compiler: Compiled 180 to 114 computations (36.7% saved)

sample1.5s (12.4%)

Algorithm

1×

intervals

Results

691.0ms	8000×	body	128	valid
173.0ms	8000×	pre	128	true

Compiler

Compiled 434 to 276 computations (36.4% saved)

Details

analyze111.0ms (0.9%)

sample45.0ms (0.4%)

simplify45.0ms (0.4%)

prune6.0ms (0%)

localize15.0ms (0.1%)

rewrite848.0ms (7.2%)

series2.6s (21.6%)

simplify398.0ms (3.4%)

prune565.0ms (4.8%)

localize14.0ms (0.1%)

rewrite108.0ms (0.9%)

series62.0ms (0.5%)

simplify87.0ms (0.7%)

prune25.0ms (0.2%)

localize20.0ms (0.2%)

rewrite152.0ms (1.3%)

series93.0ms (0.8%)

simplify103.0ms (0.9%)

prune38.0ms (0.3%)

localize19.0ms (0.2%)

rewrite675.0ms (5.7%)

series1.9s (15.8%)

simplify696.0ms (5.9%)

prune519.0ms (4.4%)

regimes1.2s (10.5%)

bsearch32.0ms (0.3%)

simplify5.0ms (0%)

end8.0ms (0.1%)

sample1.5s (12.4%)

Profiling