Details

analyze963.0ms (10.8%)

Algorithm

1×	search
2×	egg-herbie

Rules

70×	`*-commutative_binary64`
57×	`associate-/l*_binary64`
30×	`associate-/r/_binary64`
26×	`distribute-rgt-out_binary64`
24×	`associate-*r/_binary64`
18×	`associate-r_binary64`
16×	`associate-*l/_binary64`
12×	`associate-/l/_binary64` `associate-l_binary64`
9×	`+-commutative_binary64`
6×	`distribute-rgt-in_binary64`
4×	`distribute-lft-out_binary64`
3×	`associate-/r*_binary64`
1×	`swap-a1-a2`
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` `1-exp_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` `times-frac_binary64` `div-sub_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `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-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `swap-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` `distribute-lft-in_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_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	25	80
1	65	80
2	120	80
3	174	80
4	228	80
5	258	80
6	285	80
7	279	80
8	279	80
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Symmetry

(sort a1 a2)

Compiler

Compiled 20 to 16 computations (20% saved)

sample87.0ms (1%)

Algorithm

1×

intervals

Results

19.0ms	53×	body	1024	valid
14.0ms	47×	body	1024	invalid
12.0ms	166×	body	128	valid
5.0ms	22×	body	512	valid
5.0ms	20×	body	512	invalid
2.0ms	15×	body	256	valid
2.0ms	10×	body	256	invalid
2.0ms	22×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`distribute-rgt-out_binary64` `associate-*r/_binary64`
6×	`associate-r_binary64`
5×	`associate-*l/_binary64`
4×	`associate-/l/_binary64` `associate-l_binary64`
3×	`+-commutative_binary64`
2×	`distribute-rgt-in_binary64` `associate-/r*_binary64`
1×	`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` `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` `1-exp_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` `times-frac_binary64` `div-sub_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `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-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `swap-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` `distribute-lft-in_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64` `associate-+l+_binary64` `associate-+r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	26	20
2	46	20
3	66	20
4	85	20
5	97	20
6	108	20
7	106	20
8	106	20

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite159.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
22×	`sqrt-prod_binary64` `associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`pow1_binary64` `add-log-exp_binary64`
3×	`associate-/l_binary64` `unswap-sqr_binary64` `associate-l*_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
1×	`frac-2neg_binary64` `clear-num_binary64` `pow-prod-down_binary64` `associate-r/_binary64` `-commutative_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

3 → 94

Calls

3 calls:

15.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2096 to 762 computations (63.6% saved)

series186.0ms (2.1%)

Error

0.4b

Counts

3 → 42

Calls

3 calls:

94.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
43.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
27.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1297 to 1213 computations (6.5% saved)

simplify128.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

367×	`sub-neg_binary64`
341×	`unswap-sqr_binary64`
336×	`associate-/l*_binary64`
303×	`*-commutative_binary64`
272×	`associate-*r/_binary64`
269×	`associate-*l/_binary64`
169×	`associate--l+_binary64`
153×	`distribute-rgt-in_binary64`
148×	`associate-+l+_binary64`
138×	`associate--r+_binary64`
133×	`distribute-lft-in_binary64`
131×	`associate-/r*_binary64`
129×	`associate-/r/_binary64`
118×	`associate-l_binary64`
115×	`associate-r_binary64`
109×	`associate-/l/_binary64`
100×	`cancel-sign-sub-inv_binary64`
98×	`times-frac_binary64`
96×	`associate-+r+_binary64`
81×	`unsub-neg_binary64`
70×	`sqr-pow_binary64`
54×	`neg-mul-1_binary64` `neg-sub0_binary64`
46×	`*-rgt-identity_binary64`
44×	`*-lft-identity_binary64` `difference-of-squares_binary64`
40×	`+-commutative_binary64`
35×	`distribute-rgt-neg-in_binary64`
30×	`/-rgt-identity_binary64`
29×	`associate-+l-_binary64`
28×	`cube-prod_binary64` `distribute-lft-neg-in_binary64`
26×	`distribute-neg-in_binary64` `associate-+r-_binary64`
24×	`log-prod_binary64` `exp-prod_binary64`
20×	`log-div_binary64`
19×	`div-sub_binary64`
18×	`cube-div_binary64`
17×	`+-rgt-identity_binary64` `distribute-neg-frac_binary64`
16×	`distribute-rgt-out_binary64`
15×	`pow-sqr_binary64`
12×	`unpow3_binary64`
10×	`cube-unmult_binary64` `distribute-lft-neg-out_binary64`
9×	`sub0-neg_binary64`
7×	`pow-plus_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out_binary64`
6×	`cube-mult_binary64` `swap-sqr_binary64` `associate--l-_binary64`
4×	`unpow1/2_binary64` `rem-sqrt-square_binary64`
3×	`log-rec_binary64` `unpow2_binary64` `unpow1_binary64` `distribute-rgt-neg-out_binary64`
2×	`remove-double-div_binary64`
1×	`prod-exp_binary64` `exp-sum_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-square-sqrt_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` `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-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` `mul-1-neg_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate--r-_binary64`

Counts

136 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3337
1	445	3089
2	1498	2993
3	4168	2993
4	5044	2993

prune107.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	9	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	9	128

Error

0.0b

Counts

128 → 9

Compiler

Compiled 1865 to 794 computations (57.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
0.5b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
8.8b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
8.8b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite226.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

100×	`sqrt-prod_binary64`
91×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
40×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`sqrt-div_binary64` `unswap-sqr_binary64`
8×	`pow1_binary64`
6×	`associate-/l_binary64` `associate-/r_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `sqrt-undiv_binary64` `div-inv_binary64` `associate-/l/_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`frac-2neg_binary64` `clear-num_binary64` `pow-prod-down_binary64` `sqrt-unprod_binary64` `associate-r/_binary64` `-commutative_binary64`

Counts

4 → 168

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
7.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
3.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 4785 to 1281 computations (73.2% saved)

series190.0ms (2.1%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

46.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
45.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
33.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
32.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 2324 to 1762 computations (24.2% saved)

simplify191.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

762×	`times-frac_binary64`
406×	`unswap-sqr_binary64`
357×	`associate-*l/_binary64`
294×	`associate-*r/_binary64`
276×	`associate-/r*_binary64`
254×	`associate-/l/_binary64`
197×	`*-commutative_binary64`
135×	`sub-neg_binary64`
108×	`associate-l_binary64`
106×	`distribute-rgt-in_binary64`
105×	`associate-r_binary64`
96×	`distribute-lft-in_binary64` `associate-/l*_binary64`
95×	`associate-/r/_binary64`
90×	`cancel-sign-sub-inv_binary64`
77×	`neg-sub0_binary64`
75×	`neg-mul-1_binary64`
72×	`distribute-rgt-neg-in_binary64`
66×	`distribute-lft-neg-in_binary64`
64×	`*-lft-identity_binary64`
57×	`sqr-pow_binary64`
55×	`*-rgt-identity_binary64`
44×	`difference-of-squares_binary64`
43×	`+-commutative_binary64`
35×	`distribute-neg-frac_binary64`
34×	`div-sub_binary64`
27×	`associate-+l-_binary64`
26×	`associate-+r-_binary64`
22×	`log-prod_binary64`
21×	`+-rgt-identity_binary64`
20×	`log-div_binary64` `cube-prod_binary64`
17×	`associate-+l+_binary64`
16×	`exp-prod_binary64` `cube-div_binary64`
15×	`unsub-neg_binary64`
13×	`cube-unmult_binary64`
12×	`/-rgt-identity_binary64` `pow-sqr_binary64`
11×	`sub0-neg_binary64`
10×	`pow-plus_binary64` `swap-sqr_binary64`
9×	`unpow3_binary64` `associate--l+_binary64` `associate-+r+_binary64`
8×	`associate--r+_binary64`
7×	`distribute-rgt-out--_binary64`
6×	`cube-mult_binary64` `rem-sqrt-square_binary64` `distribute-lft-neg-out_binary64`
4×	`log-rec_binary64` `mul-1-neg_binary64` `distribute-neg-in_binary64` `distribute-rgt-out_binary64`
3×	`unpow1/2_binary64` `rem-square-sqrt_binary64` `associate--l-_binary64`
2×	`unpow2_binary64` `unpow1_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `div0_binary64` `+-inverses_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `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-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` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_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`

Counts

216 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	5477
1	438	5298
2	1389	5137
3	4097	5137
4	5073	5137

prune144.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	189	9	198

Error

Counts

198 → 9

Compiler

Compiled 3645 to 1245 computations (65.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
8.8b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
8.9b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

rewrite177.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

41×	`add-sqr-sqrt_binary64`
39×	`sqrt-prod_binary64`
23×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`sqrt-div_binary64` `associate-r_binary64`
15×	`pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-l_binary64`
7×	`associate-*r/_binary64`
6×	`pow-prod-down_binary64` `unswap-sqr_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`pow1/2_binary64` `add-log-exp_binary64` `sqrt-pow1_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`rem-sqrt-square_binary64`
2×	`div-inv_binary64` `*-commutative_binary64`
1×	`sqrt-unprod_binary64`

Counts

4 → 110

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
13.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
5.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3424 to 934 computations (72.7% saved)

series245.0ms (2.8%)

Error

Counts

4 → 54

Calls

4 calls:

87.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
43.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
41.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
33.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 2459 to 1994 computations (18.9% saved)

simplify184.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

511×	`times-frac_binary64`
450×	`associate-/l*_binary64`
360×	`cancel-sign-sub-inv_binary64`
241×	`associate-r_binary64`
202×	`associate-l_binary64`
156×	`distribute-rgt-in_binary64`
147×	`*-commutative_binary64`
139×	`distribute-lft-in_binary64`
134×	`neg-sub0_binary64`
129×	`neg-mul-1_binary64`
127×	`sub-neg_binary64`
126×	`distribute-rgt-neg-in_binary64`
115×	`distribute-lft-neg-in_binary64`
103×	`associate-/r/_binary64`
76×	`distribute-rgt-out_binary64`
69×	`unswap-sqr_binary64`
52×	`+-commutative_binary64`
42×	`distribute-lft-out_binary64`
41×	`sqr-pow_binary64`
39×	`unsub-neg_binary64`
36×	`distribute-neg-frac_binary64` `associate-*l/_binary64`
35×	`associate-/r*_binary64`
29×	`associate-*r/_binary64`
28×	`distribute-neg-in_binary64`
27×	`cube-prod_binary64`
26×	`log-prod_binary64` `exp-prod_binary64` `associate-/l/_binary64` `associate--l+_binary64`
25×	`associate-+l+_binary64`
24×	`*-rgt-identity_binary64`
23×	`associate--r+_binary64`
20×	`associate-+r+_binary64`
19×	`*-lft-identity_binary64`
16×	`swap-sqr_binary64`
15×	`log-div_binary64` `cube-unmult_binary64`
14×	`unpow3_binary64` `div-sub_binary64` `distribute-rgt-out--_binary64`
10×	`cube-div_binary64` `distribute-lft-neg-out_binary64`
9×	`pow-plus_binary64` `cube-mult_binary64`
8×	`log-rec_binary64` `rem-sqrt-square_binary64`
7×	`difference-of-squares_binary64`
6×	`/-rgt-identity_binary64`
5×	`mul-1-neg_binary64`
4×	`unpow1/2_binary64` `pow-sqr_binary64`
3×	`unpow2_binary64` `unpow1_binary64` `associate-+r-_binary64`
2×	`rem-square-sqrt_binary64` `+-rgt-identity_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-out--_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` `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-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` `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--r-_binary64` `associate--l-_binary64`

Counts

164 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4486
1	570	4178
2	1882	4128
3	4678	4128
4	4995	4128
5	4969	4128

prune107.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	132	7	139

Error

Counts

139 → 7

Compiler

Compiled 2769 to 970 computations (65% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (/.f64 1 2))))
0.4b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 2)))

rewrite104.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

22×	`add-sqr-sqrt_binary64`
17×	`associate-r_binary64`
16×	`sqrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`
10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-*r/_binary64`
6×	`sqrt-div_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64` `flip3-+_binary64` `flip-+_binary64`
4×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `unswap-sqr_binary64` `associate-*l/_binary64`
2×	`*-commutative_binary64`
1×	`div-inv_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

3 → 73

Calls

3 calls:

11.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 2)))
11.0ms	(.f64 (cos.f64 th) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (/.f64 1 2))))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1754 to 760 computations (56.7% saved)

series170.0ms (1.9%)

Error

Counts

3 → 42

Calls

3 calls:

84.0ms	(.f64 (cos.f64 th) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (/.f64 1 2))))
40.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (/.f64 1 2)))
27.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1357 to 1267 computations (6.6% saved)

simplify108.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

561×	`distribute-rgt-in_binary64`
547×	`distribute-lft-in_binary64`
351×	`sub-neg_binary64`
313×	`cancel-sign-sub-inv_binary64`
208×	`associate-r_binary64`
199×	`associate-l_binary64`
176×	`associate--l+_binary64`
114×	`associate--r+_binary64` `*-commutative_binary64`
85×	`neg-mul-1_binary64` `neg-sub0_binary64`
79×	`distribute-rgt-out_binary64`
73×	`exp-prod_binary64` `distribute-rgt-neg-in_binary64`
69×	`unswap-sqr_binary64`
64×	`distribute-lft-neg-in_binary64`
45×	`distribute-lft-out_binary64`
41×	`sqr-pow_binary64` `+-commutative_binary64`
40×	`unsub-neg_binary64`
32×	`cube-prod_binary64`
28×	`log-prod_binary64`
26×	`*-rgt-identity_binary64`
24×	`distribute-neg-in_binary64`
23×	`associate-+l+_binary64`
21×	`exp-sum_binary64` `*-lft-identity_binary64` `associate-+l-_binary64`
20×	`associate-+r+_binary64`
18×	`swap-sqr_binary64`
15×	`distribute-rgt-out--_binary64`
14×	`distribute-lft-neg-out_binary64`
12×	`unpow3_binary64`
11×	`associate-/l*_binary64`
10×	`cube-unmult_binary64`
9×	`times-frac_binary64` `associate-/l/_binary64` `associate-/r*_binary64`
8×	`pow-sqr_binary64`
7×	`pow-plus_binary64` `difference-of-squares_binary64`
6×	`cube-mult_binary64` `rem-sqrt-square_binary64`
5×	`distribute-rgt-neg-out_binary64` `associate-/r/_binary64` `associate-*r/_binary64`
4×	`unpow1/2_binary64`
3×	`unpow2_binary64` `unpow1_binary64` `associate--l-_binary64`
2×	`/-rgt-identity_binary64`
1×	`prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-square-sqrt_binary64` `distribute-lft-out--_binary64` `associate-*l/_binary64` `associate-+r-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_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-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `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` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate--r-_binary64`

Counts

115 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	2474
1	421	2121
2	1581	2064
3	4629	2064
4	5092	2064

prune65.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Error

Counts

113 → 7

Compiler

Compiled 1333 to 582 computations (56.3% saved)

regimes2.7s (30.2%)

Accuracy

Total 0.3b remaining (93.2%)

Threshold costs 0.3b (93.2%)

Compiler

Compiled 35244 to 25841 computations (26.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_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` `1-exp_binary64` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	34
1	17	34
2	17	34

end8.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 66 to 39 computations (40.9% saved)

sample2.6s (29.1%)

Algorithm

1×

intervals

Results

559.0ms	1772×	body	1024	valid
463.0ms	1498×	body	1024	invalid
356.0ms	4868×	body	128	valid
205.0ms	910×	body	512	valid
175.0ms	793×	body	512	invalid
68.0ms	440×	body	256	valid
61.0ms	369×	body	256	invalid
56.0ms	682×	body	128	invalid
5.0ms	10×	body	2048	valid

Compiler

Compiled 164 to 140 computations (14.6% saved)

Details

analyze963.0ms (10.8%)

sample87.0ms (1%)

simplify12.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite159.0ms (1.8%)

series186.0ms (2.1%)

simplify128.0ms (1.4%)

prune107.0ms (1.2%)

localize15.0ms (0.2%)

rewrite226.0ms (2.5%)

series190.0ms (2.1%)

simplify191.0ms (2.1%)

prune144.0ms (1.6%)

localize13.0ms (0.2%)

rewrite177.0ms (2%)

series245.0ms (2.8%)

simplify184.0ms (2.1%)

prune107.0ms (1.2%)

localize11.0ms (0.1%)

rewrite104.0ms (1.2%)

series170.0ms (1.9%)

simplify108.0ms (1.2%)

prune65.0ms (0.7%)

regimes2.7s (30.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end8.0ms (0.1%)

sample2.6s (29.1%)

Profiling