Details

analyze5.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 44 to 29 computations (34.1% saved)

sample1.3s (11.7%)

Symmetry

(sort alpha beta)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify216.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1227×	`associate-/l*_binary64`
689×	`distribute-rgt-in_binary64`
661×	`distribute-lft-in_binary64`
481×	`associate-/l/_binary64`
450×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	36	38
2	114	38
3	468	37
4	2359	37
5	2330	37
6	2458	37
7	2717	37
8	3067	37
9	3038	37
10	3136	37
11	3263	37
12	3406	37
13	3706	37
14	4273	37
15	4084	37
16	4107	37
17	4114	37
18	4121	37
19	4128	37
20	4135	37
21	4142	37
22	4149	37
23	4156	37
24	5226	37

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
▶	1.6b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

Status

Error

Program

2.1b

(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))

▶

1.6b

(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 190 to 123 computations (35.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
✓	0.0b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
✓	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
✓	17.5b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series291.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

160.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
69.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
53.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
8.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

rewrite75.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
34×	`distribute-lft-out_binary64`
34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
24×	`flip-+_binary64`

Counts

4 → 166

Calls

4 calls:

19.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
18.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
13.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
10.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify204.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

363×	`+-commutative_binary64`
342×	`distribute-rgt-in_binary64`
291×	`associate-+r+_binary64`
266×	`fma-def_binary64`
257×	`*-commutative_binary64`

Counts

262 → 350

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1061	15235
1	3719	14320
2	5141	14320

prune766.0ms (6.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	345	5	350
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	346	6	352

Error

Counts

352 → 6

Alt Table

Status	Error	Program
	2.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	27.0b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 8 (pow.f64 (+.f64 alpha beta) 3)))) (+.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (-.f64 (.f64 2 2) (.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
	1.7b	(.f64 (sqrt.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))))
	31.1b	(/.f64 (+.f64 1 alpha) (pow.f64 beta 2))
	1.7b	(.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3))))
▶	0.2b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 21267 to 14406 computations (32.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
✓	0.1b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
✓	0.2b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
✓	0.2b	(.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

series498.0ms (4.4%)

Counts

4 → 72

Calls

4 calls:

211.0ms	(*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
173.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
72.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))
41.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

rewrite143.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`*-un-lft-identity_binary64`
102×	`sqrt-div_binary64`
100×	`frac-times_binary64`
94×	`add-cbrt-cube_binary64`
94×	`add-exp-log_binary64`

Counts

4 → 300

Calls

4 calls:

37.0ms	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
27.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))
20.0ms	(*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

simplify289.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

326×	`+-commutative_binary64`
326×	`*-commutative_binary64`
303×	`distribute-rgt-in_binary64`
258×	`associate-+r+_binary64`
247×	`fma-def_binary64`

Counts

372 → 495

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1184	20850
1	3917	18947
2	5438	18947

prune1.3s (11.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	690	1	691
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	691	6	697

Error

Counts

697 → 6

Alt Table

Status	Error	Program
	2.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	27.0b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 8 (pow.f64 (+.f64 alpha beta) 3)))) (+.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (-.f64 (.f64 2 2) (.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
▶	1.7b	(.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3))))
✓	0.2b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	31.1b	(/.f64 (+.f64 1 alpha) (pow.f64 beta 2))
	1.7b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (sqrt.f64 (+.f64 beta 1))) (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 (+.f64 alpha beta) 2)))

Compiler

Compiled 43279 to 30556 computations (29.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))
✓	0.1b	(/.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3)))
✓	1.4b	(.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3))))
✓	17.5b	(/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))

series309.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

140.0ms	(.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3))))
113.0ms	(/.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3)))
48.0ms	(/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))
8.0ms	(*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))

rewrite126.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

304×	`*-un-lft-identity_binary64`
211×	`times-frac_binary64`
137×	`distribute-lft-out_binary64`
100×	`associate-/r/_binary64`
91×	`associate-r_binary64`

Counts

4 → 323

Calls

4 calls:

32.0ms	(.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3))))
19.0ms	(/.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))
10.0ms	(/.f64 (+.f64 1 beta) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))

simplify356.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

415×	`distribute-rgt-in_binary64`
360×	`+-commutative_binary64`
293×	`*-commutative_binary64`
288×	`associate-+r+_binary64`
275×	`fma-def_binary64`

Counts

419 → 435

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1173	23629
1	3992	22749
2	5669	22749

prune1.3s (11.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	434	1	435
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	435	6	441

Error

Counts

441 → 6

Alt Table

Status	Error	Program
	2.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	27.0b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 8 (pow.f64 (+.f64 alpha beta) 3)))) (+.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (-.f64 (.f64 2 2) (.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
✓	1.7b	(.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3))))
▶	0.2b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 2 (+.f64 alpha beta)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3))))
✓	0.2b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	31.1b	(/.f64 (+.f64 1 alpha) (pow.f64 beta 2))

Compiler

Compiled 27642 to 18550 computations (32.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta)))
✓	0.0b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3)))
✓	0.0b	(*.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 2 (+.f64 alpha beta))))
✓	0.1b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 2 (+.f64 alpha beta)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3))))

series258.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

154.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 2 (+.f64 alpha beta)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3))))
62.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3)))
22.0ms	(/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta)))
20.0ms	(*.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 2 (+.f64 alpha beta))))

rewrite155.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

839×	`*-un-lft-identity_binary64`
517×	`times-frac_binary64`
377×	`distribute-lft-out_binary64`
196×	`add-sqr-sqrt_binary64`
189×	`add-cube-cbrt_binary64`

Counts

4 → 464

Calls

4 calls:

38.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 2 (+.f64 alpha beta)))) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3))))
15.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3)))
11.0ms	(*.f64 (+.f64 1 alpha) (/.f64 1 (+.f64 2 (+.f64 alpha beta))))
7.0ms	(/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta)))

simplify407.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
312×	`+-commutative_binary64`
287×	`*-commutative_binary64`
238×	`associate-+r+_binary64`
233×	`associate-*r/_binary64`

Counts

560 → 573

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1158	25738
1	4063	24725
2	5079	24725

prune1.0s (9.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	571	2	573
Fresh	2	1	3
Picked	1	0	1
Done	1	1	2
Total	575	4	579

Error

Counts

579 → 4

Alt Table

Status	Error	Program
	27.0b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 8 (pow.f64 (+.f64 alpha beta) 3)))) (+.f64 (.f64 (+.f64 alpha beta) (+.f64 alpha beta)) (-.f64 (.f64 2 2) (.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
	1.3b	(/.f64 (.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 (+.f64 beta 3) alpha)) (-.f64 1 (.f64 alpha alpha))) (*.f64 (-.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))))
✓	0.2b	(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	1.7b	(/.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta)))) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 alpha (+.f64 beta 3))))

Compiler

Compiled 31385 to 21395 computations (31.8% saved)

regimes2.1s (18.6%)

Accuracy

Total 0.1b remaining (47%)

Threshold costs 0.1b (47%)

Counts

466 → 1

Compiler

Compiled 55931 to 40154 computations (28.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	25	37
2	24	37

end110.0ms (1%)

Remove: (sort alpha beta)
Compiler: Compiled 254 to 170 computations (33.1% saved)

Details

analyze5.0ms (0%)

sample1.3s (11.7%)

simplify216.0ms (1.9%)

prune5.0ms (0%)

localize12.0ms (0.1%)

series291.0ms (2.6%)

rewrite75.0ms (0.7%)

simplify204.0ms (1.8%)

prune766.0ms (6.8%)

localize13.0ms (0.1%)

series498.0ms (4.4%)

rewrite143.0ms (1.3%)

simplify289.0ms (2.6%)

prune1.3s (11.7%)

localize11.0ms (0.1%)

series309.0ms (2.7%)

rewrite126.0ms (1.1%)

simplify356.0ms (3.1%)

prune1.3s (11.3%)

localize16.0ms (0.1%)

series258.0ms (2.3%)

rewrite155.0ms (1.4%)

simplify407.0ms (3.6%)

prune1.0s (9.1%)

regimes2.1s (18.6%)

simplify2.0ms (0%)

end110.0ms (1%)

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