Details

analyze267.0ms (0.2%)

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)

sample43.0ms (0%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 83 to 55 computations (33.7% saved)

simplify220.0ms (0.1%)

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 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	36	40
2	110	40
3	444	37
4	2164	37
5	2127	37
6	2255	37
7	2514	37
8	2864	37
9	2835	37
10	2933	37
11	3060	37
12	3203	37
13	3503	37
14	4070	37
15	3881	37
16	3904	37
17	3911	37
18	3918	37
19	3925	37
20	3932	37
21	3939	37
22	3946	37
23	3953	37
24	5023	37

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

2.0b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	3.9b	(/.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))
	4.6b	(/.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

▶

3.9b

(/.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))

4.6b

(/.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 155 to 102 computations (34.2% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)
0.0b	(/.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)))
0.1b	(/.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))
3.6b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

rewrite944.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

804×	`times-frac_binary64`
586×	`*-un-lft-identity_binary64`
340×	`add-sqr-sqrt_binary64`
340×	`add-cube-cbrt_binary64`
123×	`distribute-lft-out_binary64`

Counts

4 → 465

Calls

4 calls:

33.0ms	(/.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))
16.0ms	(/.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)))
13.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))
6.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)

Compiler

Compiled 23398 to 13669 computations (41.6% saved)

series501.0ms (0.3%)

Error

0.0b

Counts

4 → 66

Calls

4 calls:

201.0ms	(/.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))
106.0ms	(/.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)))
48.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))
17.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)

Compiler

Compiled 11844 to 9115 computations (23% saved)

simplify1.4s (0.9%)

Algorithm

1×	egg-herbie

Rules

901×	`times-frac_binary64`
311×	`associate-/l/_binary64`
310×	`+-commutative_binary64`
248×	`associate-+r+_binary64`
168×	`*-commutative_binary64`

Counts

531 → 502

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1295	38047
1	3694	37000
2	4973	36724
3	4999	36724
4	4974	36724

prune808.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	495	7	502
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	497	7	504

Error

0.0b

Counts

504 → 7

Alt Table

Status	Error	Program
	27.9b	(/.f64 (-.f64 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) (+.f64 (.f64 2 (.f64 (/.f64 alpha beta) (/.f64 alpha beta))) (+.f64 (.f64 5 (/.f64 alpha (.f64 beta beta))) (/.f64 3 (.f64 beta beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	34.1b	(-.f64 (+.f64 (.f64 51 (/.f64 alpha (pow.f64 beta 4))) (+.f64 (/.f64 alpha (.f64 beta beta)) (+.f64 (.f64 31 (/.f64 (.f64 alpha alpha) (pow.f64 beta 4))) (+.f64 (/.f64 1 (.f64 beta beta)) (+.f64 (.f64 6 (/.f64 (pow.f64 alpha 3) (pow.f64 beta 4))) (/.f64 26 (pow.f64 beta 4))))))) (+.f64 (.f64 (/.f64 alpha (pow.f64 beta 3)) 9) (+.f64 (.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3))) (/.f64 6 (pow.f64 beta 3)))))
	4.0b	(.f64 (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (+.f64 (+.f64 beta alpha) 3)))
	4.0b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (.f64 (/.f64 (+.f64 2 (+.f64 beta alpha)) (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	4.5b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (cbrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha))) (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 3)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 3)))) (/.f64 (/.f64 (cbrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (cbrt.f64 (+.f64 (+.f64 beta alpha) 3))))
	4.0b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 beta alpha) 3) (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))))
▶	3.9b	(/.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 alpha beta) 3))

Compiler

Compiled 22400 to 12009 computations (46.4% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1)
0.0b	(/.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)))
0.1b	(/.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 alpha beta) 3))
3.6b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

rewrite1.0s (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

954×	`times-frac_binary64`
830×	`*-un-lft-identity_binary64`
383×	`add-sqr-sqrt_binary64`
383×	`add-cube-cbrt_binary64`
254×	`distribute-lft-out_binary64`

Counts

4 → 526

Calls

4 calls:

34.0ms	(/.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 alpha beta) 3))
19.0ms	(/.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)))
13.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))
7.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1)

Compiler

Compiled 21318 to 11547 computations (45.8% saved)

series501.0ms (0.3%)

Error

0.0b

Counts

4 → 66

Calls

4 calls:

206.0ms	(/.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 alpha beta) 3))
102.0ms	(/.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)))
52.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))
19.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1)

Compiler

Compiled 11564 to 8857 computations (23.4% saved)

simplify793.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

886×	`times-frac_binary64`
313×	`+-commutative_binary64`
311×	`associate-/l/_binary64`
249×	`associate-+r+_binary64`
169×	`*-commutative_binary64`

Counts

592 → 564

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1299	42696
1	3709	41572
2	4968	41260
3	5067	41260

prune653.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	563	1	564
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	564	7	571

Error

0.0b

Counts

571 → 7

Alt Table

Status	Error	Program
	27.9b	(/.f64 (-.f64 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) (+.f64 (.f64 2 (.f64 (/.f64 alpha beta) (/.f64 alpha beta))) (+.f64 (.f64 5 (/.f64 alpha (.f64 beta beta))) (/.f64 3 (*.f64 beta beta))))) (+.f64 (+.f64 alpha beta) 3))
	4.0b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 beta alpha) 3) (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))))
	34.1b	(-.f64 (+.f64 (.f64 51 (/.f64 alpha (pow.f64 beta 4))) (+.f64 (/.f64 alpha (.f64 beta beta)) (+.f64 (.f64 31 (/.f64 (.f64 alpha alpha) (pow.f64 beta 4))) (+.f64 (/.f64 1 (.f64 beta beta)) (+.f64 (.f64 6 (/.f64 (pow.f64 alpha 3) (pow.f64 beta 4))) (/.f64 26 (pow.f64 beta 4))))))) (+.f64 (.f64 (/.f64 alpha (pow.f64 beta 3)) 9) (+.f64 (.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3))) (/.f64 6 (pow.f64 beta 3)))))
	4.0b	(.f64 (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (+.f64 (+.f64 beta alpha) 3)))
▶	4.0b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (.f64 (/.f64 (+.f64 2 (+.f64 beta alpha)) (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	4.5b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (cbrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha))) (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 3)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 3)))) (/.f64 (/.f64 (cbrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (cbrt.f64 (+.f64 (+.f64 beta alpha) 3))))
✓	3.9b	(/.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 alpha beta) 3))

Compiler

Compiled 21899 to 11834 computations (46% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 2 (+.f64 beta alpha)) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))))
3.6b	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))
3.6b	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1))
9.5b	(/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (.f64 (/.f64 (+.f64 2 (+.f64 beta alpha)) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha))))

rewrite365.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

122×	`*-un-lft-identity_binary64`
102×	`times-frac_binary64`
56×	`sqrt-prod_binary64`
56×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`

Counts

4 → 177

Calls

4 calls:

27.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (.f64 (/.f64 (+.f64 2 (+.f64 beta alpha)) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha))))
14.0ms	(/.f64 (+.f64 2 (+.f64 beta alpha)) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1))
6.0ms	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))

Compiler

Compiled 8411 to 4198 computations (50.1% saved)

series465.0ms (0.3%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

261.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (.f64 (/.f64 (+.f64 2 (+.f64 beta alpha)) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha))))
41.0ms	(/.f64 (+.f64 2 (+.f64 beta alpha)) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))))
28.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1))
27.0ms	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))

Compiler

Compiled 9378 to 6958 computations (25.8% saved)

simplify366.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

406×	`associate-/r*_binary64`
363×	`times-frac_binary64`
343×	`associate-/l*_binary64`
204×	`+-commutative_binary64`
176×	`distribute-rgt-in_binary64`

Counts

231 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	728	12806
1	2084	11625
2	4945	11601
3	4991	11601
4	4999	11601
5	4947	11601

prune228.0ms (0.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	167	7	174

Error

0.0b

Counts

174 → 7

Alt Table

Status	Error	Program
	27.9b	(/.f64 (-.f64 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) (+.f64 (.f64 2 (.f64 (/.f64 alpha beta) (/.f64 alpha beta))) (+.f64 (.f64 5 (/.f64 alpha (.f64 beta beta))) (/.f64 3 (*.f64 beta beta))))) (+.f64 (+.f64 alpha beta) 3))
▶	4.0b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 beta alpha) 3) (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))))
	34.1b	(-.f64 (+.f64 (.f64 51 (/.f64 alpha (pow.f64 beta 4))) (+.f64 (/.f64 alpha (.f64 beta beta)) (+.f64 (.f64 31 (/.f64 (.f64 alpha alpha) (pow.f64 beta 4))) (+.f64 (/.f64 1 (.f64 beta beta)) (+.f64 (.f64 6 (/.f64 (pow.f64 alpha 3) (pow.f64 beta 4))) (/.f64 26 (pow.f64 beta 4))))))) (+.f64 (.f64 (/.f64 alpha (pow.f64 beta 3)) 9) (+.f64 (.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3))) (/.f64 6 (pow.f64 beta 3)))))
	4.0b	(.f64 (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (/.f64 (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (+.f64 (+.f64 beta alpha) 3)))
✓	4.0b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (.f64 (/.f64 (+.f64 2 (+.f64 beta alpha)) (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	4.5b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (cbrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha))) (.f64 (cbrt.f64 (+.f64 (+.f64 beta alpha) 3)) (cbrt.f64 (+.f64 (+.f64 beta alpha) 3)))) (/.f64 (/.f64 (cbrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))) (cbrt.f64 (+.f64 (+.f64 beta alpha) 3))))
✓	3.9b	(/.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 alpha beta) 3))

Compiler

Compiled 7849 to 4512 computations (42.5% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 beta alpha) 3) (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))))
0.5b	(/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))
3.6b	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))
3.6b	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1))

rewrite2.0min (82%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

287822×	`times-frac_binary64`
235685×	`*-un-lft-identity_binary64`
116914×	`sqrt-prod_binary64`
93629×	`add-sqr-sqrt_binary64`
93625×	`add-cube-cbrt_binary64`

Counts

4 → 62379

Calls

4 calls:

1.2s	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 beta alpha) 3) (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))))
13.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))
8.0ms	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1))

Compiler

Compiled 1265280 to 699567 computations (44.7% saved)

series1.5s (1%)

Error

0.0b

Counts

4 → 60

Calls

4 calls:

539.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))
407.0ms	(sqrt.f64 (+.f64 1 (+.f64 (*.f64 beta alpha) (+.f64 beta alpha))))
275.0ms	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 beta alpha) 3) (/.f64 (sqrt.f64 (+.f64 1 (+.f64 (.f64 beta alpha) (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha)))))
26.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1))

Compiler

Compiled 20621 to 16070 computations (22.1% saved)

simplify16.9s (11.3%)

Algorithm

1×	egg-herbie

Details

analyze267.0ms (0.2%)

sample43.0ms (0%)

simplify220.0ms (0.1%)

prune4.0ms (0%)

localize12.0ms (0%)

rewrite944.0ms (0.6%)

series501.0ms (0.3%)

simplify1.4s (0.9%)

prune808.0ms (0.5%)

localize13.0ms (0%)

rewrite1.0s (0.7%)

series501.0ms (0.3%)

simplify793.0ms (0.5%)

prune653.0ms (0.4%)

localize23.0ms (0%)

rewrite365.0ms (0.2%)

series465.0ms (0.3%)

simplify366.0ms (0.2%)

prune228.0ms (0.2%)

localize26.0ms (0%)

rewrite2.0min (82%)

series1.5s (1%)

simplify16.9s (11.3%)

Profiling