Details

analyze3.0ms (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 (0.9%)

Symmetry

(sort alpha beta)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify210.0ms (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 → 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

prune4.0ms (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

1.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.6b	(/.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))
	3.5b	(/.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

▶

2.6b

(/.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))

3.5b

(/.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)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
✓	2.4b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

series228.0ms (0.2%)

Counts

4 → 96

Calls

4 calls:

132.0ms	(/.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))
64.0ms	(/.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)))
29.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))
3.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)

rewrite187.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 476

Calls

4 calls:

30.0ms	(/.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))
17.0ms	(/.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)))
11.0ms	(/.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)

simplify542.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-def_binary64`
354×	`+-commutative_binary64`
311×	`associate-/l/_binary64`
282×	`associate-+r+_binary64`
198×	`*-commutative_binary64`

Counts

572 → 775

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1408	39316
1	4265	37075
2	5016	37075

prune2.0s (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	771	4	775
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	773	4	777

Error

0.2b

Counts

777 → 4

Alt Table

Status	Error	Program
	4.8b	(/.f64 (sqrt.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 beta alpha) 3) (sqrt.f64 (/.f64 (+.f64 1 (fma.f64 beta alpha (+.f64 beta alpha))) (.f64 (+.f64 2 (+.f64 beta alpha)) (+.f64 2 (+.f64 beta alpha)))))))
▶	4.0b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1) (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))))
	21.9b	(/.f64 (/.f64 (+.f64 1 alpha) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	4.8b	(/.f64 (/.f64 (+.f64 1 (fma.f64 beta alpha (+.f64 beta alpha))) (.f64 (+.f64 2 (+.f64 beta alpha)) (+.f64 2 (+.f64 beta alpha)))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))

Compiler

Compiled 52217 to 30652 computations (41.3% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))
✓	0.6b	(/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1))))
✓	2.3b	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1) (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))))
✓	2.4b	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1))

series1.5s (1%)

Counts

4 → 80

Calls

4 calls:

976.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1))))
281.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))
144.0ms	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1) (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))))
93.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1))

rewrite2.4min (96%)

Algorithm

1×	rewrite-expression-head

Rules

579714×	`times-frac_binary64`
305519×	`*-un-lft-identity_binary64`
205668×	`add-sqr-sqrt_binary64`
205664×	`add-cube-cbrt_binary64`
196084×	`sqrt-prod_binary64`

Calls

4 calls:

2.1s	(/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)))) (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1) (/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))))
21.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (sqrt.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1))))
15.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1)) 1) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1))))
7.0ms	(sqrt.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1))

Details

analyze3.0ms (0%)

sample1.3s (0.9%)

simplify210.0ms (0.1%)

prune4.0ms (0%)

localize11.0ms (0%)

series228.0ms (0.2%)

rewrite187.0ms (0.1%)

simplify542.0ms (0.4%)

prune2.0s (1.3%)

localize19.0ms (0%)

series1.5s (1%)

rewrite2.4min (96%)

Profiling