Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
56.2%	0%	43.8%	1

Compiler

Compiled 44 to 29 computations (34.1% saved)

sample1.2s (12.3%)

Infinites

0% of outputs are infinite.

Symmetry

(sort alpha beta)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify211.0ms (2.2%)

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

1.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.3b	(/.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))
▶	2.0b	(/.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

2.3b

(/.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))

▶

2.0b

(/.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)))
✓	20.5b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series251.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

131.0ms	(/.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)))
65.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
47.0ms	(/.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))

rewrite78.0ms (0.8%)

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:

21.0ms	(/.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)))
19.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
12.0ms	(/.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 (2.1%)

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

prune662.0ms (6.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	342	8	350
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	344	8	352

Error

0.0b

Counts

352 → 8

Alt Table

Status	Error	Program
	2.0b	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
▶	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	2.0b	(/.f64 (+.f64 alpha 1) (/.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
	2.0b	(.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))))
	2.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (+.f64 (.f64 4 beta) (+.f64 4 (+.f64 (pow.f64 beta 2) (+.f64 (.f64 2 (.f64 beta alpha)) (*.f64 4 alpha))))))) (+.f64 alpha (+.f64 beta 3)))
	12.0b	(cbrt.f64 (/.f64 (pow.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))) 3) (pow.f64 (+.f64 alpha (+.f64 beta 3)) 3)))

Compiler

Compiled 21325 to 14460 computations (32.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series260.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

132.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
63.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
46.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
18.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

rewrite158.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

826×	`*-un-lft-identity_binary64`
508×	`times-frac_binary64`
374×	`distribute-lft-out_binary64`
191×	`add-sqr-sqrt_binary64`
182×	`add-cube-cbrt_binary64`

Counts

4 → 430

Calls

4 calls:

38.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
24.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
16.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
7.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

simplify798.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

384×	`+-commutative_binary64`
304×	`associate-+r+_binary64`
291×	`*-commutative_binary64`
273×	`fma-def_binary64`
251×	`associate-*r/_binary64`

Counts

526 → 532

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1227	25024
1	4173	23877
2	4994	23877

prune1.2s (12.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	530	2	532
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	532	8	540

Error

Counts

540 → 8

Alt Table

Status	Error	Program
	2.0b	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
✓	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
▶	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	2.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 (+.f64 alpha beta) 2)))
	0.3b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
	2.0b	(.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))))
	2.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (+.f64 (.f64 4 beta) (+.f64 4 (+.f64 (pow.f64 beta 2) (+.f64 (.f64 2 (.f64 beta alpha)) (*.f64 4 alpha))))))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 30234 to 20219 computations (33.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))
✓	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
✓	0.3b	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))

series304.0ms (3.1%)

Counts

4 → 88

Calls

4 calls:

144.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
69.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))
49.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
42.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

rewrite224.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

769×	`*-un-lft-identity_binary64`
364×	`times-frac_binary64`
331×	`distribute-lft-out_binary64`
224×	`sqrt-prod_binary64`
206×	`add-sqr-sqrt_binary64`

Counts

4 → 396

Calls

4 calls:

41.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
34.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))
29.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
9.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

simplify361.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

373×	`+-commutative_binary64`
304×	`*-commutative_binary64`
297×	`associate-+r+_binary64`
280×	`fma-def_binary64`
251×	`associate-*r/_binary64`

Counts

484 → 474

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1190	26003
1	4147	24194
2	5010	24194

prune1.2s (12.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	571	0	571
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	571	8	579

Error

Counts

579 → 8

Alt Table

Status	Error	Program
	2.0b	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
✓	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
✓	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	2.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 (+.f64 alpha beta) 2)))
▶	0.3b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
	2.0b	(.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))))
	2.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (+.f64 (.f64 4 beta) (+.f64 4 (+.f64 (pow.f64 beta 2) (+.f64 (.f64 2 (.f64 beta alpha)) (*.f64 4 alpha))))))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 33813 to 23420 computations (30.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
	0.0b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
✓	0.1b	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))))
✓	0.2b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))

series171.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

136.0ms

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

35.0ms

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

rewrite88.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`times-frac_binary64`
66×	`add-exp-log_binary64`
57×	`*-un-lft-identity_binary64`
38×	`div-exp_binary64`
36×	`add-cbrt-cube_binary64`

Counts

2 → 132

Calls

2 calls:

41.0ms

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

28.0ms

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

simplify229.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

892×	`times-frac_binary64`
752×	`fma-def_binary64`
236×	`+-commutative_binary64`
189×	`associate-+r+_binary64`
172×	`*-commutative_binary64`

Counts

180 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	777	12961
1	2718	12074
2	4947	12049
3	4951	12049

prune1.2s (12.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	588	2	590
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	591	7	598

Error

Counts

598 → 7

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
✓	0.3b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))
	2.0b	(.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
	2.0b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (+.f64 (.f64 4 beta) (+.f64 4 (+.f64 (pow.f64 beta 2) (+.f64 (.f64 2 (.f64 beta alpha)) (*.f64 4 alpha))))))) (+.f64 alpha (+.f64 beta 3)))
	0.1b	(/.f64 (/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))))) (+.f64 (+.f64 alpha beta) 2))
	1.8b	(/.f64 (.f64 (/.f64 1 (+.f64 (+.f64 beta 3) alpha)) (.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (fma.f64 alpha alpha -1))) (*.f64 (-.f64 alpha 1) (+.f64 (+.f64 alpha beta) 2)))

Compiler

Compiled 34085 to 23170 computations (32% saved)

regimes615.0ms (6.4%)

Accuracy

Total 0.1b remaining (70%)

Threshold costs 0.1b (70%)

Counts

176 → 1

Compiler

Compiled 16109 to 11474 computations (28.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	25	37
2	24	37

end179.0ms (1.8%)

Remove: (sort alpha beta)
Compiler: Compiled 330 to 228 computations (30.9% saved)

Details

analyze1.0ms (0%)

sample1.2s (12.3%)

simplify211.0ms (2.2%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series251.0ms (2.6%)

rewrite78.0ms (0.8%)

simplify204.0ms (2.1%)

prune662.0ms (6.8%)

localize15.0ms (0.2%)

series260.0ms (2.7%)

rewrite158.0ms (1.6%)

simplify798.0ms (8.2%)

prune1.2s (12.1%)

localize12.0ms (0.1%)

series304.0ms (3.1%)

rewrite224.0ms (2.3%)

simplify361.0ms (3.7%)

prune1.2s (12.6%)

localize14.0ms (0.1%)

series171.0ms (1.8%)

rewrite88.0ms (0.9%)

simplify229.0ms (2.4%)

prune1.2s (12.8%)

regimes615.0ms (6.4%)

simplify2.0ms (0%)

end179.0ms (1.8%)

Profiling