Details

analyze5.0ms (0.1%)

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)

sample1.4s (14%)

Symmetry

(sort alpha beta)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify212.0ms (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

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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.6b	(/.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))
▶	1.9b	(/.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

4.6b

(/.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))

▶

1.9b

(/.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)

localize14.0ms (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))
✓	0.1b	(.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)))
✓	18.0b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series272.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

147.0ms	(/.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))))
49.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
7.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

rewrite76.0ms (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:

20.0ms	(/.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))

simplify210.0ms (2.2%)

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

prune651.0ms (6.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	343	7	350
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	345	7	352

Error

0.0b

Counts

352 → 7

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	2.7b	(.f64 (/.f64 (+.f64 alpha 1) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	2.0b	(/.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)))
	32.8b	(-.f64 (+.f64 (/.f64 alpha (.f64 beta beta)) (/.f64 1 (.f64 beta beta))) (fma.f64 9 (/.f64 alpha (pow.f64 beta 3)) (fma.f64 3 (/.f64 (*.f64 alpha alpha) (pow.f64 beta 3)) (/.f64 6 (pow.f64 beta 3)))))
	7.1b	(/.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))) 3)) (+.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)))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (.f64 2 beta) 4))))))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 21289 to 14432 computations (32.2% saved)

localize12.0ms (0.1%)

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

series258.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

143.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
70.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
23.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
21.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

rewrite81.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

192×	`*-un-lft-identity_binary64`
89×	`times-frac_binary64`
82×	`distribute-lft-out_binary64`
60×	`add-sqr-sqrt_binary64`
48×	`add-cube-cbrt_binary64`

Counts

4 → 210

Calls

4 calls:

25.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
19.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
9.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
7.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

simplify231.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-def_binary64`
340×	`+-commutative_binary64`
271×	`associate-+r+_binary64`
244×	`*-commutative_binary64`
216×	`sub-neg_binary64`

Counts

306 → 393

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1073	16270
1	3699	15449
2	4984	15449

prune726.0ms (7.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	388	5	393
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	393	7	400

Error

Counts

400 → 7

Alt Table

Status	Error	Program
	0.6b	(/.f64 (/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3))))
	0.9b	(*.f64 (/.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.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)))
▶	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (/.f64 (+.f64 beta 1) 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.2b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
	1.9b	(/.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 2 (+.f64 alpha beta))))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (.f64 2 beta) 4))))))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 22565 to 15270 computations (32.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series231.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

143.0ms

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

67.0ms

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

20.0ms

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

rewrite128.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

410×	`*-un-lft-identity_binary64`
331×	`times-frac_binary64`
165×	`add-sqr-sqrt_binary64`
155×	`distribute-lft-out_binary64`
137×	`add-cube-cbrt_binary64`

Counts

3 → 313

Calls

3 calls:

46.0ms

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

24.0ms

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

10.0ms

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

simplify295.0ms (3%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-def_binary64`
307×	`+-commutative_binary64`
249×	`*-commutative_binary64`
247×	`associate-+r+_binary64`
237×	`distribute-rgt-in_binary64`

Counts

385 → 433

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1036	18367
1	3458	17355
2	5159	17355

prune1.0s (10.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	519	1	520
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	520	7	527

Error

Counts

527 → 7

Alt Table

Status	Error	Program
	0.6b	(/.f64 (/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (+.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)))
✓	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (/.f64 (+.f64 beta 1) 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.2b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
	1.9b	(/.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 2 (+.f64 alpha beta))))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (.f64 2 beta) 4))))))) (+.f64 alpha (+.f64 beta 3)))
	0.8b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (/.f64 (+.f64 beta 1) 1) (+.f64 (+.f64 alpha beta) 2)))))

Compiler

Compiled 28516 to 19511 computations (31.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series315.0ms (3.2%)

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)))
70.0ms	(.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))))
54.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
45.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

rewrite191.0ms (2%)

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:

39.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
28.0ms	(/.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)))
26.0ms	(.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))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

simplify359.0ms (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%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	570	1	571
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	571	7	578

Error

Counts

578 → 7

Alt Table

Status	Error	Program
	0.8b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 1 alpha) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 2 (+.f64 alpha beta))) (+.f64 2 (+.f64 alpha beta))))))
	0.6b	(/.f64 (/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 alpha (+.f64 beta 3)))) (sqrt.f64 (+.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)))
✓	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (/.f64 (+.f64 beta 1) 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.2b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (sqrt.f64 (+.f64 beta 1))))) (+.f64 alpha (+.f64 beta 3)))
	1.9b	(/.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 2 (+.f64 alpha beta))))
	2.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (.f64 2 beta) 4))))))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 33611 to 23280 computations (30.7% saved)

regimes1.7s (17.6%)

Accuracy

Total 0.1b remaining (76.7%)

Threshold costs 0.1b (76.7%)

Counts

286 → 1

Compiler

Compiled 26231 to 18569 computations (29.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	41
1	28	41
2	27	41

end158.0ms (1.6%)

Remove: (sort alpha beta)
Compiler: Compiled 334 to 231 computations (30.8% saved)

Details

analyze5.0ms (0.1%)

sample1.4s (14%)

simplify212.0ms (2.2%)

prune5.0ms (0%)

localize14.0ms (0.1%)

series272.0ms (2.8%)

rewrite76.0ms (0.8%)

simplify210.0ms (2.2%)

prune651.0ms (6.7%)

localize12.0ms (0.1%)

series258.0ms (2.7%)

rewrite81.0ms (0.8%)

simplify231.0ms (2.4%)

prune726.0ms (7.5%)

localize16.0ms (0.2%)

series231.0ms (2.4%)

rewrite128.0ms (1.3%)

simplify295.0ms (3%)

prune1.0s (10.4%)

localize13.0ms (0.1%)

series315.0ms (3.2%)

rewrite191.0ms (2%)

simplify359.0ms (3.7%)

prune1.2s (12%)

regimes1.7s (17.6%)

simplify3.0ms (0%)

end158.0ms (1.6%)

Profiling