Details

analyze4.0ms (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)

sample178.0ms (0.7%)

Algorithm

1×

intervals

Symmetry

(sort alpha beta)

Results

20.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 83 to 55 computations (33.7% saved)

simplify215.0ms (0.9%)

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

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
	3.1b	(/.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))
▶	1.5b	(/.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

3.1b

(/.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))

▶

1.5b

(/.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)

localize12.0ms (0%)

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)))
✓	18.3b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series308.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

167.0ms	(/.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)))
77.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
55.0ms	(/.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))

rewrite121.0ms (0.5%)

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:

55.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
22.0ms	(/.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))))
12.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify221.0ms (0.9%)

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

prune696.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	344	6	350
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	345	7	352

Error

0.0b

Counts

352 → 7

Alt Table

Status	Error	Program
	34.3b	(-.f64 (+.f64 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 1 (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (/.f64 alpha (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3)))))) (fma.f64 16 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 17 (/.f64 (.f64 beta (.f64 alpha alpha)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 3 (/.f64 (.f64 beta (pow.f64 alpha 3)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (.f64 30 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))))))))
	1.5b	(/.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)))))
	29.5b	(/.f64 (.f64 (+.f64 alpha 1) (-.f64 (/.f64 1 beta) (fma.f64 2 (/.f64 alpha (.f64 beta beta)) (/.f64 3 (*.f64 beta beta))))) (+.f64 alpha (+.f64 beta 3)))
	3.1b	(/.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))
	0.9b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))))) (+.f64 alpha (+.f64 beta 3)))
	25.5b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (-.f64 (.f64 beta beta) (.f64 1 1)) (.f64 (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (-.f64 beta 1)))) (+.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 21481 to 14578 computations (32.1% saved)

localize65.0ms (0.3%)

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)))
✓	0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
✓	0.3b	(.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))))

series518.0ms (2.1%)

Counts

4 → 72

Calls

4 calls:

233.0ms	(*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
154.0ms	(/.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)))
79.0ms	(.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))))
50.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))

rewrite148.0ms (0.6%)

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:

36.0ms	(/.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))))
21.0ms	(*.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))

simplify298.0ms (1.2%)

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

prune1.6s (6.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	689	2	691
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	691	7	698

Error

0.0b

Counts

698 → 7

Alt Table

Status	Error	Program
▶	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 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
	3.1b	(/.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))
	34.3b	(-.f64 (+.f64 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 1 (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (/.f64 alpha (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3)))))) (fma.f64 16 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 17 (/.f64 (.f64 beta (.f64 alpha alpha)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 3 (/.f64 (.f64 beta (pow.f64 alpha 3)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (.f64 30 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))))))))
	1.5b	(/.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)))))
	0.9b	(/.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)) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 2 (+.f64 beta alpha))) 3)))) (+.f64 alpha (+.f64 beta 3)))
	0.9b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.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)))

Compiler

Compiled 43577 to 30790 computations (29.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
	0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
✓	0.3b	(.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 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))))
✓	0.4b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))

series282.0ms (1.1%)

Counts

3 → 56

Calls

3 calls:

145.0ms

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

87.0ms

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

50.0ms

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

rewrite306.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

1274×	`*-un-lft-identity_binary64`
1056×	`times-frac_binary64`
994×	`sqrt-prod_binary64`
483×	`distribute-lft-out_binary64`
447×	`add-sqr-sqrt_binary64`

Counts

3 → 753

Calls

3 calls:

61.0ms

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

30.0ms

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

10.0ms

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

simplify794.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

743×	`fma-def_binary64`
384×	`times-frac_binary64`
270×	`*-commutative_binary64`
207×	`+-commutative_binary64`
154×	`associate-+r+_binary64`

Counts

809 → 627

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1036	39995
1	3002	37962
2	4992	37960
3	4974	37960

prune2.2s (8.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	724	0	724
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	724	7	731

Error

0.0b

Counts

731 → 7

Alt Table

Status	Error	Program
✓	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 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
	3.1b	(/.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))
	34.3b	(-.f64 (+.f64 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 1 (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (/.f64 alpha (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3)))))) (fma.f64 16 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 17 (/.f64 (.f64 beta (.f64 alpha alpha)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 3 (/.f64 (.f64 beta (pow.f64 alpha 3)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (.f64 30 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))))))))
	1.5b	(/.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)))))
	0.9b	(/.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)) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 2 (+.f64 beta alpha))) 3)))) (+.f64 alpha (+.f64 beta 3)))
▶	0.9b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.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)))

Compiler

Compiled 49092 to 33919 computations (30.9% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta))))
✓	0.1b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))
✓	12.4b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))))

series581.0ms (2.3%)

Counts

4 → 80

Calls

4 calls:

316.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))))) (+.f64 alpha (+.f64 beta 3)))
106.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))))
88.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))
69.0ms	(/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta))))

rewrite1.8s (7.4%)

Algorithm

1×	rewrite-expression-head

Rules

6058×	`*-un-lft-identity_binary64`
4965×	`times-frac_binary64`
2553×	`distribute-lft-out_binary64`
1788×	`sqrt-prod_binary64`
1654×	`add-sqr-sqrt_binary64`

Counts

4 → 2083

Calls

4 calls:

205.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))))) (+.f64 alpha (+.f64 beta 3)))
127.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))))
40.0ms	(/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta))))
17.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 2 (+.f64 alpha beta)))

simplify3.6s (14.6%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-/r/_binary64`
299×	`+-commutative_binary64`
229×	`*-commutative_binary64`
229×	`associate-+r+_binary64`
229×	`fma-def_binary64`

Counts

2163 → 1103

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1603	122838
1	4630	120206
2	4999	120206

prune3.5s (14%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1102	1	1103
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	1103	7	1110

Error

0.0b

Counts

1110 → 7

Alt Table

Status	Error	Program
✓	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 (/.f64 (sqrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))
	3.1b	(/.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))
	34.3b	(-.f64 (+.f64 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (+.f64 (/.f64 1 (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3))) (/.f64 alpha (.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 alpha 3)))))) (fma.f64 16 (/.f64 beta (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 17 (/.f64 (.f64 beta (.f64 alpha alpha)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (fma.f64 3 (/.f64 (.f64 beta (pow.f64 alpha 3)) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))) (.f64 30 (/.f64 (.f64 alpha beta) (.f64 (pow.f64 (+.f64 2 alpha) 4) (pow.f64 (+.f64 alpha 3) 2))))))))
	1.5b	(/.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)))))
✓	0.9b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (sqrt.f64 (+.f64 beta 1)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.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)))
	0.2b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (.f64 (sqrt.f64 (+.f64 1 beta)) (/.f64 (fabs.f64 (cbrt.f64 (+.f64 1 beta))) (sqrt.f64 (+.f64 2 (+.f64 alpha beta))))) (/.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (cbrt.f64 (+.f64 1 beta))) (sqrt.f64 (+.f64 2 (+.f64 alpha beta))))))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 65613 to 44939 computations (31.5% saved)

regimes4.7s (19%)

Accuracy

Total 0.1b remaining (65.1%)

Threshold costs 0.1b (65.1%)

Counts

499 → 1

Compiler

Compiled 68540 to 49157 computations (28.3% saved)

simplify5.0ms (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	18	41
1	27	41
2	26	41

end13.0ms (0.1%)

Remove: (sort alpha beta)
Compiler: Compiled 87 to 60 computations (31% saved)

sample2.6s (10.6%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
318.0ms	8000×	pre	128	true

Compiler

Compiled 428 to 304 computations (29% saved)

Details

analyze4.0ms (0%)

sample178.0ms (0.7%)

simplify215.0ms (0.9%)

prune4.0ms (0%)

localize12.0ms (0%)

series308.0ms (1.2%)

rewrite121.0ms (0.5%)

simplify221.0ms (0.9%)

prune696.0ms (2.8%)

localize65.0ms (0.3%)

series518.0ms (2.1%)

rewrite148.0ms (0.6%)

simplify298.0ms (1.2%)

prune1.6s (6.3%)

localize21.0ms (0.1%)

series282.0ms (1.1%)

rewrite306.0ms (1.2%)

simplify794.0ms (3.2%)

prune2.2s (8.7%)

localize33.0ms (0.1%)

series581.0ms (2.3%)

rewrite1.8s (7.4%)

simplify3.6s (14.6%)

prune3.5s (14%)

regimes4.7s (19%)

simplify5.0ms (0%)

end13.0ms (0.1%)

sample2.6s (10.6%)

Profiling