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)

sample176.0ms (1.7%)

Algorithm

1×

intervals

Symmetry

(sort alpha beta)

Results

23.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 83 to 55 computations (33.7% saved)

simplify214.0ms (2.1%)

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

2.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.1b	(/.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))
▶	3.2b	(/.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

5.1b

(/.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))

▶

3.2b

(/.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))
✓	0.1b	(.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)))
✓	16.8b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series288.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

154.0ms	(/.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)))
74.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
52.0ms	(/.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))

rewrite81.0ms (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)))
20.0ms	(.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))

simplify220.0ms (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

prune706.0ms (6.8%)

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
	26.2b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 3) 3))) (+.f64 (.f64 alpha alpha) (-.f64 (.f64 (+.f64 beta 3) (+.f64 beta 3)) (.f64 alpha (+.f64 beta 3)))))
	12.4b	(/.f64 (.f64 (+.f64 alpha 1) (+.f64 beta 1)) (.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
	0.3b	(/.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)))
	5.1b	(/.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))
▶	0.1b	(/.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)))
	0.2b	(/.f64 (.f64 (.f64 (+.f64 alpha 1) (/.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)))
	3.9b	(.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)))))

Compiler

Compiled 21333 to 14460 computations (32.2% saved)

localize14.0ms (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)))

series271.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

151.0ms	(/.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)))
75.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
22.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
22.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

rewrite86.0ms (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:

27.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
21.0ms	(/.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))

simplify234.0ms (2.2%)

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

prune729.0ms (7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	389	4	393
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	393	7	400

Error

Counts

400 → 7

Alt Table

Status	Error	Program
	12.4b	(/.f64 (.f64 (+.f64 alpha 1) (+.f64 beta 1)) (.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
	0.2b	(.f64 (sqrt.f64 (/.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)))) (sqrt.f64 (/.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)))))
	29.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3)))
	26.2b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 3) 3))) (+.f64 (.f64 alpha alpha) (-.f64 (.f64 (+.f64 beta 3) (+.f64 beta 3)) (.f64 alpha (+.f64 beta 3)))))
▶	0.1b	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.1b	(/.f64 (/.f64 (*.f64 (+.f64 beta 1) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3)))
	3.9b	(.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)))))

Compiler

Compiled 22615 to 15300 computations (32.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series298.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

185.0ms	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
79.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
24.0ms	(/.f64 1 (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha)))
10.0ms	(/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))

rewrite161.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

442×	`*-un-lft-identity_binary64`
358×	`times-frac_binary64`
184×	`add-sqr-sqrt_binary64`
163×	`distribute-lft-out_binary64`
151×	`add-cube-cbrt_binary64`

Counts

4 → 380

Calls

4 calls:

47.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
28.0ms	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
10.0ms	(/.f64 1 (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha)))
8.0ms	(/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))

simplify391.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-def_binary64`
329×	`+-commutative_binary64`
259×	`associate-+r+_binary64`
244×	`*-commutative_binary64`
205×	`associate-*r/_binary64`

Counts

476 → 550

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1091	21079
1	3684	19855
2	4997	19855
3	4960	19855

prune1.5s (14.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	549	1	550
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	550	7	557

Error

Counts

557 → 7

Alt Table

Status	Error	Program
	29.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3)))
	26.2b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 3) 3))) (+.f64 (.f64 alpha alpha) (-.f64 (.f64 (+.f64 beta 3) (+.f64 beta 3)) (.f64 alpha (+.f64 beta 3)))))
	0.2b	(.f64 (sqrt.f64 (/.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)))) (sqrt.f64 (/.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)))))
✓	0.1b	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.5b	(/.f64 (.f64 1 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))))
▶	0.1b	(/.f64 (/.f64 (*.f64 (+.f64 beta 1) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3)))
	3.9b	(.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)))))

Compiler

Compiled 29238 to 20030 computations (31.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series283.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

154.0ms	(/.f64 (/.f64 (*.f64 (+.f64 beta 1) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3)))
72.0ms	(/.f64 (*.f64 (+.f64 beta 1) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 alpha beta)))
32.0ms	(*.f64 (+.f64 beta 1) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha))))
24.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha)))

rewrite87.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

221×	`*-un-lft-identity_binary64`
131×	`times-frac_binary64`
99×	`distribute-lft-out_binary64`
57×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`

Counts

4 → 229

Calls

4 calls:

21.0ms	(/.f64 (/.f64 (*.f64 (+.f64 beta 1) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3)))
16.0ms	(/.f64 (*.f64 (+.f64 beta 1) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 alpha beta)))
15.0ms	(*.f64 (+.f64 beta 1) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha))))
7.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha)))

simplify298.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

392×	`+-commutative_binary64`
333×	`distribute-rgt-in_binary64`
313×	`associate-+r+_binary64`
237×	`*-commutative_binary64`
232×	`fma-def_binary64`

Counts

325 → 425

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1176	18649
1	3965	17915
2	5408	17915

prune852.0ms (8.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	425	0	425
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	425	7	432

Error

Counts

432 → 7

Alt Table

Status	Error	Program
	29.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))) (+.f64 alpha (+.f64 beta 3)))
	26.2b	(.f64 (/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 3) 3))) (+.f64 (.f64 alpha alpha) (-.f64 (.f64 (+.f64 beta 3) (+.f64 beta 3)) (.f64 alpha (+.f64 beta 3)))))
	0.2b	(.f64 (sqrt.f64 (/.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)))) (sqrt.f64 (/.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)))))
✓	0.1b	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	0.5b	(/.f64 (.f64 1 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 alpha (+.f64 beta 3)) (/.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 1 alpha))))
✓	0.1b	(/.f64 (/.f64 (*.f64 (+.f64 beta 1) (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 alpha beta))) (+.f64 alpha (+.f64 beta 3)))
	3.9b	(.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)))))

Compiler

Compiled 24246 to 16265 computations (32.9% saved)

regimes2.1s (19.9%)

Accuracy

Total 0.1b remaining (65%)

Threshold costs 0.1b (65%)

Counts

443 → 1

Compiler

Compiled 46850 to 32867 computations (29.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
11×	`*-commutative_binary64`
10×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	39
1	38	39
2	55	37
3	73	37
4	86	37
5	96	37
6	101	37
7	102	37
8	100	37

end7.0ms (0.1%)

Remove: (sort alpha beta)
Compiler: Compiled 81 to 54 computations (33.3% saved)

sample1.3s (12.9%)

Algorithm

1×

intervals

Results

717.0ms	8000×	body	128	valid
163.0ms	8000×	pre	128	true

Compiler

Compiled 324 to 221 computations (31.8% saved)

Details

analyze4.0ms (0%)

sample176.0ms (1.7%)

simplify214.0ms (2.1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series288.0ms (2.8%)

rewrite81.0ms (0.8%)

simplify220.0ms (2.1%)

prune706.0ms (6.8%)

localize14.0ms (0.1%)

series271.0ms (2.6%)

rewrite86.0ms (0.8%)

simplify234.0ms (2.2%)

prune729.0ms (7%)

localize14.0ms (0.1%)

series298.0ms (2.9%)

rewrite161.0ms (1.5%)

simplify391.0ms (3.8%)

prune1.5s (14.9%)

localize15.0ms (0.1%)

series283.0ms (2.7%)

rewrite87.0ms (0.8%)

simplify298.0ms (2.9%)

prune852.0ms (8.2%)

regimes2.1s (19.9%)

simplify4.0ms (0%)

end7.0ms (0.1%)

sample1.3s (12.9%)

Profiling