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)

sample173.0ms (1.2%)

Algorithm

1×

intervals

Symmetry

(sort alpha beta)

Results

19.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 83 to 55 computations (33.7% saved)

simplify216.0ms (1.5%)

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
	3.4b	(/.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))
▶	1.1b	(/.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)))

Status

Error

Program

3.4b

(/.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))

▶

1.1b

(/.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)))

Compiler

Compiled 190 to 123 computations (35.3% saved)

localize13.0ms (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)))
✓	14.5b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series265.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

141.0ms	(/.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)))
68.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
48.0ms	(/.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))

rewrite80.0ms (0.6%)

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))))
14.0ms	(/.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))

simplify215.0ms (1.5%)

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

prune722.0ms (5.1%)

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
	5.7b	(/.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)))
	10.2b	(/.f64 (.f64 (-.f64 (.f64 alpha alpha) (.f64 1 1)) (+.f64 beta 1)) (.f64 (+.f64 alpha (+.f64 beta 3)) (.f64 (-.f64 alpha 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))))
	1.1b	(/.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)))))
	1.8b	(.f64 (/.f64 (+.f64 alpha 1) (.f64 (cbrt.f64 (+.f64 alpha (+.f64 beta 3))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3))))) (/.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	0.5b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (cbrt.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 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	2.1b	(.f64 (.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
	11.5b	(cbrt.f64 (.f64 (.f64 (/.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))) (/.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)))) (/.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 21561 to 14604 computations (32.3% 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 1 alpha) (+.f64 2 (+.f64 alpha beta)))
✓	0.0b	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
✓	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)))

series248.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

140.0ms	(/.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)))
64.0ms	(*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
20.0ms	(/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta)))
18.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

rewrite84.0ms (0.6%)

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:

24.0ms	(*.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))

simplify651.0ms (4.6%)

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 → 392

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1073	16270
1	3696	15449
2	4984	15449

prune839.0ms (5.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	389	3	392
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	392	8	400

Error

0.0b

Counts

400 → 8

Alt Table

Status	Error	Program
	1.8b	(.f64 (/.f64 (+.f64 alpha 1) (.f64 (cbrt.f64 (+.f64 alpha (+.f64 beta 3))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3))))) (/.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3)))))
	0.5b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	1.1b	(/.f64 (.f64 (.f64 (/.f64 (+.f64 1 alpha) (-.f64 4 (*.f64 (+.f64 beta alpha) (+.f64 beta alpha)))) (-.f64 2 (+.f64 alpha beta))) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
	5.7b	(/.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)))
✓	0.1b	(/.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)))
	2.1b	(.f64 (.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
▶	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 beta 1)))) (+.f64 alpha (+.f64 beta 3)))
	9.4b	(/.f64 (.f64 (+.f64 1 alpha) (+.f64 beta 1)) (.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) 2))))

Compiler

Compiled 22659 to 15324 computations (32.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series247.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

145.0ms

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

80.0ms

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

21.0ms

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

rewrite149.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

393×	`*-un-lft-identity_binary64`
338×	`times-frac_binary64`
172×	`add-sqr-sqrt_binary64`
142×	`distribute-lft-out_binary64`
139×	`add-cube-cbrt_binary64`

Counts

3 → 335

Calls

3 calls:

50.0ms

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

26.0ms

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

13.0ms

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

simplify288.0ms (2%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
308×	`+-commutative_binary64`
247×	`associate-+r+_binary64`
241×	`*-commutative_binary64`
208×	`associate-*r/_binary64`

Counts

407 → 474

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1044	19447
1	3520	18273
2	5189	18273

prune1.3s (8.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	558	2	560
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	561	7	568

Error

0.0b

Counts

568 → 7

Alt Table

Status	Error	Program
	1.1b	(/.f64 (.f64 (+.f64 1 alpha) 1) (.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 beta 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)))
	1.8b	(.f64 (/.f64 (+.f64 alpha 1) (.f64 (cbrt.f64 (+.f64 alpha (+.f64 beta 3))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3))))) (/.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3)))))
▶	0.2b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1)))) (+.f64 alpha (+.f64 beta 3)))
	5.7b	(/.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)))
	2.1b	(.f64 (.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
	9.4b	(/.f64 (.f64 (+.f64 1 alpha) (+.f64 beta 1)) (.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) 2))))

Compiler

Compiled 30220 to 20686 computations (31.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1)))
✓	0.1b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1)))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))
✓	0.6b	(/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))

series297.0ms (2.1%)

Counts

4 → 64

Calls

4 calls:

164.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1)))) (+.f64 alpha (+.f64 beta 3)))
61.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))
47.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))
24.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1)))

rewrite570.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

3129×	`times-frac_binary64`
2928×	`*-un-lft-identity_binary64`
1250×	`sqrt-prod_binary64`
1154×	`add-sqr-sqrt_binary64`
1154×	`add-cube-cbrt_binary64`

Counts

4 → 1411

Calls

4 calls:

93.0ms	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1)))) (+.f64 alpha (+.f64 beta 3)))
40.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1)))
10.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))

simplify1.4s (9.7%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
226×	`associate-/r/_binary64`
221×	`+-commutative_binary64`
184×	`*-commutative_binary64`
182×	`associate-/l/_binary64`

Counts

1475 → 981

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1201	75259
1	3822	72057
2	4966	72055
3	4976	72055

prune2.1s (14.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	980	1	981
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	980	8	988

Error

0.0b

Counts

988 → 8

Alt Table

Status	Error	Program
	1.1b	(/.f64 (.f64 (+.f64 1 alpha) 1) (.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 beta 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)))
	1.3b	(/.f64 (.f64 (+.f64 1 alpha) (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))) (.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1)))))
	1.8b	(.f64 (/.f64 (+.f64 alpha 1) (.f64 (cbrt.f64 (+.f64 alpha (+.f64 beta 3))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3))))) (/.f64 (/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (cbrt.f64 (+.f64 alpha (+.f64 beta 3)))))
✓	0.2b	(/.f64 (*.f64 (/.f64 (+.f64 1 alpha) (+.f64 2 (+.f64 alpha beta))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)) (+.f64 beta 1)))) (+.f64 alpha (+.f64 beta 3)))
	5.7b	(/.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)))
	2.1b	(.f64 (.f64 (cbrt.f64 (/.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)))) (cbrt.f64 (/.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))))) (cbrt.f64 (/.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)))))
	9.4b	(/.f64 (.f64 (+.f64 1 alpha) (+.f64 beta 1)) (.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 (+.f64 alpha beta) 2))))

Compiler

Compiled 59460 to 40231 computations (32.3% saved)

regimes2.5s (17.7%)

Accuracy

Total 0.1b remaining (79.4%)

Threshold costs 0.1b (79.4%)

Counts

515 → 1

Compiler

Compiled 68459 to 47915 computations (30% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	37
1	27	37
2	26	37

end7.0ms (0%)

Compiler: Compiled 81 to 54 computations (33.3% saved)

sample1.8s (12.8%)

Algorithm

1×

intervals

Results

650.0ms	8000×	body	128	valid
276.0ms	8000×	pre	128	true

Compiler

Compiled 384 to 260 computations (32.3% saved)

Details

analyze4.0ms (0%)

sample173.0ms (1.2%)

simplify216.0ms (1.5%)

prune5.0ms (0%)

localize13.0ms (0.1%)

series265.0ms (1.9%)

rewrite80.0ms (0.6%)

simplify215.0ms (1.5%)

prune722.0ms (5.1%)

localize12.0ms (0.1%)

series248.0ms (1.7%)

rewrite84.0ms (0.6%)

simplify651.0ms (4.6%)

prune839.0ms (5.9%)

localize16.0ms (0.1%)

series247.0ms (1.7%)

rewrite149.0ms (1%)

simplify288.0ms (2%)

prune1.3s (8.9%)

localize22.0ms (0.2%)

series297.0ms (2.1%)

rewrite570.0ms (4%)

simplify1.4s (9.7%)

prune2.1s (14.9%)

regimes2.5s (17.7%)

simplify3.0ms (0%)

end7.0ms (0%)

sample1.8s (12.8%)

Profiling