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)

sample171.0ms (0.9%)

Algorithm

1×

intervals

Symmetry

(sort alpha beta)

Results

21.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 83 to 55 computations (33.7% saved)

simplify213.0ms (1.1%)

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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.8b	(/.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))
▶	1.3b	(/.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

1.8b

(/.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))

▶

1.3b

(/.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)))
✓	15.1b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series279.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

144.0ms	(/.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))))
57.0ms	(/.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))

rewrite75.0ms (0.4%)

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)))
17.0ms	(.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)))
12.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify211.0ms (1.1%)

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

prune676.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	344	6	350
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	346	6	352

Error

0.0b

Counts

352 → 6

Alt Table

Status	Error	Program
	6.4b	(.f64 (/.f64 (.f64 (+.f64 1 alpha) (/.f64 (+.f64 1 beta) (.f64 (+.f64 2 (+.f64 alpha beta)) (+.f64 2 (+.f64 alpha beta))))) (-.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 3) 2))) (-.f64 alpha (+.f64 beta 3)))
	33.7b	(/.f64 (+.f64 1 alpha) (pow.f64 beta 2))
	30.3b	(/.f64 (+.f64 1 alpha) (*.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 3 alpha)))
▶	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 (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)))
	5.2b	(/.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)))

Compiler

Compiled 21153 to 14344 computations (32.2% saved)

localize13.0ms (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 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)))

series281.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

140.0ms	(/.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)))
70.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
51.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
20.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))

rewrite184.0ms (1%)

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:

44.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
27.0ms	(/.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)))
21.0ms	(/.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))

simplify349.0ms (1.9%)

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

prune917.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	528	4	532
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	531	7	538

Error

Counts

538 → 7

Alt Table

Status	Error	Program
✓	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 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	7.0b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 (+.f64 1 alpha) 3) (/.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3) (pow.f64 (+.f64 2 (+.f64 beta alpha)) 3)))) (+.f64 alpha (+.f64 beta 3)))
	1.3b	(/.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)))
	30.3b	(/.f64 (+.f64 1 alpha) (*.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 3 alpha)))
	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)))
▶	0.1b	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 30174 to 20181 computations (33.1% 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 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
✓	0.0b	(.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))))
✓	0.0b	(*.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
✓	0.1b	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

series379.0ms (2%)

Counts

3 → 64

Calls

3 calls:

160.0ms

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

145.0ms

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

73.0ms

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

rewrite168.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

380×	`*-un-lft-identity_binary64`
241×	`times-frac_binary64`
171×	`distribute-lft-out_binary64`
137×	`associate-r_binary64`
104×	`add-sqr-sqrt_binary64`

Counts

3 → 268

Calls

3 calls:

46.0ms

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

36.0ms

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

29.0ms

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

simplify293.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

349×	`+-commutative_binary64`
348×	`*-commutative_binary64`
286×	`associate-+r+_binary64`
272×	`fma-def_binary64`
224×	`associate-*r/_binary64`

Counts

332 → 394

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1173	18919
1	4019	17735
2	5247	17735

prune1.1s (6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	574	0	574
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	574	7	581

Error

Counts

581 → 7

Alt Table

Status	Error	Program
✓	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 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	7.0b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 (+.f64 1 alpha) 3) (/.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3) (pow.f64 (+.f64 2 (+.f64 beta alpha)) 3)))) (+.f64 alpha (+.f64 beta 3)))
	1.3b	(/.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)))
	30.3b	(/.f64 (+.f64 1 alpha) (*.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 3 alpha)))
	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)))
✓	0.1b	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 36542 to 25132 computations (31.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
✓	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
✓	0.2b	(/.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
✓	0.6b	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))

series558.0ms (3%)

Counts

4 → 80

Calls

4 calls:

280.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
147.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
69.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
61.0ms	(/.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))

rewrite2.9s (15.3%)

Algorithm

1×	rewrite-expression-head

Rules

12123×	`*-un-lft-identity_binary64`
10095×	`times-frac_binary64`
5166×	`distribute-lft-out_binary64`
4499×	`sqrt-prod_binary64`
3315×	`add-sqr-sqrt_binary64`

Counts

4 → 4013

Calls

4 calls:

792.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))))
114.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
69.0ms	(/.f64 (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))
19.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))

simplify3.5s (18.6%)

Algorithm

1×	egg-herbie

Rules

533×	`associate-/l/_binary64`
505×	`fma-def_binary64`
444×	`associate-*r/_binary64`
159×	`associate-/r*_binary64`
109×	`associate-/l*_binary64`

Counts

4093 → 1792

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	2301	203608
1	4917	203594
2	5037	203594

prune3.8s (20.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1792	0	1792
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	1792	7	1799

Error

Counts

1799 → 7

Alt Table

Status	Error	Program
✓	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 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	7.0b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 (+.f64 1 alpha) 3) (/.f64 (pow.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) 3) (pow.f64 (+.f64 2 (+.f64 beta alpha)) 3)))) (+.f64 alpha (+.f64 beta 3)))
	1.3b	(/.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)))
	30.3b	(/.f64 (+.f64 1 alpha) (*.f64 (pow.f64 (+.f64 2 alpha) 2) (+.f64 3 alpha)))
	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)))
✓	0.1b	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (sqrt.f64 (+.f64 alpha 1)) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 118003 to 76736 computations (35% saved)

regimes1.1s (5.7%)

Accuracy

Total 0.1b remaining (76.9%)

Threshold costs 0.1b (76.9%)

Counts

228 → 1

Compiler

Compiled 26642 to 19010 computations (28.6% saved)

simplify2.0ms (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	17	40
1	26	40
2	25	40

end7.0ms (0%)

Compiler: Compiled 87 to 60 computations (31% saved)

sample1.5s (8%)

Algorithm

1×

intervals

Results

679.0ms	8000×	body	128	valid
163.0ms	8000×	pre	128	true

Compiler

Compiled 285 to 198 computations (30.5% saved)

Details

analyze4.0ms (0%)

sample171.0ms (0.9%)

simplify213.0ms (1.1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series279.0ms (1.5%)

rewrite75.0ms (0.4%)

simplify211.0ms (1.1%)

prune676.0ms (3.6%)

localize13.0ms (0.1%)

series281.0ms (1.5%)

rewrite184.0ms (1%)

simplify349.0ms (1.9%)

prune917.0ms (4.9%)

localize15.0ms (0.1%)

series379.0ms (2%)

rewrite168.0ms (0.9%)

simplify293.0ms (1.6%)

prune1.1s (6%)

localize15.0ms (0.1%)

series558.0ms (3%)

rewrite2.9s (15.3%)

simplify3.5s (18.6%)

prune3.8s (20.6%)

regimes1.1s (5.7%)

simplify2.0ms (0%)

end7.0ms (0%)

sample1.5s (8%)

Profiling