Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
56.2%	0%	43.8%	1

Compiler

Compiled 44 to 29 computations (34.1% saved)

sample1.2s (11.1%)

Symmetry

(sort alpha beta)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify211.0ms (1.9%)

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

1.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.3b	(/.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))
▶	2.5b	(/.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

5.3b

(/.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))

▶

2.5b

(/.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 (0.1%)

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)))
✓	19.9b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series274.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

146.0ms	(/.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))))
53.0ms	(/.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))

rewrite87.0ms (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:

24.0ms	(/.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)))
21.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
14.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
13.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

simplify205.0ms (1.9%)

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

prune1.1s (10.5%)

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
	31.8b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 (+.f64 alpha 1) (+.f64 alpha 1)) (+.f64 alpha 1)) (/.f64 (.f64 (.f64 (+.f64 beta 1) (+.f64 beta 1)) (+.f64 beta 1)) (.f64 (.f64 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))) (.f64 (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 alpha (+.f64 beta 3))) (+.f64 alpha (+.f64 beta 3)))))
	2.5b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 (.f64 alpha alpha) (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
	3.1b	(.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)))))
	30.2b	(-.f64 (fma.f64 51 (/.f64 alpha (pow.f64 beta 4)) (+.f64 (/.f64 alpha (.f64 beta beta)) (fma.f64 31 (/.f64 (.f64 alpha alpha) (pow.f64 beta 4)) (+.f64 (/.f64 1 (.f64 beta beta)) (fma.f64 6 (/.f64 (pow.f64 alpha 3) (pow.f64 beta 4)) (/.f64 26 (pow.f64 beta 4))))))) (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)))))
▶	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	0.4b	(/.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)))
	7.4b	(.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)))

Compiler

Compiled 21481 to 14556 computations (32.2% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series311.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

170.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
71.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))))
54.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
15.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))

rewrite113.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`*-un-lft-identity_binary64`
105×	`add-exp-log_binary64`
62×	`times-frac_binary64`
61×	`add-cbrt-cube_binary64`
53×	`add-sqr-sqrt_binary64`

Counts

4 → 216

Calls

4 calls:

32.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
27.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))
21.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))))
6.0ms	(/.f64 1 (+.f64 (+.f64 alpha beta) 2))

simplify240.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

378×	`+-commutative_binary64`
336×	`distribute-rgt-in_binary64`
300×	`associate-+r+_binary64`
282×	`*-commutative_binary64`
273×	`fma-def_binary64`

Counts

312 → 414

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1122	17154
1	3928	16011
2	5382	16011

prune913.0ms (8.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	411	3	414
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	413	8	421

Error

Counts

421 → 8

Alt Table

Status	Error	Program
	31.8b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 (+.f64 alpha 1) (+.f64 alpha 1)) (+.f64 alpha 1)) (/.f64 (.f64 (.f64 (+.f64 beta 1) (+.f64 beta 1)) (+.f64 beta 1)) (.f64 (.f64 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))) (.f64 (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 alpha (+.f64 beta 3))) (+.f64 alpha (+.f64 beta 3)))))
	2.5b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 (.f64 alpha alpha) (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
	0.9b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))))))
	7.4b	(.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)))
▶	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	3.1b	(.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)))))
	1.2b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (*.f64 (cbrt.f64 (+.f64 2 (+.f64 beta alpha))) (cbrt.f64 (+.f64 2 (+.f64 beta alpha))))) (+.f64 2 (+.f64 beta alpha))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 2))))) (+.f64 alpha (+.f64 beta 3)))

Compiler

Compiled 24522 to 16922 computations (31% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series293.0ms (2.7%)

Counts

3 → 72

Calls

3 calls:

153.0ms

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

75.0ms

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

64.0ms

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

rewrite166.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

777×	`*-un-lft-identity_binary64`
488×	`times-frac_binary64`
353×	`distribute-lft-out_binary64`
179×	`add-sqr-sqrt_binary64`
170×	`add-cube-cbrt_binary64`

Counts

3 → 383

Calls

3 calls:

43.0ms

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

28.0ms

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

19.0ms

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

simplify349.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

378×	`distribute-rgt-in_binary64`
349×	`+-commutative_binary64`
279×	`associate-+r+_binary64`
276×	`*-commutative_binary64`
258×	`fma-def_binary64`

Counts

455 → 446

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1156	22596
1	3892	21671
2	5314	21671

prune916.0ms (8.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	445	1	446
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	446	8	454

Error

Counts

454 → 8

Alt Table

Status	Error	Program
	31.8b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 (+.f64 alpha 1) (+.f64 alpha 1)) (+.f64 alpha 1)) (/.f64 (.f64 (.f64 (+.f64 beta 1) (+.f64 beta 1)) (+.f64 beta 1)) (.f64 (.f64 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))) (.f64 (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 alpha (+.f64 beta 3))) (+.f64 alpha (+.f64 beta 3)))))
	2.5b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 (.f64 alpha alpha) (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
	0.9b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))))))
	7.4b	(.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)))
✓	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
▶	0.9b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (/.f64 (cbrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	3.1b	(.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 26727 to 17973 computations (32.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
✓	0.6b	(/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))
✓	0.6b	(/.f64 (cbrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))
✓	4.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (/.f64 (cbrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))))

series344.0ms (3.2%)

Counts

4 → 52

Calls

4 calls:

161.0ms	(/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))
124.0ms	(/.f64 (cbrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))
53.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (/.f64 (cbrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))))
6.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))

rewrite315.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

923×	`*-un-lft-identity_binary64`
701×	`times-frac_binary64`
379×	`distribute-lft-out_binary64`
342×	`add-sqr-sqrt_binary64`
323×	`associate-r_binary64`

Counts

4 → 567

Calls

4 calls:

119.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (/.f64 (cbrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))))
13.0ms	(/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))
11.0ms	(/.f64 (cbrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 2 (+.f64 beta alpha))))
11.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))

simplify387.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-/l*_binary64`
471×	`fma-def_binary64`
351×	`times-frac_binary64`
324×	`associate-/l/_binary64`
248×	`*-commutative_binary64`

Counts

619 → 590

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	806	29300
1	2436	23016
2	5301	23016

prune1.1s (9.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	590	0	590
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	590	8	598

Error

Counts

598 → 8

Alt Table

Status	Error	Program
	31.8b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 (+.f64 alpha 1) (+.f64 alpha 1)) (+.f64 alpha 1)) (/.f64 (.f64 (.f64 (+.f64 beta 1) (+.f64 beta 1)) (+.f64 beta 1)) (.f64 (.f64 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))) (.f64 (.f64 (+.f64 alpha (+.f64 beta 3)) (+.f64 alpha (+.f64 beta 3))) (+.f64 alpha (+.f64 beta 3)))))
	2.5b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (fma.f64 4 beta (+.f64 (.f64 alpha alpha) (+.f64 4 (+.f64 (.f64 beta beta) (.f64 alpha (+.f64 (*.f64 2 beta) 4)))))))) (+.f64 alpha (+.f64 beta 3)))
	0.9b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2))))))
	7.4b	(.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)))
✓	0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 2 (+.f64 beta alpha))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
✓	0.9b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (/.f64 (/.f64 (cbrt.f64 (+.f64 beta 1)) (sqrt.f64 (+.f64 2 (+.f64 beta alpha)))) (+.f64 2 (+.f64 beta alpha))))) (+.f64 alpha (+.f64 beta 3)))
✓	0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 alpha beta) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
	3.1b	(.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 36701 to 25071 computations (31.7% saved)

regimes2.0s (17.9%)

Accuracy

Total 0.1b remaining (75.4%)

Threshold costs 0.1b (75.4%)

Counts

392 → 1

Compiler

Compiled 51254 to 36254 computations (29.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	27	40
2	26	40

end324.0ms (3%)

Compiler: Compiled 437 to 298 computations (31.8% saved)

Details

analyze1.0ms (0%)

sample1.2s (11.1%)

simplify211.0ms (1.9%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series274.0ms (2.5%)

rewrite87.0ms (0.8%)

simplify205.0ms (1.9%)

prune1.1s (10.5%)

localize23.0ms (0.2%)

series311.0ms (2.8%)

rewrite113.0ms (1%)

simplify240.0ms (2.2%)

prune913.0ms (8.4%)

localize16.0ms (0.1%)

series293.0ms (2.7%)

rewrite166.0ms (1.5%)

simplify349.0ms (3.2%)

prune916.0ms (8.4%)

localize19.0ms (0.2%)

series344.0ms (3.2%)

rewrite315.0ms (2.9%)

simplify387.0ms (3.5%)

prune1.1s (9.9%)

regimes2.0s (17.9%)

simplify3.0ms (0%)

end324.0ms (3%)

Profiling