Details

analyze274.0ms (8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample38.0ms (1.1%)

Algorithm

1×

intervals

Results

10.0ms	200×	body	128	valid
6.0ms	33×	body	1024	valid
5.0ms	256×	pre	128	true
2.0ms	15×	body	512	valid
1.0ms	7×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify218.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

890×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
388×	`distribute-rgt-neg-in_binary64`
379×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	64	19
4	108	19
5	215	17
6	353	17
7	603	17
8	1141	17
9	2484	17
10	3195	17
11	3981	17
12	4235	17
13	4399	17
14	4503	17
15	4531	17
16	4533	17
17	4768	17
18	4708	17
19	4930	17
20	4826	17

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

14.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	2.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
18×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series52.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
18.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

simplify103.0ms (3%)

Algorithm

1×	egg-herbie

Rules

960×	`times-frac_binary64`
218×	`+-commutative_binary64`
206×	`fma-def_binary64`
194×	`fma-neg_binary64`
193×	`associate-+r+_binary64`

Counts

112 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	3790
1	962	3664
2	3486	3620
3	4984	3620

prune118.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	203	4	207

Error

0.0b

Counts

207 → 4

Alt Table

Status	Error	Program
▶	14.7b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
	47.7b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	46.9b	(/.f64 (+.f64 beta 1) alpha)
	15.1b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 4405 to 2711 computations (38.5% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))
✓	0.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta)))
✓	2.1b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)

rewrite39.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

273×	`*-un-lft-identity_binary64`
218×	`times-frac_binary64`
143×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
78×	`distribute-lft-out_binary64`

Counts

3 → 213

Calls

3 calls:

12.0ms

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

9.0ms

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

0.0ms

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

series76.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

36.0ms

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

23.0ms

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

17.0ms

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

simplify201.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

351×	`associate-+r+_binary64`
322×	`fma-def_binary64`
312×	`+-commutative_binary64`
277×	`associate-+l+_binary64`
239×	`fma-neg_binary64`

Counts

285 → 548

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	429	8554
1	1278	7974
2	4784	7972
3	4975	7972

prune241.0ms (7.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	548	0	548
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	548	4	552

Error

0.0b

Counts

552 → 4

Alt Table

Status	Error	Program
✓	14.7b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
	47.7b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
	46.9b	(/.f64 (+.f64 beta 1) alpha)
▶	15.1b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 9369 to 5695 computations (39.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.5b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	2.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	2.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
16×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 53

Calls

1 calls:

6.0ms

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

series34.0ms (1%)

Counts

1 → 24

Calls

1 calls:

34.0ms

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

simplify109.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-def_binary64`
781×	`times-frac_binary64`
408×	`fma-neg_binary64`
283×	`cancel-sign-sub-inv_binary64`
193×	`sub-neg_binary64`

Counts

77 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	2787
1	564	2528
2	2134	2321
3	4743	2320
4	5014	2320

prune248.0ms (7.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	465	1	466
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	466	4	470

Error

0.0b

Counts

470 → 4

Alt Table

Status	Error	Program
✓	14.7b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
	47.7b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) (/.f64 beta alpha)))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (+.f64 (/.f64 3 alpha) (/.f64 beta alpha)))))
▶	46.9b	(/.f64 (+.f64 beta 1) alpha)
✓	15.1b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 12056 to 7522 computations (37.6% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune4.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0.0b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	14.7b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
	47.7b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) (/.f64 beta alpha)))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (+.f64 (/.f64 3 alpha) (/.f64 beta alpha)))))
✓	46.9b	(/.f64 (+.f64 beta 1) alpha)
✓	15.1b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)) (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 107 to 70 computations (34.6% saved)

regimes447.0ms (13.1%)

Accuracy

Total 0.0b remaining (22.5%)

Threshold costs 0.0b (22.5%)

Compiler

Compiled 7464 to 5235 computations (29.9% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
9×	`sub-neg_binary64`
6×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	85
1	42	85
2	58	85
3	75	85
4	84	85
5	87	85
6	85	85

end1.0ms (0%)

Compiler: Compiled 60 to 33 computations (45% saved)

sample1.1s (33.3%)

Algorithm

1×

intervals

Results

287.0ms	6032×	body	128	valid
172.0ms	1005×	body	1024	valid
157.0ms	8000×	pre	128	true
77.0ms	568×	body	512	valid
27.0ms	300×	body	256	valid
20.0ms	95×	body	2048	valid

Compiler

Compiled 191 to 121 computations (36.6% saved)

Details

analyze274.0ms (8%)

sample38.0ms (1.1%)

simplify218.0ms (6.4%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite13.0ms (0.4%)

series52.0ms (1.5%)

simplify103.0ms (3%)

prune118.0ms (3.5%)

localize9.0ms (0.3%)

rewrite39.0ms (1.1%)

series76.0ms (2.2%)

simplify201.0ms (5.9%)

prune241.0ms (7.1%)

localize11.0ms (0.3%)

rewrite10.0ms (0.3%)

series34.0ms (1%)

simplify109.0ms (3.2%)

prune248.0ms (7.3%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify10.0ms (0.3%)

prune4.0ms (0.1%)

regimes447.0ms (13.1%)

bsearch2.0ms (0.1%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample1.1s (33.3%)

Profiling