Details

analyze10.0ms (0.3%)

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)

sample304.0ms (9.8%)

Algorithm

1×

intervals

Results

9.0ms	193×	body	128	valid
8.0ms	22×	body	512	valid
6.0ms	33×	body	1024	valid
5.0ms	256×	pre	128	true
1.0ms	3×	body	2048	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify212.0ms (6.8%)

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

15.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.2b	(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))
✓	0.8b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series58.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

39.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
19.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite15.0ms (0.5%)

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:

10.0ms	(/.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)

simplify96.0ms (3.1%)

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 → 142

Iterations

Useful iterations: 2 (0.0ms)

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

prune113.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	140	3	143

Error

Counts

143 → 3

Alt Table

Status	Error	Program
✓	15.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
▶	45.8b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
	47.5b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 4275 to 2621 computations (38.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 beta) (/.f64 alpha beta))

series7.0ms (0.2%)

Counts

1 → 15

Calls

1 calls:

7.0ms

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

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
13×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 36

Calls

1 calls:

13.0ms

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

simplify97.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
505×	`distribute-rgt-in_binary64`
449×	`distribute-rgt-out_binary64`
350×	`distribute-lft-in_binary64`
297×	`times-frac_binary64`

Counts

51 → 48

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	402
1	119	373
2	278	372
3	796	333
4	2572	325
5	4509	325
6	4991	325
7	4997	325
8	4952	325

prune24.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	48	3	51

Error

Counts

51 → 3

Alt Table

Status	Error	Program
✓	15.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	45.8b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
▶	47.5b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 774 to 483 computations (37.6% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.6b	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
✓	2.6b	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
✓	3.0b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	8.3b	(/.f64 beta (*.f64 alpha alpha))

series163.0ms (5.2%)

Counts

4 → 96

Calls

4 calls:

57.0ms	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
41.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
34.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
30.0ms	(/.f64 beta (*.f64 alpha alpha))

rewrite59.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`*-un-lft-identity_binary64`
48×	`prod-diff_binary64`
46×	`distribute-lft-out_binary64`
41×	`times-frac_binary64`
38×	`add-sqr-sqrt_binary64`

Counts

4 → 150

Calls

4 calls:

22.0ms	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
6.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
4.0ms	(/.f64 beta (*.f64 alpha alpha))
0.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))

simplify232.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
502×	`fma-neg_binary64`
299×	`cancel-sign-sub-inv_binary64`
192×	`distribute-rgt-neg-in_binary64`
161×	`distribute-rgt-in_binary64`

Counts

246 → 203

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	10949
1	623	9056
2	2377	7436
3	4711	7436
4	4930	7436

prune143.0ms (4.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	203	3	206

Error

Counts

206 → 3

Alt Table

Status	Error	Program
✓	15.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	45.8b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
✓	47.5b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 11486 to 4175 computations (63.7% saved)

regimes255.0ms (8.2%)

Accuracy

Total 0.1b remaining (52.4%)

Threshold costs 0.1b (52.4%)

Counts

39 → 2

Compiler

Compiled 3645 to 2436 computations (33.2% saved)

bsearch1.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	76
1	41	76
2	55	76
3	70	76
4	77	76
5	79	76
6	77	76

end1.0ms (0%)

Compiler: Compiled 54 to 30 computations (44.4% saved)

sample1.3s (40.8%)

Algorithm

1×

intervals

Results

293.0ms	5987×	body	128	valid
192.0ms	8000×	pre	128	true
190.0ms	979×	body	1024	valid
86.0ms	591×	body	512	valid
50.0ms	339×	body	256	valid
23.0ms	104×	body	2048	valid

Compiler

Compiled 133 to 81 computations (39.1% saved)

Details

analyze10.0ms (0.3%)

sample304.0ms (9.8%)

simplify212.0ms (6.8%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series58.0ms (1.9%)

rewrite15.0ms (0.5%)

simplify96.0ms (3.1%)

prune113.0ms (3.6%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite15.0ms (0.5%)

simplify97.0ms (3.1%)

prune24.0ms (0.8%)

localize14.0ms (0.5%)

series163.0ms (5.2%)

rewrite59.0ms (1.9%)

simplify232.0ms (7.5%)

prune143.0ms (4.6%)

regimes255.0ms (8.2%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.3s (40.8%)

Profiling