Details

analyze277.0ms (5.6%)

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)

sample91.0ms (1.9%)

Algorithm

1×

intervals

Results

22.0ms	256×	pre	128	true
15.0ms	190×	body	128	valid
10.0ms	33×	body	1024	valid
3.0ms	16×	body	512	valid
2.0ms	16×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify214.0ms (4.3%)

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

prune6.0ms (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

15.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.3b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series106.0ms (2.2%)

Counts

2 → 48

Calls

2 calls:

70.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
36.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite38.0ms (0.8%)

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:

15.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
1.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify181.0ms (3.7%)

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

prune246.0ms (5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	4	143

Error

0.0b

Counts

143 → 4

Alt Table

Status	Error	Program
	47.2b	(-.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)))))
	46.3b	(/.f64 (+.f64 beta 1) alpha)
	45.2b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
▶	25.9b	(fma.f64 (/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))) -1/2 1/2)

Compiler

Compiled 4319 to 2649 computations (38.7% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))
✓	1.3b	(fma.f64 (/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))) -1/2 1/2)
✓	1.4b	(-.f64 (.f64 alpha alpha) (.f64 beta beta))
✓	25.5b	(/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta)))

series202.0ms (4.1%)

Counts

4 → 96

Calls

4 calls:

105.0ms	(fma.f64 (/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))) -1/2 1/2)
69.0ms	(/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta)))
16.0ms	(*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))
12.0ms	(-.f64 (.f64 alpha alpha) (.f64 beta beta))

rewrite58.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
12×	`flip-+_binary64`
12×	`flip3-+_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`

Counts

4 → 96

Calls

4 calls:

23.0ms	(/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta)))
16.0ms	(*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))
7.0ms	(-.f64 (.f64 alpha alpha) (.f64 beta beta))
1.0ms	(fma.f64 (/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))) -1/2 1/2)

simplify189.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

496×	`fma-def_binary64`
438×	`times-frac_binary64`
391×	`associate-/r*_binary64`
266×	`associate-/l*_binary64`
203×	`distribute-rgt-in_binary64`

Counts

192 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	510	6469
1	1721	6089
2	5081	6089

prune383.0ms (7.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	236	4	240

Error

0.0b

Counts

240 → 4

Alt Table

Status	Error	Program
	47.2b	(-.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)))))
	46.3b	(/.f64 (+.f64 beta 1) alpha)
▶	45.2b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
✓	25.9b	(fma.f64 (/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))) -1/2 1/2)

Compiler

Compiled 9128 to 4784 computations (47.6% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series15.0ms (0.3%)

Counts

1 → 15

Calls

1 calls:

14.0ms

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

rewrite24.0ms (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:

20.0ms

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

simplify121.0ms (2.5%)

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

prune52.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	48	4	52

Error

0.0b

Counts

52 → 4

Alt Table

Status	Error	Program
	47.2b	(-.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)))))
▶	46.3b	(/.f64 (+.f64 beta 1) alpha)
✓	45.2b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
✓	25.9b	(fma.f64 (/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))) -1/2 1/2)

Compiler

Compiled 796 to 497 computations (37.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

12.0ms

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

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/l*_binary64`

Counts

1 → 35

Calls

1 calls:

7.0ms

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

simplify104.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

657×	`distribute-rgt-in_binary64`
554×	`distribute-lft-in_binary64`
413×	`associate-+l+_binary64`
338×	`unsub-neg_binary64`
305×	`associate-+r+_binary64`

Counts

47 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	585
1	134	551
2	294	551
3	688	518
4	1731	518
5	3257	518
6	4763	518
7	5090	518

prune56.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	56	5	61

Error

Counts

61 → 5

Alt Table

Status	Error	Program
	47.2b	(-.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)))))
✓	46.3b	(/.f64 (+.f64 beta 1) alpha)
✓	45.2b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
	47.5b	(/.f64 (-.f64 (.f64 beta beta) (.f64 1 1)) (*.f64 alpha (-.f64 beta 1)))
✓	25.9b	(fma.f64 (/.f64 (-.f64 (.f64 alpha alpha) (.f64 beta beta)) (*.f64 (+.f64 (+.f64 beta alpha) 2) (+.f64 alpha beta))) -1/2 1/2)

Compiler

Compiled 755 to 484 computations (35.9% saved)

regimes469.0ms (9.5%)

Accuracy

Total -0.0b remaining (-23%)

Threshold costs -0.0b (-23%)

Counts

39 → 2

Compiler

Compiled 3285 to 2326 computations (29.2% saved)

bsearch2.0ms (0%)

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

simplify8.0ms (0.2%)

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

end2.0ms (0%)

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

sample2.0s (40.7%)

Algorithm

1×

intervals

Results

489.0ms	5982×	body	128	valid
323.0ms	999×	body	1024	valid
261.0ms	8000×	pre	128	true
146.0ms	611×	body	512	valid
57.0ms	313×	body	256	valid
39.0ms	95×	body	2048	valid

Compiler

Compiled 163 to 101 computations (38% saved)

Details

analyze277.0ms (5.6%)

sample91.0ms (1.9%)

simplify214.0ms (4.3%)

prune6.0ms (0.1%)

localize15.0ms (0.3%)

series106.0ms (2.2%)

rewrite38.0ms (0.8%)

simplify181.0ms (3.7%)

prune246.0ms (5%)

localize25.0ms (0.5%)

series202.0ms (4.1%)

rewrite58.0ms (1.2%)

simplify189.0ms (3.8%)

prune383.0ms (7.8%)

localize11.0ms (0.2%)

series15.0ms (0.3%)

rewrite24.0ms (0.5%)

simplify121.0ms (2.5%)

prune52.0ms (1%)

localize6.0ms (0.1%)

series12.0ms (0.2%)

rewrite10.0ms (0.2%)

simplify104.0ms (2.1%)

prune56.0ms (1.1%)

regimes469.0ms (9.5%)

bsearch2.0ms (0%)

simplify8.0ms (0.2%)

end2.0ms (0%)

sample2.0s (40.7%)

Profiling