Details

analyze300.0ms (4.4%)

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)

sample58.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms	186×	body	128	valid
11.0ms	38×	body	1024	valid
7.0ms	256×	pre	128	true
5.0ms	16×	body	512	valid
2.0ms	6×	body	2048	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify232.0ms (3.4%)

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

prune5.0ms (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

17.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.3b	(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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	2.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

rewrite26.0ms (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:

16.0ms	(/.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)

series98.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

64.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
34.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

simplify189.0ms (2.8%)

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

prune243.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	203	4	207

Error

Counts

207 → 4

Alt Table

Status	Error	Program
✓	17.3b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	45.2b	(-.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)))))
	44.2b	(/.f64 (+.f64 beta 1) alpha)
▶	17.5b	(fma.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 4319 to 2653 computations (38.6% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))))
✓	0.4b	(/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
✓	0.5b	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
✓	9.5b	(fma.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

rewrite162.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

206×	`*-un-lft-identity_binary64`
156×	`add-sqr-sqrt_binary64`
150×	`times-frac_binary64`
101×	`sqrt-prod_binary64`
76×	`add-cube-cbrt_binary64`

Counts

4 → 256

Calls

4 calls:

79.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))))
20.0ms	(/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
14.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
1.0ms	(fma.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

series343.0ms (5%)

Counts

4 → 64

Calls

4 calls:

139.0ms	(/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
90.0ms	(/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))
75.0ms	(fma.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
38.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))))

simplify374.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

310×	`fma-def_binary64`
268×	`associate-r_binary64`
207×	`associate-/l*_binary64`
204×	`associate-+l+_binary64`
193×	`associate-l_binary64`

Counts

320 → 620

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	505	10510
1	1500	9281
2	5051	9281

prune678.0ms (10%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	620	0	620
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	620	4	624

Error

Counts

624 → 4

Alt Table

Status	Error	Program
✓	17.3b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	45.2b	(-.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)))))
▶	44.2b	(/.f64 (+.f64 beta 1) alpha)
✓	17.5b	(fma.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 13912 to 8883 computations (36.1% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite12.0ms (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:

9.0ms

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

series34.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

34.0ms

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

simplify128.0ms (1.9%)

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 → 87

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

prune51.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	87	4	91

Error

Counts

91 → 4

Alt Table

Status	Error	Program
✓	17.3b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
▶	45.2b	(-.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)))))
✓	44.2b	(/.f64 (+.f64 beta 1) alpha)
✓	17.5b	(fma.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 775 to 493 computations (36.4% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
✓	2.0b	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
✓	4.5b	(-.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)))))
✓	8.7b	(/.f64 beta (*.f64 alpha alpha))

rewrite114.0ms (1.7%)

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:

52.0ms	(-.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)))))
11.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
6.0ms	(/.f64 beta (*.f64 alpha alpha))
1.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))

series387.0ms (5.7%)

Counts

4 → 96

Calls

4 calls:

113.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
110.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
101.0ms	(-.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)))))
63.0ms	(/.f64 beta (*.f64 alpha alpha))

simplify449.0ms (6.6%)

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 → 462

Iterations

Useful iterations: 2 (0.0ms)

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

prune302.0ms (4.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	462	0	462
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	462	4	466

Error

Counts

466 → 4

Alt Table

Status	Error	Program
✓	17.3b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	45.2b	(-.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)))))
✓	44.2b	(/.f64 (+.f64 beta 1) alpha)
✓	17.5b	(fma.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

Compiler

Compiled 11499 to 4176 computations (63.7% saved)

regimes489.0ms (7.2%)

Accuracy

Total 0.1b remaining (60.4%)

Threshold costs 0.1b (60.4%)

Compiler

Compiled 3810 to 2596 computations (31.9% saved)

bsearch3.0ms (0%)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
6×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	61
1	37	61
2	47	61
3	53	61
4	56	61
5	55	61

end2.0ms (0%)

Compiler: Compiled 44 to 27 computations (38.6% saved)

sample2.0s (30%)

Algorithm

1×

intervals

Results

528.0ms	5943×	body	128	valid
319.0ms	1001×	body	1024	valid
291.0ms	8000×	pre	128	true
160.0ms	629×	body	512	valid
52.0ms	349×	body	256	valid
31.0ms	78×	body	2048	valid

Compiler

Compiled 143 to 92 computations (35.7% saved)

Details

analyze300.0ms (4.4%)

sample58.0ms (0.9%)

simplify232.0ms (3.4%)

prune5.0ms (0.1%)

localize15.0ms (0.2%)

rewrite26.0ms (0.4%)

series98.0ms (1.4%)

simplify189.0ms (2.8%)

prune243.0ms (3.6%)

localize24.0ms (0.4%)

rewrite162.0ms (2.4%)

series343.0ms (5%)

simplify374.0ms (5.5%)

prune678.0ms (10%)

localize7.0ms (0.1%)

rewrite12.0ms (0.2%)

series34.0ms (0.5%)

simplify128.0ms (1.9%)

prune51.0ms (0.7%)

localize28.0ms (0.4%)

rewrite114.0ms (1.7%)

series387.0ms (5.7%)

simplify449.0ms (6.6%)

prune302.0ms (4.4%)

regimes489.0ms (7.2%)

bsearch3.0ms (0%)

simplify9.0ms (0.1%)

end2.0ms (0%)

sample2.0s (30%)

Profiling