Details

analyze1.5s (33.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample47.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	199×	body	128	valid
6.0ms	18×	body	2048	valid
5.0ms	256×	pre	128	true
5.0ms	11×	body	4096	valid
3.0ms	12×	body	1024	valid
2.0ms	9×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 45 to 34 computations (24.4% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	24
2	39	22
3	45	22
4	47	22
5	49	22
6	50	22
7	47	22

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

11.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
✓	0.0b	(fma.f64 x x (.f64 p (.f64 4 p)))
✓	0.5b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	16.6b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
16×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`

Counts

4 → 147

Calls

4 calls:

14.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
9.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))
9.0ms	(fma.f64 x x (.f64 p (.f64 4 p)))
9.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)

series94.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

29.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
27.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
23.0ms	(fma.f64 x x (.f64 p (.f64 4 p)))
14.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

simplify140.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-def_binary64`
495×	`fma-neg_binary64`
469×	`cancel-sign-sub-inv_binary64`
231×	`distribute-rgt-neg-in_binary64`
210×	`distribute-lft-neg-in_binary64`

Counts

243 → 406

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	4133
1	662	3857
2	2292	3771
3	4512	3767
4	5023	3767

prune212.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	403	3	406
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	403	4	407

Error

4.2b

Counts

407 → 4

Alt Table

Status	Error	Program
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	56.8b	(sqrt.f64 (fma.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 (/.f64 p x) (/.f64 p x) (fma.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35 (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3)))))
▶	52.2b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	53.3b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))

Compiler

Compiled 6350 to 4267 computations (32.8% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
✓	0.2b	(/.f64 (*.f64 x x) p)
✓	24.2b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`

Counts

3 → 132

Calls

3 calls:

16.0ms	(/.f64 (*.f64 x x) p)
13.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
10.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

series98.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

46.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
32.0ms	(/.f64 (*.f64 x x) p)
19.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

simplify101.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

710×	`associate-/l*_binary64`
538×	`associate-l_binary64`
496×	`associate-/r*_binary64`
315×	`associate-*l/_binary64`
296×	`associate-/l/_binary64`

Counts

204 → 335

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	1829
1	232	1708
2	764	1547
3	4683	1547
4	5017	1547

prune77.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	333	2	335
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	336	3	339

Error

Counts

339 → 3

Alt Table

Status	Error	Program
▶	53.0b	(/.f64 p x)
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	55.2b	(neg.f64 (/.f64 p x))

Compiler

Compiled 2271 to 576 computations (74.6% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune2.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	53.0b	(/.f64 p x)
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
▶	55.2b	(neg.f64 (/.f64 p x))

Compiler

Compiled 34 to 23 computations (32.4% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune2.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	53.0b	(/.f64 p x)
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	55.2b	(neg.f64 (/.f64 p x))

Compiler

Compiled 28 to 19 computations (32.1% saved)

regimes339.0ms (7.7%)

Accuracy

Total 5.5b remaining (98.7%)

Threshold costs 0b (0%)

Compiler

Compiled 4109 to 3176 computations (22.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	57
1	26	57
2	26	57

end1.0ms (0%)

Compiler: Compiled 40 to 25 computations (37.5% saved)

sample1.6s (37.6%)

Algorithm

1×

intervals

Results

447.0ms	6087×	body	128	valid
283.0ms	752×	body	2048	valid
181.0ms	8000×	pre	128	true
146.0ms	485×	body	1024	valid
136.0ms	286×	body	4096	valid
51.0ms	242×	body	512	valid
20.0ms	148×	body	256	valid

Compiler

Compiled 94 to 64 computations (31.9% saved)

Details

analyze1.5s (33.6%)

sample47.0ms (1.1%)

simplify13.0ms (0.3%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite48.0ms (1.1%)

series94.0ms (2.1%)

simplify140.0ms (3.2%)

prune212.0ms (4.8%)

localize5.0ms (0.1%)

rewrite45.0ms (1%)

series98.0ms (2.2%)

simplify101.0ms (2.3%)

prune77.0ms (1.8%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0.2%)

prune2.0ms (0%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

regimes339.0ms (7.7%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (37.6%)

Profiling