Details

analyze93.0ms (2.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample139.0ms (3.9%)

Algorithm

1×

intervals

Results

7.0ms	200×	body	128	valid
3.0ms	20×	body	1024	valid
2.0ms	22×	body	512	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify197.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

1996×	`fma-def_binary64`
1626×	`fma-neg_binary64`
1098×	`div-sub_binary64`
733×	`sub-neg_binary64`
664×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	102	14
4	274	14
5	652	14
6	1272	14
7	1697	14
8	2416	14
9	2933	14
10	3278	14
11	3461	14
12	1980	14
13	1996	14
14	2659	14
15	2539	14
16	2497	14
17	2531	14
18	2531	14
19	4723	14
20	4903	14
21	5942	14

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

13.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	25.4b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	14.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series19.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
8.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

2 → 57

Calls

2 calls:

5.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
0.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

simplify84.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
491×	`associate--l+_binary64`
425×	`associate--r+_binary64`
390×	`associate-+l+_binary64`
315×	`fma-def_binary64`

Counts

105 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2086
1	416	1897
2	1275	1850
3	4701	1850
4	5402	1850

prune75.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Error

0.0b

Counts

104 → 3

Alt Table

Status	Error	Program
✓	14.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	31.3b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
▶	14.1b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

Compiler

Compiled 1870 to 1280 computations (31.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 1 y))
✓	0.0b	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
✓	1.6b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

series23.0ms (0.6%)

Counts

3 → 60

Calls

3 calls:

11.0ms	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
9.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
2.0ms	(/.f64 y (+.f64 1 y))

rewrite58.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
18×	`associate-l_binary64`

Counts

3 → 98

Calls

3 calls:

36.0ms	(/.f64 y (+.f64 1 y))
10.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
7.0ms	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

simplify100.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-neg_binary64`
621×	`distribute-rgt-in_binary64`
465×	`times-frac_binary64`
290×	`cancel-sign-sub-inv_binary64`
257×	`sub-neg_binary64`

Counts

158 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	2569
1	702	2474
2	2288	2452
3	4520	2452
4	4961	2452

prune120.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	193	3	196

Error

0.0b

Counts

196 → 3

Alt Table

Status	Error	Program
✓	14.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
▶	31.3b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	14.1b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

Compiler

Compiled 3644 to 2522 computations (30.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 y y))
✓	2.3b	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
✓	6.1b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	8.8b	(/.f64 x (*.f64 y y))

series79.0ms (2.2%)

Counts

4 → 84

Calls

4 calls:

33.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
25.0ms	(/.f64 x (*.f64 y y))
19.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
2.0ms	(/.f64 1 (*.f64 y y))

rewrite51.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
26×	`distribute-lft-out_binary64`
24×	`prod-diff_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 146

Calls

4 calls:

20.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
11.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
6.0ms	(/.f64 x (*.f64 y y))
3.0ms	(/.f64 1 (*.f64 y y))

simplify180.0ms (5%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-neg_binary64`
251×	`cancel-sign-sub-inv_binary64`
196×	`associate-/r/_binary64`
171×	`distribute-rgt-neg-in_binary64`
166×	`distribute-rgt-in_binary64`

Counts

230 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	5463
1	643	4334
2	2435	3523
3	4370	3521
4	4967	3521

prune153.0ms (4.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	188	4	192

Error

0.0b

Counts

192 → 4

Alt Table

Status	Error	Program
✓	14.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
✓	31.3b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
▶	55.7b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (fma.f64 (.f64 y y) (+.f64 x -1) y) (pow.f64 y 3)))
✓	14.1b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

Compiler

Compiled 6070 to 2809 computations (53.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.3b	(fma.f64 (*.f64 y y) (+.f64 x -1) y)
✓	6.1b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (fma.f64 (.f64 y y) (+.f64 x -1) y) (pow.f64 y 3)))
	8.8b	(/.f64 x (*.f64 y y))
✓	27.8b	(/.f64 (fma.f64 (*.f64 y y) (+.f64 x -1) y) (pow.f64 y 3))

series70.0ms (2%)

Counts

3 → 72

Calls

3 calls:

38.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (fma.f64 (.f64 y y) (+.f64 x -1) y) (pow.f64 y 3)))
24.0ms	(/.f64 (fma.f64 (*.f64 y y) (+.f64 x -1) y) (pow.f64 y 3))
8.0ms	(fma.f64 (*.f64 y y) (+.f64 x -1) y)

rewrite91.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

266×	`*-un-lft-identity_binary64`
220×	`times-frac_binary64`
192×	`add-sqr-sqrt_binary64`
179×	`add-cube-cbrt_binary64`
160×	`prod-diff_binary64`

Counts

3 → 305

Calls

3 calls:

19.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (fma.f64 (.f64 y y) (+.f64 x -1) y) (pow.f64 y 3)))
4.0ms	(/.f64 (fma.f64 (*.f64 y y) (+.f64 x -1) y) (pow.f64 y 3))
0.0ms	(fma.f64 (*.f64 y y) (+.f64 x -1) y)

simplify357.0ms (10%)

Algorithm

1×	egg-herbie

Rules

509×	`fma-neg_binary64`
299×	`associate-/r*_binary64`
287×	`log-div_binary64`
280×	`div-sub_binary64`
268×	`log-prod_binary64`

Counts

377 → 305

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	425	21054
1	957	12963
2	3051	9833
3	4371	9832
4	4801	9832

prune277.0ms (7.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	333	0	333
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	333	4	337

Error

0.0b

Counts

337 → 4

Alt Table

Status	Error	Program
✓	14.2b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
✓	31.3b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	55.7b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (fma.f64 (.f64 y y) (+.f64 x -1) y) (pow.f64 y 3)))
✓	14.1b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

Compiler

Compiled 17008 to 7789 computations (54.2% saved)

regimes589.0ms (16.4%)

Accuracy

Total 0.6b remaining (91.6%)

Threshold costs 0.6b (91.6%)

Counts

75 → 3

Compiler

Compiled 5843 to 3924 computations (32.8% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	77
1	44	77
2	54	77
3	66	77
4	75	77
5	83	77
6	90	77
7	96	77
8	101	77
9	103	77
10	99	77

end1.0ms (0%)

Compiler: Compiled 54 to 38 computations (29.6% saved)

sample773.0ms (21.6%)

Algorithm

1×

intervals

Results

249.0ms	6274×	body	128	valid
104.0ms	591×	body	1024	valid
76.0ms	693×	body	512	valid
31.0ms	437×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 138 to 94 computations (31.9% saved)

Details

analyze93.0ms (2.6%)

sample139.0ms (3.9%)

simplify197.0ms (5.5%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.5%)

rewrite9.0ms (0.3%)

simplify84.0ms (2.3%)

prune75.0ms (2.1%)

localize6.0ms (0.2%)

series23.0ms (0.6%)

rewrite58.0ms (1.6%)

simplify100.0ms (2.8%)

prune120.0ms (3.3%)

localize11.0ms (0.3%)

series79.0ms (2.2%)

rewrite51.0ms (1.4%)

simplify180.0ms (5%)

prune153.0ms (4.3%)

localize12.0ms (0.3%)

series70.0ms (2%)

rewrite91.0ms (2.6%)

simplify357.0ms (10%)

prune277.0ms (7.7%)

regimes589.0ms (16.4%)

bsearch2.0ms (0.1%)

simplify6.0ms (0.2%)

end1.0ms (0%)

sample773.0ms (21.6%)

Profiling