Details

analyze55.0ms (1.1%)

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
25%	74.9%	0.1%	3
37.5%	62.4%	0.1%	4
56.2%	43.7%	0.1%	5
65.6%	34.3%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample1.0s (21.5%)

Results

866.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify128.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
511×	`fma-neg_binary64`
365×	`times-frac_binary64`
331×	`div-sub_binary64`
156×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	30	10
4	52	10
5	81	10
6	124	10
7	191	10
8	300	10
9	641	10
10	822	10
11	1299	10
12	1328	10
13	1343	10
14	1357	10
15	1377	10
16	1377	10
17	1276	10

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series17.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

17.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64`

Counts

1 → 48

Calls

1 calls:

13.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

simplify135.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

610×	`div-sub_binary64`
586×	`fma-neg_binary64`
530×	`cancel-sign-sub-inv_binary64`
194×	`distribute-neg-frac_binary64`
184×	`fma-def_binary64`

Counts

72 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1287
1	283	1239
2	748	1195
3	2488	1183
4	4383	1183
5	5485	1183

prune67.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	54	5	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	5	60

Error

Counts

60 → 5

Alt Table

Status	Error	Program
	0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 3))
	30.8b	(fma.f64 2 (*.f64 (/.f64 y x) (/.f64 y x)) (fma.f64 (/.f64 y x) -2 1))
▶	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
	32.4b	(fma.f64 2 (/.f64 x y) -1)
	31.0b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))

Compiler

Compiled 1014 to 335 computations (67% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series59.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(/.f64 y (+.f64 x y))
18.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
14.0ms	(/.f64 x (+.f64 x y))

rewrite236.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Rules

595×	`*-un-lft-identity_binary64`
496×	`times-frac_binary64`
339×	`add-sqr-sqrt_binary64`
327×	`add-cube-cbrt_binary64`
324×	`prod-diff_binary64`

Counts

3 → 459

Calls

3 calls:

49.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
7.0ms	(/.f64 y (+.f64 x y))
6.0ms	(/.f64 x (+.f64 x y))

simplify1.4s (30%)

Algorithm

1×	egg-herbie

Rules

764×	`fma-neg_binary64`
542×	`times-frac_binary64`
251×	`unsub-neg_binary64`
239×	`sub-neg_binary64`
210×	`fma-udef_binary64`

Counts

531 → 445

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	463	25191
1	1077	16096
2	2498	11283
3	4634	11271
4	4896	11271

prune398.0ms (8.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	444	1	445
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	446	4	450

Error

Counts

450 → 4

Alt Table

Status	Error	Program
▶	30.7b	(+.f64 1 (.f64 2 (.f64 (/.f64 y x) (+.f64 (/.f64 y x) -1))))
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
	32.4b	(fma.f64 2 (/.f64 x y) -1)
	31.0b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))

Compiler

Compiled 18588 to 3305 computations (82.2% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y x) -1)
✓	0.1b	(*.f64 (/.f64 y x) (+.f64 (/.f64 y x) -1))

series32.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

23.0ms	(*.f64 (/.f64 y x) (+.f64 (/.f64 y x) -1))
9.0ms	(+.f64 (/.f64 y x) -1)

rewrite49.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 72

Calls

2 calls:

29.0ms	(*.f64 (/.f64 y x) (+.f64 (/.f64 y x) -1))
11.0ms	(+.f64 (/.f64 y x) -1)

simplify166.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

393×	`associate-*l/_binary64`
318×	`associate-*r/_binary64`
317×	`distribute-rgt-in_binary64`
291×	`fma-def_binary64`
278×	`distribute-lft-in_binary64`

Counts

120 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1490
1	336	1319
2	1007	1308
3	3532	1288
4	4695	1288
5	5000	1288
6	4957	1288

prune128.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	123	4	127

Error

Counts

127 → 4

Alt Table

Status	Error	Program
✓	30.7b	(+.f64 1 (.f64 2 (.f64 (/.f64 y x) (+.f64 (/.f64 y x) -1))))
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
	32.4b	(fma.f64 2 (/.f64 x y) -1)
▶	31.0b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))

Compiler

Compiled 2542 to 1313 computations (48.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 x y))
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y))
✓	0.1b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))

series118.0ms (2.5%)

Counts

3 → 36

Calls

3 calls:

58.0ms	(/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y))
36.0ms	(sqrt.f64 (-.f64 x y))
23.0ms	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))

rewrite88.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
81×	`add-sqr-sqrt_binary64`
68×	`times-frac_binary64`
60×	`sqrt-prod_binary64`
42×	`add-cube-cbrt_binary64`

Counts

3 → 153

Calls

3 calls:

34.0ms	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))
10.0ms	(/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y))
7.0ms	(sqrt.f64 (-.f64 x y))

simplify217.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-def_binary64`
316×	`associate-/l/_binary64`
305×	`cancel-sign-sub-inv_binary64`
269×	`fma-neg_binary64`
173×	`associate-/r/_binary64`

Counts

189 → 201

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	269	4187
1	700	3896
2	2350	3775
3	4569	3763
4	4961	3763

prune136.0ms (2.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	235	4	239

Error

Counts

239 → 4

Alt Table

Status	Error	Program
✓	30.7b	(+.f64 1 (.f64 2 (.f64 (/.f64 y x) (+.f64 (/.f64 y x) -1))))
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
	32.4b	(fma.f64 2 (/.f64 x y) -1)
✓	31.0b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))

Compiler

Compiled 5601 to 1447 computations (74.2% saved)

regimes174.0ms (3.6%)

Accuracy

Total 0.0b remaining (67.1%)

Threshold costs 0.0b (67.1%)

Counts

39 → 1

Compiler

Compiled 1629 to 1016 computations (37.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	10	16
2	17	16
3	21	16
4	24	16
5	25	16
6	25	16

end54.0ms (1.1%)

Compiler: Compiled 77 to 41 computations (46.8% saved)

Details

analyze55.0ms (1.1%)

sample1.0s (21.5%)

simplify128.0ms (2.7%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series17.0ms (0.4%)

rewrite19.0ms (0.4%)

simplify135.0ms (2.8%)

prune67.0ms (1.4%)

localize14.0ms (0.3%)

series59.0ms (1.2%)

rewrite236.0ms (4.9%)

simplify1.4s (30%)

prune398.0ms (8.3%)

localize12.0ms (0.3%)

series32.0ms (0.7%)

rewrite49.0ms (1%)

simplify166.0ms (3.5%)

prune128.0ms (2.7%)

localize6.0ms (0.1%)

series118.0ms (2.5%)

rewrite88.0ms (1.8%)

simplify217.0ms (4.5%)

prune136.0ms (2.9%)

regimes174.0ms (3.6%)

simplify3.0ms (0.1%)

end54.0ms (1.1%)

Profiling