Details

analyze871.0ms (15.3%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
21.8%	78%	0.1%	6
26.5%	73.3%	0.1%	7
32%	67.9%	0.1%	8
46.4%	52.7%	0.9%	9
50.9%	47.2%	1.9%	10
54.3%	43.3%	2.4%	11
62.1%	32.5%	5.4%	12
64.3%	28.1%	7.6%	13
66.3%	24.6%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample52.0ms (0.9%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
4.0ms	43×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify112.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1167×	`fma-def_binary64`
1073×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	43	18
3	75	18
4	123	16
5	213	16
6	302	16
7	472	16
8	1009	13
9	1328	13
10	1542	13
11	1559	13
12	1556	13
13	1556	13
14	1453	13

prune7.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	3.8b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	2.4b	(*.f64 (/.f64 x y) z)

series73.0ms (1.3%)

Counts

2 → 72

Calls

2 calls:

45.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
27.0ms	(*.f64 (/.f64 x y) z)

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

2 → 82

Calls

2 calls:

15.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
8.0ms	(*.f64 (/.f64 x y) z)

simplify169.0ms (3%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-neg_binary64`
414×	`associate-l_binary64`
348×	`associate-*l/_binary64`
343×	`associate-r_binary64`
327×	`fma-def_binary64`

Counts

154 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	2469
1	383	2220
2	1060	1685
3	3521	1673
4	4720	1673
5	4999	1673
6	4896	1673

prune118.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	135	5	140

Error

Counts

140 → 5

Alt Table

Status	Error	Program
✓	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
▶	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
	32.2b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.8b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 2892 to 1331 computations (54% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	1.2b	(*.f64 (/.f64 x (cbrt.f64 y)) z)
✓	4.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))

series957.0ms (16.8%)

Counts

4 → 96

Calls

4 calls:

799.0ms	(*.f64 (/.f64 x (cbrt.f64 y)) z)
63.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
50.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))
45.0ms	(cbrt.f64 y)

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
45×	`add-sqr-sqrt_binary64`
35×	`associate-l_binary64`
35×	`add-cbrt-cube_binary64`

Counts

4 → 152

Calls

4 calls:

15.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))
10.0ms	(*.f64 (/.f64 x (cbrt.f64 y)) z)
8.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify250.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-neg_binary64`
610×	`associate-/l/_binary64`
454×	`*-commutative_binary64`
384×	`unswap-sqr_binary64`
192×	`associate-r_binary64`

Counts

248 → 224

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3394
1	393	2332
2	1491	2271
3	2499	2256
4	4837	2256
5	5214	2256

prune427.0ms (7.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	260	5	265

Error

Counts

265 → 5

Alt Table

Status	Error	Program
✓	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
	32.2b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	3.8b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 7080 to 2960 computations (58.2% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z)))
✓	0.2b	(*.f64 (/.f64 1 y) z)
✓	5.0b	(.f64 x (.f64 (/.f64 1 y) z))

series64.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

32.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z)))
20.0ms	(.f64 x (.f64 (/.f64 1 y) z))
11.0ms	(*.f64 (/.f64 1 y) z)

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
35×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64`

Counts

3 → 110

Calls

3 calls:

14.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z)))
10.0ms	(.f64 x (.f64 (/.f64 1 y) z))
9.0ms	(*.f64 (/.f64 1 y) z)

simplify221.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-def_binary64`
405×	`fma-neg_binary64`
334×	`associate-*l/_binary64`
312×	`cancel-sign-sub-inv_binary64`
299×	`*-commutative_binary64`

Counts

206 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2789
1	410	2567
2	1204	1918
3	3298	1906
4	4681	1906
5	4856	1906

prune280.0ms (4.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	176	5	181

Error

Counts

181 → 5

Alt Table

Status	Error	Program
✓	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (pow.f64 (/.f64 z y) 1))))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
	3.8b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 3785 to 2277 computations (39.8% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (pow.f64 (/.f64 z y) 1)))
✓	5.0b	(*.f64 x (pow.f64 (/.f64 z y) 1))

series68.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

49.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (pow.f64 (/.f64 z y) 1)))
19.0ms	(*.f64 x (pow.f64 (/.f64 z y) 1))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
17×	`associate-r_binary64`

Counts

2 → 86

Calls

2 calls:

19.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (pow.f64 (/.f64 z y) 1)))
15.0ms	(*.f64 x (pow.f64 (/.f64 z y) 1))

simplify145.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

573×	`unswap-sqr_binary64`
434×	`fma-neg_binary64`
386×	`fma-def_binary64`
377×	`associate-*l/_binary64`
359×	`associate-*r/_binary64`

Counts

158 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	2538
1	372	2403
2	1291	1761
3	3628	1750
4	4737	1750
5	4900	1750

prune120.0ms (2.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	146	5	151

Error

Counts

151 → 5

Alt Table

Status	Error	Program
✓	1.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (pow.f64 (/.f64 z y) 1))))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
✓	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
	3.8b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 3311 to 1817 computations (45.1% saved)

regimes187.0ms (3.3%)

Accuracy

Total 0.1b remaining (87.4%)

Threshold costs 0.1b (87.4%)

Counts

25 → 2

Compiler

Compiled 2207 to 1481 computations (32.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
11×	`sub-neg_binary64`
8×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	54
1	34	54
2	53	54
3	69	54
4	84	54
5	90	54
6	91	54
7	90	54

end1.0ms (0%)

Compiler: Compiled 39 to 23 computations (41% saved)

sample1.3s (23.3%)

Algorithm

1×

intervals

Results

690.0ms	8000×	body	128	valid
100.0ms	1168×	body	128	invalid

Compiler

Compiled 143 to 94 computations (34.3% saved)

Details

analyze871.0ms (15.3%)

sample52.0ms (0.9%)

simplify112.0ms (2%)

prune7.0ms (0.1%)

localize16.0ms (0.3%)

series73.0ms (1.3%)

rewrite33.0ms (0.6%)

simplify169.0ms (3%)

prune118.0ms (2.1%)

localize17.0ms (0.3%)

series957.0ms (16.8%)

rewrite57.0ms (1%)

simplify250.0ms (4.4%)

prune427.0ms (7.5%)

localize12.0ms (0.2%)

series64.0ms (1.1%)

rewrite49.0ms (0.9%)

simplify221.0ms (3.9%)

prune280.0ms (4.9%)

localize11.0ms (0.2%)

series68.0ms (1.2%)

rewrite42.0ms (0.7%)

simplify145.0ms (2.6%)

prune120.0ms (2.1%)

regimes187.0ms (3.3%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.3s (23.3%)

Profiling