Details

analyze603.0ms (15.6%)

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
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)

sample25.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	31×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify71.0ms (1.8%)

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

prune3.0ms (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
	4.1b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	3.7b	(*.f64 (/.f64 x y) z)

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

3 → 117

Calls

3 calls:

9.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
5.0ms	(*.f64 (/.f64 x y) z)
4.0ms	(/.f64 (+.f64 x 4) y)

series219.0ms (5.6%)

Counts

3 → 96

Calls

3 calls:

131.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
72.0ms	(*.f64 (/.f64 x y) z)
15.0ms	(/.f64 (+.f64 x 4) y)

simplify139.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-l_binary64`
381×	`fma-def_binary64`
379×	`associate-*l/_binary64`
369×	`associate-r_binary64`
310×	`fma-neg_binary64`

Counts

213 → 353

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	187	3147
1	457	2896
2	1229	2394
3	3977	2382
4	4927	2330
5	4911	2330

prune188.0ms (4.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	349	4	353
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	350	5	355

Error

0.0b

Counts

355 → 5

Alt Table

Status	Error	Program
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
	4.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	28.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
✓	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))

Compiler

Compiled 3671 to 1732 computations (52.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
✓	7.0b	(*.f64 x (/.f64 z y))

rewrite19.0ms (0.5%)

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:

9.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
6.0ms	(*.f64 x (/.f64 z y))

series107.0ms (2.8%)

Counts

2 → 72

Calls

2 calls:

64.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
43.0ms	(*.f64 x (/.f64 z y))

simplify111.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

381×	`associate-r_binary64`
373×	`associate-*r/_binary64`
365×	`associate-*l/_binary64`
350×	`fma-def_binary64`
341×	`fma-neg_binary64`

Counts

154 → 258

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2478
1	386	2346
2	1212	1703
3	3481	1689
4	4636	1689
5	4914	1689

prune146.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	348	0	348
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	348	5	353

Error

0.0b

Counts

353 → 5

Alt Table

Status	Error	Program
▶	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
	4.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	28.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
✓	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))

Compiler

Compiled 3499 to 1672 computations (52.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z)))
✓	0.2b	(*.f64 (/.f64 1 y) z)
✓	7.0b	(.f64 x (.f64 (/.f64 1 y) z))

rewrite26.0ms (0.7%)

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:

9.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z)))
6.0ms	(.f64 x (.f64 (/.f64 1 y) z))
5.0ms	(*.f64 (/.f64 1 y) z)

series127.0ms (3.3%)

Counts

3 → 96

Calls

3 calls:

66.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z)))
41.0ms	(.f64 x (.f64 (/.f64 1 y) z))
19.0ms	(*.f64 (/.f64 1 y) z)

simplify123.0ms (3.2%)

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 → 342

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

prune163.0ms (4.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	522	0	522
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	522	5	527

Error

0.0b

Counts

527 → 5

Alt Table

Status	Error	Program
✓	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
▶	4.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	28.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
✓	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))

Compiler

Compiled 4633 to 2827 computations (39% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))
✓	0.0b	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
✓	7.0b	(/.f64 (*.f64 z x) y)

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
28×	`prod-diff_binary64`
27×	`times-frac_binary64`

Counts

3 → 112

Calls

3 calls:

11.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
6.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))
3.0ms	(/.f64 (*.f64 z x) y)

series138.0ms (3.6%)

Counts

3 → 54

Calls

3 calls:

66.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
46.0ms	(/.f64 (*.f64 z x) y)
25.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))

simplify140.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-def_binary64`
584×	`times-frac_binary64`
452×	`fma-neg_binary64`
244×	`cancel-sign-sub-inv_binary64`
197×	`distribute-rgt-neg-in_binary64`

Counts

166 → 289

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	201	3145
1	525	2728
2	1842	2393
3	4099	2379
4	4956	2278
5	4866	2278

prune134.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	288	1	289
Fresh	0	1	1
Picked	1	0	1
Done	1	2	3
Total	290	4	294

Error

Counts

294 → 4

Alt Table

Status	Error	Program
✓	1.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	1.6b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x))))
	28.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) z))))
✓	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))

Compiler

Compiled 4890 to 2101 computations (57% saved)

regimes397.0ms (10.3%)

Accuracy

Total 0.6b remaining (95.8%)

Threshold costs 0.6b (95.8%)

Compiler

Compiled 6487 to 4486 computations (30.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
12×	`*-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	27	42
2	41	42
3	63	42
4	85	42
5	99	42
6	105	42
7	106	42
8	105	42

end1.0ms (0%)

Compiler: Compiled 29 to 16 computations (44.8% saved)

sample900.0ms (23.3%)

Algorithm

1×

intervals

Results

403.0ms	8000×	body	128	valid
58.0ms	1217×	body	128	invalid

Compiler

Compiled 118 to 75 computations (36.4% saved)

Details

analyze603.0ms (15.6%)

sample25.0ms (0.6%)

simplify71.0ms (1.8%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite23.0ms (0.6%)

series219.0ms (5.6%)

simplify139.0ms (3.6%)

prune188.0ms (4.9%)

localize8.0ms (0.2%)

rewrite19.0ms (0.5%)

series107.0ms (2.8%)

simplify111.0ms (2.9%)

prune146.0ms (3.8%)

localize10.0ms (0.2%)

rewrite26.0ms (0.7%)

series127.0ms (3.3%)

simplify123.0ms (3.2%)

prune163.0ms (4.2%)

localize10.0ms (0.3%)

rewrite26.0ms (0.7%)

series138.0ms (3.6%)

simplify140.0ms (3.6%)

prune134.0ms (3.5%)

regimes397.0ms (10.3%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample900.0ms (23.3%)

Profiling