Details

analyze447.0ms (13.2%)

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)

sample152.0ms (4.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
2.0ms	45×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify63.0ms (1.9%)

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
▶	1.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	3.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize7.0ms (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))
✓	2.5b	(*.f64 (/.f64 x y) z)

series38.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

19.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
14.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

rewrite26.0ms (0.8%)

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)

simplify119.0ms (3.5%)

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 → 177

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

prune128.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	172	7	179

Error

Counts

179 → 7

Alt Table

Status	Error	Program
	40.0b	(fabs.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y) 3)))
	27.8b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	1.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	3.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	36.2b	(fabs.f64 (/.f64 (.f64 y (fma.f64 -1 (fma.f64 z x -4) x)) (.f64 y y)))
▶	3.4b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
	34.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 (/.f64 x (sqrt.f64 y)) z))))

Compiler

Compiled 3697 to 1761 computations (52.4% saved)

localize11.0ms (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))
✓	5.9b	(/.f64 (*.f64 z x) y)

series40.0ms (1.2%)

Counts

3 → 54

Calls

3 calls:

20.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
12.0ms	(/.f64 (*.f64 z x) y)
8.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))

rewrite29.0ms (0.9%)

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:

10.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
8.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))
3.0ms	(/.f64 (*.f64 z x) y)

simplify126.0ms (3.7%)

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 → 175

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

prune131.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	176	6	182

Error

Counts

182 → 6

Alt Table

Status	Error	Program
	36.2b	(fabs.f64 (/.f64 (.f64 y (fma.f64 -1 (fma.f64 z x -4) x)) (.f64 y y)))
▶	1.5b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x))))
	40.0b	(fabs.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y) 3)))
	27.8b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	1.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	3.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 4981 to 2170 computations (56.4% 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 z (/.f64 y x)))
✓	2.5b	(/.f64 z (/.f64 y x))

series32.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

19.0ms	(-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x)))
13.0ms	(/.f64 z (/.f64 y x))

rewrite81.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

409×	`times-frac_binary64`
273×	`add-sqr-sqrt_binary64`
267×	`*-un-lft-identity_binary64`
264×	`add-cube-cbrt_binary64`
176×	`prod-diff_binary64`

Counts

2 → 320

Calls

2 calls:

23.0ms	(-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x)))
4.0ms	(/.f64 z (/.f64 y x))

simplify356.0ms (10.5%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary64`
441×	`associate-*r/_binary64`
371×	`associate-*l/_binary64`
267×	`associate-/r/_binary64`
226×	`div-sub_binary64`

Counts

392 → 432

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	630	22384
1	1770	11864
2	4109	11390
3	5196	11390

prune342.0ms (10.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	474	0	474
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	474	6	480

Error

Counts

480 → 6

Alt Table

Status	Error	Program
	36.2b	(fabs.f64 (/.f64 (.f64 y (fma.f64 -1 (fma.f64 z x -4) x)) (.f64 y y)))
✓	1.5b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x))))
	40.0b	(fabs.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y) 3)))
	27.8b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	1.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	3.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))

Compiler

Compiled 20116 to 7146 computations (64.5% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.1b	(/.f64 (-.f64 x (fma.f64 x z -4)) y)

series15.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

15.0ms

(/.f64 (-.f64 x (fma.f64 x z -4)) y)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

1 → 40

Calls

1 calls:

5.0ms

(/.f64 (-.f64 x (fma.f64 x z -4)) y)

simplify75.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

552×	`distribute-rgt-in_binary64`
532×	`distribute-lft-in_binary64`
426×	`fma-def_binary64`
406×	`times-frac_binary64`
357×	`div-sub_binary64`

Counts

76 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1438
1	224	1392
2	495	1134
3	1230	1134
4	4511	1134
5	4991	1134

prune50.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	71	5	76

Error

Counts

76 → 5

Alt Table

Status	Error	Program
	34.4b	(fabs.f64 (/.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) (sqrt.f64 y)) (sqrt.f64 y)))
✓	1.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	3.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
✓	1.5b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x))))
	27.8b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))

Compiler

Compiled 1294 to 779 computations (39.8% saved)

regimes255.0ms (7.5%)

Accuracy

Total 0.6b remaining (97.9%)

Threshold costs 0.6b (97.9%)

Counts

50 → 1

Compiler

Compiled 4270 to 2860 computations (33% saved)

simplify5.0ms (0.2%)

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)

sample826.0ms (24.4%)

Algorithm

1×

intervals

Results

403.0ms	8000×	body	128	valid
56.0ms	1189×	body	128	invalid

Compiler

Compiled 123 to 80 computations (35% saved)

Details

analyze447.0ms (13.2%)

sample152.0ms (4.5%)

simplify63.0ms (1.9%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series38.0ms (1.1%)

rewrite26.0ms (0.8%)

simplify119.0ms (3.5%)

prune128.0ms (3.8%)

localize11.0ms (0.3%)

series40.0ms (1.2%)

rewrite29.0ms (0.9%)

simplify126.0ms (3.7%)

prune131.0ms (3.9%)

localize10.0ms (0.3%)

series32.0ms (0.9%)

rewrite81.0ms (2.4%)

simplify356.0ms (10.5%)

prune342.0ms (10.1%)

localize7.0ms (0.2%)

series15.0ms (0.4%)

rewrite7.0ms (0.2%)

simplify75.0ms (2.2%)

prune50.0ms (1.5%)

regimes255.0ms (7.5%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample826.0ms (24.4%)

Profiling