Details

analyze455.0ms (11.6%)

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)

sample155.0ms (3.9%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
2.0ms	37×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify64.0ms (1.6%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.1b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.9b	(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))
✓	3.4b	(*.f64 (/.f64 x y) z)

series42.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

21.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
14.0ms	(*.f64 (/.f64 x y) z)
6.0ms	(/.f64 (+.f64 x 4) y)

rewrite25.0ms (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)

simplify133.0ms (3.4%)

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

prune154.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	173	6	179

Error

0.0b

Counts

179 → 6

Alt Table

Status	Error	Program
	33.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (sqrt.f64 x) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 y)) z))))
	2.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) z))))
	31.0b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
▶	2.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
✓	1.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	32.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (sqrt.f64 z)) (sqrt.f64 z))))

Compiler

Compiled 3707 to 1751 computations (52.8% saved)

localize10.0ms (0.2%)

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))
✓	4.7b	(/.f64 (*.f64 z x) y)

series45.0ms (1.2%)

Counts

3 → 54

Calls

3 calls:

22.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
14.0ms	(/.f64 (*.f64 z x) y)
9.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))

rewrite27.0ms (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:

9.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y))
7.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))
3.0ms	(/.f64 (*.f64 z x) y)

simplify123.0ms (3.1%)

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

prune148.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	175	6	181

Error

Counts

181 → 6

Alt Table

Status	Error	Program
▶	2.0b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x))))
	32.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (sqrt.f64 z)) (sqrt.f64 z))))
	31.0b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	2.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
✓	1.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	2.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (*.f64 z x) (/.f64 1 y))))

Compiler

Compiled 4990 to 2175 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)))
✓	3.6b	(/.f64 z (/.f64 y x))

series86.0ms (2.2%)

Counts

2 → 72

Calls

2 calls:

71.0ms	(-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x)))
14.0ms	(/.f64 z (/.f64 y x))

rewrite86.0ms (2.2%)

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))

simplify320.0ms (8.1%)

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

prune399.0ms (10.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	474	0	474
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	474	6	480

Error

Counts

480 → 6

Alt Table

Status	Error	Program
✓	2.0b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x))))
	32.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (sqrt.f64 z)) (sqrt.f64 z))))
	31.0b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	2.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
✓	1.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	2.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (*.f64 z x) (/.f64 1 y))))

Compiler

Compiled 20125 to 7151 computations (64.5% saved)

localize10.0ms (0.2%)

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) (/.f64 1 y)))
✓	4.8b	(.f64 (.f64 z x) (/.f64 1 y))

series36.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

22.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (*.f64 z x) (/.f64 1 y)))
14.0ms	(.f64 (.f64 z x) (/.f64 1 y))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
12×	`prod-exp_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 72

Calls

2 calls:

8.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (*.f64 z x) (/.f64 1 y)))
7.0ms	(.f64 (.f64 z x) (/.f64 1 y))

simplify89.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
342×	`distribute-rgt-in_binary64`
319×	`distribute-lft-in_binary64`
233×	`cancel-sign-sub-inv_binary64`
225×	`associate-/l*_binary64`

Counts

144 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	2252
1	445	2005
2	1535	1767
3	4460	1764
4	4935	1764

prune144.0ms (3.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	163	6	169

Error

Counts

169 → 6

Alt Table

Status	Error	Program
✓	2.0b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y))) (/.f64 z (/.f64 y x))))
	32.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (sqrt.f64 z)) (sqrt.f64 z))))
	31.0b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
✓	2.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (/.f64 (.f64 z x) y)))
✓	1.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	2.1b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (*.f64 z x) (/.f64 1 y))))

Compiler

Compiled 4146 to 2274 computations (45.2% saved)

regimes500.0ms (12.7%)

Accuracy

Total 0.1b remaining (88.2%)

Threshold costs 0.1b (88.2%)

Counts

77 → 2

Compiler

Compiled 6312 to 4306 computations (31.8% saved)

bsearch2.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
15×	`sub-neg_binary64`
14×	`*-commutative_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	65
1	41	65
2	61	65
3	88	65
4	116	65
5	130	65
6	134	65
7	135	65
8	132	65

end1.0ms (0%)

Compiler: Compiled 46 to 27 computations (41.3% saved)

sample836.0ms (21.2%)

Algorithm

1×

intervals

Results

390.0ms	8000×	body	128	valid
53.0ms	1189×	body	128	invalid

Compiler

Compiled 171 to 113 computations (33.9% saved)

Details

analyze455.0ms (11.6%)

sample155.0ms (3.9%)

simplify64.0ms (1.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series42.0ms (1.1%)

rewrite25.0ms (0.6%)

simplify133.0ms (3.4%)

prune154.0ms (3.9%)

localize10.0ms (0.2%)

series45.0ms (1.2%)

rewrite27.0ms (0.7%)

simplify123.0ms (3.1%)

prune148.0ms (3.8%)

localize10.0ms (0.3%)

series86.0ms (2.2%)

rewrite86.0ms (2.2%)

simplify320.0ms (8.1%)

prune399.0ms (10.1%)

localize10.0ms (0.2%)

series36.0ms (0.9%)

rewrite20.0ms (0.5%)

simplify89.0ms (2.3%)

prune144.0ms (3.7%)

regimes500.0ms (12.7%)

bsearch2.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample836.0ms (21.2%)

Profiling