Details

analyze614.0ms (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
6.2%	93.6%	0.1%	6
20.3%	79.6%	0.1%	7
28.9%	71%	0.1%	8
39.8%	60.1%	0.1%	9
57.5%	42.3%	0.1%	10
63.9%	36%	0.1%	11
68.6%	31.3%	0.1%	12
79.5%	20.3%	0.1%	13
82.9%	17%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.0s (22.4%)

Results

901.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify218.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

2674×	`fma-neg_binary64`
2270×	`div-sub_binary64`
1877×	`fma-def_binary64`
968×	`associate-/l/_binary64`
705×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	14	13
2	20	13
3	28	13
4	41	13
5	55	13
6	72	13
7	85	13
8	102	13
9	127	13
10	155	13
11	215	13
12	356	13
13	666	13
14	1204	13
15	1746	13
16	1897	13
17	2006	13
18	2246	13
19	2452	13
20	1993	13
21	2354	13
22	2400	13
23	2609	13
24	2737	13
25	2812	13
26	2982	13
27	2984	13
28	3004	13
29	3004	13
30	3850	13
31	5135	13

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

9.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	9.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series25.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

25.0ms

(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

rewrite58.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

816×	`prod-diff_binary64`
190×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`
105×	`add-sqr-sqrt_binary64`
100×	`log1p-expm1-u_binary64`

Counts

1 → 35

Calls

1 calls:

57.0ms

(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	203	13
2	2855	13
3	5099	13
0	0	0
1	0	0

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

338×	`fma-def_binary64`
330×	`+-commutative_binary64`
304×	`distribute-neg-in_binary64`
284×	`sub-neg_binary64`
246×	`times-frac_binary64`

Counts

71 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	1140
1	265	1140
2	934	1004
3	3610	983
4	4808	980
5	4998	980

prune60.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	5	70

Error

0.0b

Counts

70 → 5

Alt Table

Status	Error	Program
	20.1b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
✓	9.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
▶	9.3b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	35.3b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	32.5b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))

Compiler

Compiled 1478 to 732 computations (50.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (-.f64 1 (/.f64 y z)))
✓	8.7b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

series42.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

27.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
15.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))

rewrite74.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

807×	`prod-diff_binary64`
202×	`log1p-udef_binary64`
115×	`add-sqr-sqrt_binary64`
109×	`log1p-expm1-u_binary64`
109×	`expm1-log1p-u_binary64`

Counts

2 → 67

Calls

2 calls:

72.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))
72.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	226	23
2	3029	23
3	4992	23
0	0	0
1	0	0

simplify71.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

455×	`fma-def_binary64`
367×	`+-commutative_binary64`
347×	`sub-neg_binary64`
266×	`times-frac_binary64`
233×	`associate-/l*_binary64`

Counts

127 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1602
1	319	1602
2	1135	1355
3	4313	1343
4	4988	1343

prune73.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	115	5	120

Error

0.0b

Counts

120 → 5

Alt Table

Status	Error	Program
▶	20.1b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
✓	9.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
✓	9.3b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	35.3b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	32.5b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))

Compiler

Compiled 2214 to 1101 computations (50.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 y z))
✓	0.2b	(pow.f64 (/.f64 y z) 2)
✓	4.4b	(/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2)))
✓	15.4b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))

series274.0ms (5.9%)

Counts

4 → 102

Calls

4 calls:

152.0ms	(/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2)))
95.0ms	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
19.0ms	(pow.f64 (/.f64 y z) 2)
8.0ms	(+.f64 1 (/.f64 y z))

rewrite139.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

263×	`fma-neg_binary64`
261×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`
165×	`egg-rr`
148×	`add-sqr-sqrt_binary64`

Counts

4 → 165

Calls

4 calls:

131.0ms	(+.f64 1 (/.f64 y z))
131.0ms	(pow.f64 (/.f64 y z) 2)
131.0ms	(/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2)))
131.0ms	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	300	43
2	4111	43
3	5110	43
0	0	0
1	0	0

simplify155.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
721×	`times-frac_binary64`
264×	`associate-+r+_binary64`
264×	`distribute-neg-in_binary64`
250×	`distribute-rgt-in_binary64`

Counts

267 → 234

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3237
1	489	3219
2	1741	2705
3	4977	2705

prune338.0ms (7.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	234	5	239

Error

0.0b

Counts

239 → 5

Alt Table

Status	Error	Program
✓	20.1b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
✓	9.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
✓	9.3b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	35.3b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
▶	32.5b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))

Compiler

Compiled 6040 to 3149 computations (47.9% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 z (/.f64 z (/.f64 y z)))
✓	0.2b	(/.f64 z (/.f64 y z))
✓	6.8b	(fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z))))

series82.0ms (1.8%)

Counts

3 → 84

Calls

3 calls:

48.0ms	(fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z))))
18.0ms	(/.f64 z (/.f64 y z))
16.0ms	(+.f64 z (/.f64 z (/.f64 y z)))

rewrite122.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

570×	`log-prod_binary64`
315×	`fma-def_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`
178×	`log-div_binary64`

Counts

3 → 150

Calls

3 calls:

116.0ms	(+.f64 z (/.f64 z (/.f64 y z)))
116.0ms	(/.f64 z (/.f64 y z))
115.0ms	(fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	202	30
2	2851	30
3	5454	30
0	0	0
1	0	0

simplify168.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

907×	`fma-def_binary64`
868×	`associate-/l/_binary64`
763×	`distribute-rgt-out_binary64`
344×	`distribute-rgt-in_binary64`
263×	`*-commutative_binary64`

Counts

234 → 167

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	25	948
1	39	945
2	63	889
3	110	743
4	299	689
5	756	689
6	1623	689
7	3077	689
8	3105	689
9	3373	689
10	4175	689
11	4303	689
12	5029	689

prune164.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	167	5	172

Error

0.0b

Counts

172 → 5

Alt Table

Status	Error	Program
	31.5b	(neg.f64 (fma.f64 (/.f64 x y) z z))
✓	20.1b	(*.f64 (/.f64 (+.f64 x y) (-.f64 1 (pow.f64 (/.f64 y z) 2))) (+.f64 1 (/.f64 y z)))
✓	9.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
✓	9.3b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	35.3b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))

Compiler

Compiled 3068 to 918 computations (70.1% saved)

regimes634.0ms (13.6%)

Accuracy

Total 0.1b remaining (92.4%)

Threshold costs 0.1b (92.4%)

Counts

44 → 3

Compiler

Compiled 2675 to 1783 computations (33.3% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	90
1	30	90
2	37	90
3	42	90
4	45	90
5	46	90
6	45	90

end179.0ms (3.8%)

Compiler: Compiled 196 to 113 computations (42.3% saved)

Details

analyze614.0ms (13.2%)

sample1.0s (22.4%)

simplify218.0ms (4.7%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series25.0ms (0.5%)

rewrite58.0ms (1.2%)

simplify76.0ms (1.6%)

prune60.0ms (1.3%)

localize7.0ms (0.1%)

series42.0ms (0.9%)

rewrite74.0ms (1.6%)

simplify71.0ms (1.5%)

prune73.0ms (1.6%)

localize9.0ms (0.2%)

series274.0ms (5.9%)

rewrite139.0ms (3%)

simplify155.0ms (3.3%)

prune338.0ms (7.3%)

localize16.0ms (0.4%)

series82.0ms (1.8%)

rewrite122.0ms (2.6%)

simplify168.0ms (3.6%)

prune164.0ms (3.5%)

regimes634.0ms (13.6%)

bsearch2.0ms (0.1%)

simplify9.0ms (0.2%)

end179.0ms (3.8%)

Profiling