Details

analyze546.0ms (15.2%)

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
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.1s (29.7%)

Results

842.0ms	8256×	body	128	valid
120.0ms	1138×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	11

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

12.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.4b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 44 to 26 computations (40.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 (-.f64 y z) 1))
✓	11.6b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

series25.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

14.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
11.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))

rewrite95.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

623×	`prod-diff_binary64`
353×	`fma-def_binary64`
308×	`fma-neg_binary64`
183×	`log1p-udef_binary64`
181×	`expm1-udef_binary64`

Counts

2 → 90

Calls

2 calls:

93.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))
93.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	206	19
2	2863	19
3	4968	19
4	4988	19
0	0	0
1	0	0

simplify101.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

651×	`div-sub_binary64`
545×	`sub-neg_binary64`
410×	`neg-mul-1_binary64`
396×	`associate-/l*_binary64`
395×	`fma-neg_binary64`

Counts

162 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	760
1	64	760
2	118	760
3	282	637
4	524	637
5	1437	637
6	2897	637
7	4071	637
8	4983	637
9	5062	637

prune71.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Error

Counts

109 → 5

Alt Table

Status	Error	Program
▶	5.1b	(*.f64 (/.f64 x 1) (/.f64 (+.f64 (-.f64 y z) 1) z))
	5.8b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	37.1b	(/.f64 (fma.f64 (sqrt.f64 (.f64 x (-.f64 y z))) (sqrt.f64 (.f64 x (-.f64 y z))) x) z)
	35.9b	(/.f64 (fma.f64 (sqrt.f64 (-.f64 y z)) (*.f64 (sqrt.f64 (-.f64 y z)) x) x) z)
	5.8b	(*.f64 (/.f64 x z) (+.f64 (-.f64 y z) 1))

Compiler

Compiled 1517 to 506 computations (66.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (-.f64 y z) 1) z)
✓	4.8b	(*.f64 (/.f64 x 1) (/.f64 (+.f64 (-.f64 y z) 1) z))

series20.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

14.0ms	(*.f64 (/.f64 x 1) (/.f64 (+.f64 (-.f64 y z) 1) z))
6.0ms	(/.f64 (+.f64 (-.f64 y z) 1) z)

rewrite132.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

495×	`prod-diff_binary64`
400×	`fma-udef_binary64`
373×	`fma-def_binary64`
277×	`fma-neg_binary64`
186×	`log1p-udef_binary64`

Counts

2 → 79

Calls

2 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	213	23
2	2911	21
3	4830	21
4	4834	21
5	5068	21
0	0	0
1	0	0

simplify88.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

943×	`fma-neg_binary64`
877×	`fma-def_binary64`
472×	`times-frac_binary64`
462×	`neg-mul-1_binary64`
439×	`neg-sub0_binary64`

Counts

139 → 94

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	688
1	57	688
2	111	626
3	179	623
4	466	569
5	1130	569
6	2741	569
7	4355	569
8	5030	569

prune65.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	94	5	99

Error

Counts

99 → 5

Alt Table

Status	Error	Program
	5.8b	(*.f64 (/.f64 x z) (+.f64 (-.f64 y z) 1))
▶	4.5b	(/.f64 x (/.f64 z (+.f64 1 (-.f64 y z))))
✓	5.1b	(*.f64 (/.f64 x 1) (/.f64 (+.f64 (-.f64 y z) 1) z))
	5.8b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	35.9b	(/.f64 (fma.f64 (sqrt.f64 (-.f64 y z)) (*.f64 (sqrt.f64 (-.f64 y z)) x) x) z)

Compiler

Compiled 1346 to 688 computations (48.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (+.f64 1 (-.f64 y z)))
✓	4.2b	(/.f64 x (/.f64 z (+.f64 1 (-.f64 y z))))

series30.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

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

rewrite99.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

607×	`prod-diff_binary64`
444×	`fma-udef_binary64`
337×	`fma-def_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`

Counts

2 → 97

Calls

2 calls:

97.0ms	(/.f64 z (+.f64 1 (-.f64 y z)))
97.0ms	(/.f64 x (/.f64 z (+.f64 1 (-.f64 y z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	206	23
2	2946	23
3	4959	23
4	4991	23
0	0	0
1	0	0

simplify73.0ms (2%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-neg_binary64`
443×	`fma-def_binary64`
363×	`times-frac_binary64`
279×	`associate-/l*_binary64`
218×	`associate-/r*_binary64`

Counts

157 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	1433
1	318	1409
2	1195	1292
3	4858	1292
4	5469	1292

prune87.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
✓	5.1b	(*.f64 (/.f64 x 1) (/.f64 (+.f64 (-.f64 y z) 1) z))
	5.8b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
▶	5.8b	(fma.f64 (-.f64 y z) (/.f64 x z) (/.f64 x z))
	35.9b	(/.f64 (fma.f64 (sqrt.f64 (-.f64 y z)) (*.f64 (sqrt.f64 (-.f64 y z)) x) x) z)
✓	4.5b	(/.f64 x (/.f64 z (+.f64 1 (-.f64 y z))))

Compiler

Compiled 2413 to 1260 computations (47.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.8b	(fma.f64 (-.f64 y z) (/.f64 x z) (/.f64 x z))

series19.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

18.0ms

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

rewrite55.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

866×	`log1p-expm1-u_binary64`
866×	`expm1-log1p-u_binary64`
584×	`prod-diff_binary64`
82×	`add-sqr-sqrt_binary64`
76×	`add-log-exp_binary64`

Counts

1 → 25

Calls

1 calls:

54.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	155	13
2	2132	13
3	6463	13
0	0	0
1	0	0

simplify79.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
572×	`fma-neg_binary64`
160×	`distribute-rgt-in_binary64`
145×	`distribute-lft-in_binary64`
127×	`associate-l_binary64`

Counts

61 → 36

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	515
1	52	515
2	116	455
3	251	455
4	564	365
5	917	365
6	1311	365
7	1390	365
8	1402	365
9	1402	365
10	1323	365

prune40.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	36	5	41

Error

Counts

41 → 5

Alt Table

Status	Error	Program
✓	5.8b	(fma.f64 (-.f64 y z) (/.f64 x z) (/.f64 x z))
	35.9b	(/.f64 (fma.f64 (sqrt.f64 (-.f64 y z)) (*.f64 (sqrt.f64 (-.f64 y z)) x) x) z)
✓	4.5b	(/.f64 x (/.f64 z (+.f64 1 (-.f64 y z))))
	5.8b	(-.f64 (/.f64 (fma.f64 x y x) z) x)
✓	5.1b	(*.f64 (/.f64 x 1) (/.f64 (+.f64 (-.f64 y z) 1) z))

Compiler

Compiled 525 to 219 computations (58.3% saved)

regimes720.0ms (20%)

Accuracy

Total 0.3b remaining (97.5%)

Threshold costs 0.3b (97.5%)

Counts

79 → 3

Compiler

Compiled 4104 to 2586 computations (37% 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`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	77
1	36	77
2	44	77
3	48	77
4	50	77
5	49	77

end89.0ms (2.5%)

Compiler: Compiled 179 to 100 computations (44.1% saved)

Details

analyze546.0ms (15.2%)

sample1.1s (29.7%)

simplify58.0ms (1.6%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series25.0ms (0.7%)

rewrite95.0ms (2.6%)

simplify101.0ms (2.8%)

prune71.0ms (2%)

localize6.0ms (0.2%)

series20.0ms (0.6%)

rewrite132.0ms (3.7%)

simplify88.0ms (2.5%)

prune65.0ms (1.8%)

localize5.0ms (0.2%)

series30.0ms (0.8%)

rewrite99.0ms (2.8%)

simplify73.0ms (2%)

prune87.0ms (2.4%)

localize5.0ms (0.1%)

series19.0ms (0.5%)

rewrite55.0ms (1.5%)

simplify79.0ms (2.2%)

prune40.0ms (1.1%)

regimes720.0ms (20%)

bsearch2.0ms (0.1%)

simplify9.0ms (0.2%)

end89.0ms (2.5%)

Profiling