Details

analyze276.0ms (6.5%)

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
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
46.8%	53.1%	0.1%	7
60.9%	39%	0.1%	8
67.9%	31.2%	0.9%	9
74.5%	22.2%	3.2%	10
77.9%	17.2%	5%	11
81.1%	11.8%	7.1%	12
82.7%	9%	8.3%	13
84.3%	6.1%	9.7%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.6s (37%)

Results

1.4s	8256×	body	128	valid
43.0ms	257×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify119.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1151×	`distribute-rgt-in_binary64`
1143×	`distribute-lft-in_binary64`
971×	`fma-def_binary64`
653×	`associate-/l*_binary64`
535×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	22	14
2	30	14
3	75	14
4	112	14
5	222	14
6	406	14
7	419	14
8	783	14
9	937	14
10	1259	14
11	1611	14
12	1778	14
13	2015	14
14	2939	14
15	3245	14
16	5075	14

prune6.0ms (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

11.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	11.1b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
▶	11.1b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))

Compiler

Compiled 73 to 45 computations (38.4% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) 1)
✓	0.1b	(*.f64 x (+.f64 (/.f64 x y) 1))
✓	10.3b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))

series47.0ms (1.1%)

Counts

3 → 63

Calls

3 calls:

21.0ms	(*.f64 x (+.f64 (/.f64 x y) 1))
19.0ms	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
7.0ms	(+.f64 (/.f64 x y) 1)

rewrite203.0ms (4.8%)

Algorithm

2×	batch-egg-rewrite

Rules

488×	`prod-diff_binary64`
356×	`fma-udef_binary64`
282×	`fma-def_binary64`
270×	`fma-neg_binary64`
185×	`log1p-udef_binary64`

Counts

3 → 141

Calls

3 calls:

199.0ms	(+.f64 (/.f64 x y) 1)
199.0ms	(*.f64 x (+.f64 (/.f64 x y) 1))
199.0ms	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	209	29
2	2964	29
3	4808	29
4	4838	29
5	4978	29
6	4961	29
0	0	0
1	0	0

simplify137.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
530×	`associate-+l-_binary64`
372×	`cancel-sign-sub-inv_binary64`
370×	`associate--r+_binary64`
317×	`sub-neg_binary64`

Counts

204 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	789
1	130	785
2	408	727
3	1548	663
4	4387	663
5	4864	663
6	4963	663

prune252.0ms (5.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	161	6	167
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	162	7	169

Error

Counts

169 → 7

Alt Table

Status	Error	Program
	11.1b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
	0.1b	(.f64 (+.f64 (/.f64 x y) 1) (.f64 x (/.f64 1 (+.f64 x 1))))
	14.3b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
	47.2b	(/.f64 (*.f64 x x) (fma.f64 x y y))
	33.4b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))) 2)
▶	0.1b	(*.f64 (/.f64 x (+.f64 x 1)) (+.f64 (/.f64 x y) 1))
	0.2b	(*.f64 x (/.f64 1 (/.f64 (+.f64 x 1) (+.f64 (/.f64 x y) 1))))

Compiler

Compiled 2874 to 1458 computations (49.3% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (/.f64 x y) 1)
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.1b	(*.f64 (/.f64 x (+.f64 x 1)) (+.f64 (/.f64 x y) 1))

series27.0ms (0.6%)

Counts

2 → 36

Calls

2 calls:

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

rewrite93.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

778×	`prod-diff_binary64`
183×	`log1p-udef_binary64`
181×	`expm1-udef_binary64`
106×	`add-sqr-sqrt_binary64`
102×	`log1p-expm1-u_binary64`

Counts

2 → 86

Calls

2 calls:

89.0ms	(/.f64 x (+.f64 x 1))
89.0ms	(*.f64 (/.f64 x (+.f64 x 1)) (+.f64 (/.f64 x y) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	209	23
2	2961	23
3	5063	23
0	0	0
1	0	0

simplify139.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-+l-_binary64`
485×	`cancel-sign-sub-inv_binary64`
388×	`associate--r+_binary64`
382×	`sub-neg_binary64`
296×	`fma-neg_binary64`

Counts

122 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	645
1	161	639
2	499	574
3	1792	566
4	4533	566
5	4757	566
6	5003	566

prune231.0ms (5.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	170	6	176

Error

Counts

176 → 6

Alt Table

Status	Error	Program
	0.1b	(/.f64 (+.f64 1 (/.f64 x y)) (/.f64 (+.f64 x 1) x))
	14.3b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
	47.2b	(/.f64 (*.f64 x x) (fma.f64 x y y))
▶	0.1b	(/.f64 x (/.f64 (+.f64 x 1) (+.f64 1 (/.f64 x y))))
	33.4b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))) 2)
	0.1b	(.f64 (+.f64 (/.f64 x y) 1) (.f64 x (/.f64 1 (+.f64 x 1))))

Compiler

Compiled 3027 to 1789 computations (40.9% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 x y))
✓	0.0b	(/.f64 x (/.f64 (+.f64 x 1) (+.f64 1 (/.f64 x y))))
✓	0.1b	(/.f64 (+.f64 x 1) (+.f64 1 (/.f64 x y)))

series57.0ms (1.3%)

Counts

3 → 63

Calls

3 calls:

28.0ms	(/.f64 (+.f64 x 1) (+.f64 1 (/.f64 x y)))
21.0ms	(/.f64 x (/.f64 (+.f64 x 1) (+.f64 1 (/.f64 x y))))
8.0ms	(+.f64 1 (/.f64 x y))

rewrite178.0ms (4.2%)

Algorithm

2×	batch-egg-rewrite

Rules

418×	`prod-diff_binary64`
368×	`fma-udef_binary64`
339×	`fma-def_binary64`
238×	`fma-neg_binary64`
188×	`log1p-udef_binary64`

Counts

3 → 145

Calls

3 calls:

173.0ms	(+.f64 1 (/.f64 x y))
173.0ms	(/.f64 x (/.f64 (+.f64 x 1) (+.f64 1 (/.f64 x y))))
173.0ms	(/.f64 (+.f64 x 1) (+.f64 1 (/.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	209	36
2	3046	36
3	4857	36
4	4870	36
5	5130	36
0	0	0
1	0	0

simplify92.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
653×	`associate--l+_binary64`
501×	`associate-+l+_binary64`
452×	`associate--r+_binary64`
283×	`fma-def_binary64`

Counts

208 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	1356
1	282	1352
2	1036	1234
3	4890	1218
4	5775	1218

prune220.0ms (5.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	195	4	199

Error

Counts

199 → 4

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (+.f64 1 (/.f64 x y)) (/.f64 (+.f64 x 1) x))
	14.3b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
✓	0.1b	(/.f64 x (/.f64 (+.f64 x 1) (+.f64 1 (/.f64 x y))))
	38.6b	(/.f64 x (-.f64 (+.f64 (/.f64 y x) y) (/.f64 (pow.f64 y 2) x)))

Compiler

Compiled 3676 to 2075 computations (43.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (/.f64 x y))
✓	0.0b	(/.f64 (+.f64 x 1) x)
✓	0.1b	(/.f64 (+.f64 1 (/.f64 x y)) (/.f64 (+.f64 x 1) x))

series15.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

13.0ms	(/.f64 (+.f64 1 (/.f64 x y)) (/.f64 (+.f64 x 1) x))
2.0ms	(/.f64 (+.f64 x 1) x)

rewrite144.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

418×	`prod-diff_binary64`
368×	`fma-udef_binary64`
322×	`fma-def_binary64`
236×	`fma-neg_binary64`
188×	`log1p-udef_binary64`

Counts

2 → 76

Calls

2 calls:

143.0ms	(/.f64 (+.f64 x 1) x)
143.0ms	(/.f64 (+.f64 1 (/.f64 x y)) (/.f64 (+.f64 x 1) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	209	23
2	3043	23
3	4858	23
4	4871	23
5	5068	23
0	0	0
1	0	0

simplify84.0ms (2%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-def_binary64`
530×	`associate-+l-_binary64`
372×	`cancel-sign-sub-inv_binary64`
370×	`associate--r+_binary64`
317×	`sub-neg_binary64`

Counts

112 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	576
1	132	572
2	410	514
3	1550	486
4	4389	486
5	4866	486
6	4965	486

prune96.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	147	4	151

Error

Counts

151 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (+.f64 1 (/.f64 x y)) (/.f64 (+.f64 x 1) x))
	14.3b	(+.f64 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 1 x) y)) (/.f64 x (+.f64 1 x)))
✓	0.1b	(/.f64 x (/.f64 (+.f64 x 1) (+.f64 1 (/.f64 x y))))
	38.6b	(/.f64 x (-.f64 (+.f64 (/.f64 y x) y) (/.f64 (pow.f64 y 2) x)))

Compiler

Compiled 2461 to 1469 computations (40.3% saved)

regimes169.0ms (4%)

Accuracy

Total 0.0b remaining (71%)

Threshold costs 0.0b (71%)

Counts

62 → 1

Compiler

Compiled 2426 to 1631 computations (32.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	14	16
2	13	16

end61.0ms (1.4%)

Compiler: Compiled 84 to 57 computations (32.1% saved)

Details

analyze276.0ms (6.5%)

sample1.6s (37%)

simplify119.0ms (2.8%)

prune6.0ms (0.1%)

localize11.0ms (0.3%)

series47.0ms (1.1%)

rewrite203.0ms (4.8%)

simplify137.0ms (3.2%)

prune252.0ms (5.9%)

localize11.0ms (0.3%)

series27.0ms (0.6%)

rewrite93.0ms (2.2%)

simplify139.0ms (3.2%)

prune231.0ms (5.4%)

localize12.0ms (0.3%)

series57.0ms (1.3%)

rewrite178.0ms (4.2%)

simplify92.0ms (2.2%)

prune220.0ms (5.2%)

localize6.0ms (0.2%)

series15.0ms (0.4%)

rewrite144.0ms (3.4%)

simplify84.0ms (2%)

prune96.0ms (2.3%)

regimes169.0ms (4%)

simplify3.0ms (0.1%)

end61.0ms (1.4%)

Profiling