Details

analyze110.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	24.7%	75.3%	0
0%	24.7%	75.3%	1
0%	24.7%	75.3%	2
12.4%	12.4%	75.3%	3
12.4%	12.4%	75.3%	4
18.5%	6.2%	75.3%	5
18.5%	6.2%	75.3%	6
21.6%	3.1%	75.3%	7
21.6%	3.1%	75.3%	8
23.2%	1.5%	75.3%	9
23.2%	1.5%	75.3%	10
23.9%	0.8%	75.3%	11
23.9%	0.8%	75.3%	12
24.3%	0.4%	75.3%	13
24.3%	0.4%	75.3%	14

Compiler

Compiled 35 to 18 computations (48.6% saved)

sample1.4s (36.1%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 70 to 36 computations (48.6% saved)

preprocess31.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

1068×	`fma-def_binary32`
462×	`associate-/l*_binary32`
340×	`distribute-rgt-in_binary32`
266×	`associate-/l/_binary32`
263×	`associate-/r*_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	86
1	69	86
2	207	82
3	485	82
4	1076	78
5	2341	60
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 28 to 13 computations (53.6% saved)

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-def_binary32`
440×	`times-frac_binary32`
346×	`distribute-rgt-in_binary32`
272×	`distribute-rgt-out_binary32`
271×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	38	43
2	107	41
3	246	41
4	518	39
5	1075	30
6	3430	29
7	4946	29

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
▶	0.3b	(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)

Status

Error

Program

0.3b

(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (*.f32 (*.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))

▶

0.3b

(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)

Compiler

Compiled 142 to 78 computations (45.1% saved)

localize55.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2)))
✓	0.0b	(exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s)))
✓	0.1b	(exp.f32 (/.f32 (fabs.f32 x) s))
✓	0.2b	(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)

series134.0ms (3.5%)

Counts

4 → 80

Calls

24 calls:

16.0ms	(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)	x	-inf
15.0ms	(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)	x	inf
14.0ms	(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)	x	0
14.0ms	(/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2)))	x	inf
13.0ms	(/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2)))	x	-inf

rewrite66.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

678×	`prod-diff_binary32`
165×	`add-sqr-sqrt_binary32`
156×	`log1p-expm1-u_binary32`
156×	`expm1-log1p-u_binary32`
155×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	71
1	331	55
2	4941	55

Stop Event

1×	node limit

Counts

4 → 98

simplify56.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

386×	`times-frac_binary32`
371×	`fma-neg_binary32`
370×	`unswap-sqr_binary32`
359×	`distribute-rgt-neg-in_binary32`
306×	`distribute-neg-frac_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	1764
1	208	1716
2	624	1688
3	3071	1654

Stop Event

1×	node limit

Counts

178 → 110

prune94.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	107	5	112

Error

0.3b

Counts

112 → 5

Alt Table

Status	Error	Program
	12.8b	(/.f32 (/.f32 1 (+.f32 (pow.f32 (E.f32) (/.f32 x s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
	27.1b	(fma.f32 (/.f32 x (/.f32 (pow.f32 s 3) x)) -1/16 (/.f32 1/4 s))
	0.3b	(/.f32 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)) (.f32 (.f32 s (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 (fabs.f32 x)) s)))))
✓	0.3b	(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
▶	0.3b	(/.f32 1 (fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))))

Compiler

Compiled 2631 to 1305 computations (50.4% saved)

localize32.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2)
✓	0.0b	(/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))
	0.1b	(exp.f32 (/.f32 (fabs.f32 x) s))
✓	0.2b	(fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))))

series74.0ms (2%)

Counts

3 → 40

Calls

18 calls:

9.0ms	(fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))))	x	inf
8.0ms	(fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))))	x	-inf
7.0ms	(fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))))	x	0
6.0ms	(fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s))))	s	-inf
6.0ms	(/.f32 s (exp.f32 (/.f32 (fabs.f32 x) s)))	x	0

rewrite54.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

382×	`prod-diff_binary32`
187×	`expm1-udef_binary32`
187×	`log1p-udef_binary32`
162×	`log-pow_binary32`
142×	`fma-def_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	47
1	219	39
2	3013	39

Stop Event

1×	node limit

Counts

3 → 94

simplify33.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

831×	`fma-def_binary32`
674×	`associate-*l/_binary32`
357×	`associate-/l/_binary32`
285×	`associate-/r/_binary32`
256×	`unswap-sqr_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	870
1	166	826
2	467	820
3	1793	800

Stop Event

1×	node limit

Counts

134 → 117

prune268.0ms (7.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	169	7	176

Error

0.2b

Counts

176 → 7

Alt Table

Status	Error	Program
	12.8b	(/.f32 (/.f32 1 (+.f32 (pow.f32 (E.f32) (/.f32 x s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
	27.1b	(fma.f32 (/.f32 x (/.f32 (pow.f32 s 3) x)) -1/16 (/.f32 1/4 s))
	0.9b	(/.f32 1 (exp.f32 (log.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s)))))))
	0.4b	(/.f32 1 (pow.f32 (sqrt.f32 (fma.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2) (/.f32 s (exp.f32 (/.f32 x s))))) 2))
✓	0.3b	(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
▶	0.3b	(/.f32 1 (+.f32 (/.f32 s (exp.f32 (/.f32 x s))) (*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2))))
	0.8b	(/.f32 1 (fma.f32 s (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) 2) (/.f32 s (+.f32 (fma.f32 (/.f32 1/2 s) (/.f32 (*.f32 x x) s) 1) (fma.f32 1/6 (pow.f32 (/.f32 (fabs.f32 x) s) 3) (/.f32 (fabs.f32 x) s))))))

Compiler

Compiled 4183 to 1773 computations (57.6% saved)

localize32.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (exp.f32 (/.f32 x s)) 2)
✓	0.0b	(exp.f32 (/.f32 x s))
✓	0.1b	(/.f32 s (exp.f32 (/.f32 x s)))
✓	0.2b	(*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2))

series51.0ms (1.4%)

Counts

4 → 72

Calls

24 calls:

20.0ms	(*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2))	x	0
3.0ms	(/.f32 s (exp.f32 (/.f32 x s)))	x	-inf
3.0ms	(/.f32 s (exp.f32 (/.f32 x s)))	x	inf
3.0ms	(/.f32 s (exp.f32 (/.f32 x s)))	s	0
2.0ms	(exp.f32 (/.f32 x s))	s	inf

rewrite62.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`log-prod_binary32`
329×	`prod-diff_binary32`
187×	`expm1-udef_binary32`
187×	`log1p-udef_binary32`
162×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	203	36
2	2883	36

Stop Event

1×	node limit

Counts

4 → 146

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary32`
555×	`associate-/l*_binary32`
358×	`associate-*l/_binary32`
331×	`associate-/r*_binary32`
255×	`associate-*r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	936
1	127	912
2	338	894
3	1161	870

Stop Event

1×	node limit

Counts

218 → 176

prune259.0ms (6.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	206	7	213

Error

0.1b

Counts

213 → 7

Alt Table

Status	Error	Program
▶	0.3b	(/.f32 1 (+.f32 (/.f32 s (exp.f32 (/.f32 x s))) (fma.f32 s (exp.f32 (/.f32 x s)) (*.f32 s 2))))
	4.0b	(/.f32 1 (+.f32 (/.f32 s (pow.f32 (exp.f32 x) (/.f32 1 s))) (*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2))))
	12.8b	(/.f32 (/.f32 1 (+.f32 (pow.f32 (E.f32) (/.f32 x s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
	27.1b	(fma.f32 (/.f32 x (/.f32 (pow.f32 s 3) x)) -1/16 (/.f32 1/4 s))
	0.3b	(/.f32 1 (+.f32 (/.f32 s (pow.f32 (pow.f32 (exp.f32 (/.f32 x s)) 3) 1/3)) (*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2))))
✓	0.3b	(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
	0.5b	(/.f32 1 (+.f32 (exp.f32 (-.f32 (log.f32 s) (/.f32 x s))) (*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2))))

Compiler

Compiled 5038 to 2204 computations (56.3% saved)

localize48.0ms (1.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 1 (+.f32 (/.f32 s (exp.f32 (/.f32 x s))) (fma.f32 s (exp.f32 (/.f32 x s)) (*.f32 s 2))))
	0.0b	(exp.f32 (/.f32 x s))
	0.1b	(/.f32 s (exp.f32 (/.f32 x s)))
✓	0.2b	(fma.f32 s (exp.f32 (/.f32 x s)) (*.f32 s 2))

series78.0ms (2.1%)

Counts

2 → 48

Calls

12 calls:

18.0ms	(/.f32 1 (+.f32 (/.f32 s (exp.f32 (/.f32 x s))) (fma.f32 s (exp.f32 (/.f32 x s)) (*.f32 s 2))))	x	-inf
18.0ms	(/.f32 1 (+.f32 (/.f32 s (exp.f32 (/.f32 x s))) (fma.f32 s (exp.f32 (/.f32 x s)) (*.f32 s 2))))	x	inf
16.0ms	(/.f32 1 (+.f32 (/.f32 s (exp.f32 (/.f32 x s))) (fma.f32 s (exp.f32 (/.f32 x s)) (*.f32 s 2))))	s	0
8.0ms	(/.f32 1 (+.f32 (/.f32 s (exp.f32 (/.f32 x s))) (fma.f32 s (exp.f32 (/.f32 x s)) (*.f32 s 2))))	s	-inf
6.0ms	(/.f32 1 (+.f32 (/.f32 s (exp.f32 (/.f32 x s))) (fma.f32 s (exp.f32 (/.f32 x s)) (*.f32 s 2))))	s	inf

rewrite55.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

336×	`fma-def_binary32`
227×	`expm1-udef_binary32`
227×	`log1p-udef_binary32`
201×	`log-pow_binary32`
200×	`fma-neg_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	257	38
2	3477	36

Stop Event

1×	node limit

Counts

2 → 52

simplify36.0ms (1%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/r*_binary32`
520×	`fma-def_binary32`
402×	`associate-*l/_binary32`
226×	`cancel-sign-sub-inv_binary32`
184×	`associate-/r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	900
1	170	900
2	444	876
3	1554	864

Stop Event

1×	node limit

Counts

100 → 72

prune217.0ms (5.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	174	7	181

Error

0.1b

Counts

181 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f32 1 (+.f32 (/.f32 s (exp.f32 (/.f32 x s))) (fma.f32 s (exp.f32 (/.f32 x s)) (*.f32 s 2))))
	4.0b	(/.f32 1 (+.f32 (/.f32 s (pow.f32 (exp.f32 x) (/.f32 1 s))) (*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2))))
	12.8b	(/.f32 (/.f32 1 (+.f32 (pow.f32 (E.f32) (/.f32 x s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
	27.1b	(fma.f32 (/.f32 x (/.f32 (pow.f32 s 3) x)) -1/16 (/.f32 1/4 s))
	0.3b	(/.f32 1 (+.f32 (/.f32 s (pow.f32 (pow.f32 (exp.f32 (/.f32 x s)) 3) 1/3)) (*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2))))
✓	0.3b	(/.f32 (/.f32 1 (+.f32 (exp.f32 (/.f32 (fabs.f32 x) s)) (+.f32 (exp.f32 (/.f32 (fabs.f32 x) (neg.f32 s))) 2))) s)
	0.5b	(/.f32 1 (+.f32 (exp.f32 (-.f32 (log.f32 s) (/.f32 x s))) (*.f32 s (+.f32 (exp.f32 (/.f32 x s)) 2))))

Compiler

Compiled 4144 to 1808 computations (56.4% saved)

regimes385.0ms (10.2%)

Accuracy

Total 0.0b remaining (26.6%)

Threshold costs 0.0b (26.6%)

Counts

77 → 1

Compiler

Compiled 7394 to 4757 computations (35.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	12	24

Stop Event

1×

saturated

end104.0ms (2.8%)

Stop Event

1×

fuel

Compiler

Compiled 174 to 113 computations (35.1% saved)

Details

analyze110.0ms (2.9%)

sample1.4s (36.1%)

preprocess31.0ms (0.8%)

simplify35.0ms (0.9%)

prune4.0ms (0.1%)

localize55.0ms (1.5%)

series134.0ms (3.5%)

rewrite66.0ms (1.7%)

simplify56.0ms (1.5%)

prune94.0ms (2.5%)

localize32.0ms (0.9%)

series74.0ms (2%)

rewrite54.0ms (1.4%)

simplify33.0ms (0.9%)

prune268.0ms (7.1%)

localize32.0ms (0.8%)

series51.0ms (1.4%)

rewrite62.0ms (1.6%)

simplify35.0ms (0.9%)

prune259.0ms (6.9%)

localize48.0ms (1.3%)

series78.0ms (2.1%)

rewrite55.0ms (1.5%)

simplify36.0ms (1%)

prune217.0ms (5.7%)

regimes385.0ms (10.2%)

simplify2.0ms (0.1%)

end104.0ms (2.8%)

Profiling