Details

analyze96.0ms (2.4%)

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 18 to 14 computations (22.2% saved)

sample1.2s (29.7%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 36 to 28 computations (22.2% saved)

preprocess34.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

434×	`fma-def_binary32`
401×	`associate-/l*_binary32`
298×	`associate-/l/_binary32`
270×	`associate-/r*_binary32`
208×	`unswap-sqr_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	27	28
2	45	28
3	69	28
4	96	28
5	160	28
6	306	28
7	665	28
8	1503	28
9	4050	28
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify20.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

518×	`unswap-sqr_binary32`
340×	`times-frac_binary32`
331×	`associate-l_binary32`
260×	`associate-r_binary32`
208×	`fma-def_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	27	14
3	40	14
4	54	14
5	88	14
6	162	14
7	344	14
8	773	14
9	2616	14

Stop Event

1×	node limit

Counts

1 → 1

prune2.0ms (0%)

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize22.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

series31.0ms (0.8%)

Counts

3 → 72

Calls

18 calls:

4.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))	s	0
4.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))	x	-inf
4.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))	x	inf
3.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))	s	inf
2.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))	x	0

rewrite48.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

822×	`log1p-expm1-u_binary32`
822×	`expm1-log1p-u_binary32`
97×	`add-sqr-sqrt_binary32`
94×	`*-un-lft-identity_binary32`
94×	`pow1_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	192	27
2	2671	27
0	9	33

Stop Event

1×	saturated
1×	node limit

Counts

3 → 83

simplify36.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

727×	`cancel-sign-sub-inv_binary32`
632×	`fma-def_binary32`
551×	`associate-/r*_binary32`
320×	`fma-neg_binary32`
192×	`associate-/r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	1020
1	128	966
2	368	918
3	1575	906

Stop Event

1×	node limit

Counts

155 → 108

prune52.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	3	109

Error

0.0b

Counts

109 → 3

Alt Table

Status	Error	Program
✓	0.1b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
▶	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))
	24.1b	(fma.f32 (/.f32 x s) 1/4 (fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 1/2))

Compiler

Compiled 1528 to 909 computations (40.5% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s))))
✓	0.0b	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))
✓	0.0b	(exp.f32 (/.f32 x s))
✓	0.0b	(/.f32 1 (exp.f32 (/.f32 x s)))

series70.0ms (1.7%)

Counts

4 → 72

Calls

24 calls:

10.0ms	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))	x	inf
9.0ms	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))	x	-inf
7.0ms	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))	s	0
4.0ms	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))	s	inf
3.0ms	(+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s))))	x	-inf

rewrite54.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

452×	`log-prod_binary32`
168×	`expm1-udef_binary32`
168×	`log1p-udef_binary32`
166×	`fma-def_binary32`
158×	`pow3_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	39
1	195	39
2	2594	39
0	9	42

Stop Event

1×	saturated
1×	node limit

Counts

4 → 135

simplify54.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-def_binary32`
727×	`cancel-sign-sub-inv_binary32`
547×	`associate-/r*_binary32`
317×	`fma-neg_binary32`
190×	`associate-/r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	1113
1	137	1053
2	393	996
3	1633	978

Stop Event

1×	node limit

Counts

207 → 163

prune148.0ms (3.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	159	4	163
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	162	4	166

Error

0.0b

Counts

166 → 4

Alt Table

Status	Error	Program
	0.1b	(pow.f32 (pow.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) 3) 1/3)
▶	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (*.f32 -3 (/.f32 x s))) 1/3)))
	5.8b	(/.f32 1 (+.f32 1 (/.f32 1 (pow.f32 (exp.f32 x) (/.f32 1 s)))))

Compiler

Compiled 2600 to 1516 computations (41.7% saved)

localize22.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))
	0.1b	(exp.f32 (/.f32 (neg.f32 x) s))
✓	1.7b	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))

series534.0ms (13.1%)

Counts

2 → 48

Calls

12 calls:

94.0ms	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))	x	-inf
87.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))	s	0
84.0ms	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))	s	0
83.0ms	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))	x	inf
82.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))	x	inf

rewrite41.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

708×	`pow1_binary32`
650×	`expm1-log1p-u_binary32`
649×	`log1p-expm1-u_binary32`
91×	`add-sqr-sqrt_binary32`
89×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	181	17
2	2446	17
0	9	24

Stop Event

1×	saturated
1×	node limit

Counts

2 → 59

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary32`
498×	`cancel-sign-sub-inv_binary32`
363×	`associate-/l/_binary32`
261×	`fma-neg_binary32`
227×	`distribute-lft-neg-in_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	972
1	163	750
2	510	738
3	2194	678

Stop Event

1×	node limit

Counts

107 → 78

prune71.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	107	4	111

Error

0.0b

Counts

111 → 4

Alt Table

Status	Error	Program
	0.1b	(pow.f32 (pow.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) 3) 1/3)
▶	0.1b	(exp.f32 (neg.f32 (log1p.f32 (/.f32 1 (exp.f32 (/.f32 x s))))))
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))
	5.8b	(/.f32 1 (+.f32 1 (/.f32 1 (pow.f32 (exp.f32 x) (/.f32 1 s)))))

Compiler

Compiled 1427 to 802 computations (43.8% saved)

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f32 (/.f32 x s))
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (/.f32 1 (exp.f32 (/.f32 x s))))))
	0.0b	(/.f32 1 (exp.f32 (/.f32 x s)))
✓	1.7b	(log1p.f32 (/.f32 1 (exp.f32 (/.f32 x s))))

series695.0ms (17.1%)

Counts

2 → 48

Calls

12 calls:

139.0ms	(log1p.f32 (/.f32 1 (exp.f32 (/.f32 x s))))	x	inf
111.0ms	(log1p.f32 (/.f32 1 (exp.f32 (/.f32 x s))))	s	0
111.0ms	(exp.f32 (neg.f32 (log1p.f32 (/.f32 1 (exp.f32 (/.f32 x s))))))	x	-inf
109.0ms	(exp.f32 (neg.f32 (log1p.f32 (/.f32 1 (exp.f32 (/.f32 x s))))))	x	inf
102.0ms	(log1p.f32 (/.f32 1 (exp.f32 (/.f32 x s))))	x	-inf

rewrite41.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

776×	`expm1-log1p-u_binary32`
775×	`log1p-expm1-u_binary32`
95×	`add-sqr-sqrt_binary32`
95×	`pow1_binary32`
93×	`*-un-lft-identity_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	197	21
2	2417	21
0	10	26

Stop Event

1×	saturated
1×	node limit

Counts

2 → 59

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary32`
498×	`cancel-sign-sub-inv_binary32`
358×	`associate-/l/_binary32`
261×	`fma-neg_binary32`
229×	`distribute-rgt-neg-in_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	1044
1	158	750
2	500	738
3	2163	678

Stop Event

1×	node limit

Counts

107 → 77

prune133.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	151	4	155

Error

0.0b

Counts

155 → 4

Alt Table

Status	Error	Program
	0.1b	(pow.f32 (pow.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) 3) 1/3)
✓	0.1b	(exp.f32 (neg.f32 (log1p.f32 (/.f32 1 (exp.f32 (/.f32 x s))))))
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))
	5.8b	(/.f32 1 (+.f32 1 (/.f32 1 (pow.f32 (exp.f32 x) (/.f32 1 s)))))

Compiler

Compiled 2191 to 1176 computations (46.3% saved)

regimes435.0ms (10.7%)

Accuracy

Total 0.0b remaining (35.5%)

Threshold costs 0.0b (35.5%)

Counts

71 → 1

Compiler

Compiled 7064 to 5796 computations (18% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary32`
3×	`*-commutative_binary32`
3×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	23	14
3	27	14
4	28	14

Stop Event

1×

saturated

end58.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 70 to 58 computations (17.1% saved)

Details

analyze96.0ms (2.4%)

sample1.2s (29.7%)

preprocess34.0ms (0.8%)

simplify20.0ms (0.5%)

prune2.0ms (0%)

localize22.0ms (0.5%)

series31.0ms (0.8%)

rewrite48.0ms (1.2%)

simplify36.0ms (0.9%)

prune52.0ms (1.3%)

localize22.0ms (0.5%)

series70.0ms (1.7%)

rewrite54.0ms (1.3%)

simplify54.0ms (1.3%)

prune148.0ms (3.6%)

localize22.0ms (0.6%)

series534.0ms (13.1%)

rewrite41.0ms (1%)

simplify76.0ms (1.9%)

prune71.0ms (1.7%)

localize25.0ms (0.6%)

series695.0ms (17.1%)

rewrite41.0ms (1%)

simplify37.0ms (0.9%)

prune133.0ms (3.3%)

regimes435.0ms (10.7%)

simplify2.0ms (0.1%)

end58.0ms (1.4%)

Profiling