Details

analyze94.0ms (2.7%)

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)

sample1.3s (38.5%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 47 to 37 computations (21.3% saved)

simplify19.0ms (0.6%)

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

prune1.0ms (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)

localize23.0ms (0.7%)

Local error

Found 3 expressions with local error:

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

series28.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

18.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
5.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
4.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

rewrite45.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

822×	`log1p-expm1-u_binary32`
822×	`expm1-log1p-u_binary32`
96×	`prod-diff_binary32`
95×	`add-sqr-sqrt_binary32`
88×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	193	27
2	2659	27

Stop Event

1×	node limit

Counts

3 → 83

Calls

3 calls:

44.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
44.0ms	(exp.f32 (/.f32 (neg.f32 x) s))
44.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

simplify33.0ms (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`
193×	`associate-/r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	1020
1	128	966
2	368	918
3	1574	906

Stop Event

1×	node limit

Counts

155 → 108

prune47.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Error

0.0b

Counts

109 → 4

Alt Table

Status	Error	Program
▶	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))
	26.4b	(-.f32 (+.f32 1/2 (.f32 1/4 (/.f32 x s))) (.f32 1/48 (/.f32 (pow.f32 x 3) (pow.f32 s 3))))
	22.1b	(fma.f32 1/4 (/.f32 x s) 1/2)
✓	0.1b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

Compiler

Compiled 1552 to 931 computations (40% saved)

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

series64.0ms (1.8%)

Counts

4 → 72

Calls

4 calls:

32.0ms	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))
15.0ms	(+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s))))
13.0ms	(/.f32 1 (exp.f32 (/.f32 x s)))
4.0ms	(exp.f32 (/.f32 x s))

rewrite54.0ms (1.6%)

Algorithm

1×	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	196	39
2	2583	39

Stop Event

1×	node limit

Counts

4 → 135

Calls

4 calls:

52.0ms	(/.f32 1 (exp.f32 (/.f32 x s)))
52.0ms	(+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s))))
52.0ms	(exp.f32 (/.f32 x s))
52.0ms	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))

simplify37.0ms (1.1%)

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	1634	978

Stop Event

1×	node limit

Counts

207 → 164

prune181.0ms (5.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	159	5	164
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	163	5	168

Error

0.0b

Counts

168 → 5

Alt Table

Status	Error	Program
	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (pow.f32 (E.f32) (/.f32 x s)))))
	0.2b	(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 (/.f32 1 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 3))))
	0.2b	(/.f32 1 (+.f32 1 (pow.f32 (pow.f32 (exp.f32 (/.f32 x s)) -3) 1/3)))

Compiler

Compiled 2641 to 1540 computations (41.7% saved)

localize23.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(exp.f32 (/.f32 (neg.f32 x) s))
✓	0.1b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))
✓	1.0b	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))

series498.0ms (14.3%)

Counts

2 → 48

Calls

2 calls:

256.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))
241.0ms	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))

rewrite38.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`expm1-log1p-u_binary32`
649×	`log1p-expm1-u_binary32`
128×	`log1p-udef_binary32`
91×	`add-sqr-sqrt_binary32`
84×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	181	17
2	2466	17

Stop Event

1×	node limit

Counts

2 → 59

Calls

2 calls:

37.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))
37.0ms	(log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))

simplify33.0ms (1%)

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

prune47.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	107	5	112

Error

0.0b

Counts

112 → 5

Alt Table

Status	Error	Program
	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (pow.f32 (E.f32) (/.f32 x s)))))
	0.2b	(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 (/.f32 1 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 3))))
	0.2b	(/.f32 1 (+.f32 1 (pow.f32 (pow.f32 (exp.f32 (/.f32 x s)) -3) 1/3)))

Compiler

Compiled 1461 to 838 computations (42.6% saved)

localize31.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f32 (/.f32 x s))
✓	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 3))))
✓	0.1b	(pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 3)
✓	0.1b	(cbrt.f32 (exp.f32 (/.f32 x s)))

series101.0ms (2.9%)

Counts

3 → 72

Calls

3 calls:

40.0ms	(pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 3)
33.0ms	(/.f32 1 (+.f32 1 (/.f32 1 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 3))))
29.0ms	(cbrt.f32 (exp.f32 (/.f32 x s)))

rewrite49.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`log-prod_binary32`
198×	`expm1-udef_binary32`
198×	`log1p-udef_binary32`
189×	`log-pow_binary32`
177×	`fma-def_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	258	28
2	3097	28

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

48.0ms	(/.f32 1 (+.f32 1 (/.f32 1 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 3))))
48.0ms	(pow.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) 3)
48.0ms	(cbrt.f32 (exp.f32 (/.f32 x s)))

simplify33.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

724×	`associate-*l/_binary32`
628×	`associate-/r*_binary32`
289×	`cancel-sign-sub-inv_binary32`
215×	`associate-/l/_binary32`
209×	`associate-/r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	957
1	152	927
2	422	873
3	1727	849

Stop Event

1×	node limit

Counts

154 → 104

prune138.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	140	5	145

Error

0.0b

Counts

145 → 5

Alt Table

Status	Error	Program
	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (pow.f32 (E.f32) (/.f32 x s)))))
	0.2b	(pow.f32 (pow.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) 3) 1/3)
	0.2b	(/.f32 1 (+.f32 1 (pow.f32 (pow.f32 (exp.f32 (/.f32 x s)) -3) 1/3)))
	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (.f32 (cbrt.f32 (exp.f32 (/.f32 x s))) (exp.f32 (.f32 2/3 (/.f32 x s)))))))
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (/.f32 (neg.f32 x) s)))))

Compiler

Compiled 2489 to 1591 computations (36.1% saved)

regimes435.0ms (12.5%)

Accuracy

Total 0.0b remaining (54.4%)

Threshold costs 0.0b (54.4%)

Counts

82 → 1

Compiler

Compiled 8386 to 6927 computations (17.4% 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

end66.0ms (1.9%)

Compiler: Compiled 92 to 75 computations (18.5% saved)

Details

analyze94.0ms (2.7%)

sample1.3s (38.5%)

simplify19.0ms (0.6%)

prune1.0ms (0%)

localize23.0ms (0.7%)

series28.0ms (0.8%)

rewrite45.0ms (1.3%)

simplify33.0ms (0.9%)

prune47.0ms (1.3%)

localize22.0ms (0.6%)

series64.0ms (1.8%)

rewrite54.0ms (1.6%)

simplify37.0ms (1.1%)

prune181.0ms (5.2%)

localize23.0ms (0.7%)

series498.0ms (14.3%)

rewrite38.0ms (1.1%)

simplify33.0ms (1%)

prune47.0ms (1.4%)

localize31.0ms (0.9%)

series101.0ms (2.9%)

rewrite49.0ms (1.4%)

simplify33.0ms (0.9%)

prune138.0ms (4%)

regimes435.0ms (12.5%)

simplify2.0ms (0.1%)

end66.0ms (1.9%)

Profiling