Details

analyze101.0ms (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 18 to 14 computations (22.2% saved)

sample1.3s (36.8%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 47 to 37 computations (21.3% saved)

simplify55.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-neg_binary32`
518×	`unswap-sqr_binary32`
432×	`exp-prod_binary32`
340×	`times-frac_binary32`
333×	`associate-l_binary32`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	27	14
3	36	14
4	50	14
5	79	14
6	147	14
7	261	14
8	528	14
9	1676	14
10	3160	14
11	4121	14
12	4850	14

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

Compiler

Compiled 33 to 27 computations (18.2% saved)

localize24.0ms (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	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
✓	0.0b	(exp.f32 (/.f32 (neg.f32 x) s))

series32.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

21.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
6.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
5.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary32`
42×	`times-frac_binary32`
34×	`exp-prod_binary32`
33×	`add-sqr-sqrt_binary32`
33×	`add-cube-cbrt_binary32`

Counts

3 → 102

Calls

3 calls:

6.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
4.0ms	(exp.f32 (/.f32 (neg.f32 x) s))
4.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))

simplify117.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary32`
322×	`associate-/l/_binary32`
269×	`associate-/r/_binary32`
197×	`distribute-rgt-neg-in_binary32`
190×	`distribute-lft-neg-in_binary32`

Counts

174 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	2521
1	346	2365
2	806	2311
3	2414	2287
4	4850	2287
5	5089	2287

prune121.0ms (3.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
▶	0.0b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
	0.0b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
	22.4b	(fma.f32 (/.f32 x s) 1/4 1/2)
	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

Compiler

Compiled 2699 to 1443 computations (46.5% saved)

localize28.0ms (0.8%)

Local error

Found 3 expressions with local error:

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

series39.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
6.0ms	(+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))
6.0ms	(pow.f32 (E.f32) (/.f32 (neg.f32 x) s))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary32`
42×	`times-frac_binary32`
34×	`pow-unpow_binary32`
34×	`add-sqr-sqrt_binary32`
34×	`add-cube-cbrt_binary32`

Counts

3 → 109

Calls

3 calls:

5.0ms	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
4.0ms	(pow.f32 (E.f32) (/.f32 (neg.f32 x) s))
4.0ms	(+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))

simplify141.0ms (4%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-neg_binary32`
261×	`associate-r_binary32`
229×	`associate-/l*_binary32`
228×	`times-frac_binary32`
223×	`associate-/l/_binary32`

Counts

181 → 172

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	184	2820
1	462	2541
2	1212	2486
3	4036	2473
4	4811	2469
5	4949	2469
6	4875	2469

prune115.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	172	4	176

Error

Counts

176 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
▶	0.0b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
	22.4b	(fma.f32 (/.f32 x s) 1/4 1/2)
	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

Compiler

Compiled 3020 to 1505 computations (50.2% saved)

localize26.0ms (0.7%)

Local error

Found 3 expressions with local error:

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

series38.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

23.0ms	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
8.0ms	(pow.f32 (exp.f32 -1) (/.f32 x s))
7.0ms	(+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary32`
22×	`add-sqr-sqrt_binary32`
22×	`add-cube-cbrt_binary32`
21×	`times-frac_binary32`
13×	`pow-unpow_binary32`

Counts

3 → 88

Calls

3 calls:

5.0ms	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
4.0ms	(+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))
3.0ms	(pow.f32 (exp.f32 -1) (/.f32 x s))

simplify103.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-neg_binary32`
238×	`associate-r_binary32`
236×	`distribute-rgt-neg-in_binary32`
215×	`unswap-sqr_binary32`
212×	`fma-def_binary32`

Counts

160 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2396
1	348	2254
2	869	2200
3	3038	2188
4	4756	2188
5	4929	2188

prune105.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	146	4	150

Error

Counts

150 → 4

Alt Table

Status	Error	Program
✓	0.0b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
✓	0.0b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
	22.4b	(fma.f32 (/.f32 x s) 1/4 1/2)
▶	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

Compiler

Compiled 2532 to 1679 computations (33.7% saved)

localize24.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
✓	0.0b	(exp.f32 (neg.f32 (/.f32 x s)))
✓	1.1b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series555.0ms (15.8%)

Counts

3 → 64

Calls

3 calls:

274.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
274.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))
7.0ms	(exp.f32 (neg.f32 (/.f32 x s)))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`exp-prod_binary32`
21×	`*-un-lft-identity_binary32`
21×	`add-sqr-sqrt_binary32`
21×	`add-cube-cbrt_binary32`
18×	`times-frac_binary32`

Counts

3 → 78

Calls

3 calls:

4.0ms	(exp.f32 (neg.f32 (/.f32 x s)))
2.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
0.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

simplify129.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

452×	`fma-neg_binary32`
354×	`distribute-neg-frac_binary32`
292×	`times-frac_binary32`
241×	`associate-/l*_binary32`
200×	`associate-/r*_binary32`

Counts

142 → 118

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	172	2142
1	367	1839
2	964	1802
3	3283	1774
4	4792	1772
5	4934	1772
6	4991	1772
7	4918	1772

prune70.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	0	1
Picked	1	0	1
Done	1	1	2
Total	120	2	122

Error

Counts

122 → 2

Alt Table

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

Compiler

Compiled 1756 to 797 computations (54.6% saved)

regimes278.0ms (7.9%)

Accuracy

Total 0.0b remaining (33.8%)

Threshold costs 0.0b (33.8%)

Counts

21 → 1

Compiler

Compiled 1994 to 1649 computations (17.3% 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	10	16
1	20	16
2	27	16
3	31	16
4	32	16
5	31	16

end41.0ms (1.2%)

Compiler: Compiled 45 to 37 computations (17.8% saved)

Details

analyze101.0ms (2.9%)

sample1.3s (36.8%)

simplify55.0ms (1.6%)

prune2.0ms (0%)

localize24.0ms (0.7%)

series32.0ms (0.9%)

rewrite20.0ms (0.6%)

simplify117.0ms (3.3%)

prune121.0ms (3.4%)

localize28.0ms (0.8%)

series39.0ms (1.1%)

rewrite25.0ms (0.7%)

simplify141.0ms (4%)

prune115.0ms (3.3%)

localize26.0ms (0.7%)

series38.0ms (1.1%)

rewrite25.0ms (0.7%)

simplify103.0ms (2.9%)

prune105.0ms (3%)

localize24.0ms (0.7%)

series555.0ms (15.8%)

rewrite10.0ms (0.3%)

simplify129.0ms (3.7%)

prune70.0ms (2%)

regimes278.0ms (7.9%)

simplify2.0ms (0.1%)

end41.0ms (1.2%)

Profiling