Details

analyze91.0ms (1.7%)

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)

sample1.4s (26.9%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 47 to 37 computations (21.3% saved)

simplify57.0ms (1.1%)

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

0.1b

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 (0.4%)

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 (0.6%)

Counts

3 → 72

Calls

3 calls:

19.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
7.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
5.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

rewrite20.0ms (0.4%)

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)))

simplify109.0ms (2.1%)

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

prune150.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	156	5	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	5	162

Error

Counts

162 → 5

Alt Table

Status	Error	Program
▶	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	24.3b	(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 (/.f32 x s) 1/4 1/2))
	0.0b	(/.f32 1 (exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	17.7b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (neg.f32 x) s))) (sqrt.f32 (/.f32 (neg.f32 x) s)))))
	0.1b	(/.f32 1 (+.f32 1 (.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))) (cbrt.f32 (exp.f32 (/.f32 (neg.f32 x) s)))) (cbrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 2775 to 1475 computations (46.8% saved)

localize22.0ms (0.4%)

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))))))
✓	0.1b	(exp.f32 (neg.f32 (/.f32 x s)))
✓	1.1b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series661.0ms (12.5%)

Counts

3 → 64

Calls

3 calls:

383.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
273.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))
5.0ms	(exp.f32 (neg.f32 (/.f32 x s)))

rewrite12.0ms (0.2%)

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))))

simplify136.0ms (2.6%)

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

prune85.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	119	4	123

Error

Counts

123 → 4

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
▶	0.0b	(/.f32 1 (exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	17.7b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (neg.f32 x) s))) (sqrt.f32 (/.f32 (neg.f32 x) s)))))
	0.2b	(exp.f32 (neg.f32 (*.f32 (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))) (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))

Compiler

Compiled 1839 to 846 computations (54% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))
✓	0.0b	(/.f32 1 (exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.1b	(exp.f32 (neg.f32 (/.f32 x s)))
	1.1b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series589.0ms (11.2%)

Counts

2 → 48

Calls

2 calls:

295.0ms	(exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))
294.0ms	(/.f32 1 (exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary32`
12×	`add-sqr-sqrt_binary32`
12×	`add-cube-cbrt_binary32`
9×	`times-frac_binary32`
6×	`exp-prod_binary32`

Counts

2 → 50

Calls

2 calls:

3.0ms	(/.f32 1 (exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
1.0ms	(exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))

simplify111.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

597×	`cancel-sign-sub-inv_binary32`
561×	`associate-/r*_binary32`
558×	`fma-def_binary32`
483×	`fma-neg_binary32`
196×	`associate-/r/_binary32`

Counts

98 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	1665
1	188	1548
2	424	1509
3	1542	1499
4	4538	1499
5	4968	1499
6	4999	1499
7	4924	1499

prune112.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	156	4	160

Error

Counts

160 → 4

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
✓	0.0b	(/.f32 1 (exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	17.7b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (neg.f32 x) s))) (sqrt.f32 (/.f32 (neg.f32 x) s)))))
▶	0.2b	(exp.f32 (neg.f32 (*.f32 (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))) (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))

Compiler

Compiled 2498 to 1098 computations (56% saved)

localize34.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (neg.f32 (*.f32 (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))) (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))
	0.1b	(exp.f32 (neg.f32 (/.f32 x s)))
✓	0.2b	(*.f32 (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))) (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	1.1b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series560.0ms (10.6%)

Counts

2 → 48

Calls

2 calls:

285.0ms

(exp.f32 (neg.f32 (*.f32 (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))) (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))

275.0ms

(*.f32 (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))) (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary32`
18×	`sqrt-prod_binary32`
17×	`pow1_binary32`
11×	`*-un-lft-identity_binary32`
11×	`add-cube-cbrt_binary32`

Counts

2 → 72

Calls

2 calls:

6.0ms

(*.f32 (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))) (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

2.0ms

(exp.f32 (neg.f32 (*.f32 (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))) (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

593×	`cancel-sign-sub-inv_binary32`
474×	`fma-neg_binary32`
221×	`associate-l_binary32`
218×	`times-frac_binary32`
211×	`distribute-neg-frac_binary32`

Counts

120 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	126	2213
1	254	1801
2	697	1733
3	2684	1668
4	4824	1668
5	4949	1668

prune189.0ms (3.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	264	0	264
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	264	4	268

Error

Counts

268 → 4

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
✓	0.0b	(/.f32 1 (exp.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	17.7b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 (neg.f32 x) s))) (sqrt.f32 (/.f32 (neg.f32 x) s)))))
✓	0.2b	(exp.f32 (neg.f32 (*.f32 (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))) (sqrt.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))

Compiler

Compiled 6019 to 1851 computations (69.2% saved)

regimes657.0ms (12.5%)

Accuracy

Total 0.0b remaining (34.5%)

Threshold costs 0.0b (34.5%)

Counts

89 → 1

Compiler

Compiled 11300 to 9175 computations (18.8% saved)

simplify2.0ms (0%)

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
5	28	14

end56.0ms (1.1%)

Compiler: Compiled 78 to 54 computations (30.8% saved)

Details

analyze91.0ms (1.7%)

sample1.4s (26.9%)

simplify57.0ms (1.1%)

prune2.0ms (0%)

localize23.0ms (0.4%)

series31.0ms (0.6%)

rewrite20.0ms (0.4%)

simplify109.0ms (2.1%)

prune150.0ms (2.8%)

localize22.0ms (0.4%)

series661.0ms (12.5%)

rewrite12.0ms (0.2%)

simplify136.0ms (2.6%)

prune85.0ms (1.6%)

localize25.0ms (0.5%)

series589.0ms (11.2%)

rewrite6.0ms (0.1%)

simplify111.0ms (2.1%)

prune112.0ms (2.1%)

localize34.0ms (0.6%)

series560.0ms (10.6%)

rewrite14.0ms (0.3%)

simplify96.0ms (1.8%)

prune189.0ms (3.6%)

regimes657.0ms (12.5%)

simplify2.0ms (0%)

end56.0ms (1.1%)

Profiling