Details

analyze153.0ms (3.9%)

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)

sample36.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify57.0ms (1.4%)

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)

localize22.0ms (0.6%)

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))

series37.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

24.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
6.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
6.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

rewrite23.0ms (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:

8.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
4.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
4.0ms	(exp.f32 (/.f32 (neg.f32 x) s))

simplify104.0ms (2.7%)

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

prune138.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	155	6	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	6	162

Error

0.0b

Counts

162 → 6

Alt Table

Status	Error	Program
	0.1b	(/.f32 1 (expm1.f32 (log1p.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	23.1b	(fma.f32 (/.f32 x s) 1/4 1/2)
	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))
▶	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
	0.1b	(/.f32 1 (+.f32 1 (*.f32 (sqrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))) (sqrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 2767 to 1491 computations (46.1% 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))))
✓	0.1b	(pow.f32 (exp.f32 -1) (/.f32 x s))

series40.0ms (1%)

Counts

3 → 72

Calls

3 calls:

25.0ms	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s))))
8.0ms	(+.f32 1 (pow.f32 (exp.f32 -1) (/.f32 x s)))
7.0ms	(pow.f32 (exp.f32 -1) (/.f32 x s))

rewrite19.0ms (0.5%)

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

simplify104.0ms (2.7%)

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

prune182.0ms (4.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	145	7	152

Error

0.0b

Counts

152 → 7

Alt Table

Status	Error	Program
▶	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
	0.1b	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)))))
	0.1b	(/.f32 1 (expm1.f32 (log1p.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	23.1b	(fma.f32 (/.f32 x s) 1/4 1/2)
	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))
	0.5b	(/.f32 1 (+.f32 1 (pow.f32 (pow.f32 (exp.f32 -1) (/.f32 (*.f32 (cbrt.f32 x) (cbrt.f32 x)) (sqrt.f32 s))) (/.f32 (cbrt.f32 x) (sqrt.f32 s)))))
	0.1b	(/.f32 1 (+.f32 1 (*.f32 (sqrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))) (sqrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 2688 to 1789 computations (33.4% saved)

localize25.0ms (0.6%)

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))))
✓	0.1b	(pow.f32 (E.f32) (/.f32 (neg.f32 x) s))

series39.0ms (1%)

Counts

3 → 72

Calls

3 calls:

25.0ms	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
7.0ms	(+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))
7.0ms	(pow.f32 (E.f32) (/.f32 (neg.f32 x) s))

rewrite20.0ms (0.5%)

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	(pow.f32 (E.f32) (/.f32 (neg.f32 x) s))
5.0ms	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
3.0ms	(+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))

simplify144.0ms (3.7%)

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

prune181.0ms (4.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	172	7	179

Error

0.0b

Counts

179 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
▶	0.1b	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)))))
	0.1b	(/.f32 1 (expm1.f32 (log1p.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	23.1b	(fma.f32 (/.f32 x s) 1/4 1/2)
	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))
	0.5b	(/.f32 1 (+.f32 1 (pow.f32 (pow.f32 (exp.f32 -1) (/.f32 (*.f32 (cbrt.f32 x) (cbrt.f32 x)) (sqrt.f32 s))) (/.f32 (cbrt.f32 x) (sqrt.f32 s)))))
	0.1b	(/.f32 1 (+.f32 1 (*.f32 (sqrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))) (sqrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 3152 to 1595 computations (49.4% saved)

localize34.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

series145.0ms (3.7%)

Counts

4 → 96

Calls

4 calls:

91.0ms	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)))))
22.0ms	(+.f32 1 (*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s))))
20.0ms	(*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)))
11.0ms	(pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary32`
50×	`unpow-prod-down_binary32`
35×	`*-un-lft-identity_binary32`
35×	`add-cube-cbrt_binary32`
25×	`sqrt-prod_binary32`

Counts

4 → 161

Calls

4 calls:

8.0ms	(*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)))
4.0ms	(/.f32 1 (+.f32 1 (*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)))))
4.0ms	(+.f32 1 (*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s))))
4.0ms	(pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s))

simplify191.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

523×	`times-frac_binary32`
515×	`fma-def_binary32`
362×	`associate-/l*_binary32`
343×	`fma-neg_binary32`
251×	`associate-/r*_binary32`

Counts

257 → 229

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	222	6177
1	516	5411
2	1595	5290
3	4511	4634
4	4927	4598
5	4961	4598

prune437.0ms (11.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	279	2	281
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	281	7	288

Error

0.0b

Counts

288 → 7

Alt Table

Status	Error	Program
	0.1b	(/.f32 1 (expm1.f32 (log1p.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	23.1b	(fma.f32 (/.f32 x s) 1/4 1/2)
	0.1b	(/.f32 1 (+.f32 1 (/.f32 1 (exp.f32 (/.f32 x s)))))
	0.5b	(/.f32 1 (+.f32 1 (.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 (.f32 (cbrt.f32 x) (cbrt.f32 x)) (sqrt.f32 s))) (/.f32 (cbrt.f32 x) (sqrt.f32 s))))))
	0.1b	(/.f32 1 (+.f32 1 (.f32 (.f32 (cbrt.f32 (.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)))) (cbrt.f32 (.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s))))) (cbrt.f32 (*.f32 (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)) (pow.f32 (sqrt.f32 (exp.f32 -1)) (/.f32 x s)))))))
✓	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
	0.1b	(/.f32 1 (+.f32 1 (*.f32 (sqrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))) (sqrt.f32 (exp.f32 (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 7906 to 5605 computations (29.1% saved)

regimes468.0ms (12%)

Accuracy

Total 0.0b remaining (47.4%)

Threshold costs 0.0b (47.4%)

Counts

72 → 1

Compiler

Compiled 9089 to 7278 computations (19.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary32`
1×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	17	20
2	16	20

end1.0ms (0%)

Compiler: Compiled 15 to 13 computations (13.3% saved)

sample1.3s (32%)

Algorithm

1×

intervals

Results

458.0ms	8000×	body	128	valid
136.0ms	8000×	pre	128	true

Compiler

Compiled 187 to 138 computations (26.2% saved)

Details

analyze153.0ms (3.9%)

sample36.0ms (0.9%)

simplify57.0ms (1.4%)

prune2.0ms (0%)

localize22.0ms (0.6%)

series37.0ms (0.9%)

rewrite23.0ms (0.6%)

simplify104.0ms (2.7%)

prune138.0ms (3.5%)

localize26.0ms (0.7%)

series40.0ms (1%)

rewrite19.0ms (0.5%)

simplify104.0ms (2.7%)

prune182.0ms (4.6%)

localize25.0ms (0.6%)

series39.0ms (1%)

rewrite20.0ms (0.5%)

simplify144.0ms (3.7%)

prune181.0ms (4.6%)

localize34.0ms (0.9%)

series145.0ms (3.7%)

rewrite33.0ms (0.8%)

simplify191.0ms (4.9%)

prune437.0ms (11.2%)

regimes468.0ms (12%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample1.3s (32%)

Profiling