Details

analyze182.0ms (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)

sample2.6s (23.9%)

Results

2.5s

8256×

body

128

valid

Compiler

Compiled 47 to 37 computations (21.3% saved)

simplify69.0ms (0.6%)

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

0.1b

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)

localize26.0ms (0.2%)

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 (0.3%)

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))

rewrite24.0ms (0.2%)

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

simplify143.0ms (1.3%)

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

prune229.0ms (2.1%)

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

0.0b

Counts

162 → 5

Alt Table

Status	Error	Program
	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))))))
	0.3b	(/.f32 1 (*.f32 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2)) (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
▶	0.1b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (/.f32 (neg.f32 x) s)) (cbrt.f32 (/.f32 (neg.f32 x) s)))) (cbrt.f32 (/.f32 (neg.f32 x) s)))))
	22.8b	(fma.f32 (/.f32 x s) 1/4 1/2)

Compiler

Compiled 2815 to 1499 computations (46.7% saved)

localize59.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))
✓	0.1b	(/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2)))
✓	0.1b	(exp.f32 (/.f32 x s))
	0.1b	(exp.f32 (/.f32 (neg.f32 x) s))

series1.1s (9.8%)

Counts

3 → 60

Calls

3 calls:

621.0ms

(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

439.0ms

(/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2)))

7.0ms

(exp.f32 (/.f32 x s))

rewrite67.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`times-frac_binary32`
130×	`*-un-lft-identity_binary32`
102×	`add-sqr-sqrt_binary32`
102×	`add-cube-cbrt_binary32`
56×	`sqrt-prod_binary32`

Counts

3 → 188

Calls

3 calls:

18.0ms

(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

5.0ms

(exp.f32 (/.f32 x s))

5.0ms

(/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2)))

simplify433.0ms (4%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary32`
437×	`associate-/l/_binary32`
220×	`associate-/r*_binary32`
217×	`times-frac_binary32`
157×	`cancel-sign-sub-inv_binary32`

Counts

248 → 244

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	319	11137
1	796	10804
2	2968	10528
3	4900	10522
4	5013	10522

prune807.0ms (7.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	308	3	311
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	310	6	316

Error

0.0b

Counts

316 → 6

Alt Table

Status	Error	Program
	0.2b	(/.f32 (/.f32 (/.f32 1 (hypot.f32 1 (exp.f32 (.f32 (/.f32 x s) -1/2)))) (.f32 (cbrt.f32 (sqrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))) (cbrt.f32 (sqrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))))) (cbrt.f32 (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	22.8b	(fma.f32 (/.f32 x s) 1/4 1/2)
	0.3b	(/.f32 1 (*.f32 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2)) (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))))
	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (/.f32 (neg.f32 x) s)) (cbrt.f32 (/.f32 (neg.f32 x) s)))) (cbrt.f32 (/.f32 (neg.f32 x) s)))))
	15.4b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (/.f32 x s)))) (sqrt.f32 (/.f32 (neg.f32 x) s))))))
▶	0.1b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

Compiler

Compiled 11244 to 6931 computations (38.4% saved)

localize75.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))
✓	0.1b	(/.f32 1 (hypot.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 x s)) -1/2)))
	0.1b	(exp.f32 (/.f32 (neg.f32 x) s))
✓	0.1b	(pow.f32 (E.f32) (/.f32 x s))

series1.4s (12.8%)

Counts

3 → 72

Calls

3 calls:

833.0ms

(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

550.0ms

(/.f32 1 (hypot.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 x s)) -1/2)))

7.0ms

(pow.f32 (E.f32) (/.f32 x s))

rewrite61.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`times-frac_binary32`
131×	`*-un-lft-identity_binary32`
103×	`add-sqr-sqrt_binary32`
103×	`add-cube-cbrt_binary32`
56×	`sqrt-prod_binary32`

Counts

3 → 195

Calls

3 calls:

10.0ms

(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

6.0ms

(pow.f32 (E.f32) (/.f32 x s))

3.0ms

(/.f32 1 (hypot.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 x s)) -1/2)))

simplify660.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

887×	`fma-def_binary32`
227×	`times-frac_binary32`
221×	`associate-/r*_binary32`
158×	`cancel-sign-sub-inv_binary32`
156×	`associate-r_binary32`

Counts

267 → 254

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	333	11871
1	860	10931
2	3188	10647
3	4746	9856
4	4898	9841
5	4980	9841
6	4996	9841
7	4926	9841

prune762.0ms (7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	318	3	321
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	321	6	327

Error

0.0b

Counts

327 → 6

Alt Table

Status	Error	Program
▶	0.1b	(/.f32 1 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))
	15.4b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (/.f32 x s)))) (sqrt.f32 (/.f32 (neg.f32 x) s))))))
	0.1b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (*.f32 (log.f32 (E.f32)) (/.f32 x s))) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))
	22.8b	(fma.f32 (/.f32 x s) 1/4 1/2)
	0.1b	(sqrt.f32 (/.f32 1 (pow.f32 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2)) 4)))
✓	0.1b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

Compiler

Compiled 11526 to 6832 computations (40.7% saved)

localize53.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

series75.0ms (0.7%)

Counts

3 → 48

Calls

3 calls:

51.0ms	(/.f32 1 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))
12.0ms	(+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))
11.0ms	(exp.f32 (neg.f32 (/.f32 x s)))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary32`
30×	`times-frac_binary32`
30×	`exp-prod_binary32`
28×	`add-sqr-sqrt_binary32`
28×	`add-cube-cbrt_binary32`

Counts

3 → 99

Calls

3 calls:

12.0ms	(/.f32 1 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))
9.0ms	(+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))
9.0ms	(exp.f32 (neg.f32 (/.f32 x s)))

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-neg_binary32`
301×	`associate-/l/_binary32`
210×	`distribute-neg-frac_binary32`
203×	`distribute-rgt-neg-in_binary32`
195×	`distribute-lft-neg-in_binary32`

Counts

147 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2180
1	352	2024
2	819	1970
3	2461	1946
4	4757	1946
5	4975	1946

prune176.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	136	6	142

Error

0.0b

Counts

142 → 6

Alt Table

Status	Error	Program
✓	0.1b	(/.f32 1 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))
	15.4b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (/.f32 x s)))) (sqrt.f32 (/.f32 (neg.f32 x) s))))))
	0.1b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (exp.f32 (*.f32 (log.f32 (E.f32)) (/.f32 x s))) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))
	22.8b	(fma.f32 (/.f32 x s) 1/4 1/2)
	0.1b	(sqrt.f32 (/.f32 1 (pow.f32 (hypot.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -1/2)) 4)))
✓	0.1b	(/.f32 (/.f32 1 (hypot.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 x s)) -1/2))) (sqrt.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))

Compiler

Compiled 2290 to 1263 computations (44.8% saved)

regimes1.5s (14.2%)

Accuracy

Total 0.0b remaining (60.5%)

Threshold costs 0.0b (60.5%)

Counts

119 → 1

Compiler

Compiled 17782 to 13781 computations (22.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	13	15
2	12	15

end173.0ms (1.6%)

Compiler: Compiled 132 to 107 computations (18.9% saved)

Details

analyze182.0ms (1.7%)

sample2.6s (23.9%)

simplify69.0ms (0.6%)

prune2.0ms (0%)

localize26.0ms (0.2%)

series37.0ms (0.3%)

rewrite24.0ms (0.2%)

simplify143.0ms (1.3%)

prune229.0ms (2.1%)

localize59.0ms (0.5%)

series1.1s (9.8%)

rewrite67.0ms (0.6%)

simplify433.0ms (4%)

prune807.0ms (7.4%)

localize75.0ms (0.7%)

series1.4s (12.8%)

rewrite61.0ms (0.6%)

simplify660.0ms (6.1%)

prune762.0ms (7%)

localize53.0ms (0.5%)

series75.0ms (0.7%)

rewrite35.0ms (0.3%)

simplify128.0ms (1.2%)

prune176.0ms (1.6%)

regimes1.5s (14.2%)

simplify4.0ms (0%)

end173.0ms (1.6%)

Profiling