Details

analyze92.0ms (2%)

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)

sample90.0ms (2%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify53.0ms (1.2%)

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)

localize42.0ms (0.9%)

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))

series34.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(/.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))

rewrite26.0ms (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	(exp.f32 (/.f32 (neg.f32 x) s))
6.0ms	(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
4.0ms	(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))

simplify107.0ms (2.4%)

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

prune127.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	3	162

Error

0.0b

Counts

162 → 3

Alt Table

Status	Error	Program
▶	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	0.1b	(.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))) (cbrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.0b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))

Compiler

Compiled 2727 to 1455 computations (46.6% saved)

localize24.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
✓	0.1b	(exp.f32 (neg.f32 (/.f32 x s)))
✓	1.4b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series753.0ms (16.7%)

Counts

3 → 64

Calls

3 calls:

379.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
368.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))
6.0ms	(exp.f32 (neg.f32 (/.f32 x s)))

rewrite12.0ms (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:

5.0ms	(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))))

simplify135.0ms (3%)

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

prune89.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	118	3	121

Error

0.0b

Counts

121 → 3

Alt Table

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

Compiler

Compiled 1829 to 828 computations (54.7% saved)

localize26.0ms (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))

series40.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(/.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 (0.4%)

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

simplify140.0ms (3.1%)

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

prune129.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	172	3	175

Error

0.0b

Counts

175 → 3

Alt Table

Status	Error	Program
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
▶	18.1b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))) (-.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))))

Compiler

Compiled 3012 to 1499 computations (50.2% saved)

localize48.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f32 (exp.f32 (/.f32 x s)) -2)
✓	1.6b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))) (-.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
✓	5.2b	(-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))
✓	5.3b	(-.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))

series156.0ms (3.5%)

Counts

4 → 96

Calls

4 calls:

99.0ms	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))) (-.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
27.0ms	(-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))
19.0ms	(pow.f32 (exp.f32 (/.f32 x s)) -2)
11.0ms	(-.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))

rewrite66.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`add-sqr-sqrt_binary32`
121×	`*-un-lft-identity_binary32`
90×	`add-cube-cbrt_binary32`
84×	`prod-diff_binary32`
63×	`unpow-prod-down_binary32`

Counts

4 → 263

Calls

4 calls:

21.0ms	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))) (-.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	(-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))
4.0ms	(pow.f32 (exp.f32 (/.f32 x s)) -2)

simplify415.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

869×	`times-frac_binary32`
353×	`fma-neg_binary32`
309×	`cancel-sign-sub-inv_binary32`
250×	`exp-prod_binary32`
222×	`associate-r_binary32`

Counts

359 → 399

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	376	14181
1	832	11121
2	2524	7989
3	4305	7971
4	4947	7971
5	4732	7971

prune358.0ms (7.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	397	2	399
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	398	4	402

Error

Counts

402 → 4

Alt Table

Status	Error	Program
	18.1b	(.f32 (/.f32 1 (.f32 (*.f32 (cbrt.f32 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))) (cbrt.f32 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2)))) (cbrt.f32 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))))) (-.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
✓	0.0b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	17.9b	(.f32 (/.f32 1 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))) (/.f32 (-.f32 1 (pow.f32 (E.f32) (.f32 (/.f32 x s) -2))) (+.f32 1 (pow.f32 (E.f32) (neg.f32 (/.f32 x s))))))
✓	0.0b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))

Compiler

Compiled 15425 to 7017 computations (54.5% saved)

regimes337.0ms (7.5%)

Accuracy

Total 0.0b remaining (62.3%)

Threshold costs 0.0b (62.3%)

Counts

43 → 1

Compiler

Compiled 7971 to 4987 computations (37.4% saved)

simplify3.0ms (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

end0.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample1.2s (26.2%)

Algorithm

1×

intervals

Results

463.0ms	8000×	body	128	valid
147.0ms	8000×	pre	128	true

Compiler

Compiled 126 to 95 computations (24.6% saved)

Details

analyze92.0ms (2%)

sample90.0ms (2%)

simplify53.0ms (1.2%)

prune2.0ms (0%)

localize42.0ms (0.9%)

series34.0ms (0.8%)

rewrite26.0ms (0.6%)

simplify107.0ms (2.4%)

prune127.0ms (2.8%)

localize24.0ms (0.5%)

series753.0ms (16.7%)

rewrite12.0ms (0.3%)

simplify135.0ms (3%)

prune89.0ms (2%)

localize26.0ms (0.6%)

series40.0ms (0.9%)

rewrite20.0ms (0.4%)

simplify140.0ms (3.1%)

prune129.0ms (2.9%)

localize48.0ms (1.1%)

series156.0ms (3.5%)

rewrite66.0ms (1.5%)

simplify415.0ms (9.2%)

prune358.0ms (7.9%)

regimes337.0ms (7.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (26.2%)

Profiling