Details

analyze92.0ms (1.2%)

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)

sample91.0ms (1.2%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify58.0ms (0.8%)

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 (0.3%)

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 (0.4%)

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))

rewrite21.0ms (0.3%)

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)))

simplify103.0ms (1.4%)

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

prune133.0ms (1.8%)

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

0.1b

Counts

162 → 4

Alt Table

Status	Error	Program
	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 (E.f32) (/.f32 (neg.f32 x) s))))
	0.3b	(*.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) (sqrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
	0.1b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

Compiler

Compiled 2747 to 1473 computations (46.4% saved)

localize25.0ms (0.3%)

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 (0.5%)

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 (0.3%)

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 (1.9%)

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

prune159.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	170	6	176

Error

0.0b

Counts

176 → 6

Alt Table

Status	Error	Program
	0.3b	(*.f32 (sqrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))) (sqrt.f32 (/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
▶	0.1b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	17.4b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))) (-.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
	11.3b	(.f32 (/.f32 1 (+.f32 (pow.f32 1 3) (pow.f32 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)) 3))) (+.f32 (.f32 1 1) (-.f32 (.f32 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)) (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))) (.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))
	0.3b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))) (/.f32 1 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))
✓	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))

Compiler

Compiled 3224 to 1627 computations (49.5% saved)

localize23.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (neg.f32 (/.f32 x s)))
✓	0.1b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
✓	0.7b	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series855.0ms (11.2%)

Counts

3 → 64

Calls

3 calls:

492.0ms	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
357.0ms	(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))
6.0ms	(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))))

simplify173.0ms (2.3%)

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

prune144.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	118	6	124

Error

0.0b

Counts

124 → 6

Alt Table

Status	Error	Program
	0.3b	(*.f32 (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))) (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))
✓	0.1b	(exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
	17.4b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))) (-.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
	11.3b	(.f32 (/.f32 1 (+.f32 (pow.f32 1 3) (pow.f32 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)) 3))) (+.f32 (.f32 1 1) (-.f32 (.f32 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)) (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))) (.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))
▶	0.3b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))) (/.f32 1 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))
✓	0.1b	(/.f32 1 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))

Compiler

Compiled 1995 to 938 computations (53% saved)

localize56.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))) (/.f32 1 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))
✓	0.0b	(/.f32 1 (*.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))
	0.1b	(pow.f32 (E.f32) (/.f32 (neg.f32 x) s))
✓	0.2b	(*.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))

series1.2s (15.5%)

Counts

3 → 72

Calls

3 calls:

673.0ms

(/.f32 1 (*.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))

479.0ms

(*.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))

29.0ms

(*.f32 (/.f32 1 (*.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))) (/.f32 1 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))

rewrite93.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-exp-log_binary32`
68×	`add-sqr-sqrt_binary32`
61×	`*-un-lft-identity_binary32`
50×	`times-frac_binary32`
44×	`prod-exp_binary32`

Counts

3 → 221

Calls

3 calls:

31.0ms

(*.f32 (/.f32 1 (*.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))) (/.f32 1 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))

13.0ms

(/.f32 1 (*.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))

12.0ms

(*.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))

simplify277.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-/l*_binary32`
531×	`associate-*l/_binary32`
382×	`fma-def_binary32`
239×	`fma-neg_binary32`
218×	`cancel-sign-sub-inv_binary32`

Counts

293 → 329

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	11904
1	563	8335
2	1768	7184
3	4462	6980
4	4987	6980
5	4922	6980

prune1.0s (13.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	559	4	563
Fresh	0	3	3
Picked	1	0	1
Done	2	0	2
Total	562	7	569

Error

0.0b

Counts

569 → 7

Alt Table

Status	Error	Program
	0.3b	(*.f32 (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))) (sqrt.f32 (exp.f32 (neg.f32 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))
	17.4b	(*.f32 (/.f32 1 (-.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -2))) (-.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))
	11.3b	(.f32 (/.f32 1 (+.f32 (pow.f32 1 3) (pow.f32 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)) 3))) (+.f32 (.f32 1 1) (-.f32 (.f32 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)) (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))) (.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))
	15.3b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))) (/.f32 1 (cbrt.f32 (+.f32 1 (pow.f32 (pow.f32 (E.f32) (/.f32 (sqrt.f32 (neg.f32 x)) (sqrt.f32 s))) (/.f32 (sqrt.f32 (neg.f32 x)) (sqrt.f32 s)))))))
	0.3b	(.f32 (/.f32 1 (.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))) (/.f32 1 (cbrt.f32 (+.f32 1 (*.f32 (pow.f32 (sqrt.f32 (E.f32)) (neg.f32 (/.f32 x s))) (pow.f32 (sqrt.f32 (E.f32)) (neg.f32 (/.f32 x s))))))))
	0.3b	(.f32 (/.f32 1 (.f32 (.f32 (cbrt.f32 (.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))) (cbrt.f32 (.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))) (cbrt.f32 (.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))) (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s)))))))) (/.f32 1 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))
	0.3b	(.f32 (/.f32 1 (exp.f32 (.f32 2 (log.f32 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (neg.f32 (/.f32 x s))))))))) (/.f32 1 (cbrt.f32 (+.f32 1 (pow.f32 (E.f32) (/.f32 (neg.f32 x) s))))))

Compiler

Compiled 23372 to 11137 computations (52.3% saved)

regimes1.5s (20.2%)

Accuracy

Total 0.0b remaining (50.4%)

Threshold costs 0.0b (50.4%)

Counts

152 → 1

Compiler

Compiled 40544 to 25950 computations (36% saved)

simplify3.0ms (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	11	16
1	21	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)

sample1.3s (17.1%)

Algorithm

1×

intervals

Results

470.0ms	8000×	body	128	valid
207.0ms	8000×	pre	128	true

Compiler

Compiled 311 to 191 computations (38.6% saved)

Details

analyze92.0ms (1.2%)

sample91.0ms (1.2%)

simplify58.0ms (0.8%)

prune2.0ms (0%)

localize23.0ms (0.3%)

series34.0ms (0.4%)

rewrite21.0ms (0.3%)

simplify103.0ms (1.4%)

prune133.0ms (1.8%)

localize25.0ms (0.3%)

series39.0ms (0.5%)

rewrite20.0ms (0.3%)

simplify144.0ms (1.9%)

prune159.0ms (2.1%)

localize23.0ms (0.3%)

series855.0ms (11.2%)

rewrite12.0ms (0.2%)

simplify173.0ms (2.3%)

prune144.0ms (1.9%)

localize56.0ms (0.7%)

series1.2s (15.5%)

rewrite93.0ms (1.2%)

simplify277.0ms (3.6%)

prune1.0s (13.3%)

regimes1.5s (20.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3s (17.1%)

Profiling