Details

analyze642.0ms (15.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample440.0ms (10.8%)

Algorithm

1×

intervals

Results

289.0ms	88×	body	1024	valid
9.0ms	48×	body	512	valid
5.0ms	94×	body	128	valid
3.0ms	7×	body	2048	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify46.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

667×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
380×	`fma-def_binary64`
279×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	123	11
5	318	8
6	1056	8
7	4350	8
8	4987	8

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	42.3b	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

Compiler

Compiled 56 to 46 computations (17.9% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	0.0b	(+.f64 1 (exp.f64 x))

series6.0ms (0.2%)

Counts

2 → 8

Calls

2 calls:

5.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
4×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

3.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

simplify81.0ms (2%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
283×	`fma-neg_binary64`
235×	`fma-def_binary64`
177×	`associate-/r/_binary64`
165×	`associate-+l+_binary64`

Counts

46 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	538
1	218	494
2	595	470
3	2140	454
4	4978	454
5	4938	454
6	5008	454

prune45.0ms (1.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	56	1	57

Error

Counts

57 → 1

Alt Table

Status	Error	Program
▶	0b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))

Compiler

Compiled 679 to 492 computations (27.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
✓	0.0b	(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))

series24.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

14.0ms	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
10.0ms	(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

201×	`times-frac_binary64`
132×	`add-sqr-sqrt_binary64`
129×	`*-un-lft-identity_binary64`
129×	`add-cube-cbrt_binary64`
126×	`distribute-lft-neg-in_binary64`

Counts

2 → 254

Calls

2 calls:

8.0ms	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
5.0ms	(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))

simplify331.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
635×	`associate-/l*_binary64`
298×	`associate-/r/_binary64`
294×	`div-sub_binary64`
280×	`associate-/l/_binary64`

Counts

278 → 341

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	360	8231
1	635	7873
2	1908	7608
3	4461	7604
4	4951	7604

prune116.0ms (2.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	341	1	342

Error

Counts

342 → 1

Alt Table

Status	Error	Program
✓	0b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))

Compiler

Compiled 7230 to 1408 computations (80.5% saved)

regimes61.0ms (1.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

23 → 1

Compiler

Compiled 685 to 579 computations (15.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	7	13

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample2.2s (54.3%)

Algorithm

1×

intervals

Results

1.2s	2623×	body	1024	valid
371.0ms	1314×	body	512	valid
219.0ms	3131×	body	128	valid
109.0ms	269×	body	2048	valid
85.0ms	663×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 35 to 27 computations (22.9% saved)

Details

analyze642.0ms (15.8%)

sample440.0ms (10.8%)

simplify46.0ms (1.1%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify81.0ms (2%)

prune45.0ms (1.1%)

localize7.0ms (0.2%)

series24.0ms (0.6%)

rewrite42.0ms (1%)

simplify331.0ms (8.2%)

prune116.0ms (2.9%)

regimes61.0ms (1.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (54.3%)

Profiling