Details

analyze989.0ms (17%)

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)

sample465.0ms (8%)

Algorithm

1×

intervals

Results

309.0ms	89×	body	1024	valid
9.0ms	47×	body	512	valid
5.0ms	89×	body	128	valid
5.0ms	12×	body	2048	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify46.0ms (0.8%)

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

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 30 to 24 computations (20% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.1%)

Counts

2 → 8

Calls

2 calls:

6.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

4.0ms	(+.f64 1 (exp.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

simplify87.0ms (1.5%)

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

prune42.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	3	56

Error

Counts

56 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	0.0b	(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
	0.0b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))

Compiler

Compiled 717 to 523 computations (27.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (exp.f64 x))
✓	0.0b	(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
✓	0.0b	(exp.f64 (log1p.f64 (exp.f64 x)))

series741.0ms (12.7%)

Counts

3 → 36

Calls

3 calls:

330.0ms	(exp.f64 (log1p.f64 (exp.f64 x)))
212.0ms	(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
198.0ms	(log1p.f64 (exp.f64 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`exp-prod_binary64`
6×	`add-cube-cbrt_binary64`
4×	`sqrt-pow1_binary64`

Counts

3 → 43

Calls

3 calls:

2.0ms	(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
1.0ms	(exp.f64 (log1p.f64 (exp.f64 x)))
0.0ms	(log1p.f64 (exp.f64 x))

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
323×	`fma-neg_binary64`
194×	`fma-def_binary64`
168×	`associate-+l+_binary64`
161×	`distribute-rgt-neg-in_binary64`

Counts

79 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	800
1	213	733
2	571	703
3	2170	691
4	4886	691
5	4942	691

prune142.0ms (2.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	81	2	83

Error

Counts

83 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	0.0b	(sqrt.f64 (exp.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))))

Compiler

Compiled 894 to 513 computations (42.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))))
✓	0.0b	(exp.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)))
✓	0.7b	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 3)

series1.1s (18.2%)

Counts

4 → 48

Calls

4 calls:

347.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))
297.0ms	(exp.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)))
212.0ms	(sqrt.f64 (exp.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))))
202.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64`
30×	`exp-prod_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`

Counts

4 → 103

Calls

4 calls:

4.0ms	(sqrt.f64 (exp.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))))
3.0ms	(exp.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)))
2.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
2.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

467×	`associate-l_binary64`
451×	`fma-def_binary64`
416×	`associate-r_binary64`
351×	`fma-neg_binary64`
294×	`associate-+l+_binary64`

Counts

151 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	171	1683
1	346	1546
2	1039	1486
3	4477	1484
4	5009	1484

prune92.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	167	2	169

Error

Counts

169 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	0.0b	(sqrt.f64 (exp.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))))

Compiler

Compiled 2436 to 1595 computations (34.5% saved)

regimes74.0ms (1.3%)

Accuracy

Total 0.0b remaining (6.5%)

Threshold costs 0.0b (6.5%)

Counts

26 → 1

Compiler

Compiled 1163 to 877 computations (24.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	9	8
2	8	8

end0.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

sample1.9s (32.1%)

Algorithm

1×

intervals

Results

917.0ms	2599×	body	1024	valid
273.0ms	1357×	body	512	valid
198.0ms	3087×	body	128	valid
132.0ms	308×	body	2048	valid
80.0ms	649×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

Details

analyze989.0ms (17%)

sample465.0ms (8%)

simplify46.0ms (0.8%)

prune4.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify87.0ms (1.5%)

prune42.0ms (0.7%)

localize6.0ms (0.1%)

series741.0ms (12.7%)

rewrite4.0ms (0.1%)

simplify67.0ms (1.2%)

prune142.0ms (2.5%)

localize8.0ms (0.1%)

series1.1s (18.2%)

rewrite15.0ms (0.3%)

simplify86.0ms (1.5%)

prune92.0ms (1.6%)

regimes74.0ms (1.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.9s (32.1%)

Profiling