Details

analyze826.0ms (15.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
12.5%	75%	12.5%	4
18.7%	62.5%	18.8%	5
21.9%	56.2%	21.9%	6
23.4%	53.1%	23.5%	7
24.2%	51.5%	24.3%	8
24.6%	51.1%	24.3%	9
24.8%	51%	24.3%	10
24.8%	51%	24.3%	11
24.8%	50.9%	24.3%	12
24.9%	50.8%	24.3%	13
24.9%	50.8%	24.3%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.7s (49.7%)

Results

1.4s	2769×	body	1024	valid
454.0ms	3139×	body	128	valid
432.0ms	1381×	body	512	valid
164.0ms	286×	body	2048	valid
147.0ms	681×	body	256	valid
80.0ms	39×	body	8192	exit

Compiler

Compiled 27 to 23 computations (14.8% saved)

simplify44.0ms (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

prune6.0ms (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)

localize3.0ms (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:

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

rewrite6.0ms (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:

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

simplify78.0ms (1.4%)

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

prune44.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	2	56

Error

Counts

56 → 2

Alt Table

Status	Error	Program
	0.0b	(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
▶	0.0b	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))

Compiler

Compiled 705 to 514 computations (27.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (exp.f64 x))
✓	0.0b	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))
✓	0.0b	(log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x))))
✓	0.6b	(*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))

series1.1s (20.4%)

Counts

4 → 24

Calls

4 calls:

819.0ms	(log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x))))
293.0ms	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))
4.0ms	(*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))
2.0ms	(exp.f64 (exp.f64 x))

rewrite91.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
19×	`pow1_binary64`
15×	`exp-prod_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`log-pow_binary64`

Counts

4 → 73

Calls

4 calls:

79.0ms	(*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))
4.0ms	(log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x))))
4.0ms	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))
1.0ms	(exp.f64 (exp.f64 x))

simplify114.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
393×	`fma-neg_binary64`
358×	`associate-l_binary64`
344×	`distribute-lft-out_binary64`
308×	`distribute-rgt-out_binary64`

Counts

97 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1019
1	324	926
2	944	905
3	2790	896
4	4777	896
5	4958	896

prune83.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	128	2	130

Error

Counts

130 → 2

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (log.f64 (expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x)))))))
✓	0.0b	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))

Compiler

Compiled 1746 to 1230 computations (29.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (log.f64 (expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x)))))))
✓	0.0b	(log.f64 (expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x))))))
✓	0.0b	(exp.f64 (+.f64 1 (exp.f64 x)))
✓	1.0b	(expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x)))))

series15.0ms (0.3%)

Counts

4 → 40

Calls

4 calls:

7.0ms	(sqrt.f64 (log.f64 (expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x)))))))
3.0ms	(expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x)))))
3.0ms	(exp.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(log.f64 (expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x))))))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`
7×	`pow1_binary64`

Counts

4 → 57

Calls

4 calls:

3.0ms	(exp.f64 (+.f64 1 (exp.f64 x)))
1.0ms	(sqrt.f64 (log.f64 (expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x)))))))
1.0ms	(log.f64 (expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x))))))
0.0ms	(expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x)))))

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
268×	`fma-neg_binary64`
248×	`fma-def_binary64`
187×	`associate-+l+_binary64`
155×	`distribute-rgt-out_binary64`

Counts

97 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1093
1	218	1007
2	647	969
3	2346	957
4	4881	957
5	4957	957

prune59.0ms (1.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	96	2	98

Error

Counts

98 → 2

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (log.f64 (expm1.f64 (log1p.f64 (exp.f64 (+.f64 1 (exp.f64 x)))))))
✓	0.0b	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))

Compiler

Compiled 1339 to 1062 computations (20.7% saved)

regimes99.0ms (1.8%)

Accuracy

Total 0.0b remaining (1.4%)

Threshold costs 0.0b (1.4%)

Counts

41 → 1

Compiler

Compiled 1250 to 1072 computations (14.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`e-exp-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	11	13
2	13	13
3	12	13

end55.0ms (1%)

Compiler: Compiled 35 to 31 computations (11.4% saved)

Details

analyze826.0ms (15.1%)

sample2.7s (49.7%)

simplify44.0ms (0.8%)

prune6.0ms (0.1%)

localize3.0ms (0.1%)

series7.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify78.0ms (1.4%)

prune44.0ms (0.8%)

localize10.0ms (0.2%)

series1.1s (20.4%)

rewrite91.0ms (1.7%)

simplify114.0ms (2.1%)

prune83.0ms (1.5%)

localize10.0ms (0.2%)

series15.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify82.0ms (1.5%)

prune59.0ms (1.1%)

regimes99.0ms (1.8%)

simplify2.0ms (0%)

end55.0ms (1%)

Profiling