Details

analyze1.4s (25.4%)

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)

sample57.0ms (1%)

Algorithm

1×

intervals

Results

28.0ms	84×	body	1024	valid
9.0ms	46×	body	512	valid
5.0ms	93×	body	128	valid
5.0ms	12×	body	2048	valid
3.0ms	21×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify43.0ms (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

prune3.0ms (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))

rewrite7.0ms (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))

simplify79.0ms (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

prune41.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	4	56

Error

Counts

56 → 4

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
	0.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x)))))
	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 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 739 to 539 computations (27.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
✓	0.0b	(+.f64 1 (pow.f64 (exp.f64 x) 3))
✓	0.0b	(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
✓	0.0b	(pow.f64 (exp.f64 x) 3)

series126.0ms (2.2%)

Counts

4 → 32

Calls

4 calls:

64.0ms	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
50.0ms	(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
6.0ms	(+.f64 1 (pow.f64 (exp.f64 x) 3))
6.0ms	(pow.f64 (exp.f64 x) 3)

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 110

Calls

4 calls:

7.0ms	(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
5.0ms	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
4.0ms	(+.f64 1 (pow.f64 (exp.f64 x) 3))
2.0ms	(pow.f64 (exp.f64 x) 3)

simplify142.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-def_binary64`
561×	`fma-neg_binary64`
244×	`log-prod_binary64`
226×	`associate-/l*_binary64`
226×	`unswap-sqr_binary64`

Counts

142 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	3224
1	424	3011
2	1286	2957
3	4007	2957
4	4654	2957
5	4950	2957

prune131.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
	0.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x)))))
▶	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 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 3542 to 2276 computations (35.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
✓	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	(hypot.f64 1 (pow.f64 (exp.f64 x) 3/2))
✓	0.0b	(pow.f64 (exp.f64 x) 3/2)

series752.0ms (13.3%)

Counts

4 → 48

Calls

4 calls:

314.0ms	(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
236.0ms	(pow.f64 (exp.f64 x) 3/2)
194.0ms	(hypot.f64 1 (pow.f64 (exp.f64 x) 3/2))
8.0ms	(sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
15×	`sqrt-prod_binary64`

Counts

4 → 89

Calls

4 calls:

4.0ms	(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
2.0ms	(pow.f64 (exp.f64 x) 3/2)
1.0ms	(sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
0.0ms	(hypot.f64 1 (pow.f64 (exp.f64 x) 3/2))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
415×	`associate-+l+_binary64`
288×	`associate--l+_binary64`
242×	`associate-r_binary64`
225×	`cancel-sign-sub-inv_binary64`

Counts

137 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	3067
1	455	2841
2	1295	2773
3	4947	2773

prune249.0ms (4.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	164	4	168

Error

Counts

168 → 4

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
▶	0.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x)))))
✓	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 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 3926 to 2641 computations (32.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x)))))
✓	0.0b	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
✓	0.7b	(log1p.f64 (+.f64 1 (exp.f64 x)))

series204.0ms (3.6%)

Counts

3 → 36

Calls

3 calls:

197.0ms	(log1p.f64 (+.f64 1 (exp.f64 x)))
5.0ms	(sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x)))))
2.0ms	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`
4×	`expm1-log1p-u_binary64`

Counts

3 → 37

Calls

3 calls:

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

simplify114.0ms (2%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
268×	`fma-neg_binary64`
240×	`fma-def_binary64`
178×	`associate-+l+_binary64`
177×	`associate-/r/_binary64`

Counts

73 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	785
1	207	731
2	591	704
3	2122	691
4	4808	691
5	4978	691
6	4997	691
7	4944	691

prune71.0ms (1.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	110	4	114

Error

Counts

114 → 4

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
✓	0.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x)))))
✓	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 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 1348 to 1028 computations (23.7% saved)

regimes75.0ms (1.3%)

Accuracy

Total 0.0b remaining (20.8%)

Threshold costs 0.0b (20.8%)

Counts

26 → 1

Compiler

Compiled 1059 to 857 computations (19.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	14	11
2	15	11
3	13	11

end0.0ms (0%)

Compiler: Compiled 8 to 7 computations (12.5% saved)

sample2.0s (34.8%)

Algorithm

1×

intervals

Results

910.0ms	2643×	body	1024	valid
335.0ms	1327×	body	512	valid
221.0ms	3106×	body	128	valid
127.0ms	283×	body	2048	valid
89.0ms	641×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 67 to 54 computations (19.4% saved)

Details

analyze1.4s (25.4%)

sample57.0ms (1%)

simplify43.0ms (0.8%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series7.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify79.0ms (1.4%)

prune41.0ms (0.7%)

localize8.0ms (0.1%)

series126.0ms (2.2%)

rewrite25.0ms (0.4%)

simplify142.0ms (2.5%)

prune131.0ms (2.3%)

localize9.0ms (0.2%)

series752.0ms (13.3%)

rewrite12.0ms (0.2%)

simplify78.0ms (1.4%)

prune249.0ms (4.4%)

localize7.0ms (0.1%)

series204.0ms (3.6%)

rewrite3.0ms (0%)

simplify114.0ms (2%)

prune71.0ms (1.2%)

regimes75.0ms (1.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (34.8%)

Profiling