Details

analyze1.2s (25.7%)

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)

sample128.0ms (2.7%)

Algorithm

1×

intervals

Results

35.0ms	100×	body	1024	valid
8.0ms	43×	body	512	valid
4.0ms	84×	body	128	valid
4.0ms	10×	body	2048	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify44.0ms (0.9%)

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)

localize4.0ms (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))

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-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))

simplify87.0ms (1.8%)

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

prune127.0ms (2.6%)

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
	18.4b	(sqrt.f64 (+.f64 2 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))))
▶	0.0b	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))

Compiler

Compiled 705 to 514 computations (27.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x))))
✓	0.0b	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))
✓	0.0b	(exp.f64 (exp.f64 x))
✓	0.7b	(*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))

series515.0ms (10.7%)

Counts

4 → 24

Calls

4 calls:

279.0ms	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))
230.0ms	(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))

rewrite32.0ms (0.7%)

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:

20.0ms	(*.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))

simplify82.0ms (1.7%)

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

prune184.0ms (3.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

Counts

130 → 2

Alt Table

Status	Error	Program
▶	18.4b	(sqrt.f64 (+.f64 2 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))))
✓	0.0b	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))

Compiler

Compiled 1756 to 1234 computations (29.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 2 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))))
✓	0.0b	(fma.f64 1/6 (pow.f64 x 3) x)
✓	9.3b	(fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))

series21.0ms (0.4%)

Counts

3 → 28

Calls

3 calls:

14.0ms	(sqrt.f64 (+.f64 2 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))))
3.0ms	(fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))
3.0ms	(fma.f64 1/6 (pow.f64 x 3) x)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

3.0ms	(sqrt.f64 (+.f64 2 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))))
0.0ms	(fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))
0.0ms	(fma.f64 1/6 (pow.f64 x 3) x)

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

751×	`times-frac_binary64`
444×	`fma-neg_binary64`
254×	`distribute-rgt-in_binary64`
246×	`distribute-lft-in_binary64`
236×	`fma-def_binary64`

Counts

67 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1170
1	207	1122
2	696	1062
3	3481	1060
4	4933	1060

prune51.0ms (1.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	68	2	70

Error

Counts

70 → 2

Alt Table

Status	Error	Program
✓	18.4b	(sqrt.f64 (+.f64 2 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))))
✓	0.0b	(sqrt.f64 (log.f64 (*.f64 (exp.f64 1) (exp.f64 (exp.f64 x)))))

Compiler

Compiled 1497 to 1080 computations (27.9% saved)

regimes156.0ms (3.2%)

Accuracy

Total 0.0b remaining (10.7%)

Threshold costs 0.0b (10.7%)

Counts

56 → 1

Compiler

Compiled 1748 to 1489 computations (14.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	16	21
2	15	21

end0.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

sample2.1s (42.6%)

Algorithm

1×

intervals

Results

1.0s	2690×	body	1024	valid
336.0ms	1354×	body	512	valid
233.0ms	3035×	body	128	valid
114.0ms	277×	body	2048	valid
81.0ms	644×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 51 to 41 computations (19.6% saved)

Details

analyze1.2s (25.7%)

sample128.0ms (2.7%)

simplify44.0ms (0.9%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify87.0ms (1.8%)

prune127.0ms (2.6%)

localize8.0ms (0.2%)

series515.0ms (10.7%)

rewrite32.0ms (0.7%)

simplify82.0ms (1.7%)

prune184.0ms (3.8%)

localize10.0ms (0.2%)

series21.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify55.0ms (1.1%)

prune51.0ms (1.1%)

regimes156.0ms (3.2%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (42.6%)

Profiling