Details

analyze1.7s (30.6%)

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)

sample100.0ms (1.8%)

Algorithm

1×

intervals

Results

47.0ms	69×	body	1024	valid
17.0ms	46×	body	512	valid
11.0ms	111×	body	128	valid
7.0ms	11×	body	2048	valid
4.0ms	19×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify60.0ms (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

prune5.0ms (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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 30 to 24 computations (20% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	0.2b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series12.0ms (0.2%)

Counts

2 → 8

Calls

2 calls:

9.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
3.0ms	(+.f64 1 (exp.f64 x))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

5.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
3.0ms	(+.f64 1 (exp.f64 x))

simplify85.0ms (1.6%)

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

prune48.0ms (0.9%)

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

0.2b

Counts

56 → 2

Alt Table

Status	Error	Program
▶	0.3b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
	23.1b	(-.f64 (+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/48))

Status

Error

Program

▶

0.3b

(hypot.f64 1 (sqrt.f64 (exp.f64 x)))

23.1b

(-.f64 (+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))) (*.f64 (*.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/48))

Compiler

Compiled 743 to 550 computations (26% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
✓	0.3b	(sqrt.f64 (exp.f64 x))

series11.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

8.0ms	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
3.0ms	(sqrt.f64 (exp.f64 x))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

2.0ms	(sqrt.f64 (exp.f64 x))
0.0ms	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))

simplify47.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

795×	`times-frac_binary64`
699×	`associate-/l*_binary64`
289×	`fma-neg_binary64`
186×	`associate-/r/_binary64`
169×	`fma-def_binary64`

Counts

44 → 51

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	503
1	173	470
2	482	443
3	1872	430
4	5251	430

prune131.0ms (2.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	51	2	53

Error

0.0b

Counts

53 → 2

Alt Table

Status	Error	Program
✓	0.3b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
▶	0.0b	(hypot.f64 1 (pow.f64 (exp.f64 1) (/.f64 x 2)))

Compiler

Compiled 615 to 429 computations (30.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 (pow.f64 (exp.f64 1) (/.f64 x 2)))
✓	0.1b	(pow.f64 (exp.f64 1) (/.f64 x 2))

series28.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

24.0ms	(hypot.f64 1 (pow.f64 (exp.f64 1) (/.f64 x 2)))
4.0ms	(pow.f64 (exp.f64 1) (/.f64 x 2))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow-unpow_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`

Counts

2 → 42

Calls

2 calls:

6.0ms	(pow.f64 (exp.f64 1) (/.f64 x 2))
1.0ms	(hypot.f64 1 (pow.f64 (exp.f64 1) (/.f64 x 2)))

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
176×	`fma-def_binary64`
172×	`distribute-neg-frac_binary64`
168×	`distribute-rgt-neg-in_binary64`
163×	`associate-/l*_binary64`

Counts

66 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	858
1	281	777
2	759	721
3	2693	653
4	4787	653
5	5204	653

prune186.0ms (3.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	90	2	92

Error

Counts

92 → 2

Alt Table

Status	Error	Program
✓	0.3b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
▶	0.0b	(hypot.f64 1 (exp.f64 (*.f64 1/2 x)))

Compiler

Compiled 1254 to 1010 computations (19.5% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 (exp.f64 (*.f64 1/2 x)))

series19.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

19.0ms

(hypot.f64 1 (exp.f64 (*.f64 1/2 x)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(hypot.f64 1 (exp.f64 (*.f64 1/2 x)))

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

796×	`associate-/l*_binary64`
405×	`associate-/r*_binary64`
268×	`fma-neg_binary64`
182×	`associate-/r/_binary64`
153×	`distribute-neg-frac_binary64`

Counts

22 → 26

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	400
1	135	326
2	411	281
3	1699	269
4	4944	269

prune31.0ms (0.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	26	2	28

Error

Counts

28 → 2

Alt Table

Status	Error	Program
✓	0.3b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
✓	0.0b	(hypot.f64 1 (exp.f64 (*.f64 1/2 x)))

Compiler

Compiled 379 to 320 computations (15.6% saved)

regimes230.0ms (4.2%)

Accuracy

Total 0.0b remaining (22.9%)

Threshold costs 0.0b (22.9%)

Counts

37 → 1

Compiler

Compiled 1743 to 1412 computations (19% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	9	9

end1.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

sample2.6s (47.6%)

Algorithm

1×

intervals

Results

1.4s	2685×	body	1024	valid
381.0ms	1354×	body	512	valid
248.0ms	3080×	body	128	valid
127.0ms	243×	body	2048	valid
99.0ms	638×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 35 to 30 computations (14.3% saved)

Details

analyze1.7s (30.6%)

sample100.0ms (1.8%)

simplify60.0ms (1.1%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series12.0ms (0.2%)

rewrite10.0ms (0.2%)

simplify85.0ms (1.6%)

prune48.0ms (0.9%)

localize6.0ms (0.1%)

series11.0ms (0.2%)

rewrite3.0ms (0.1%)

simplify47.0ms (0.9%)

prune131.0ms (2.4%)

localize10.0ms (0.2%)

series28.0ms (0.5%)

rewrite11.0ms (0.2%)

simplify85.0ms (1.5%)

prune186.0ms (3.4%)

localize8.0ms (0.1%)

series19.0ms (0.3%)

rewrite1.0ms (0%)

simplify58.0ms (1.1%)

prune31.0ms (0.6%)

regimes230.0ms (4.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.6s (47.6%)

Profiling