Details

analyze1.7s (24.8%)

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)

sample121.0ms (1.8%)

Algorithm

1×

intervals

Results

73.0ms	100×	body	1024	valid
14.0ms	36×	body	512	valid
10.0ms	92×	body	128	valid
7.0ms	9×	body	2048	valid
5.0ms	19×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify57.0ms (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

prune8.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	42.5b	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

Compiler

Compiled 56 to 46 computations (17.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite14.0ms (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:

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

series15.0ms (0.2%)

Counts

2 → 8

Calls

2 calls:

13.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

simplify214.0ms (3.1%)

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 → 63

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

prune92.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	3	65

Error

0.2b

Counts

65 → 3

Alt Table

Status	Error	Program
	0.3b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
▶	0.3b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
	20.2b	(-.f64 (+.f64 (.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))

Compiler

Compiled 811 to 610 computations (24.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (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:

3.0ms	(sqrt.f64 (exp.f64 x))
1.0ms	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))

series61.0ms (0.9%)

Counts

2 → 16

Calls

2 calls:

41.0ms	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
19.0ms	(sqrt.f64 (exp.f64 x))

simplify75.0ms (1.1%)

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 → 62

Iterations

Useful iterations: 3 (0.0ms)

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

prune72.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	62	3	65

Error

0.0b

Counts

65 → 3

Alt Table

Status	Error	Program
	0.3b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
✓	0.3b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
▶	0.1b	(hypot.f64 1 (pow.f64 (exp.f64 1) (/.f64 x 2)))

Compiler

Compiled 637 to 445 computations (30.1% saved)

localize108.0ms (1.6%)

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))

rewrite10.0ms (0.1%)

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)))

series35.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

32.0ms	(hypot.f64 1 (pow.f64 (exp.f64 1) (/.f64 x 2)))
3.0ms	(pow.f64 (exp.f64 1) (/.f64 x 2))

simplify158.0ms (2.3%)

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 → 126

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

prune127.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	126	3	129

Error

Counts

129 → 3

Alt Table

Status	Error	Program
	0.3b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
✓	0.3b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
▶	0.0b	(hypot.f64 1 (exp.f64 (*.f64 1/2 x)))

Compiler

Compiled 1276 to 1026 computations (19.6% 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)))

rewrite2.0ms (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)))

series30.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

30.0ms

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

simplify67.0ms (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 → 41

Iterations

Useful iterations: 3 (0.0ms)

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

prune75.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	41	3	44

Error

Counts

44 → 3

Alt Table

Status	Error	Program
	0.3b	(sqrt.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x))))
✓	0.3b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
✓	0.0b	(hypot.f64 1 (exp.f64 (*.f64 1/2 x)))

Compiler

Compiled 390 to 328 computations (15.9% saved)

regimes128.0ms (1.9%)

Accuracy

Total 0.0b remaining (54%)

Threshold costs 0.0b (54%)

Compiler

Compiled 942 to 800 computations (15.1% saved)

simplify6.0ms (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)

sample3.7s (53.4%)

Algorithm

1×

intervals

Results

1.8s	2628×	body	1024	valid
537.0ms	1368×	body	512	valid
426.0ms	3101×	body	128	valid
213.0ms	270×	body	2048	valid
158.0ms	633×	body	256	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 46 to 38 computations (17.4% saved)

Details

analyze1.7s (24.8%)

sample121.0ms (1.8%)

simplify57.0ms (0.8%)

prune8.0ms (0.1%)

localize7.0ms (0.1%)

rewrite14.0ms (0.2%)

series15.0ms (0.2%)

simplify214.0ms (3.1%)

prune92.0ms (1.3%)

localize7.0ms (0.1%)

rewrite5.0ms (0.1%)

series61.0ms (0.9%)

simplify75.0ms (1.1%)

prune72.0ms (1%)

localize108.0ms (1.6%)

rewrite10.0ms (0.1%)

series35.0ms (0.5%)

simplify158.0ms (2.3%)

prune127.0ms (1.8%)

localize8.0ms (0.1%)

rewrite2.0ms (0%)

series30.0ms (0.4%)

simplify67.0ms (1%)

prune75.0ms (1.1%)

regimes128.0ms (1.9%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample3.7s (53.4%)

Profiling