Details

analyze18.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample48.0ms (0.6%)

Algorithm

1×

intervals

Results

18.0ms	59×	body	2048	valid
11.0ms	143×	body	128	valid
7.0ms	30×	body	1024	valid
3.0ms	18×	body	512	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 28 to 26 computations (7.1% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	35	15
4	42	15
5	52	15
6	60	15
7	69	15
8	72	15
9	53	15

prune3.0ms (0%)

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

14.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	1.6b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
24×	`sqrt-prod_binary64`
21×	`prod-diff_binary64`

Counts

4 → 117

Calls

4 calls:

9.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
5.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
2.0ms	(/.f64 1/2 (hypot.f64 1 x))

series23.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

8.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
5.0ms	(/.f64 1/2 (hypot.f64 1 x))
4.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify129.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary64`
471×	`associate-l_binary64`
406×	`associate-r_binary64`
399×	`fma-neg_binary64`
286×	`cancel-sign-sub-inv_binary64`

Counts

165 → 258

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3449
1	643	3086
2	1772	2766
3	4772	2766
4	4875	2766

prune204.0ms (2.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	254	4	258
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	255	4	259

Error

0.0b

Counts

259 → 4

Alt Table

Status	Error	Program
▶	14.3b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	14.8b	(/.f64 (-.f64 1 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) 3)) (+.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (+.f64 3/2 (/.f64 1/2 (hypot.f64 1 x)))))
	14.8b	(log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	34.3b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))

Compiler

Compiled 4490 to 4000 computations (10.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	1.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`add-sqr-sqrt_binary64`
109×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
58×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

2 → 138

Calls

2 calls:

15.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series32.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

27.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
5.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify216.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
230×	`fma-def_binary64`
191×	`associate-r_binary64`
183×	`fma-neg_binary64`
177×	`associate-/r*_binary64`

Counts

162 → 281

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	407	7612
1	1109	5376
2	3422	5334
3	4984	5334
4	4941	5334

prune351.0ms (4.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	452	3	455
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	456	3	459

Error

Counts

459 → 3

Alt Table

Status	Error	Program
▶	14.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	34.3b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
	14.3b	(*.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 10463 to 9347 computations (10.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
	1.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64`
64×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
28×	`distribute-lft-out_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 66

Calls

1 calls:

14.0ms

(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series16.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

16.0ms

(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

simplify134.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
434×	`associate--l+_binary64`
397×	`fma-neg_binary64`
299×	`associate-/r*_binary64`
172×	`associate-+r+_binary64`

Counts

78 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	3489
1	548	3360
2	1834	3344
3	4893	3341
4	5158	3341

prune346.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	972	0	972
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	972	3	975

Error

Counts

975 → 3

Alt Table

Status	Error	Program
✓	14.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	34.3b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
▶	14.3b	(*.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 10275 to 9163 computations (10.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
	1.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune308.0ms (4.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	3140	0	3140
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	3140	3	3143

Error

Counts

3143 → 3

Alt Table

Status	Error	Program
✓	14.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	34.3b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	14.3b	(*.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 8539 to 7620 computations (10.8% saved)

regimes2.4s (32.5%)

Accuracy

Total 0.0b remaining (6.3%)

Threshold costs 0.0b (6.3%)

Compiler

Compiled 23787 to 21564 computations (9.3% saved)

bsearch71.0ms (1%)

Steps

Iters	Range		Point
9	2.0477836685004104e-7	106.18091515429026	0.002673467331980555
9	-527.769203384588	-4.240002696744291e-6	-0.002203921674884077

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	86
1	37	86
2	44	86
3	46	86
4	47	86
5	45	86

end2.0ms (0%)

Compiler: Compiled 59 to 50 computations (15.3% saved)

sample2.9s (38.9%)

Algorithm

1×

intervals

Results

1.3s	2106×	body	2048	valid
459.0ms	970×	body	1024	valid
415.0ms	4140×	body	128	valid
169.0ms	520×	body	512	valid
53.0ms	264×	body	256	valid

Compiler

Compiled 127 to 110 computations (13.4% saved)

Details

analyze18.0ms (0.2%)

sample48.0ms (0.6%)

simplify11.0ms (0.2%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite28.0ms (0.4%)

series23.0ms (0.3%)

simplify129.0ms (1.8%)

prune204.0ms (2.8%)

localize8.0ms (0.1%)

rewrite33.0ms (0.5%)

series32.0ms (0.4%)

simplify216.0ms (2.9%)

prune351.0ms (4.8%)

localize9.0ms (0.1%)

rewrite19.0ms (0.3%)

series16.0ms (0.2%)

simplify134.0ms (1.8%)

prune346.0ms (4.7%)

localize9.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify65.0ms (0.9%)

prune308.0ms (4.2%)

regimes2.4s (32.5%)

bsearch71.0ms (1%)

simplify8.0ms (0.1%)

end2.0ms (0%)

sample2.9s (38.9%)

Profiling