Details

analyze21.0ms (0.3%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample62.0ms (1%)

Algorithm

1×

intervals

Results

30.0ms	67×	body	2048	valid
11.0ms	35×	body	1024	valid
10.0ms	139×	body	128	valid
3.0ms	12×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 28 to 26 computations (7.1% saved)

simplify13.0ms (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

13.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize6.0ms (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))
✓	0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite28.0ms (0.5%)

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:

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))))
4.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
2.0ms	(/.f64 1/2 (hypot.f64 1 x))

series24.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

9.0ms	(-.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)))

simplify128.0ms (2.1%)

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

prune168.0ms (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
▶	13.1b	(/.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))))))
	34.4b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
	13.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
	14.0b	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))

Compiler

Compiled 4456 to 3970 computations (10.9% saved)

localize9.0ms (0.2%)

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))
✓	0.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
37×	`times-frac_binary64`

Counts

1 → 71

Calls

1 calls:

6.0ms

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

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

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

simplify124.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-def_binary64`
384×	`associate-*l/_binary64`
374×	`fma-neg_binary64`
350×	`associate-*r/_binary64`
237×	`associate-/l*_binary64`

Counts

83 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	1994
1	516	1332
2	1253	978
3	3914	978
4	4325	978
5	4895	978
6	4565	978

prune234.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	377	0	377
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	377	4	381

Error

0.0b

Counts

381 → 4

Alt Table

Status	Error	Program
✓	13.1b	(/.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))))))
	34.4b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
▶	13.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
	14.0b	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))

Compiler

Compiled 7981 to 7068 computations (11.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`sqrt-prod_binary64`
10×	`times-frac_binary64`

Counts

3 → 68

Calls

3 calls:

3.0ms	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
2.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
0.0ms	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))

series70.0ms (1.2%)

Counts

3 → 16

Calls

3 calls:

30.0ms	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
30.0ms	(hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
10.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

simplify101.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

461×	`sub-neg_binary64`
420×	`fma-def_binary64`
302×	`associate-l_binary64`
280×	`associate-r_binary64`
205×	`associate-+l+_binary64`

Counts

84 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	2158
1	388	1926
2	1185	1723
3	4577	1723
4	4967	1723

prune122.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	353	4	357

Error

0.0b

Counts

357 → 4

Alt Table

Status	Error	Program
✓	13.1b	(/.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))))))
	34.4b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
✓	13.7b	(-.f64 1 (hypot.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
▶	14.0b	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))

Compiler

Compiled 3753 to 3403 computations (9.3% 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	(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)
✓	0.5b	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
	0.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
26×	`cbrt-prod_binary64`
20×	`cube-prod_binary64`
20×	`unpow-prod-down_binary64`

Counts

2 → 80

Calls

2 calls:

9.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))
8.0ms	(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)

series25.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

17.0ms	(pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)
8.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))

simplify130.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
348×	`distribute-rgt-in_binary64`
256×	`cancel-sign-sub-inv_binary64`
232×	`sub-neg_binary64`
229×	`unswap-sqr_binary64`

Counts

104 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	3182
1	677	2883
2	2438	2855
3	4883	2855
4	4930	2855

prune211.0ms (3.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	761	1	762
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	763	3	766

Error

0.0b

Counts

766 → 3

Alt Table

Status	Error	Program
✓	13.1b	(/.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))))))
	34.4b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
	14.4b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))) (cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3)))) (cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))) 3))))

Compiler

Compiled 6362 to 5751 computations (9.6% saved)

regimes1.4s (23.7%)

Accuracy

Total 0.1b remaining (53.7%)

Threshold costs 0.1b (53.7%)

Compiler

Compiled 12871 to 11806 computations (8.3% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-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	22	50
1	29	50
2	36	50
3	38	50
4	39	50
5	37	50

end2.0ms (0%)

Compiler: Compiled 35 to 29 computations (17.1% saved)

sample3.0s (50.3%)

Algorithm

1×

intervals

Results

1.4s	2149×	body	2048	valid
476.0ms	1032×	body	1024	valid
437.0ms	4110×	body	128	valid
161.0ms	465×	body	512	valid
49.0ms	244×	body	256	valid

Compiler

Compiled 125 to 110 computations (12% saved)

Details

analyze21.0ms (0.3%)

sample62.0ms (1%)

simplify13.0ms (0.2%)

prune3.0ms (0%)

localize6.0ms (0.1%)

rewrite28.0ms (0.5%)

series24.0ms (0.4%)

simplify128.0ms (2.1%)

prune168.0ms (2.8%)

localize9.0ms (0.2%)

rewrite13.0ms (0.2%)

series6.0ms (0.1%)

simplify124.0ms (2.1%)

prune234.0ms (3.9%)

localize9.0ms (0.1%)

rewrite10.0ms (0.2%)

series70.0ms (1.2%)

simplify101.0ms (1.7%)

prune122.0ms (2%)

localize8.0ms (0.1%)

rewrite23.0ms (0.4%)

series25.0ms (0.4%)

simplify130.0ms (2.2%)

prune211.0ms (3.5%)

regimes1.4s (23.7%)

bsearch7.0ms (0.1%)

simplify8.0ms (0.1%)

end2.0ms (0%)

sample3.0s (50.3%)

Profiling