Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample61.0ms (2.1%)

Algorithm

1×

intervals

Results

20.0ms	61×	body	2048	valid
10.0ms	46×	body	1024	valid
6.0ms	121×	body	128	valid
3.0ms	19×	body	512	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 28 to 26 computations (7.1% saved)

simplify9.0ms (0.3%)

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 (0.1%)

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

19.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.9b	(-.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 (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(hypot.f64 1 x)
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	1.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series18.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
4.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
4.0ms	(hypot.f64 1 x)
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

rewrite20.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
24×	`sqrt-prod_binary64`
21×	`prod-diff_binary64`

Counts

4 → 110

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

simplify133.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
463×	`fma-neg_binary64`
398×	`times-frac_binary64`
372×	`associate-l_binary64`
332×	`associate-r_binary64`

Counts

158 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	3244
1	653	2896
2	1804	2575
3	4560	2539
4	4860	2539
5	5266	2539

prune154.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	194	3	197

Error

0.0b

Counts

197 → 3

Alt Table

Status	Error	Program
	29.4b	(*.f64 1/8 (pow.f64 x 2))
▶	19.4b	(/.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))))))
✓	19.9b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 4396 to 3906 computations (11.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(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))))))
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	1.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series27.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

24.0ms	(/.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))))))
3.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite36.0ms (1.2%)

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:

16.0ms	(/.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)))

simplify171.0ms (5.8%)

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 → 186

Iterations

Useful iterations: 2 (0.0ms)

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

prune306.0ms (10.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	294	1	295
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	295	3	298

Error

Counts

298 → 3

Alt Table

Status	Error	Program
✓	19.4b	(/.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))))))
✓	19.9b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
▶	30.1b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))

Compiler

Compiled 10520 to 9368 computations (11% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
✓	0.3b	(*.f64 (pow.f64 x 4) -11/128)

series9.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))
3.0ms	(*.f64 (pow.f64 x 4) -11/128)

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-l_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 (pow.f64 x 4) -11/128)
0.0ms	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))

simplify72.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

461×	`unsub-neg_binary64`
423×	`*-commutative_binary64`
388×	`distribute-rgt-neg-in_binary64`
343×	`exp-prod_binary64`
304×	`log-prod_binary64`

Counts

61 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	70	724
1	123	683
2	317	665
3	1110	665
4	2628	659
5	4199	659
6	5084	659

prune38.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	63	3	66

Error

Counts

66 → 3

Alt Table

Status	Error	Program
✓	19.4b	(/.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))))))
✓	19.9b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	30.1b	(fma.f64 x (.f64 x 1/8) (.f64 (pow.f64 x 4) -11/128))

Compiler

Compiled 1025 to 749 computations (26.9% saved)

regimes305.0ms (10.4%)

Accuracy

Total 0.2b remaining (79.3%)

Threshold costs 0.2b (79.3%)

Counts

27 → 2

Compiler

Compiled 6022 to 5442 computations (9.6% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-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	21	50
1	29	50
2	36	50
3	38	50
4	39	50
5	37	50

end1.0ms (0%)

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

sample1.5s (52.3%)

Algorithm

1×

intervals

Results

666.0ms	2099×	body	2048	valid
260.0ms	1017×	body	1024	valid
224.0ms	4110×	body	128	valid
91.0ms	534×	body	512	valid
26.0ms	240×	body	256	valid

Compiler

Compiled 91 to 78 computations (14.3% saved)

Details

analyze4.0ms (0.1%)

sample61.0ms (2.1%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series18.0ms (0.6%)

rewrite20.0ms (0.7%)

simplify133.0ms (4.5%)

prune154.0ms (5.3%)

localize9.0ms (0.3%)

series27.0ms (0.9%)

rewrite36.0ms (1.2%)

simplify171.0ms (5.8%)

prune306.0ms (10.5%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify72.0ms (2.5%)

prune38.0ms (1.3%)

regimes305.0ms (10.4%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.5s (52.3%)

Profiling