Details

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.1s (27.7%)

Results

1.0s	2101×	body	2048	valid
464.0ms	4365×	body	128	valid
396.0ms	1020×	body	1024	valid
149.0ms	515×	body	512	valid
48.0ms	255×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify8.0ms (0.1%)

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

13.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.5b	(-.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	2.1b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series13.0ms (0.2%)

Counts

3 → 36

Calls

3 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))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

rewrite88.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

466×	`prod-diff_binary64`
406×	`log-prod_binary64`
205×	`fma-def_binary64`
170×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`

Counts

3 → 100

Calls

3 calls:

86.0ms	(/.f64 1/2 (hypot.f64 1 x))
86.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
86.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	200	34
2	2408	34
3	4933	34
4	5094	34

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

717×	`fma-neg_binary64`
480×	`sub-neg_binary64`
479×	`times-frac_binary64`
353×	`fma-def_binary64`
210×	`associate--l+_binary64`

Counts

136 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	784
1	354	766
2	1067	746
3	3436	746
4	4852	746
5	5215	746

prune132.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	3	163

Error

0.0b

Counts

163 → 3

Alt Table

Status	Error	Program
	34.6b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
	13.0b	(/.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))))))
▶	13.0b	(*.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 3076 to 2742 computations (10.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series26.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

18.0ms

(*.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)))))))

4.0ms

(+.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)))

rewrite77.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`prod-diff_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`
131×	`egg-rr`

Counts

3 → 131

Calls

3 calls:

75.0ms

(*.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)))))))

75.0ms

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

75.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	52
1	273	40
2	3414	40
3	4966	40

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-def_binary64`
455×	`distribute-rgt-in_binary64`
407×	`distribute-lft-in_binary64`
222×	`cancel-sign-sub-inv_binary64`
178×	`associate-/r*_binary64`

Counts

167 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	1608
1	664	1428
2	2355	1385
3	5162	1385

prune321.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	247	3	250

Error

0.0b

Counts

250 → 3

Alt Table

Status	Error	Program
	34.6b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
▶	13.0b	(.f64 (.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x)))) (/.f64 1 (+.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)))))))
✓	13.0b	(*.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 7783 to 6937 computations (10.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (.f64 x x)))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	0.0b	(/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.6b	(/.f64 1/4 (+.f64 1 (*.f64 x x)))
✓	1.5b	(-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x))))

series11.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (.f64 x x)))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
3.0ms	(-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x))))
3.0ms	(/.f64 1/4 (+.f64 1 (*.f64 x x)))
2.0ms	(/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

rewrite79.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

443×	`prod-diff_binary64`
260×	`log1p-udef_binary64`
154×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`

Counts

4 → 141

Calls

4 calls:

76.0ms	(.f64 (-.f64 1/4 (/.f64 1/4 (+.f64 1 (.f64 x x)))) (/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
76.0ms	(/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
76.0ms	(/.f64 1/4 (+.f64 1 (*.f64 x x)))
76.0ms	(-.f64 1/4 (/.f64 1/4 (+.f64 1 (*.f64 x x))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	61
1	324	42
2	3904	42
3	5098	42

simplify109.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

863×	`fma-neg_binary64`
435×	`fma-def_binary64`
368×	`times-frac_binary64`
324×	`sub-neg_binary64`
225×	`distribute-rgt-neg-in_binary64`

Counts

189 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	96	729
1	327	715
2	894	695
3	2650	695
4	4851	695
5	4972	695
6	4999	695
7	4931	695

prune312.0ms (4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	209	3	212

Error

Counts

212 → 3

Alt Table

Status	Error	Program
▶	13.0b	(.f64 (.f64 (/.f64 (-.f64 1/16 (*.f64 (/.f64 -1/4 (fma.f64 x x 1)) (/.f64 -1/4 (fma.f64 x x 1)))) (-.f64 1/4 (/.f64 -1/4 (fma.f64 x x 1)))) (/.f64 1 (+.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)))))))
	34.6b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
✓	13.0b	(*.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 7543 to 6501 computations (13.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	0.1b	(*.f64 (/.f64 -1/4 (fma.f64 x x 1)) (/.f64 -1/4 (fma.f64 x x 1)))
✓	0.6b	(/.f64 -1/4 (fma.f64 x x 1))
✓	1.5b	(-.f64 1/16 (*.f64 (/.f64 -1/4 (fma.f64 x x 1)) (/.f64 -1/4 (fma.f64 x x 1))))

series10.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(/.f64 -1/4 (fma.f64 x x 1))
3.0ms	(*.f64 (/.f64 -1/4 (fma.f64 x x 1)) (/.f64 -1/4 (fma.f64 x x 1)))
3.0ms	(-.f64 1/16 (*.f64 (/.f64 -1/4 (fma.f64 x x 1)) (/.f64 -1/4 (fma.f64 x x 1))))

rewrite52.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

851×	`log1p-expm1-u_binary64`
851×	`expm1-log1p-u_binary64`
104×	`egg-rr`
92×	`add-sqr-sqrt_binary64`
90×	`add-cbrt-cube_binary64`

Counts

3 → 104

Calls

3 calls:

50.0ms	(*.f64 (/.f64 -1/4 (fma.f64 x x 1)) (/.f64 -1/4 (fma.f64 x x 1)))
50.0ms	(/.f64 -1/4 (fma.f64 x x 1))
50.0ms	(-.f64 1/16 (*.f64 (/.f64 -1/4 (fma.f64 x x 1)) (/.f64 -1/4 (fma.f64 x x 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	200	33
2	2185	33
3	5184	33

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Rules

578×	`cancel-sign-sub-inv_binary64`
526×	`associate-/r*_binary64`
491×	`fma-neg_binary64`
353×	`sub-neg_binary64`
259×	`div-sub_binary64`

Counts

140 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	68	621
1	224	615
2	610	603
3	1702	603
4	4394	603
5	4780	603
6	5049	603

prune484.0ms (6.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

298 → 3

Alt Table

Status	Error	Program
✓	13.0b	(.f64 (.f64 (/.f64 (-.f64 1/16 (*.f64 (/.f64 -1/4 (fma.f64 x x 1)) (/.f64 -1/4 (fma.f64 x x 1)))) (-.f64 1/4 (/.f64 -1/4 (fma.f64 x x 1)))) (/.f64 1 (+.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)))))))
	34.6b	(fma.f64 (pow.f64 x 4) -11/128 (.f64 1/8 (.f64 x x)))
✓	13.0b	(*.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 14974 to 12567 computations (16.1% saved)

regimes3.5s (44.8%)

Accuracy

Total 0.2b remaining (78%)

Threshold costs 0.2b (78%)

Counts

250 → 2

Compiler

Compiled 53891 to 47598 computations (11.7% saved)

bsearch11.0ms (0.1%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	87
1	45	87
2	54	87
3	58	87
4	60	87
5	58	87

end122.0ms (1.6%)

Compiler: Compiled 200 to 167 computations (16.5% saved)

Details

analyze1.0ms (0%)

sample2.1s (27.7%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series13.0ms (0.2%)

rewrite88.0ms (1.1%)

simplify66.0ms (0.9%)

prune132.0ms (1.7%)

localize9.0ms (0.1%)

series26.0ms (0.3%)

rewrite77.0ms (1%)

simplify55.0ms (0.7%)

prune321.0ms (4.2%)

localize16.0ms (0.2%)

series11.0ms (0.1%)

rewrite79.0ms (1%)

simplify109.0ms (1.4%)

prune312.0ms (4%)

localize19.0ms (0.2%)

series10.0ms (0.1%)

rewrite52.0ms (0.7%)

simplify78.0ms (1%)

prune484.0ms (6.3%)

regimes3.5s (44.8%)

bsearch11.0ms (0.1%)

simplify4.0ms (0%)

end122.0ms (1.6%)

Profiling