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 (44.9%)

Results

1.1s	2156×	body	2048	valid
461.0ms	4333×	body	128	valid
372.0ms	991×	body	1024	valid
151.0ms	529×	body	512	valid
49.0ms	247×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify8.0ms (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 (0.1%)

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

16.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.1b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	1.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series13.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

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

rewrite94.0ms (2%)

Algorithm

2×	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

4 → 143

Calls

4 calls:

91.0ms	(/.f64 1/2 (hypot.f64 1 x))
91.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
91.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
91.0ms	(-.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	44
1	200	44
2	2408	44
3	4933	44
4	5094	44
0	0	0
1	0	0

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-neg_binary64`
538×	`sub-neg_binary64`
430×	`fma-def_binary64`
239×	`associate--l+_binary64`
232×	`cancel-sign-sub-inv_binary64`

Counts

191 → 223

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	934
1	399	916
2	1174	892
3	3690	892
4	4978	892

prune178.0ms (3.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	220	3	223
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	221	3	224

Error

0.0b

Counts

224 → 3

Alt Table

Status	Error	Program
	16.4b	(pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
	33.5b	(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 8) -1843/32768 (.f64 (pow.f64 x 4) -11/128))))
▶	15.6b	(*.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 4147 to 3682 computations (11.2% 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 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	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)))))))
✓	1.3b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series30.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

17.0ms

(*.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)))))))

10.0ms

(/.f64 1 (+.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)))

rewrite71.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

492×	`prod-diff_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`
127×	`log1p-expm1-u_binary64`

Counts

3 → 119

Calls

3 calls:

68.0ms

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

68.0ms

(*.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)))))))

68.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	55
1	273	43
2	3414	43
3	4966	43
0	0	0
1	0	0

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

866×	`fma-def_binary64`
507×	`distribute-rgt-in_binary64`
254×	`times-frac_binary64`
248×	`fma-neg_binary64`
204×	`cancel-sign-sub-inv_binary64`

Counts

155 → 182

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	2084
1	703	1778
2	2422	1721
3	4929	1721
4	4985	1721

prune229.0ms (4.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	234	3	237

Error

Counts

237 → 3

Alt Table

Status	Error	Program
▶	16.4b	(pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
	33.5b	(fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 (pow.f64 x 8) -1843/32768 (.f64 (pow.f64 x 4) -11/128))))
✓	15.6b	(*.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 7872 to 7039 computations (10.6% saved)

localize8.0ms (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	(sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	0.0b	(pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
	1.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series27.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

15.0ms	(pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
11.0ms	(sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

rewrite61.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

461×	`log-prod_binary64`
387×	`prod-diff_binary64`
224×	`fma-def_binary64`
195×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`

Counts

2 → 75

Calls

2 calls:

59.0ms	(sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
59.0ms	(pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	245	32
2	2735	32
3	5327	32
0	0	0
1	0	0

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary64`
660×	`associate-/r*_binary64`
610×	`times-frac_binary64`
288×	`cancel-sign-sub-inv_binary64`
241×	`associate-/l*_binary64`

Counts

99 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	1246
1	472	1071
2	1694	991
3	5324	991

prune179.0ms (3.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	231	3	234

Error

Counts

234 → 3

Alt Table

Status	Error	Program
✓	16.4b	(pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
▶	33.5b	(fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 (pow.f64 x 8) -1843/32768 (.f64 (pow.f64 x 4) -11/128))))
✓	15.6b	(*.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 5730 to 5208 computations (9.1% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 8) -1843/32768 (*.f64 (pow.f64 x 4) -11/128))
✓	0.1b	(*.f64 (pow.f64 x 4) -11/128)
✓	27.8b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 (pow.f64 x 8) -1843/32768 (*.f64 (pow.f64 x 4) -11/128)))

series11.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(fma.f64 (pow.f64 x 8) -1843/32768 (*.f64 (pow.f64 x 4) -11/128))
4.0ms	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 (pow.f64 x 8) -1843/32768 (*.f64 (pow.f64 x 4) -11/128)))
3.0ms	(*.f64 (pow.f64 x 4) -11/128)

rewrite88.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

476×	`log-prod_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
189×	`pow3_binary64`
184×	`log-pow_binary64`

Counts

3 → 78

Calls

3 calls:

86.0ms	(fma.f64 (pow.f64 x 8) -1843/32768 (*.f64 (pow.f64 x 4) -11/128))
86.0ms	(*.f64 (pow.f64 x 4) -11/128)
86.0ms	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 (pow.f64 x 8) -1843/32768 (*.f64 (pow.f64 x 4) -11/128)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	298	42
2	2750	42
3	5000	42
4	4795	42
0	0	0
1	0	0

simplify81.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-neg_binary64`
591×	`cancel-sign-sub-inv_binary64`
517×	`unswap-sqr_binary64`
369×	`distribute-rgt-neg-in_binary64`
358×	`*-commutative_binary64`

Counts

114 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	456
1	58	450
2	126	420
3	352	420
4	1231	420
5	2769	420
6	4572	420
7	4911	420

prune81.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	89	3	92

Error

Counts

92 → 3

Alt Table

Status	Error	Program
✓	16.4b	(pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) 2)
✓	33.5b	(fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 (pow.f64 x 8) -1843/32768 (.f64 (pow.f64 x 4) -11/128))))
✓	15.6b	(*.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 2329 to 1833 computations (21.3% saved)

regimes1.2s (24.3%)

Accuracy

Total 0.0b remaining (39.2%)

Threshold costs 0.0b (39.2%)

Counts

154 → 2

Compiler

Compiled 17203 to 15409 computations (10.4% saved)

bsearch4.0ms (0.1%)

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	31	67
1	39	67
2	46	67
3	48	67
4	49	67
5	47	67

end89.0ms (1.9%)

Compiler: Compiled 150 to 126 computations (16% saved)

Details

analyze1.0ms (0%)

sample2.1s (44.9%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series13.0ms (0.3%)

rewrite94.0ms (2%)

simplify56.0ms (1.2%)

prune178.0ms (3.7%)

localize9.0ms (0.2%)

series30.0ms (0.6%)

rewrite71.0ms (1.5%)

simplify77.0ms (1.6%)

prune229.0ms (4.8%)

localize8.0ms (0.2%)

series27.0ms (0.6%)

rewrite61.0ms (1.3%)

simplify46.0ms (1%)

prune179.0ms (3.8%)

localize11.0ms (0.2%)

series11.0ms (0.2%)

rewrite88.0ms (1.9%)

simplify81.0ms (1.7%)

prune81.0ms (1.7%)

regimes1.2s (24.3%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end89.0ms (1.9%)

Profiling