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 (42.7%)

Results

1.0s	2147×	body	2048	valid
445.0ms	4258×	body	128	valid
411.0ms	1089×	body	1024	valid
140.0ms	503×	body	512	valid
48.0ms	259×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify7.0ms (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`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	29	15
3	37	15
4	44	15
5	54	15
6	65	15
7	77	15
8	80	15

Stop Event

1×

saturated

Counts

1 → 2

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

17.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize7.0ms (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))
✓	2.5b	(-.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)))))
3.0ms	(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)))

rewrite60.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	44
1	202	44
2	2576	44

Stop Event

1×	node limit

Counts

4 → 139

Calls

4 calls:

55.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
55.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
55.0ms	(/.f64 1/2 (hypot.f64 1 x))
55.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify47.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-neg_binary64`
422×	`fma-def_binary64`
239×	`associate--l+_binary64`
232×	`cancel-sign-sub-inv_binary64`
188×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	934
1	400	916
2	1253	892
3	4392	892

Stop Event

1×	node limit

Counts

187 → 219

prune187.0ms (3.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	217	2	219
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	2	220

Error

0.0b

Counts

220 → 2

Alt Table

Status	Error	Program
	29.2b	(fma.f64 1/8 (.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
▶	16.8b	(/.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))))))

Status

Error

Program

29.2b

(fma.f64 1/8 (*.f64 x x) (fma.f64 69/1024 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))))

▶

16.8b

(/.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))))))

Compiler

Compiled 4077 to 3612 computations (11.4% saved)

localize9.0ms (0.2%)

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 (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 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	2.0b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series24.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

17.0ms

(/.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))))))

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)))

rewrite128.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`prod-diff_binary64`
219×	`log1p-udef_binary64`
217×	`egg-rr`
124×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	255	40
2	3616	40

Stop Event

1×	node limit

Counts

3 → 217

Calls

3 calls:

119.0ms

(/.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))))))

119.0ms

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

119.0ms

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

simplify47.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-def_binary64`
455×	`distribute-rgt-in_binary64`
222×	`cancel-sign-sub-inv_binary64`
178×	`associate-/r*_binary64`
163×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	1608
1	736	1428
2	2762	1385

Stop Event

1×	node limit

Counts

253 → 281

prune509.0ms (10.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	371	2	373
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	372	3	375

Error

Counts

375 → 3

Alt Table

Status	Error	Program
	29.2b	(/.f64 (-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (+.f64 (.f64 3/16 (pow.f64 x 4)) (.f64 35/256 (pow.f64 x 8)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
▶	29.2b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
✓	16.8b	(/.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))))))

Compiler

Compiled 19905 to 17832 computations (10.4% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))
✓	0.1b	(*.f64 (pow.f64 x 8) -1843/32768)
✓	23.8b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))

series11.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms

(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))

4.0ms

(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))))

3.0ms

(*.f64 (pow.f64 x 8) -1843/32768)

rewrite53.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

271×	`expm1-udef_binary64`
271×	`log1p-udef_binary64`
221×	`prod-diff_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	361	49
2	3750	49

Stop Event

1×	node limit

Counts

3 → 60

Calls

3 calls:

52.0ms

(fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))

52.0ms

(*.f64 (pow.f64 x 8) -1843/32768)

52.0ms

(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (*.f64 (pow.f64 x 8) -1843/32768))))

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

622×	`associate-l_binary64`
475×	`fma-def_binary64`
417×	`associate-r_binary64`
413×	`unswap-sqr_binary64`
315×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	477
1	79	469
2	197	441
3	702	441
4	4339	441

Stop Event

1×	node limit

Counts

96 → 78

prune75.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	78	3	81

Error

Counts

81 → 3

Alt Table

Status	Error	Program
▶	29.2b	(/.f64 (-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (+.f64 (.f64 3/16 (pow.f64 x 4)) (.f64 35/256 (pow.f64 x 8)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	29.2b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
✓	16.8b	(/.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))))))

Compiler

Compiled 1942 to 1521 computations (21.7% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 5/32 (pow.f64 x 6))
✓	0.0b	(*.f64 35/256 (pow.f64 x 8))
✓	0.1b	(*.f64 3/16 (pow.f64 x 4))
✓	23.8b	(-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (+.f64 (.f64 3/16 (pow.f64 x 4)) (.f64 35/256 (pow.f64 x 8))))

series14.0ms (0.3%)

Counts

4 → 9

Calls

4 calls:

4.0ms	(*.f64 5/32 (pow.f64 x 6))
4.0ms	(-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (+.f64 (.f64 3/16 (pow.f64 x 4)) (.f64 35/256 (pow.f64 x 8))))
3.0ms	(*.f64 35/256 (pow.f64 x 8))
3.0ms	(*.f64 3/16 (pow.f64 x 4))

rewrite41.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

214×	`log1p-expm1-u_binary64`
214×	`expm1-log1p-u_binary64`
210×	`add-cbrt-cube_binary64`
205×	`add-sqr-sqrt_binary64`
201×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	51
1	471	51

Stop Event

1×	node limit

Counts

4 → 82

Calls

4 calls:

39.0ms	(*.f64 5/32 (pow.f64 x 6))
39.0ms	(*.f64 35/256 (pow.f64 x 8))
39.0ms	(*.f64 3/16 (pow.f64 x 4))
39.0ms	(-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (+.f64 (.f64 3/16 (pow.f64 x 4)) (.f64 35/256 (pow.f64 x 8))))

simplify26.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-neg-in_binary64`
551×	`associate-l_binary64`
413×	`unswap-sqr_binary64`
405×	`associate-r_binary64`
279×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	138
1	68	130
2	161	126
3	562	126
4	3466	126

Stop Event

1×	node limit

Counts

91 → 93

prune122.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	93	3	96

Error

Counts

96 → 3

Alt Table

Status	Error	Program
✓	29.2b	(/.f64 (-.f64 (+.f64 (.f64 5/32 (pow.f64 x 6)) (.f64 1/4 (pow.f64 x 2))) (+.f64 (.f64 3/16 (pow.f64 x 4)) (.f64 35/256 (pow.f64 x 8)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	29.2b	(fma.f64 (pow.f64 x 6) 69/1024 (fma.f64 x (.f64 x 1/8) (fma.f64 (pow.f64 x 4) -11/128 (.f64 (pow.f64 x 8) -1843/32768))))
✓	16.8b	(/.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))))))

Compiler

Compiled 4359 to 3578 computations (17.9% saved)

regimes1.2s (25.1%)

Accuracy

Total 0.0b remaining (14.7%)

Threshold costs 0.0b (14.7%)

Counts

146 → 2

Compiler

Compiled 16600 to 14754 computations (11.1% saved)

bsearch4.0ms (0.1%)

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

simplify3.0ms (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	30	64
1	38	64
2	45	64
3	47	64
4	48	64

Stop Event

1×

saturated

end138.0ms (2.8%)

Compiler: Compiled 165 to 137 computations (17% saved)

Details

analyze1.0ms (0%)

sample2.1s (42.7%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series13.0ms (0.3%)

rewrite60.0ms (1.2%)

simplify47.0ms (0.9%)

prune187.0ms (3.8%)

localize9.0ms (0.2%)

series24.0ms (0.5%)

rewrite128.0ms (2.6%)

simplify47.0ms (0.9%)

prune509.0ms (10.3%)

localize12.0ms (0.2%)

series11.0ms (0.2%)

rewrite53.0ms (1.1%)

simplify38.0ms (0.8%)

prune75.0ms (1.5%)

localize20.0ms (0.4%)

series14.0ms (0.3%)

rewrite41.0ms (0.8%)

simplify26.0ms (0.5%)

prune122.0ms (2.5%)

regimes1.2s (25.1%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end138.0ms (2.8%)

Profiling