Details

analyze132.0ms (4.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.1s (39.3%)

Results

1.0s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify77.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
623×	`fma-def_binary64`
311×	`fma-neg_binary64`
283×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	60	21
3	159	21
4	518	17
5	1687	17
6	3597	17
7	5026	17

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 59 to 40 computations (32.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

series42.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
9.0ms	(hypot.f64 a b)

rewrite74.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`prod-diff_binary64`
447×	`log-prod_binary64`
243×	`fma-def_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`

Counts

2 → 80

Calls

2 calls:

70.0ms	(hypot.f64 a b)
70.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	212	21
2	2417	21
3	5319	21

simplify65.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-neg_binary64`
562×	`cancel-sign-sub-inv_binary64`
297×	`neg-mul-1_binary64`
289×	`neg-sub0_binary64`
280×	`fma-def_binary64`

Counts

128 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	1045
1	211	1007
2	639	925
3	2618	925
4	4315	925
5	5122	925

prune85.0ms (3.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	124	2	126

Error

Counts

126 → 2

Alt Table

Status	Error	Program
▶	57.1b	(pow.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3) 1/3)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2538 to 1659 computations (34.6% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a b)
	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.1b	(pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3)
✓	17.5b	(pow.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3) 1/3)

series445.0ms (16.2%)

Counts

2 → 48

Calls

2 calls:

395.0ms	(pow.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3) 1/3)
50.0ms	(pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3)

rewrite114.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`prod-diff_binary64`
483×	`fma-udef_binary64`
275×	`fma-def_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`

Counts

2 → 91

Calls

2 calls:

112.0ms	(pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3)
112.0ms	(pow.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3) 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	284	37
2	3002	37
3	4824	37
4	4737	37
5	4864	37

simplify112.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

669×	`times-frac_binary64`
534×	`associate-/l*_binary64`
291×	`+-commutative_binary64`
264×	`fma-def_binary64`
263×	`associate-+r+_binary64`

Counts

139 → 143

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	764	7397
1	2594	7339
2	5126	7339

prune338.0ms (12.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	268	2	270

Error

Counts

270 → 2

Alt Table

Status	Error	Program
✓	57.1b	(pow.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3) 1/3)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 15050 to 11184 computations (25.7% saved)

regimes108.0ms (3.9%)

Accuracy

Total 0.0b remaining (1.6%)

Threshold costs 0.0b (1.6%)

Counts

16 → 1

Compiler

Compiled 1439 to 1082 computations (24.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17
2	12	17

end55.0ms (2%)

Compiler: Compiled 60 to 44 computations (26.7% saved)

Details

analyze132.0ms (4.8%)

sample1.1s (39.3%)

simplify77.0ms (2.8%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series42.0ms (1.5%)

rewrite74.0ms (2.7%)

simplify65.0ms (2.4%)

prune85.0ms (3.1%)

localize10.0ms (0.4%)

series445.0ms (16.2%)

rewrite114.0ms (4.1%)

simplify112.0ms (4.1%)

prune338.0ms (12.3%)

regimes108.0ms (3.9%)

simplify2.0ms (0.1%)

end55.0ms (2%)

Profiling