Details

analyze141.0ms (8.6%)

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%	62.4%	12.6%	6
25%	46.8%	28.2%	7
31.2%	35.9%	32.9%	8
39%	25%	36%	9
42.9%	18.7%	38.3%	10
47.2%	12.9%	39.9%	11
49.4%	9.6%	41.1%	12
51.6%	6.5%	41.9%	13
52.7%	4.8%	42.4%	14

Compiler

Compiled 16 to 10 computations (37.5% saved)

sample840.0ms (51.4%)

Symmetry

(sort x y)

Results

782.0ms	8256×	body	128	valid
19.0ms	212×	body	128	invalid

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify8.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

33×	`fma-def_binary64`
8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	14
2	47	12
3	81	12
4	83	12

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

series12.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

6.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))
6.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))

rewrite58.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

667×	`fma-def_binary64`
292×	`fma-neg_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
172×	`egg-rr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	223	24
2	3123	20

Stop Event

1×	node limit

Counts

2 → 172

Calls

2 calls:

55.0ms	(+.f64 (.f64 x x) (.f64 (*.f64 x 2) y))
55.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

simplify78.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-def_binary64`
391×	`sqr-pow_binary64`
374×	`*-commutative_binary64`
372×	`unswap-sqr_binary64`
362×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	525
1	32	480
2	69	399
3	151	393
4	412	393
5	1498	393
6	2779	393
7	3051	393
8	3237	393
9	3481	393
10	3784	393
11	4175	393
12	4682	393

Stop Event

1×	node limit

Counts

220 → 184

prune119.0ms (7.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	183	2	185

Error

Counts

185 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x x (*.f64 y (fma.f64 x 2 y)))
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

Compiler

Compiled 3092 to 1523 computations (50.7% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (fma.f64 x 2 y))

series5.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(*.f64 y (fma.f64 x 2 y))

rewrite35.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

507×	`log1p-expm1-u_binary64`
507×	`expm1-log1p-u_binary64`
315×	`unpow-prod-down_binary64`
268×	`log-prod_binary64`
153×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	120	8
2	1374	8

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

34.0ms

(*.f64 y (fma.f64 x 2 y))

simplify65.0ms (4%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary64`
469×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
292×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	231
1	19	231
2	37	213
3	75	177
4	168	177
5	464	177
6	1534	177
7	2777	177
8	3132	177
9	3354	177
10	3576	177
11	3880	177
12	4302	177
13	4812	177

Stop Event

1×	node limit

Counts

45 → 27

prune21.0ms (1.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	27	2	29

Error

Counts

29 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y (fma.f64 x 2 y)))
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x 2) y)) (.f64 y y))

Compiler

Compiled 348 to 192 computations (44.8% saved)

regimes159.0ms (9.8%)

Accuracy

Total 0.0b remaining (58.2%)

Threshold costs 0.0b (58.2%)

Counts

60 → 1

Compiler

Compiled 2220 to 1340 computations (39.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	9	15

Stop Event

1×

saturated

end73.0ms (4.5%)

Remove: (sort x y)
Compiler: Compiled 78 to 43 computations (44.9% saved)

Details

analyze141.0ms (8.6%)

sample840.0ms (51.4%)

simplify8.0ms (0.5%)

prune4.0ms (0.3%)

localize7.0ms (0.4%)

series12.0ms (0.7%)

rewrite58.0ms (3.6%)

simplify78.0ms (4.8%)

prune119.0ms (7.3%)

localize5.0ms (0.3%)

series5.0ms (0.3%)

rewrite35.0ms (2.1%)

simplify65.0ms (4%)

prune21.0ms (1.3%)

regimes159.0ms (9.8%)

simplify2.0ms (0.1%)

end73.0ms (4.5%)

Profiling