Details

analyze60.0ms (2.1%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.2s (79.6%)

Symmetry

(sort a x)

Results

859.0ms	1557×	body	2048	valid
618.0ms	1760×	body	1024	valid
338.0ms	3159×	body	128	valid
254.0ms	1152×	body	512	valid
102.0ms	628×	body	256	valid
12.0ms	136×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify75.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
455×	`*-commutative_binary64`
440×	`unswap-sqr_binary64`
344×	`associate-l_binary64`
274×	`associate-+l+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	16	6
2	23	6
3	35	6
4	70	6
5	160	6
6	432	6
7	1564	6
8	3490	6
9	4954	6
10	4993	6
11	4874	6

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	(expm1.f64 (*.f64 a x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 a x))

series6.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(expm1.f64 (*.f64 a x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`log1p-expm1-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (*.f64 a x))

simplify69.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
844×	`distribute-lft-out_binary64`
785×	`fma-neg_binary64`
383×	`*-commutative_binary64`
308×	`unswap-sqr_binary64`

Counts

35 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	382
1	96	369
2	262	363
3	966	347
4	2376	333
5	3696	333
6	4842	333
7	5375	333

prune12.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	2	20

Error

0.0b

Counts

20 → 2

Alt Table

Status	Error	Program
▶	22.3b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 279 to 139 computations (50.2% saved)

localize20.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 a x) 4)
✓	0.3b	(pow.f64 (*.f64 a x) 3)
✓	5.3b	(fma.f64 x (.f64 1/2 (.f64 a a)) a)
✓	11.5b	(fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4)))

series78.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

37.0ms	(fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4)))
16.0ms	(pow.f64 (*.f64 a x) 4)
13.0ms	(pow.f64 (*.f64 a x) 3)
11.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
7×	`add-cbrt-cube_binary64`
6×	`pow-unpow_binary64`
6×	`*-un-lft-identity_binary64`

Counts

4 → 63

Calls

4 calls:

2.0ms	(pow.f64 (*.f64 a x) 3)
2.0ms	(pow.f64 (*.f64 a x) 4)
0.0ms	(fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4)))
0.0ms	(fma.f64 x (.f64 1/2 (.f64 a a)) a)

simplify85.0ms (3%)

Algorithm

1×	egg-herbie

Rules

538×	`sqr-pow_binary64`
379×	`distribute-rgt-in_binary64`
354×	`exp-prod_binary64`
340×	`distribute-lft-in_binary64`
269×	`log-prod_binary64`

Counts

159 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	1930
1	168	1716
2	499	1702
3	1311	1702
4	2862	1702
5	4973	1702

prune68.0ms (2.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	88	2	90

Error

0.0b

Counts

90 → 2

Alt Table

Status	Error	Program
✓	22.3b	(fma.f64 x (fma.f64 x (.f64 1/2 (.f64 a a)) a) (fma.f64 1/6 (pow.f64 (.f64 a x) 3) (.f64 1/24 (pow.f64 (*.f64 a x) 4))))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 2531 to 1342 computations (47% saved)

regimes38.0ms (1.3%)

Accuracy

Total 0.0b remaining (10.5%)

Threshold costs 0.0b (10.5%)

Counts

6 → 1

Compiler

Compiled 405 to 249 computations (38.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
2	6	6

end50.0ms (1.8%)

Remove: (sort a x)
Compiler: Compiled 56 to 36 computations (35.7% saved)

Details

analyze60.0ms (2.1%)

sample2.2s (79.6%)

simplify75.0ms (2.7%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.2%)

rewrite1.0ms (0%)

simplify69.0ms (2.4%)

prune12.0ms (0.4%)

localize20.0ms (0.7%)

series78.0ms (2.8%)

rewrite8.0ms (0.3%)

simplify85.0ms (3%)

prune68.0ms (2.4%)

regimes38.0ms (1.3%)

simplify2.0ms (0.1%)

end50.0ms (1.8%)

Profiling