Details

analyze111.0ms (2.3%)

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)

sample3.8s (78.8%)

Symmetry

(sort a x)

Results

1.5s	1586×	body	2048	valid
1.0s	1747×	body	1024	valid
487.0ms	3185×	body	128	valid
446.0ms	1106×	body	512	valid
171.0ms	632×	body	256	valid
26.0ms	172×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify105.0ms (2.2%)

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

prune6.0ms (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)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite94.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

736×	`log1p-udef_binary64`
405×	`log1p-expm1-u_binary64`
405×	`expm1-log1p-u_binary64`
342×	`pow1_binary64`
287×	`unpow-prod-down_binary64`

Counts

1 → 36

Calls

1 calls:

93.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	95	6
2	1080	6
3	4662	6
4	5883	6
0	0	0
1	0	0

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1324×	`distribute-lft-out_binary64`
882×	`fma-def_binary64`
423×	`associate-/l/_binary64`
368×	`*-commutative_binary64`
362×	`associate-/r/_binary64`

Counts

60 → 44

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	284
1	86	284
2	234	278
3	888	262
4	2148	248
5	2915	248
6	3566	248
7	5038	248

prune36.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	2	45

Error

Counts

45 → 2

Alt Table

Status	Error	Program
▶	19.6b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 538 to 244 computations (54.6% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))
✓	0.3b	(pow.f64 (*.f64 a x) 2)

series42.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))
13.0ms	(pow.f64 (*.f64 a x) 2)

rewrite73.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

721×	`log1p-expm1-u_binary64`
721×	`expm1-log1p-u_binary64`
416×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
82×	`add-cube-cbrt_binary64`

Counts

2 → 46

Calls

2 calls:

71.0ms	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))
71.0ms	(pow.f64 (*.f64 a x) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	185	21
2	1904	21
3	5125	21
0	0	0
1	0	0

simplify244.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

743×	`unswap-sqr_binary64`
738×	`fma-def_binary64`
718×	`sqr-pow_binary64`
653×	`fabs-mul_binary64`
584×	`cube-prod_binary64`

Counts

94 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	606
1	26	606
2	55	588
3	156	552
4	588	552
5	1035	552
6	1210	552
7	1316	552
8	1450	552
9	1560	552
10	1707	552
11	2799	552
12	2800	552
13	3046	552
14	3266	552
15	3584	552
16	4011	552
17	4303	552
18	4485	552
19	4700	552
20	4950	552

prune50.0ms (1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	52	2	54

Error

Counts

54 → 2

Alt Table

Status	Error	Program
✓	19.6b	(fma.f64 a x (.f64 1/2 (pow.f64 (.f64 a x) 2)))
✓	0.0b	(expm1.f64 (*.f64 a x))

Compiler

Compiled 763 to 412 computations (46% saved)

regimes55.0ms (1.1%)

Accuracy

Total 0.0b remaining (20%)

Threshold costs 0.0b (20%)

Counts

4 → 1

Compiler

Compiled 205 to 139 computations (32.2% saved)

simplify3.0ms (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

end83.0ms (1.7%)

Remove: (sort a x)
Compiler: Compiled 42 to 28 computations (33.3% saved)

Details

analyze111.0ms (2.3%)

sample3.8s (78.8%)

simplify105.0ms (2.2%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite94.0ms (2%)

simplify94.0ms (2%)

prune36.0ms (0.7%)

localize11.0ms (0.2%)

series42.0ms (0.9%)

rewrite73.0ms (1.5%)

simplify244.0ms (5.1%)

prune50.0ms (1%)

regimes55.0ms (1.1%)

simplify3.0ms (0.1%)

end83.0ms (1.7%)

Profiling