Details

analyze19.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	1.6%	48.5%	9
50.4%	1.2%	48.5%	10
50.4%	1.2%	48.5%	11
50.4%	1.1%	48.6%	12
50.4%	1%	48.6%	13
50.5%	0.9%	48.6%	14

Compiler

Compiled 15 to 8 computations (46.7% saved)

sample3.0s (79.7%)

Results

1.8s	3934×	body	1024	valid
560.0ms	2038×	body	512	valid
240.0ms	428×	body	2048	valid
192.0ms	1039×	body	256	valid
86.0ms	817×	body	128	valid

Compiler

Compiled 44 to 23 computations (47.7% saved)

simplify70.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
658×	`unswap-sqr_binary64`
478×	`fma-neg_binary64`
464×	`times-frac_binary64`
388×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	20	22
2	34	22
3	58	22
4	125	22
5	288	22
6	624	22
7	1577	22
8	3798	22
9	4553	22
10	5023	22

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

58.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	58.3b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 42 to 21 computations (50% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	2.2b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	6.9b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series18.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

14.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite75.0ms (2%)

Algorithm

2×	batch-egg-rewrite
3×	egg-rewrite

Rules

97×	`add-sqr-sqrt_binary64`
92×	`log1p-expm1-u_binary64`
92×	`expm1-log1p-u_binary64`
91×	`add-log-exp_binary64`
89×	`add-cbrt-cube_binary64`

Counts

3 → 0

Calls

3 calls:

75.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
75.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
75.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	186	18
2	26	18
0	6	6
1	130	6
2	71	6
0	8	3
1	186	3
2	26	3
0	6	6
1	129	6
2	19	6
0	0	0
1	0	0

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-def_binary64`
752×	`fma-neg_binary64`
514×	`cancel-sign-sub-inv_binary64`
508×	`unswap-sqr_binary64`
480×	`associate-l_binary64`

Counts

24 → 27

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	321
1	137	317
2	336	311
3	910	309
4	2632	309
5	4822	309
6	4911	309
7	4936	309

prune22.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Error

2.0b

Counts

28 → 3

Alt Table

Status	Error	Program
✓	58.3b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	3.2b	(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x)))
	3.3b	x

Compiler

Compiled 454 to 243 computations (46.5% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x)))
✓	0.0b	(fma.f64 (pow.f64 x 5) 2/15 x)
✓	0.0b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))

series13.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x)))
3.0ms	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
3.0ms	(fma.f64 (pow.f64 x 5) 2/15 x)

rewrite57.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

507×	`log-prod_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
201×	`log-pow_binary64`
152×	`prod-diff_binary64`

Counts

3 → 92

Calls

3 calls:

54.0ms	(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x)))
54.0ms	(fma.f64 (pow.f64 x 5) 2/15 x)
54.0ms	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	45
1	302	45
2	3025	45
3	4921	45
0	0	0
1	0	0

simplify171.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

921×	`distribute-rgt-neg-in_binary64`
534×	`sqr-pow_binary64`
477×	`fma-neg_binary64`
432×	`sub-neg_binary64`
398×	`cancel-sign-sub-inv_binary64`

Counts

128 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	438
1	74	430
2	166	408
3	431	402
4	1180	402
5	1924	402
6	2643	402
7	3577	402
8	3489	402
9	3665	402
10	3867	402
11	4057	402
12	3819	402
13	4825	402
14	4889	402

prune79.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	110	3	113

Error

2.0b

Counts

113 → 3

Alt Table

Status	Error	Program
✓	58.3b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	3.2b	(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x)))
▶	3.3b	x

Compiler

Compiled 2408 to 1884 computations (21.8% saved)

localize1.0ms (0%)

prune2.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

2.0b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	58.3b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	3.2b	(fma.f64 (pow.f64 x 7) -17/315 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x)))
✓	3.3b	x

Compiler

Compiled 33 to 21 computations (36.4% saved)

regimes28.0ms (0.7%)

Accuracy

Total 0.7b remaining (40.2%)

Threshold costs 0.7b (40.2%)

Counts

14 → 1

Compiler

Compiled 422 to 306 computations (27.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	30
1	23	30
2	25	30
3	26	30
4	26	30

end120.0ms (3.2%)

Compiler: Compiled 75 to 53 computations (29.3% saved)

Details

analyze19.0ms (0.5%)

sample3.0s (79.7%)

simplify70.0ms (1.9%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series18.0ms (0.5%)

rewrite75.0ms (2%)

simplify69.0ms (1.8%)

prune22.0ms (0.6%)

localize10.0ms (0.3%)

series13.0ms (0.3%)

rewrite57.0ms (1.5%)

simplify171.0ms (4.6%)

prune79.0ms (2.1%)

localize1.0ms (0%)

prune2.0ms (0%)

regimes28.0ms (0.7%)

simplify2.0ms (0.1%)

end120.0ms (3.2%)

Profiling