Details

analyze19.0ms (0.4%)

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)

sample3.3s (73.2%)

Results

2.0s	3983×	body	1024	valid
636.0ms	2061×	body	512	valid
258.0ms	1009×	body	256	valid
228.0ms	417×	body	2048	valid
88.0ms	786×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 44 to 23 computations (47.7% saved)

simplify66.0ms (1.5%)

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

57.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	57.8b	(/.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 (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	0.3b	(/.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 (0.4%)

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)))

rewrite77.0ms (1.7%)

Algorithm

3×	egg-rewrite
1×	batch-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:

77.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
77.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
77.0ms	(-.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

simplify72.0ms (1.6%)

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

prune24.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	24	3	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	4	28

Error

0.2b

Counts

28 → 4

Alt Table

Status	Error	Program
	0.8b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
	1.4b	x
✓	57.8b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	0.6b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 496 to 275 computations (44.6% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	0.0b	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
✓	0.0b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.1b	(*.f64 1/3 (pow.f64 x 3))

series16.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

9.0ms

(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

4.0ms

(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))

3.0ms

(*.f64 1/3 (pow.f64 x 3))

rewrite168.0ms (3.7%)

Algorithm

3×	egg-rewrite
1×	batch-egg-rewrite

Rules

1073×	`log1p-udef_binary64`
679×	`log-prod_binary64`
589×	`log1p-expm1-u_binary64`
589×	`expm1-log1p-u_binary64`
423×	`pow2_binary64`

Counts

3 → 49

Calls

3 calls:

167.0ms

(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))

167.0ms

(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

167.0ms

(*.f64 1/3 (pow.f64 x 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	21
1	456	21
2	73	21
0	6	7
1	125	7
2	1261	7
3	4816	7
4	6163	7
0	21	33
1	456	33
2	73	33
0	12	18
1	254	18
2	2520	18
3	4842	18

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-/r/_binary64`
590×	`associate-/l/_binary64`
488×	`fma-neg_binary64`
446×	`fma-def_binary64`
406×	`distribute-rgt-neg-in_binary64`

Counts

73 → 77

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	591
1	136	591
2	299	587
3	685	585
4	1704	561
5	2988	561
6	5130	561

prune79.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	87	3	90

Error

0.2b

Counts

90 → 3

Alt Table

Status	Error	Program
	0.8b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
▶	0.6b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 2))))
✓	57.8b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 2483 to 1606 computations (35.3% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 2)))
	0.0b	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
✓	0.0b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 2))))
	0.1b	(*.f64 1/3 (pow.f64 x 3))

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

5.0ms

(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 2))))

3.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 2)))

rewrite63.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

434×	`log1p-udef_binary64`
250×	`add-sqr-sqrt_binary64`
250×	`log1p-expm1-u_binary64`
250×	`expm1-log1p-u_binary64`
244×	`add-log-exp_binary64`

Counts

2 → 36

Calls

2 calls:

62.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 2)))

62.0ms

(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 2))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	65
1	558	65
2	4769	65
3	5169	65

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-neg_binary64`
673×	`fma-def_binary64`
558×	`cancel-sign-sub-inv_binary64`
506×	`unswap-sqr_binary64`
438×	`associate-l_binary64`

Counts

60 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	337
1	144	321
2	348	311
3	894	309
4	2640	309
5	5134	309

prune132.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	4	124

Error

0.2b

Counts

124 → 4

Alt Table

Status	Error	Program
▶	0.8b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
	53.5b	(*.f64 1/7 x)
✓	0.6b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 2))))
✓	57.8b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 4112 to 3185 computations (22.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))

rewrite40.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

835×	`log1p-expm1-u_binary64`
835×	`expm1-log1p-u_binary64`
103×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
95×	`add-cbrt-cube_binary64`

Counts

1 → 25

Calls

1 calls:

39.0ms

(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	10	15
1	214	15
2	2151	15
3	5047	15

simplify119.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

992×	`fma-neg_binary64`
552×	`distribute-rgt-neg-in_binary64`
422×	`distribute-lft-neg-in_binary64`
416×	`unswap-sqr_binary64`
405×	`cancel-sign-sub-inv_binary64`

Counts

37 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	159
1	42	155
2	88	141
3	223	141
4	500	141
5	1264	141
6	1975	141
7	3745	141
8	4307	141
9	4647	141
10	4957	141
11	4997	141
12	4831	141

prune23.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	33	4	37

Error

0.2b

Counts

37 → 4

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 5) 2/15 x))
	53.5b	(*.f64 1/7 x)
✓	0.6b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x 2))))
✓	57.8b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 560 to 430 computations (23.2% saved)

regimes30.0ms (0.7%)

Accuracy

Total 0.5b remaining (32%)

Threshold costs 0.5b (32%)

Counts

15 → 1

Compiler

Compiled 508 to 372 computations (26.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	46
1	27	46
2	27	46

end103.0ms (2.3%)

Compiler: Compiled 132 to 97 computations (26.5% saved)

Details

analyze19.0ms (0.4%)

sample3.3s (73.2%)

simplify66.0ms (1.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series18.0ms (0.4%)

rewrite77.0ms (1.7%)

simplify72.0ms (1.6%)

prune24.0ms (0.5%)

localize16.0ms (0.4%)

series16.0ms (0.3%)

rewrite168.0ms (3.7%)

simplify56.0ms (1.2%)

prune79.0ms (1.8%)

localize20.0ms (0.4%)

series8.0ms (0.2%)

rewrite63.0ms (1.4%)

simplify42.0ms (0.9%)

prune132.0ms (2.9%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite40.0ms (0.9%)

simplify119.0ms (2.6%)

prune23.0ms (0.5%)

regimes30.0ms (0.7%)

simplify2.0ms (0%)

end103.0ms (2.3%)

Profiling