Details

analyze1.3s (28.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.3s (28.2%)

Results

1.1s	8254×	body	128	valid
104.0ms	775×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess51.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

956×	`div-sub_binary64`
390×	`fma-def_binary64`
299×	`distribute-rgt-in_binary64`
254×	`distribute-lft-in_binary64`
253×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
1	138	154
2	292	154
3	605	154
4	1447	154
5	3922	154
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify23.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary64`
577×	`div-sub_binary64`
529×	`fma-neg_binary64`
259×	`fma-def_binary64`
192×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	41	14
3	82	14
4	188	14
5	381	14
6	902	14
7	2369	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
▶	1.1b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

Compiler

Compiled 88 to 52 computations (40.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	2.0b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

series54.0ms (1.2%)

Counts

2 → 84

Calls

21 calls:

9.0ms	(/.f64 (-.f64 z t) (-.f64 a t))	t	0
4.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))	y	inf
3.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))	a	-inf
3.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))	t	-inf
3.0ms	(/.f64 (-.f64 z t) (-.f64 a t))	a	-inf

rewrite131.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
257×	`egg-rr`
111×	`add-sqr-sqrt_binary64`
106×	`log1p-expm1-u_binary64`
106×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	208	23
2	3217	23

Stop Event

1×	node limit

Counts

2 → 257

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-def_binary64`
725×	`cancel-sign-sub-inv_binary64`
627×	`times-frac_binary64`
351×	`sub-neg_binary64`
189×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	2597
1	526	2549
2	1906	2271

Stop Event

1×	node limit

Counts

341 → 330

prune238.0ms (5.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	328	2	330
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	328	4	332

Error

0.0b

Counts

332 → 4

Alt Table

Status	Error	Program
▶	4.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
	23.6b	(+.f64 x (/.f64 (neg.f64 (-.f64 z t)) (/.f64 t y)))
✓	1.1b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	12.3b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 15235 to 4284 computations (71.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 t a))
✓	3.9b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)

series79.0ms (1.7%)

Counts

2 → 84

Calls

24 calls:

29.0ms	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)	t	0
6.0ms	(/.f64 y (-.f64 t a))	a	-inf
4.0ms	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)	y	inf
3.0ms	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)	a	0
3.0ms	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)	x	inf

rewrite54.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
220×	`log1p-udef_binary64`
120×	`add-sqr-sqrt_binary64`
114×	`log1p-expm1-u_binary64`
114×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	224	21
2	3274	21

Stop Event

1×	node limit

Counts

2 → 58

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
651×	`times-frac_binary64`
590×	`cancel-sign-sub-inv_binary64`
189×	`sub-neg_binary64`
132×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	2442
1	541	2442
2	1822	1825

Stop Event

1×	node limit

Counts

142 → 123

prune78.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	123	4	127

Error

0.0b

Counts

127 → 4

Alt Table

Status	Error	Program
✓	4.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
✓	1.1b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	22.9b	(+.f64 x (-.f64 y (*.f64 (/.f64 y t) z)))
▶	12.3b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 2629 to 868 computations (67% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 z t) y)
✓	13.4b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

series38.0ms (0.8%)

Counts

2 → 60

Calls

21 calls:

3.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))	a	-inf
3.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))	y	-inf
3.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))	z	0
3.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))	t	inf
3.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))	a	inf

rewrite56.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

745×	`prod-diff_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
109×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	205	20
2	3128	20

Stop Event

1×	node limit

Counts

2 → 67

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

526×	`times-frac_binary64`
525×	`cancel-sign-sub-inv_binary64`
492×	`fma-def_binary64`
473×	`associate-/l*_binary64`
253×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1594
1	364	1558
2	1280	1235

Stop Event

1×	node limit

Counts

127 → 111

prune104.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	111	4	115

Error

Counts

115 → 4

Alt Table

Status	Error	Program
✓	4.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
	30.7b	(+.f64 x (+.f64 (.f64 (/.f64 y t) (+.f64 a (/.f64 a (/.f64 t a)))) (-.f64 y (fma.f64 (/.f64 y t) z (.f64 (/.f64 z t) (*.f64 (/.f64 y t) (+.f64 a (/.f64 a (/.f64 t a)))))))))
✓	1.1b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
▶	12.2b	(+.f64 x (/.f64 (-.f64 (.f64 y z) (.f64 y t)) (-.f64 a t)))

Compiler

Compiled 2507 to 876 computations (65.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.6b	(-.f64 (.f64 y z) (.f64 y t))
✓	13.4b	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) (-.f64 a t))

series64.0ms (1.4%)

Counts

2 → 66

Calls

21 calls:

28.0ms	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) (-.f64 a t))	t	0
5.0ms	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) (-.f64 a t))	a	-inf
4.0ms	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) (-.f64 a t))	y	inf
3.0ms	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) (-.f64 a t))	a	inf
3.0ms	(/.f64 (-.f64 (.f64 y z) (.f64 y t)) (-.f64 a t))	a	0

rewrite78.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

640×	`fma-def_binary64`
314×	`fma-neg_binary64`
243×	`egg-rr`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	240	20
2	3749	20

Stop Event

1×	node limit

Counts

2 → 243

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Rules

526×	`cancel-sign-sub-inv_binary64`
526×	`times-frac_binary64`
510×	`fma-def_binary64`
488×	`associate-/l*_binary64`
251×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	115	1637
1	384	1607
2	1335	1365

Stop Event

1×	node limit

Counts

309 → 291

prune194.0ms (4.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	291	0	291
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	291	4	295

Error

Counts

295 → 4

Alt Table

Status	Error	Program
✓	4.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
	30.7b	(+.f64 x (+.f64 (.f64 (/.f64 y t) (+.f64 a (/.f64 a (/.f64 t a)))) (-.f64 y (fma.f64 (/.f64 y t) z (.f64 (/.f64 z t) (*.f64 (/.f64 y t) (+.f64 a (/.f64 a (/.f64 t a)))))))))
✓	1.1b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
✓	12.2b	(+.f64 x (/.f64 (-.f64 (.f64 y z) (.f64 y t)) (-.f64 a t)))

Compiler

Compiled 6988 to 1855 computations (73.5% saved)

regimes464.0ms (10.1%)

Accuracy

Total 1.0b remaining (98.6%)

Threshold costs 0b (0%)

Counts

63 → 1

Compiler

Compiled 9122 to 5500 computations (39.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	20	16
2	25	16
3	27	16
4	28	16

Stop Event

1×

saturated

end61.0ms (1.3%)

Stop Event

1×

fuel

Compiler

Compiled 122 to 66 computations (45.9% saved)

Details

analyze1.3s (28.1%)

sample1.3s (28.2%)

preprocess51.0ms (1.1%)

simplify23.0ms (0.5%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series54.0ms (1.2%)

rewrite131.0ms (2.9%)

simplify64.0ms (1.4%)

prune238.0ms (5.2%)

localize7.0ms (0.2%)

series79.0ms (1.7%)

rewrite54.0ms (1.2%)

simplify48.0ms (1%)

prune78.0ms (1.7%)

localize8.0ms (0.2%)

series38.0ms (0.8%)

rewrite56.0ms (1.2%)

simplify38.0ms (0.8%)

prune104.0ms (2.3%)

localize9.0ms (0.2%)

series64.0ms (1.4%)

rewrite78.0ms (1.7%)

simplify48.0ms (1%)

prune194.0ms (4.2%)

regimes464.0ms (10.1%)

simplify3.0ms (0.1%)

end61.0ms (1.3%)

Profiling