Details

analyze2.4s (26.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	99.6%	0.4%	8
0%	99.6%	0.4%	9
0%	99.6%	0.4%	10
0%	99.6%	0.4%	11
0%	99.6%	0.4%	12
0%	99.6%	0.4%	13
0%	99.6%	0.4%	14

Compiler

Compiled 28 to 19 computations (32.1% saved)

sample2.8s (30.5%)

Results

1.5s	8256×	body	128	valid
1.3s	7448×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

preprocess54.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

647×	`fma-def_binary64`
618×	`distribute-lft-in_binary64`
618×	`distribute-rgt-in_binary64`
548×	`cancel-sign-sub-inv_binary64`
330×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	188	754
1	558	696
2	1885	696
0	8	8
1	8	8

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort x y)

(sort z t)

Compiler

Compiled 27 to 18 computations (33.3% saved)

simplify22.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-def_binary64`
441×	`fma-neg_binary64`
435×	`distribute-rgt-in_binary64`
372×	`distribute-lft-in_binary64`
298×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	37	24
2	104	24
3	371	24
4	1368	24
5	3595	24

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.8b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))
	6.4b	(.f64 2 (-.f64 (+.f64 (.f64 x y) (.f64 z t)) (.f64 (.f64 (+.f64 a (.f64 b c)) c) i)))

Compiler

Compiled 148 to 93 computations (37.2% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))
✓	2.6b	(fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (.f64 x y))

series124.0ms (1.4%)

Counts

2 → 168

Calls

42 calls:

8.0ms	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))	y	-inf
6.0ms	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))	i	0
6.0ms	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))	b	0
4.0ms	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))	x	0
4.0ms	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))	y	0

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

334×	`prod-diff_binary64`
296×	`log1p-udef_binary64`
175×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	41
1	341	37
2	4159	37

Stop Event

1×	node limit

Counts

2 → 38

simplify107.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
632×	`cancel-sign-sub-inv_binary64`
361×	`distribute-rgt-neg-in_binary64`
282×	`fma-def_binary64`
260×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	4101
1	219	3484
2	609	3350
3	1918	3350
4	4112	3350

Stop Event

1×	node limit

Counts

206 → 81

prune77.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	76	7	83

Error

0.0b

Counts

83 → 7

Alt Table

Status	Error	Program
	54.0b	(.f64 c (.f64 -2 (.f64 c (.f64 i b))))
	15.7b	(.f64 2 (fma.f64 c (.f64 i (neg.f64 a)) (fma.f64 t z (*.f64 y x))))
	6.4b	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (.f64 y x))))
▶	6.1b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (+.f64 a (*.f64 c b))))))
✓	1.8b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))
	27.8b	(.f64 2 (fma.f64 z t (.f64 -1 (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i))))
	22.3b	(.f64 2 (fma.f64 t z (.f64 y x)))

Compiler

Compiled 1750 to 687 computations (60.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (+.f64 a (.f64 c b)))))
✓	0.0b	(+.f64 a (*.f64 c b))
✓	0.3b	(.f64 i (+.f64 a (.f64 c b)))
✓	5.8b	(.f64 c (.f64 i (+.f64 a (*.f64 c b))))

series106.0ms (1.2%)

Counts

4 → 228

Calls

57 calls:

8.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (+.f64 a (.f64 c b)))))	i	-inf
6.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (+.f64 a (.f64 c b)))))	z	-inf
6.0ms	(.f64 i (+.f64 a (.f64 c b)))	i	-inf
3.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (+.f64 a (.f64 c b)))))	x	0
3.0ms	(-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (+.f64 a (.f64 c b)))))	x	inf

rewrite77.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

326×	`log1p-udef_binary64`
182×	`add-sqr-sqrt_binary64`
179×	`associate-r_binary64`
171×	`log1p-expm1-u_binary64`
171×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	53
1	346	45
2	4921	45

Stop Event

1×	node limit

Counts

4 → 126

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
646×	`cancel-sign-sub-inv_binary64`
469×	`fma-def_binary64`
264×	`associate-l_binary64`
258×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	3462
1	157	2766
2	376	2766
3	912	2766
4	2675	2766

Stop Event

1×	node limit

Counts

354 → 173

prune208.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	169	4	173
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	173	7	180

Error

0.0b

Counts

180 → 7

Alt Table

Status	Error	Program
	15.9b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 c (*.f64 i b)))))
✓	1.8b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))
	15.7b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 a i))))
▶	6.4b	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (.f64 y x))))
	31.4b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (fma.f64 c b a) (.f64 c i)))) 2))
	27.8b	(.f64 2 (fma.f64 z t (.f64 -1 (.f64 (+.f64 (.f64 (pow.f64 c 2) b) (*.f64 c a)) i))))
	12.9b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (*.f64 c b)))))

Compiler

Compiled 4367 to 1363 computations (68.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (.f64 y x))))
✓	0.0b	(-.f64 (neg.f64 a) (*.f64 c b))
✓	0.1b	(.f64 c (-.f64 (neg.f64 a) (.f64 c b)))
✓	6.4b	(fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (*.f64 y x))

series159.0ms (1.7%)

Counts

4 → 240

Calls

60 calls:

6.0ms	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (.f64 y x))))	z	inf
6.0ms	(fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (*.f64 y x))	x	inf
6.0ms	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (.f64 y x))))	y	0
6.0ms	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (.f64 y x))))	i	0
5.0ms	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (.f64 y x))))	x	-inf

rewrite68.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

329×	`log1p-udef_binary64`
193×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
178×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	66
1	373	58
2	4816	58

Stop Event

1×	node limit

Counts

4 → 100

simplify139.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-neg_binary64`
321×	`distribute-rgt-neg-in_binary64`
293×	`sub-neg_binary64`
280×	`fma-def_binary64`
247×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	75	4720
1	246	4135
2	657	3652
3	1938	3652
4	3562	3652
5	4825	3652

Stop Event

1×	node limit

Counts

340 → 155

prune151.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	154	8	162

Error

0.0b

Counts

162 → 8

Alt Table

Status	Error	Program
	15.7b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 a i))))
	18.6b	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 -1 (.f64 (pow.f64 c 2) b)) (.f64 y x))))
	15.9b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 c (*.f64 i b)))))
✓	1.8b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))
✓	6.4b	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (.f64 y x))))
	31.4b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (fma.f64 c b a) (.f64 c i)))) 2))
	55.8b	(.f64 b (.f64 i (.f64 (.f64 c c) -2)))
▶	12.9b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (*.f64 c b)))))

Compiler

Compiled 3515 to 1302 computations (63% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 t z (*.f64 y x))
✓	0.0b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (*.f64 c b)))))
✓	2.5b	(.f64 c (.f64 i (*.f64 c b)))
✓	4.0b	(.f64 i (.f64 c b))

series98.0ms (1.1%)

Counts

4 → 204

Calls

51 calls:

7.0ms	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (*.f64 c b)))))	t	-inf
6.0ms	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (*.f64 c b)))))	i	0
3.0ms	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (*.f64 c b)))))	i	inf
3.0ms	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (*.f64 c b)))))	b	inf
3.0ms	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (*.f64 c b)))))	z	0

rewrite63.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

307×	`expm1-udef_binary64`
307×	`log1p-udef_binary64`
174×	`associate-r_binary64`
172×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	48
1	334	48
2	4367	48

Stop Event

1×	node limit

Counts

4 → 70

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-neg_binary64`
462×	`cancel-sign-sub-inv_binary64`
376×	`associate-l_binary64`
342×	`*-commutative_binary64`
331×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	2829
1	77	2640
2	220	2640
3	649	2640
4	2091	2640
5	3483	2640

Stop Event

1×	node limit

Counts

274 → 90

prune90.0ms (1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	90	8	98

Error

0.0b

Counts

98 → 8

Alt Table

Status	Error	Program
	15.7b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 a i))))
	18.6b	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 -1 (.f64 (pow.f64 c 2) b)) (.f64 y x))))
	15.9b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 c (*.f64 i b)))))
	34.3b	(.f64 2 (fma.f64 b (.f64 (.f64 c i) (neg.f64 c)) (.f64 t z)))
✓	1.8b	(.f64 2 (fma.f64 z t (fma.f64 (fma.f64 b c a) (.f64 i (neg.f64 c)) (*.f64 x y))))
✓	6.4b	(.f64 2 (fma.f64 z t (fma.f64 i (.f64 c (-.f64 (neg.f64 a) (.f64 c b))) (.f64 y x))))
	31.4b	(.f64 2 (pow.f64 (sqrt.f64 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 (fma.f64 c b a) (.f64 c i)))) 2))
✓	12.9b	(.f64 2 (-.f64 (fma.f64 t z (.f64 y x)) (.f64 c (.f64 i (*.f64 c b)))))

Compiler

Compiled 1928 to 671 computations (65.2% saved)

regimes1.9s (20.2%)

Accuracy

Total 1.5b remaining (98.3%)

Threshold costs 0b (0%)

Counts

82 → 3

Compiler

Compiled 28591 to 20299 computations (29% saved)

bsearch63.0ms (0.7%)

Algorithm

2×	binary-search

Calls

2 calls:

56.0ms	i
5.0ms	i

Steps

Iters	Point		Range
4.85756880567276e-284	∈ [	2.161457816042519e-287	,	1.0830790664377225e-280	]
-3.5147571057147903e-28	∈ [	-7.359570094831268e-28	,	-2.114428990928486e-28	]

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify23.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	84
1	58	84
2	81	84
3	99	84
4	106	84
5	108	84

Stop Event

1×

saturated

end175.0ms (1.9%)

Stop Event

1×

fuel

Remove

(sort z t)

(sort x y)

Compiler

Compiled 597 to 342 computations (42.7% saved)

Details

analyze2.4s (26.2%)

sample2.8s (30.5%)

preprocess54.0ms (0.6%)

simplify22.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.2%)

series124.0ms (1.4%)

rewrite63.0ms (0.7%)

simplify107.0ms (1.2%)

prune77.0ms (0.8%)

localize15.0ms (0.2%)

series106.0ms (1.2%)

rewrite77.0ms (0.8%)

simplify88.0ms (1%)

prune208.0ms (2.3%)

localize13.0ms (0.1%)

series159.0ms (1.7%)

rewrite68.0ms (0.7%)

simplify139.0ms (1.5%)

prune151.0ms (1.7%)

localize14.0ms (0.2%)

series98.0ms (1.1%)

rewrite63.0ms (0.7%)

simplify93.0ms (1%)

prune90.0ms (1%)

regimes1.9s (20.2%)

bsearch63.0ms (0.7%)

simplify23.0ms (0.3%)

end175.0ms (1.9%)

Profiling