Details

analyze718.0ms (13.8%)

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
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.1s (21.5%)

Results

1.0s	8256×	body	128	valid
59.0ms	488×	body	128	invalid

Compiler

Compiled 40 to 24 computations (40% saved)

preprocess66.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

905×	`fma-def_binary64`
532×	`associate-/l*_binary64`
381×	`fma-neg_binary64`
305×	`div-sub_binary64`
300×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	140
1	122	140
2	243	140
3	398	140
4	872	140
5	1687	140
6	3097	140
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 11 computations (42.1% saved)

simplify42.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

832×	`fma-def_binary64`
768×	`times-frac_binary64`
756×	`fma-neg_binary64`
281×	`associate-/l*_binary64`
228×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	25	20
2	51	20
3	82	20
4	166	20
5	297	20
6	488	20
7	738	20
8	1199	20
9	1800	20
10	2769	20
11	4928	20

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

28.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.4b	(/.f64 (fma.f64 d (neg.f64 a) (.f64 b c)) (fma.f64 c c (.f64 d d)))

Compiler

Compiled 69 to 35 computations (49.3% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 d (neg.f64 a) (*.f64 b c))
✓	27.9b	(/.f64 (fma.f64 d (neg.f64 a) (.f64 b c)) (fma.f64 c c (.f64 d d)))

series82.0ms (1.6%)

Counts

2 → 96

Calls

24 calls:

13.0ms	(/.f64 (fma.f64 d (neg.f64 a) (.f64 b c)) (fma.f64 c c (.f64 d d)))	b	inf
10.0ms	(/.f64 (fma.f64 d (neg.f64 a) (.f64 b c)) (fma.f64 c c (.f64 d d)))	a	-inf
10.0ms	(/.f64 (fma.f64 d (neg.f64 a) (.f64 b c)) (fma.f64 c c (.f64 d d)))	a	inf
9.0ms	(/.f64 (fma.f64 d (neg.f64 a) (.f64 b c)) (fma.f64 c c (.f64 d d)))	b	-inf
9.0ms	(/.f64 (fma.f64 d (neg.f64 a) (.f64 b c)) (fma.f64 c c (.f64 d d)))	b	0

rewrite49.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`log-prod_binary64`
286×	`prod-diff_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`
164×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	226	25
2	2902	25

Stop Event

1×	node limit

Counts

2 → 65

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-def_binary64`
483×	`associate-*l/_binary64`
469×	`cancel-sign-sub-inv_binary64`
382×	`fma-neg_binary64`
359×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	1722
1	133	1638
2	386	1599
3	1781	1554

Stop Event

1×	node limit

Counts

161 → 92

prune62.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Error

1.4b

Counts

93 → 9

Alt Table

Status	Error	Program
	44.6b	(sqrt.f64 (pow.f64 (/.f64 (fma.f64 d a (*.f64 b c)) (pow.f64 (hypot.f64 d c) 2)) 2))
	41.7b	(/.f64 c (/.f64 (fma.f64 c c (*.f64 d d)) b))
	34.9b	(fma.f64 (/.f64 (/.f64 a c) c) (neg.f64 d) (/.f64 b c))
	37.9b	(/.f64 b c)
	32.1b	(-.f64 (.f64 (/.f64 (/.f64 c d) d) (+.f64 b (/.f64 (.f64 c a) d))) (/.f64 a d))
	30.5b	(fma.f64 b (/.f64 (/.f64 c d) d) (/.f64 (neg.f64 a) d))
▶	28.6b	(.f64 (-.f64 (.f64 d a) (*.f64 b c)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2))))
	36.5b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d a (.f64 b c)) (hypot.f64 d c)))
	38.0b	(-.f64 (/.f64 b c) (.f64 (/.f64 d (.f64 c c)) (+.f64 a (/.f64 (*.f64 b d) c))))

Compiler

Compiled 1968 to 719 computations (63.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 d c)
✓	0.5b	(/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2)))
✓	0.7b	(-.f64 (.f64 d a) (.f64 b c))
✓	27.7b	(.f64 (-.f64 (.f64 d a) (*.f64 b c)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2))))

series157.0ms (3%)

Counts

4 → 144

Calls

36 calls:

27.0ms	(/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2)))	c	inf
16.0ms	(.f64 (-.f64 (.f64 d a) (*.f64 b c)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2))))	a	inf
15.0ms	(.f64 (-.f64 (.f64 d a) (*.f64 b c)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2))))	b	0
15.0ms	(.f64 (-.f64 (.f64 d a) (*.f64 b c)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2))))	b	-inf
14.0ms	(.f64 (-.f64 (.f64 d a) (*.f64 b c)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2))))	b	inf

rewrite65.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
161×	`add-sqr-sqrt_binary64`
157×	`pow1_binary64`
155×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	327	43
2	4259	43

Stop Event

1×	node limit

Counts

4 → 143

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

498×	`times-frac_binary64`
332×	`associate-/l*_binary64`
307×	`sub-neg_binary64`
235×	`associate-/r*_binary64`
232×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	2816
1	312	2714
2	960	2653
3	4662	2653

Stop Event

1×	node limit

Counts

287 → 215

prune157.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	210	5	215
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	214	10	224

Error

1.4b

Counts

224 → 10

Alt Table

Status	Error	Program
	41.2b	(.f64 (.f64 (-.f64 (pow.f64 (.f64 d a) 2) (pow.f64 (.f64 b c) 2)) (/.f64 1 (fma.f64 d a (*.f64 b c)))) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2))))
	34.9b	(fma.f64 (/.f64 (/.f64 a c) c) (neg.f64 d) (/.f64 b c))
	39.1b	(.f64 (-.f64 (.f64 d a) (.f64 b c)) (/.f64 1 (neg.f64 (pow.f64 (fma.f64 1/2 (.f64 (/.f64 c d) c) d) 2))))
	32.1b	(-.f64 (.f64 (/.f64 (/.f64 c d) d) (+.f64 b (/.f64 (.f64 c a) d))) (/.f64 a d))
	28.4b	(/.f64 (neg.f64 (-.f64 (.f64 d a) (.f64 b c))) (pow.f64 (hypot.f64 d c) 2))
▶	28.3b	(-.f64 (.f64 b (/.f64 c (fma.f64 c c (.f64 d d)))) (.f64 d (/.f64 a (fma.f64 c c (.f64 d d)))))
	28.8b	(.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 d a)) 2) (cbrt.f64 (.f64 d a)) (.f64 b (neg.f64 c))) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 d c) 2))))
	30.5b	(fma.f64 b (/.f64 (/.f64 c d) d) (/.f64 (neg.f64 a) d))
	36.5b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d a (.f64 b c)) (hypot.f64 d c)))
	38.0b	(-.f64 (/.f64 b c) (.f64 (/.f64 d (.f64 c c)) (+.f64 a (/.f64 (*.f64 b d) c))))

Compiler

Compiled 5355 to 2403 computations (55.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(.f64 b (/.f64 c (fma.f64 c c (.f64 d d))))
✓	9.7b	(/.f64 a (fma.f64 c c (*.f64 d d)))
✓	9.8b	(.f64 d (/.f64 a (fma.f64 c c (.f64 d d))))
✓	19.3b	(/.f64 c (fma.f64 c c (*.f64 d d)))

series198.0ms (3.8%)

Counts

4 → 132

Calls

33 calls:

18.0ms	(/.f64 a (fma.f64 c c (*.f64 d d)))	a	-inf
16.0ms	(.f64 d (/.f64 a (fma.f64 c c (.f64 d d))))	a	-inf
16.0ms	(.f64 d (/.f64 a (fma.f64 c c (.f64 d d))))	a	inf
16.0ms	(.f64 b (/.f64 c (fma.f64 c c (.f64 d d))))	b	-inf
16.0ms	(.f64 d (/.f64 a (fma.f64 c c (.f64 d d))))	a	0

rewrite58.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`log-prod_binary64`
210×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`
184×	`log-pow_binary64`
123×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	50
1	230	46
2	3090	46

Stop Event

1×	node limit

Counts

4 → 126

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

796×	`times-frac_binary64`
544×	`associate-/l*_binary64`
410×	`associate-/r*_binary64`
292×	`cancel-sign-sub-inv_binary64`
197×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	3228
1	319	3156
2	1021	2982

Stop Event

1×	node limit

Counts

258 → 193

prune141.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	193	10	203

Error

0.4b

Counts

203 → 10

Alt Table

Status	Error	Program
▶	23.6b	(-.f64 (.f64 b (/.f64 c (fma.f64 c c (.f64 d d)))) (/.f64 (/.f64 (*.f64 d a) (hypot.f64 c d)) (hypot.f64 c d)))
	40.7b	(-.f64 (.f64 (/.f64 (/.f64 b d) d) c) (.f64 d (/.f64 a (fma.f64 c c (*.f64 d d)))))
	39.1b	(.f64 (-.f64 (.f64 d a) (.f64 b c)) (/.f64 1 (neg.f64 (pow.f64 (fma.f64 1/2 (.f64 (/.f64 c d) c) d) 2))))
	32.1b	(-.f64 (.f64 (/.f64 (/.f64 c d) d) (+.f64 b (/.f64 (.f64 c a) d))) (/.f64 a d))
	43.6b	(-.f64 (.f64 b (/.f64 c (fma.f64 c c (.f64 d d)))) (*.f64 (/.f64 d c) (/.f64 a c)))
	34.9b	(fma.f64 (/.f64 (/.f64 a c) c) (neg.f64 d) (/.f64 b c))
	28.4b	(/.f64 (neg.f64 (-.f64 (.f64 d a) (.f64 b c))) (pow.f64 (hypot.f64 d c) 2))
	30.5b	(fma.f64 b (/.f64 (/.f64 c d) d) (/.f64 (neg.f64 a) d))
	36.5b	(.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d a (.f64 b c)) (hypot.f64 d c)))
	38.0b	(-.f64 (/.f64 b c) (.f64 (/.f64 d (.f64 c c)) (+.f64 a (/.f64 (*.f64 b d) c))))

Compiler

Compiled 5611 to 2148 computations (61.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (/.f64 (*.f64 d a) (hypot.f64 c d)) (hypot.f64 c d))
	3.8b	(.f64 b (/.f64 c (fma.f64 c c (.f64 d d))))
✓	10.2b	(/.f64 (*.f64 d a) (hypot.f64 c d))
	19.3b	(/.f64 c (fma.f64 c c (*.f64 d d)))

series150.0ms (2.9%)

Counts

2 → 72

Calls

18 calls:

21.0ms	(/.f64 (/.f64 (*.f64 d a) (hypot.f64 c d)) (hypot.f64 c d))	a	-inf
18.0ms	(/.f64 (*.f64 d a) (hypot.f64 c d))	a	-inf
18.0ms	(/.f64 (/.f64 (*.f64 d a) (hypot.f64 c d)) (hypot.f64 c d))	a	inf
18.0ms	(/.f64 (*.f64 d a) (hypot.f64 c d))	a	inf
16.0ms	(/.f64 (/.f64 (*.f64 d a) (hypot.f64 c d)) (hypot.f64 c d))	a	0

rewrite52.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

917×	`log1p-expm1-u_binary64`
917×	`expm1-log1p-u_binary64`
88×	`add-sqr-sqrt_binary64`
88×	`pow1_binary64`
87×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	171	23
2	2448	23

Stop Event

1×	node limit

Counts

2 → 84

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

749×	`times-frac_binary64`
445×	`associate-/l*_binary64`
349×	`associate-/r*_binary64`
232×	`associate-r_binary64`
205×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	1888
1	276	1816
2	956	1733

Stop Event

1×	node limit

Counts

156 → 134

prune183.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	225	4	229
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	231	8	239

Error

0.2b

Counts

239 → 8

Alt Table

Status	Error	Program
	25.1b	(-.f64 (/.f64 (.f64 c b) (pow.f64 (hypot.f64 c d) 2)) (/.f64 (/.f64 (.f64 d a) (hypot.f64 c d)) (hypot.f64 c d)))
	43.6b	(-.f64 (.f64 b (/.f64 c (fma.f64 c c (.f64 d d)))) (*.f64 (/.f64 d c) (/.f64 a c)))
	34.9b	(fma.f64 (/.f64 (/.f64 a c) c) (neg.f64 d) (/.f64 b c))
	36.6b	(-.f64 (.f64 (/.f64 (/.f64 b d) d) c) (/.f64 (/.f64 (.f64 d a) (hypot.f64 c d)) (hypot.f64 c d)))
	30.5b	(fma.f64 b (/.f64 (/.f64 c d) d) (/.f64 (neg.f64 a) d))
	10.5b	(-.f64 (.f64 b (.f64 (/.f64 (pow.f64 (cbrt.f64 c) 2) (hypot.f64 c d)) (/.f64 (cbrt.f64 c) (hypot.f64 c d)))) (/.f64 (/.f64 (*.f64 d a) (hypot.f64 c d)) (hypot.f64 c d)))
	16.2b	(-.f64 (.f64 b (/.f64 c (fma.f64 c c (.f64 d d)))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 d (hypot.f64 c d)) a)) 2) 1) (/.f64 (cbrt.f64 (*.f64 (/.f64 d (hypot.f64 c d)) a)) (hypot.f64 c d))))
	38.0b	(-.f64 (/.f64 b c) (.f64 (/.f64 d (.f64 c c)) (+.f64 a (/.f64 (*.f64 b d) c))))

Compiler

Compiled 6818 to 2234 computations (67.2% saved)

regimes1.5s (28.2%)

Accuracy

Total 5.6b remaining (91.3%)

Threshold costs 0b (0%)

Counts

125 → 3

Compiler

Compiled 13928 to 8539 computations (38.7% saved)

bsearch44.0ms (0.8%)

Algorithm

2×	binary-search

Calls

2 calls:

22.0ms	d
18.0ms	d

Steps

Iters	Point		Range
1.0364479188939085e+154	∈ [	4.283640888235788e+153	,	1.9292525623115435e+163	]
-1.692033155006485e+165	∈ [	-4.3389664077513974e+167	,	-1.342296805634099e+164	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	81
1	37	81
2	48	81
3	58	81
4	71	81
5	77	81
6	80	81
7	81	81

Stop Event

1×

saturated

end115.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 312 to 152 computations (51.3% saved)

Details

analyze718.0ms (13.8%)

sample1.1s (21.5%)

preprocess66.0ms (1.3%)

simplify42.0ms (0.8%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series82.0ms (1.6%)

rewrite49.0ms (0.9%)

simplify48.0ms (0.9%)

prune62.0ms (1.2%)

localize11.0ms (0.2%)

series157.0ms (3%)

rewrite65.0ms (1.3%)

simplify77.0ms (1.5%)

prune157.0ms (3%)

localize11.0ms (0.2%)

series198.0ms (3.8%)

rewrite58.0ms (1.1%)

simplify58.0ms (1.1%)

prune141.0ms (2.7%)

localize12.0ms (0.2%)

series150.0ms (2.9%)

rewrite52.0ms (1%)

simplify39.0ms (0.8%)

prune183.0ms (3.5%)

regimes1.5s (28.2%)

bsearch44.0ms (0.8%)

simplify5.0ms (0.1%)

end115.0ms (2.2%)

Profiling