Details

analyze620.0ms (8.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.2s (30.6%)

Results

713.0ms	5464×	body	128	valid
588.0ms	1114×	body	2048	valid
300.0ms	712×	body	1024	valid
266.0ms	408×	body	4096	valid
165.0ms	1125×	body	128	invalid
117.0ms	377×	body	512	valid
39.0ms	181×	body	256	valid

Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess37.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

531×	`associate-/l*_binary64`
461×	`fma-neg_binary64`
449×	`div-sub_binary64`
277×	`fma-def_binary64`
251×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	104
1	115	96
2	308	96
3	784	88
4	1482	88
5	2839	88
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 20 to 14 computations (30% saved)

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
544×	`div-sub_binary64`
489×	`fma-neg_binary64`
405×	`times-frac_binary64`
262×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	100	24
3	259	22
4	460	22
5	840	22
6	1790	22
7	2999	22
8	3682	22
9	4742	22

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

35.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	35.2b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	35.3b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.5b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series120.0ms (1.7%)

Counts

4 → 96

Calls

36 calls:

10.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	a	-inf
9.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	a	inf
7.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	c	-inf
7.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))	c	inf
5.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))	c	-inf

rewrite80.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

169×	`add-sqr-sqrt_binary64`
165×	`log1p-expm1-u_binary64`
165×	`expm1-log1p-u_binary64`
164×	`add-cbrt-cube_binary64`
160×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	347	62

Stop Event

1×	node limit

Counts

4 → 160

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

743×	`times-frac_binary64`
469×	`associate-/l*_binary64`
434×	`fma-def_binary64`
425×	`associate-/r*_binary64`
158×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	2060
1	415	1984
2	1475	1904

Stop Event

1×	node limit

Counts

256 → 236

prune183.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	229	7	236
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	229	9	238

Error

6.1b

Counts

238 → 9

Alt Table

Status	Error	Program
	36.9b	(/.f64 (-.f64 (neg.f64 b) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))) (.f64 2 a))
✓	35.2b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	48.1b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4))) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	50.4b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (pow.f64 b 2))) (*.f64 2 a))
	48.1b	(/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4))) (/.f64 1 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))) (*.f64 2 a))
	39.5b	(/.f64 (neg.f64 c) b)
	44.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	44.3b	(neg.f64 (/.f64 b a))
▶	35.3b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))

Compiler

Compiled 6277 to 3647 computations (41.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
✓	1.5b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	24.6b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series117.0ms (1.6%)

Counts

4 → 96

Calls

36 calls:

10.0ms	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))	a	-inf
9.0ms	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))	a	inf
8.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))	c	-inf
7.0ms	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))	c	-inf
7.0ms	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))	c	inf

rewrite66.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

954×	`prod-diff_binary64`
137×	`add-sqr-sqrt_binary64`
131×	`log1p-expm1-u_binary64`
131×	`expm1-log1p-u_binary64`
130×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	279	62
2	3616	62

Stop Event

1×	node limit

Counts

4 → 130

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
465×	`associate-/l*_binary64`
423×	`associate-/r*_binary64`
372×	`fma-def_binary64`
147×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	2045
1	381	1971
2	1339	1891

Stop Event

1×	node limit

Counts

226 → 204

prune180.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	198	6	204
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	203	10	213

Error

6.0b

Counts

213 → 10

Alt Table

Status	Error	Program
✓	35.2b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	44.4b	(*.f64 (+.f64 b b) (/.f64 -1/2 a))
	39.5b	(/.f64 (neg.f64 c) b)
	42.0b	(.f64 (.f64 2 (*.f64 (/.f64 c b) a)) (/.f64 -1/2 a))
	44.7b	(.f64 (.f64 2 (-.f64 b (*.f64 (/.f64 c b) a))) (/.f64 -1/2 a))
	45.6b	(/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 -1/2 a)) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
	50.4b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (pow.f64 b 2))) (*.f64 2 a))
	44.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	47.1b	(/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 (.f64 a -2) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
▶	35.3b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))

Compiler

Compiled 5147 to 3007 computations (41.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2))
✓	0.2b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
	1.5b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	24.6b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series188.0ms (2.6%)

Counts

2 → 40

Calls

18 calls:

36.0ms	(/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2))	c	inf
30.0ms	(/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2))	a	-inf
27.0ms	(/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2))	c	-inf
24.0ms	(/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2))	a	inf
11.0ms	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))	a	inf

rewrite70.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

972×	`prod-diff_binary64`
156×	`add-sqr-sqrt_binary64`
148×	`add-cbrt-cube_binary64`
148×	`log1p-expm1-u_binary64`
148×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	47
1	320	44
2	4211	44

Stop Event

1×	node limit

Counts

2 → 89

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

801×	`times-frac_binary64`
498×	`associate-/l*_binary64`
432×	`associate-/r*_binary64`
306×	`fma-def_binary64`
116×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1185
1	360	1168
2	1268	1105

Stop Event

1×	node limit

Counts

129 → 135

prune184.0ms (2.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	238	10	248

Error

6.0b

Counts

248 → 10

Alt Table

Status	Error	Program
✓	35.2b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	44.4b	(*.f64 (+.f64 b b) (/.f64 -1/2 a))
▶	39.5b	(/.f64 (neg.f64 c) b)
	39.6b	(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))
	44.7b	(.f64 (.f64 2 (-.f64 b (*.f64 (/.f64 c b) a))) (/.f64 -1/2 a))
	45.6b	(/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 -1/2 a)) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
	50.4b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (pow.f64 b 2))) (*.f64 2 a))
	44.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	47.1b	(/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 (.f64 a -2) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
✓	35.3b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))

Compiler

Compiled 6174 to 3775 computations (38.9% saved)

localize3.0ms (0%)

prune5.0ms (0.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	2	2
Total	10	10

Error

6.0b

Counts

10 → 10

Alt Table

Status	Error	Program
✓	35.2b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	44.4b	(*.f64 (+.f64 b b) (/.f64 -1/2 a))
✓	39.5b	(/.f64 (neg.f64 c) b)
	39.6b	(/.f64 1 (-.f64 (/.f64 a b) (/.f64 b c)))
	44.7b	(.f64 (.f64 2 (-.f64 b (*.f64 (/.f64 c b) a))) (/.f64 -1/2 a))
	45.6b	(/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 -1/2 a)) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
	50.4b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (pow.f64 b 2))) (*.f64 2 a))
	44.5b	(-.f64 (/.f64 c b) (/.f64 b a))
	47.1b	(/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 (.f64 a -2) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
✓	35.3b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))

Compiler

Compiled 171 to 110 computations (35.7% saved)

regimes2.7s (37.9%)

Accuracy

Total 5.0b remaining (47.1%)

Threshold costs 0b (0%)

Counts

201 → 3

Compiler

Compiled 16832 to 11622 computations (31% saved)

bsearch80.0ms (1.1%)

Algorithm

2×	binary-search

Calls

2 calls:

55.0ms	b
18.0ms	b

Steps

Iters	Point		Range
8.78674791955544e+79	∈ [	4.512357091273017e+79	,	9.269001199721543e+79	]
-2.0142789486219722e-102	∈ [	-5.237301060789583e-99	,	-1.9894619644440475e-115	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	35	50
2	44	50
3	51	50
4	55	50
5	56	50

Stop Event

1×

saturated

end124.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 245 to 156 computations (36.3% saved)

Details

analyze620.0ms (8.6%)

sample2.2s (30.6%)

preprocess37.0ms (0.5%)

simplify40.0ms (0.5%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series120.0ms (1.7%)

rewrite80.0ms (1.1%)

simplify59.0ms (0.8%)

prune183.0ms (2.5%)

localize9.0ms (0.1%)

series117.0ms (1.6%)

rewrite66.0ms (0.9%)

simplify47.0ms (0.6%)

prune180.0ms (2.5%)

localize11.0ms (0.1%)

series188.0ms (2.6%)

rewrite70.0ms (1%)

simplify33.0ms (0.5%)

prune184.0ms (2.6%)

localize3.0ms (0%)

prune5.0ms (0.1%)

regimes2.7s (37.9%)

bsearch80.0ms (1.1%)

simplify3.0ms (0%)

end124.0ms (1.7%)

Profiling