Details

analyze3.2s (10.7%)

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%	98.2%	1.8%	7
0%	92%	8%	8
0%	91.2%	8.8%	9
0.4%	89.3%	10.3%	10
7.1%	79.2%	13.6%	11
11.9%	70.2%	17.9%	12
13.8%	67.4%	18.7%	13
16.6%	63.3%	20.1%	14

Compiler

Compiled 45 to 33 computations (26.7% saved)

sample7.1s (24.1%)

Symmetry

(sort A C)

Results

1.7s	5748×	body	128	valid
944.0ms	882×	body	1024	valid
829.0ms	681×	body	2048	valid
795.0ms	2593×	body	128	invalid
779.0ms	788×	body	1024	invalid
736.0ms	634×	body	2048	invalid
538.0ms	589×	body	512	valid
396.0ms	561×	body	512	invalid
169.0ms	354×	body	256	valid
150.0ms	322×	body	256	invalid
3.0ms	2×	body	4096	valid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify49.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

759×	`neg-mul-1_binary64`
493×	`associate-l_binary64`
463×	`associate-r_binary64`
420×	`distribute-rgt-in_binary64`
410×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	61	49
2	176	49
3	648	49
4	2727	49
5	4869	49
6	5512	49

prune6.0ms (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

50.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
▶	50.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

Status

Error

Program

55.4b

(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))

▶

50.9b

(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))

Compiler

Compiled 239 to 156 computations (34.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	4.4b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	12.9b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
✓	25.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

series7.9s (26.6%)

Counts

4 → 124

Calls

4 calls:

4.5s	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
3.2s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
147.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
40.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite118.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`distribute-lft-in_binary64`
204×	`distribute-rgt-in_binary64`
164×	`*-un-lft-identity_binary64`
108×	`prod-diff_binary64`
105×	`add-sqr-sqrt_binary64`

Counts

4 → 284

Calls

4 calls:

23.0ms	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
13.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
5.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
5.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

simplify663.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

721×	`times-frac_binary64`
670×	`fma-def_binary64`
277×	`associate-/l*_binary64`
190×	`associate-/r*_binary64`
93×	`sub-neg_binary64`

Counts

408 → 499

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	2765	55201
1	4842	49427
2	5911	49427

prune1.3s (4.3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	476	23	499
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	477	24	501

Error

20.0b

Counts

501 → 24

Alt Table

Status	Error	Program
	52.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	50.9b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
	51.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	61.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (fma.f64 A A (.f64 C C)) (.f64 2 (.f64 A C)))))) (*.f64 A C)))) (sqrt.f64 2)))
	50.9b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	63.0b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (sqrt.f64 (+.f64 A C)) (sqrt.f64 (+.f64 A C)) (neg.f64 (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	55.9b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 A A) (.f64 F (.f64 B B))) C) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.8b	(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	51.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	54.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.4b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	62.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	51.3b	(/.f64 (neg.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
▶	45.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	50.8b	(/.f64 (neg.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	63.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.9b	(/.f64 (neg.f64 (-.f64 (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 C B))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 C B))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (fma.f64 C C (.f64 B B)) (-.f64 C (hypot.f64 C B)))))) (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 C B)))) (.f64 (sqrt.f64 2) B))))) (.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 C B)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	52.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 1/2 (+.f64 (/.f64 (.f64 C (.f64 B B)) (.f64 A A)) (/.f64 (.f64 B B) A))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 69455 to 36738 computations (47.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.9b	(.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C))))
✓	6.4b	(/.f64 (*.f64 B B) C)
✓	13.9b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C)))))))
✓	23.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

series492.0ms (1.7%)

Counts

4 → 120

Calls

4 calls:

226.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
213.0ms	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C)))))))
42.0ms	(.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C))))
10.0ms	(/.f64 (*.f64 B B) C)

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
16×	`distribute-lft-neg-in_binary64`

Counts

4 → 127

Calls

4 calls:

5.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
5.0ms	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C)))))))
3.0ms	(/.f64 (*.f64 B B) C)
3.0ms	(.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C))))

simplify191.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

581×	`fma-def_binary64`
354×	`times-frac_binary64`
327×	`associate-/l*_binary64`
318×	`associate-r_binary64`
254×	`associate-l_binary64`

Counts

247 → 250

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	372	10053
1	992	9704
2	4476	9704
3	5049	9704

prune335.0ms (1.1%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	244	6	250
Fresh	3	20	23
Picked	0	1	1
Done	0	0	0
Total	247	27	274

Error

19.3b

Counts

274 → 27

Alt Table

Status	Error	Program
	51.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	61.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (fma.f64 A A (.f64 C C)) (.f64 2 (.f64 A C)))))) (*.f64 A C)))) (sqrt.f64 2)))
	50.9b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
▶	45.6b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C)))))))))
	63.0b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (sqrt.f64 (+.f64 A C)) (sqrt.f64 (+.f64 A C)) (neg.f64 (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	51.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	62.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (.f64 (/.f64 F C) (pow.f64 B 4)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	55.9b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 A A) (.f64 F (.f64 B B))) C) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.8b	(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.9b	(.f64 (sqrt.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	47.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	51.3b	(/.f64 (neg.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
✓	45.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	50.8b	(/.f64 (neg.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	63.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.9b	(/.f64 (neg.f64 (-.f64 (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 C B))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 C B))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (fma.f64 C C (.f64 B B)) (-.f64 C (hypot.f64 C B)))))) (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 C B)))) (.f64 (sqrt.f64 2) B))))) (.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 C B)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	52.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	46.8b	(/.f64 (neg.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.6b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	52.6b	(.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 -1/2 (/.f64 (.f64 B B) C) (.f64 2 A)))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))

Compiler

Compiled 15963 to 8975 computations (43.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.9b	(.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C))))
	6.4b	(/.f64 (*.f64 B B) C)
	13.9b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C)))))))
✓	23.1b	(/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C))))))))

series449.0ms (1.5%)

Counts

1 → 24

Calls

1 calls:

449.0ms

(/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C))))))))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

1 → 33

Calls

1 calls:

6.0ms

(/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C))))))))

simplify115.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-/r/_binary64`
442×	`distribute-rgt-in_binary64`
441×	`distribute-lft-in_binary64`
404×	`*-commutative_binary64`
342×	`div-sub_binary64`

Counts

57 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	81	2696
1	140	2502
2	375	2502
3	1493	2502
4	3654	2502
5	4798	2502
6	5621	2502

prune225.0ms (0.8%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	2	23	25
Picked	0	1	1
Done	0	1	1
Total	169	28	197

Error

19.1b

Counts

197 → 28

Alt Table

Status	Error	Program
	51.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	61.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (fma.f64 A A (.f64 C C)) (.f64 2 (.f64 A C)))))) (*.f64 A C)))) (sqrt.f64 2)))
	50.9b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
✓	45.6b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C)))))))))
	63.0b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (sqrt.f64 (+.f64 A C)) (sqrt.f64 (+.f64 A C)) (neg.f64 (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.6b	(/.f64 -1 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 C F))) (sqrt.f64 2)))
	51.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	62.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (.f64 (/.f64 F C) (pow.f64 B 4)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	55.9b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 A A) (.f64 F (.f64 B B))) C) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.8b	(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.9b	(.f64 (sqrt.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	47.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	51.3b	(/.f64 (neg.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
✓	45.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	50.8b	(/.f64 (neg.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	63.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.9b	(/.f64 (neg.f64 (-.f64 (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 C B))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 C B))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (fma.f64 C C (.f64 B B)) (-.f64 C (hypot.f64 C B)))))) (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 C B)))) (.f64 (sqrt.f64 2) B))))) (.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 C B)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.8b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 F C))))))))
	62.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	52.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
▶	46.8b	(/.f64 (neg.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.6b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 F C)))))))
	52.6b	(.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 -1/2 (/.f64 (.f64 B B) C) (.f64 2 A)))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))

Compiler

Compiled 11100 to 6494 computations (41.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.4b	(/.f64 (*.f64 B B) C)
	13.9b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C)))))))
✓	18.2b	(log.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C))))))))
✓	23.5b	(/.f64 (neg.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

series1.1s (3.8%)

Counts

2 → 48

Calls

2 calls:

912.0ms

(log.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C))))))))

215.0ms

(/.f64 (neg.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C)))))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))

rewrite38.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
42×	`add-cube-cbrt_binary64`
36×	`log-prod_binary64`

Counts

2 → 111

Calls

2 calls:

9.0ms

(/.f64 (neg.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C)))))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))

4.0ms

(log.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C))))))))

simplify235.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
292×	`sub-neg_binary64`
252×	`times-frac_binary64`
248×	`associate-/l*_binary64`
183×	`associate-/r*_binary64`

Counts

159 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	362	11066
1	885	10189
2	3655	10167
3	4986	10167
4	4967	10167

prune583.0ms (2%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	301	3	304
Fresh	2	23	25
Picked	1	0	1
Done	0	2	2
Total	304	28	332

Error

19.1b

Counts

332 → 28

Alt Table

Status	Error	Program
	51.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	52.3b	(/.f64 (neg.f64 (exp.f64 (-.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (log.f64 (/.f64 -1 A))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
	62.0b	(/.f64 (neg.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (.f64 (/.f64 F C) (pow.f64 B 4)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (fma.f64 A A (.f64 C C)) (.f64 2 (.f64 A C)))))) (*.f64 A C)))) (sqrt.f64 2)))
	50.9b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
✓	45.6b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (*.f64 B B) C)))))))))
	63.0b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (sqrt.f64 (+.f64 A C)) (sqrt.f64 (+.f64 A C)) (neg.f64 (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.6b	(/.f64 -1 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 C F))) (sqrt.f64 2)))
	55.9b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 A A) (.f64 F (.f64 B B))) C) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.8b	(/.f64 (neg.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	51.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	54.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.9b	(.f64 (sqrt.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	47.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	51.3b	(/.f64 (neg.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
✓	45.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	63.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.3b	(expm1.f64 (log1p.f64 (/.f64 (neg.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	60.9b	(/.f64 (neg.f64 (-.f64 (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 C B))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 C B))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (fma.f64 C C (.f64 B B)) (-.f64 C (hypot.f64 C B)))))) (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 C B)))) (.f64 (sqrt.f64 2) B))))) (.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 C B)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.8b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 F C))))))))
	62.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	52.5b	(.f64 (/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	58.6b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 F C)))))))
	52.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	52.6b	(.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 -1/2 (/.f64 (.f64 B B) C) (.f64 2 A)))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))

Compiler

Compiled 20173 to 11783 computations (41.6% saved)

regimes3.9s (13%)

Accuracy

Total 19.2b remaining (51.1%)

Threshold costs 0b (0%)

Counts

187 → 7

Compiler

Compiled 57085 to 34913 computations (38.8% saved)

bsearch818.0ms (2.8%)

Steps

Iters	Range		Point
8	9.912144652867839e+190	1.2100023927345213e+194	1.8496276951365653e+192
9	8.203240183861041e+33	3.773699742197884e+42	8.349140996588686e+33
8	0.004697436003505001	2.223001051033467	1.780894702735933
11	1.9362127990883291e-88	5.359290456521385e-65	1.7199397216927585e-66
4	-1.0119369454341328e-281	-6.649221107619406e-282	-1.0003519539071463e-281
8	-4.196835802278004e-160	-6.825824764939317e-164	-4.127320517617318e-160

Compiler

Compiled 5 to 4 computations (20% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

51×	`distribute-rgt-neg-in_binary64`
37×	`*-commutative_binary64`
37×	`distribute-lft-neg-in_binary64`
35×	`neg-sub0_binary64`
34×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	259
1	135	259
2	195	259
3	248	259
4	287	259
5	310	259
6	336	259
7	354	259
8	361	259
9	363	259
10	359	259

end714.0ms (2.4%)

Compiler: Compiled 1772 to 1101 computations (37.9% saved)

Iter	Nodes	Cost
0	82	259
1	135	259
2	195	259
3	248	259
4	287	259
5	310	259
6	336	259
7	354	259
8	361	259
9	363	259
10	359	259

Iter	Nodes	Cost
0	82	259
1	135	259
2	195	259
3	248	259
4	287	259
5	310	259
6	336	259
7	354	259
8	361	259
9	363	259
10	359	259

Details

analyze3.2s (10.7%)

sample7.1s (24.1%)

simplify49.0ms (0.2%)

prune6.0ms (0%)

localize17.0ms (0.1%)

series7.9s (26.6%)

rewrite118.0ms (0.4%)

simplify663.0ms (2.2%)

prune1.3s (4.3%)

localize17.0ms (0.1%)

series492.0ms (1.7%)

rewrite30.0ms (0.1%)

simplify191.0ms (0.6%)

prune335.0ms (1.1%)

localize16.0ms (0.1%)

series449.0ms (1.5%)

rewrite11.0ms (0%)

simplify115.0ms (0.4%)

prune225.0ms (0.8%)

localize19.0ms (0.1%)

series1.1s (3.8%)

rewrite38.0ms (0.1%)

simplify235.0ms (0.8%)

prune583.0ms (2%)

regimes3.9s (13%)

bsearch818.0ms (2.8%)

simplify20.0ms (0.1%)

end714.0ms (2.4%)

Profiling

Iter	Nodes	Cost
0	82	259
1	135	259
2	195	259
3	248	259
4	287	259
5	310	259
6	336	259
7	354	259
8	361	259
9	363	259
10	359	259