Details

analyze3.1s (5.4%)

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
3.1%	95.1%	1.8%	7
10.9%	81.1%	8%	8
10.9%	80.3%	8.8%	9
12.1%	77.6%	10.3%	10
15.6%	70.8%	13.6%	11
20.5%	61.6%	17.9%	12
20.5%	60.8%	18.7%	13
21.6%	58.2%	20.1%	14

Compiler

Compiled 45 to 33 computations (26.7% saved)

sample6.1s (10.6%)

Symmetry

(sort A C)

Results

1.4s	5653×	body	128	valid
840.0ms	708×	body	2048	valid
813.0ms	906×	body	1024	valid
675.0ms	817×	body	1024	invalid
610.0ms	2443×	body	128	invalid
591.0ms	565×	body	2048	invalid
423.0ms	612×	body	512	valid
372.0ms	593×	body	512	invalid
157.0ms	374×	body	256	valid
152.0ms	336×	body	256	invalid
4.0ms	3×	body	4096	valid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify49.0ms (0.1%)

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
	53.6b	(/.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)))
▶	50.8b	(/.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

53.6b

(/.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)))

▶

50.8b

(/.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)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(-.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))))))
✓	17.7b	(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)))))))
✓	19.3b	(/.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)))

series16.9s (29.5%)

Counts

4 → 124

Calls

4 calls:

9.8s	(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)))))))
6.8s	(/.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)))
251.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
58.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite110.0ms (0.2%)

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)))))))
16.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
6.0ms	(/.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)))

simplify679.0ms (1.2%)

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 (2.3%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	471	28	499
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	472	29	501

Error

22.0b

Counts

501 → 29

Alt Table

Status	Error	Program
	60.7b	(/.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)))
	55.3b	(/.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)))
	63.0b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (/.f64 (.f64 A C) B))) (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) B)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.8b	(.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	(/.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)))
	53.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	48.7b	(/.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)))
	54.5b	(-.f64 (.f64 1/16 (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (.f64 A (.f64 (pow.f64 C 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))))) (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	50.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
▶	47.6b	(.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)))))
	56.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	48.4b	(.f64 (sqrt.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))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	63.0b	(/.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)))
	50.5b	(/.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)))
	50.4b	(/.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)))
	59.1b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))))) (/.f64 (sqrt.f64 2) B)))
	48.4b	(.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)))))
	62.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (fma.f64 (sqrt.f64 (+.f64 A C)) (sqrt.f64 (+.f64 A C)) (neg.f64 (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (cbrt.f64 (hypot.f64 B (-.f64 A C))))))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C)))) (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (cbrt.f64 (hypot.f64 B (-.f64 A C)))) (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (cbrt.f64 (hypot.f64 B (-.f64 A C)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	48.5b	(/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 10 (.f64 A (.f64 C (.f64 F B)))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (fma.f64 A A (.f64 C C))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) (+.f64 C B)))) (/.f64 (.f64 A C) B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.6b	(/.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)))
	57.9b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (/.f64 (sqrt.f64 2) B)))
	47.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.6b	(/.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)))
	57.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (+.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))

Compiler

Compiled 69809 to 36922 computations (47.1% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.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))))
	1.4b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	9.0b	(sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	17.0b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series3.8s (6.6%)

Counts

3 → 60

Calls

3 calls:

2.8s

(/.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))))

955.0ms

(sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

46.0ms

(sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

15.0ms

(sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

9.0ms

(/.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))))

1.0ms

(sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))

simplify254.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

666×	`*-commutative_binary64`
325×	`fma-def_binary64`
300×	`associate-r_binary64`
285×	`associate-+r+_binary64`
176×	`associate-*l/_binary64`

Counts

142 → 189

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1541	26234
1	5173	26234

prune832.0ms (1.4%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	277	10	287
Fresh	8	20	28
Picked	1	0	1
Done	0	0	0
Total	286	30	316

Error

17.5b

Counts

316 → 30

Alt Table

Status	Error	Program
	60.7b	(/.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)))
	55.3b	(/.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)))
	63.0b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	50.4b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	59.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (/.f64 (.f64 A C) B))) (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) B)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (/.f64 (.f64 A C) B))) (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) B)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.8b	(.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))))
	59.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) (+.f64 C B)))) (/.f64 (.f64 A C) B))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	51.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	63.0b	(/.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)))
	53.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	57.9b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (/.f64 (sqrt.f64 2) B)))
▶	47.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (fma.f64 1 (+.f64 A C) (neg.f64 (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	53.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	48.7b	(/.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)))
	54.5b	(-.f64 (.f64 1/16 (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (.f64 A (.f64 (pow.f64 C 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))))) (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	61.6b	(/.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)))
	48.2b	(.f64 -1 (sqrt.f64 (/.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	63.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 2 C)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	50.4b	(/.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)))
	55.9b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))))) (sqrt.f64 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 10 (.f64 A (.f64 C (.f64 F B)))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (fma.f64 A A (.f64 C C))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.0b	(.f64 -1 (/.f64 (sqrt.f64 (.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))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) (+.f64 C B)))) (/.f64 (.f64 A C) B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.6b	(/.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)))
	50.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	50.5b	(/.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)))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (fma.f64 (sqrt.f64 (+.f64 A C)) (sqrt.f64 (+.f64 A C)) (neg.f64 (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (cbrt.f64 (hypot.f64 B (-.f64 A C))))))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C)))) (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (cbrt.f64 (hypot.f64 B (-.f64 A C)))) (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) (cbrt.f64 (hypot.f64 B (-.f64 A C)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (+.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))

Compiler

Compiled 41904 to 23239 computations (44.5% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.6b	(fma.f64 1 (+.f64 A C) (neg.f64 (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))
✓	10.7b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (fma.f64 1 (+.f64 A C) (neg.f64 (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))))))
	17.0b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))
✓	62.5b	(fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))

series13.0s (22.6%)

Counts

3 → 66

Calls

3 calls:

6.8s

(fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))

6.1s

(sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (fma.f64 1 (+.f64 A C) (neg.f64 (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))))))

61.0ms

(fma.f64 1 (+.f64 A C) (neg.f64 (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
4×	`associate-*r/_binary64`
3×	`sqrt-pow1_binary64`
3×	`pow-prod-down_binary64`
3×	`*-un-lft-identity_binary64`

Counts

3 → 36

Calls

3 calls:

5.0ms

(sqrt.f64 (*.f64 2 (*.f64 F (+.f64 (fma.f64 1 (+.f64 A C) (neg.f64 (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))))))

0.0ms

(fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))

0.0ms

(fma.f64 1 (+.f64 A C) (neg.f64 (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))

simplify290.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

407×	`*-commutative_binary64`
250×	`associate-/l*_binary64`
240×	`+-commutative_binary64`
209×	`fma-def_binary64`
201×	`times-frac_binary64`

Counts

102 → 164

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1009	19072
1	2919	14952
2	4957	14952
3	4949	14952

prune526.0ms (0.9%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	197	4	201
Fresh	3	26	29
Picked	1	0	1
Done	0	0	0
Total	201	30	231

Error

17.3b

Counts

231 → 30

Alt Table

Status	Error	Program
	62.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (.f64 1/2 (+.f64 (/.f64 (.f64 B B) C) (+.f64 (/.f64 (.f64 (.f64 B B) (.f64 A A)) (pow.f64 C 3)) (/.f64 (.f64 (.f64 B B) A) (.f64 C C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	53.6b	(/.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)))
	60.7b	(/.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)))
	55.3b	(/.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)))
	63.0b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	50.4b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	59.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (/.f64 (.f64 A C) B))) (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) B)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (/.f64 (.f64 A C) B))) (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) B)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (fma.f64 1 (+.f64 A C) (neg.f64 (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))) (-.f64 B (.f64 2 (/.f64 (*.f64 A C) B)))))
	62.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (.f64 2 C) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	50.8b	(.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	(/.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)))
	53.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	51.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	57.9b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (/.f64 (sqrt.f64 2) B)))
	53.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	48.7b	(/.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)))
	52.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (fma.f64 1 (+.f64 A C) (neg.f64 (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))) (-.f64 (.f64 2 (/.f64 (*.f64 A C) B)) B)))
	54.5b	(-.f64 (.f64 1/16 (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (.f64 A (.f64 (pow.f64 C 2) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))))) (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	63.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 2 C)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
▶	48.2b	(.f64 -1 (sqrt.f64 (/.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	50.4b	(/.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)))
	55.9b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2)))))) (sqrt.f64 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 10 (.f64 A (.f64 C (.f64 F B)))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (fma.f64 A A (.f64 C C))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.0b	(.f64 -1 (/.f64 (sqrt.f64 (.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))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) (+.f64 C B)))) (/.f64 (.f64 A C) B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	50.5b	(/.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)))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (+.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))

Compiler

Compiled 35639 to 18444 computations (48.2% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))
	1.4b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	9.5b	(sqrt.f64 (/.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (fma.f64 A (.f64 C -4) (.f64 B B))))
✓	14.5b	(/.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

series3.4s (5.9%)

Counts

3 → 116

Calls

3 calls:

3.0s

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

310.0ms

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

115.0ms

(*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))

rewrite39.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
24×	`prod-diff_binary64`
17×	`distribute-lft-in_binary64`

Counts

3 → 106

Calls

3 calls:

13.0ms

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

8.0ms

(*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))

6.0ms

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

simplify285.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

448×	`fma-def_binary64`
385×	`associate-+r+_binary64`
307×	`associate-r_binary64`
230×	`associate-/l*_binary64`
187×	`associate-*l/_binary64`

Counts

222 → 292

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1840	29251
1	5490	29251

prune837.0ms (1.5%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	384	6	390
Fresh	5	24	29
Picked	0	1	1
Done	0	0	0
Total	389	31	420

Error

12.3b

Counts

420 → 31

Alt Table

Status	Error	Program
	62.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (.f64 1/2 (+.f64 (/.f64 (.f64 B B) C) (+.f64 (/.f64 (.f64 (.f64 B B) (.f64 A A)) (pow.f64 C 3)) (/.f64 (.f64 (.f64 B B) A) (.f64 C C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	50.2b	(*.f64 -1 (sqrt.f64 (neg.f64 (/.f64 F C))))
	53.6b	(/.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)))
	60.7b	(/.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)))
	55.3b	(/.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)))
	59.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (/.f64 (.f64 A C) B))) (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) B)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (/.f64 (.f64 A C) B))) (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) B)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (fma.f64 1 (+.f64 A C) (neg.f64 (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))) (-.f64 B (.f64 2 (/.f64 (*.f64 A C) B)))))
	62.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (.f64 2 C) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	50.8b	(.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	(/.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)))
	53.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	51.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	55.9b	(.f64 -1 (sqrt.f64 (fma.f64 2 (/.f64 (.f64 A F) (.f64 B B)) (.f64 2 (+.f64 (/.f64 (.f64 C F) (.f64 B B)) (/.f64 F B))))))
	57.9b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (/.f64 (sqrt.f64 2) B)))
	53.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	48.7b	(/.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)))
	52.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (fma.f64 1 (+.f64 A C) (neg.f64 (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))) (-.f64 (.f64 2 (/.f64 (*.f64 A C) B)) B)))
	55.8b	(.f64 -1 (sqrt.f64 (.f64 2 (/.f64 F B))))
	50.3b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	50.4b	(/.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)))
	58.6b	(.f64 -1 (sqrt.f64 (/.f64 (.f64 2 (neg.f64 (.f64 F B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 10 (.f64 A (.f64 C (.f64 F B)))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (fma.f64 A A (.f64 C C))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.0b	(.f64 -1 (/.f64 (sqrt.f64 (.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))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) (+.f64 C B)))) (/.f64 (.f64 A C) B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.4b	(.f64 -1 (sqrt.f64 (neg.f64 (+.f64 (/.f64 F C) (.f64 1/4 (/.f64 (.f64 F (pow.f64 B 2)) (.f64 A (pow.f64 C 2))))))))
	57.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (+.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))
	55.3b	(.f64 -1 (sqrt.f64 (.f64 -2 (/.f64 F B))))
	50.5b	(/.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)))
✓	48.2b	(.f64 -1 (sqrt.f64 (/.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 45181 to 24187 computations (46.5% saved)

regimes4.4s (7.7%)

Accuracy

Total 23.4b remaining (68.8%)

Threshold costs 0b (0%)

Counts

232 → 7

Compiler

Compiled 59622 to 36525 computations (38.7% saved)

bsearch640.0ms (1.1%)

Steps

Iters	Range		Point
9	2.479563745998034e+47	1.8737000550549857e+56	2.9540844299171573e+47
8	9.302875860552211e+32	2.6609228424298234e+36	2.629658228729529e+36
8	1.8407748816491138e-6	0.000865310049757441	1.857244320432199e-6
7	2.582898942222175e-83	6.159322476042253e-82	6.5483964685949686e-83
9	3.643365405653367e-170	1.1842999559596716e-160	2.906967315898597e-164
6	-0.6486877683920249	-0.09497303084972727	-0.09632938194503413

Compiler

Compiled 5 to 4 computations (20% saved)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Rules

37×	`*-commutative_binary64`
26×	`+-commutative_binary64`
24×	`sub-neg_binary64`
20×	`neg-sub0_binary64`
17×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	265
1	138	265
2	181	265
3	212	265
4	228	265
5	230	265
6	230	265

end737.0ms (1.3%)

Compiler: Compiled 1900 to 1114 computations (41.4% saved)

Details

analyze3.1s (5.4%)

sample6.1s (10.6%)

simplify49.0ms (0.1%)

prune6.0ms (0%)

localize16.0ms (0%)

series16.9s (29.5%)

rewrite110.0ms (0.2%)

simplify679.0ms (1.2%)

prune1.3s (2.3%)

localize16.0ms (0%)

series3.8s (6.6%)

rewrite33.0ms (0.1%)

simplify254.0ms (0.4%)

prune832.0ms (1.4%)

localize26.0ms (0%)

series13.0s (22.6%)

rewrite9.0ms (0%)

simplify290.0ms (0.5%)

prune526.0ms (0.9%)

localize16.0ms (0%)

series3.4s (5.9%)

rewrite39.0ms (0.1%)

simplify285.0ms (0.5%)

prune837.0ms (1.5%)

regimes4.4s (7.7%)

bsearch640.0ms (1.1%)

simplify12.0ms (0%)

end737.0ms (1.3%)

Profiling