Details

analyze3.3s (8.7%)

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)

sample253.0ms (0.7%)

Algorithm

1×

intervals

Symmetry

(sort A C)

Results

33.0ms	173×	body	128	valid
29.0ms	37×	body	1024	valid
23.0ms	25×	body	2048	valid
22.0ms	20×	body	2048	nan
14.0ms	78×	body	128	nan
13.0ms	20×	body	1024	nan
12.0ms	21×	body	512	nan
9.0ms	18×	body	512	valid
2.0ms	6×	body	256	nan
1.0ms	3×	body	256	valid

Compiler

Compiled 93 to 69 computations (25.8% saved)

simplify53.0ms (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

49.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	50.8b	(/.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)))
▶	49.4b	(/.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

50.8b

(/.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)))

▶

49.4b

(/.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)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	2.8b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	12.8b	(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)))))))
✓	21.6b	(/.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)))

series17.5s (46.1%)

Counts

4 → 124

Calls

4 calls:

10.1s	(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)))))))
7.1s	(/.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)))
239.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
60.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite126.0ms (0.3%)

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:

30.0ms	(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)))))))
18.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
7.0ms	(/.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)))
6.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

simplify673.0ms (1.8%)

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 (3.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	477	22	499
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	479	22	501

Error

19.1b

Counts

501 → 22

Alt Table

Status	Error	Program
	62.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.3b	(/.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)))
	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)))
	56.5b	(/.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)))))))
	48.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (+.f64 (/.f64 (.f64 B B) C) (/.f64 (.f64 A (.f64 B B)) (.f64 C C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.4b	(.f64 (sqrt.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 (neg.f64 (sqrt.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))))
	60.5b	(/.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)))
	59.9b	(/.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)))
	53.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	49.7b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 A C) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	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)))))
	47.2b	(/.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)))
	49.3b	(/.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)))
	52.3b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 A (.f64 F (.f64 B B))) (.f64 -16 (.f64 (.f64 A A) (.f64 C F)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	52.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	60.5b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 B C)))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B) (fma.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (-.f64 C (hypot.f64 B C)))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))) (.f64 1/2 (.f64 (/.f64 (*.f64 A (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))))))))
▶	46.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	50.1b	(/.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) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.3b	(/.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)))))))))
	59.8b	(/.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)))
	49.5b	(/.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)))

Compiler

Compiled 69469 to 36688 computations (47.2% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2))
✓	13.7b	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

series53.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

30.0ms	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2))
22.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`sqrt-prod_binary64`
6×	`sqrt-pow1_binary64`

Counts

2 → 44

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2))
3.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

simplify91.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

408×	`associate-*l/_binary64`
404×	`associate-*r/_binary64`
396×	`fma-def_binary64`
390×	`associate-/l*_binary64`
328×	`*-commutative_binary64`

Counts

44 → 46

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	636
1	95	600
2	236	596
3	514	596
4	997	596
5	1905	596
6	2041	596
7	2369	596
8	3387	596
9	4728	596
10	4986	596

prune88.0ms (0.2%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	38	8	46
Fresh	1	20	21
Picked	1	0	1
Done	0	0	0
Total	40	28	68

Error

18.2b

Counts

68 → 28

Alt Table

Status	Error	Program
	62.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.3b	(/.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)))
	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)))
	56.5b	(/.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)))))))
	48.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (+.f64 (/.f64 (.f64 B B) C) (/.f64 (.f64 A (.f64 B B)) (.f64 C C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.4b	(.f64 (sqrt.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 (neg.f64 (sqrt.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))))
	42.5b	(neg.f64 (.f64 (/.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 C)) (sqrt.f64 2)))
	60.5b	(/.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)))
	46.8b	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C)))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C)))) (sqrt.f64 2))))
	47.1b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C)))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	59.9b	(/.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)))
	53.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	46.7b	(neg.f64 (sqrt.f64 (neg.f64 (/.f64 F C))))
	47.8b	(neg.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C)))) (log.f64 (sqrt.f64 2)))))
	49.7b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 A C) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.8b	(neg.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	50.1b	(/.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) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	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)))))
	47.2b	(/.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)))
	49.3b	(/.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)))
	52.3b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 A (.f64 F (.f64 B B))) (.f64 -16 (.f64 (.f64 A A) (.f64 C F)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	52.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	60.5b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 B C)))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B) (fma.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (-.f64 C (hypot.f64 B C)))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))) (.f64 1/2 (.f64 (/.f64 (*.f64 A (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))))))))
	50.8b	(neg.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 (.f64 -1/2 (/.f64 F C)))) (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	49.3b	(/.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)))))))))
	59.8b	(/.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)))
▶	42.5b	(neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (sqrt.f64 C)))

Compiler

Compiled 2756 to 1769 computations (35.8% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 -1/2 F))
✓	0.2b	(/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (sqrt.f64 C))
✓	0.4b	(.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))

series102.0ms (0.3%)

Counts

3 → 0

Calls

3 calls:

86.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (sqrt.f64 C))
9.0ms	(.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))
7.0ms	(sqrt.f64 (*.f64 -1/2 F))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64`
12×	`sqrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

8.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (sqrt.f64 C))
6.0ms	(.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))
2.0ms	(sqrt.f64 (*.f64 -1/2 F))

simplify105.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

935×	`div-sub_binary64`
607×	`times-frac_binary64`
551×	`associate-/l*_binary64`
461×	`fma-def_binary64`
242×	`neg-mul-1_binary64`

Counts

72 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	96	1123
1	181	994
2	618	989
3	2839	989
4	2952	989
5	3710	989
6	4538	989
7	5860	989

prune143.0ms (0.4%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	3	24	27
Picked	1	0	1
Done	0	0	0
Total	77	33	110

Error

18.1b

Counts

110 → 33

Alt Table

Status	Error	Program
	49.3b	(/.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)))
	43.8b	(neg.f64 (/.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))) (sqrt.f64 C)))
	52.3b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 A (.f64 F (.f64 B B))) (.f64 -16 (.f64 (.f64 A A) (.f64 C F)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	43.8b	(neg.f64 (/.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 F))) (log.f64 (sqrt.f64 2)))) (sqrt.f64 C)))
	62.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.3b	(/.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)))
	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)))
	56.5b	(/.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)))))))
	48.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (+.f64 (/.f64 (.f64 B B) C) (/.f64 (.f64 A (.f64 B B)) (.f64 C C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	42.5b	(neg.f64 (/.f64 (sqrt.f64 (*.f64 -1/2 F)) (/.f64 (sqrt.f64 C) (sqrt.f64 2))))
	52.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	49.4b	(.f64 (sqrt.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 (neg.f64 (sqrt.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))))
	42.8b	(neg.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -1/2 F))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 F)))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 -1/2 F))) (sqrt.f64 2))) (sqrt.f64 C)))
	60.5b	(/.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)))
	60.5b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 B C)))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B) (fma.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (-.f64 C (hypot.f64 B C)))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))) (.f64 1/2 (.f64 (/.f64 (*.f64 A (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))))))))
	43.8b	(neg.f64 (/.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -1/2 F)))) (sqrt.f64 2)) (sqrt.f64 C)))
	59.9b	(/.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)))
	53.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	46.7b	(neg.f64 (sqrt.f64 (neg.f64 (/.f64 F C))))
	47.8b	(neg.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C)))) (log.f64 (sqrt.f64 2)))))
	49.7b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 A C) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.8b	(neg.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	61.8b	(neg.f64 (/.f64 (.f64 (log.f64 (exp.f64 (sqrt.f64 (.f64 -1/2 F)))) (sqrt.f64 2)) (sqrt.f64 C)))
	50.1b	(/.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) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.3b	(/.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)))))))))
▶	42.5b	(neg.f64 (/.f64 (sqrt.f64 (neg.f64 F)) (sqrt.f64 C)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	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)))))
	47.2b	(/.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)))
	43.0b	(neg.f64 (/.f64 (.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 -1/2 F)))) (sqrt.f64 2)) (sqrt.f64 C)))
	47.1b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C)))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	44.2b	(neg.f64 (exp.f64 (-.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 F))) (log.f64 (sqrt.f64 2))) (log.f64 (sqrt.f64 C)))))
	59.8b	(/.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)))

Compiler

Compiled 3543 to 2390 computations (32.5% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (neg.f64 F)) (sqrt.f64 C))

series29.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

29.0ms

(/.f64 (sqrt.f64 (neg.f64 F)) (sqrt.f64 C))

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`sqrt-prod_binary64`
78×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
57×	`add-cube-cbrt_binary64`

Counts

1 → 113

Calls

1 calls:

8.0ms

(/.f64 (sqrt.f64 (neg.f64 F)) (sqrt.f64 C))

simplify220.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1342×	`fma-neg_binary64`
788×	`div-sub_binary64`
474×	`fma-def_binary64`
417×	`associate-/l*_binary64`
402×	`times-frac_binary64`

Counts

113 → 112

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	139	2274
1	201	2232
2	361	2232
3	644	2232
4	1301	2232
5	1725	2232
6	2250	2232
7	2702	2232
8	3029	2232
9	3654	2232
10	4573	2232
11	4794	2232

prune113.0ms (0.3%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	31	32
Picked	0	1	1
Done	0	0	0
Total	112	33	145

Error

18.1b

Counts

145 → 33

Alt Table

Status	Error	Program
	52.3b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 A (.f64 F (.f64 B B))) (.f64 -16 (.f64 (.f64 A A) (.f64 C F)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	43.8b	(neg.f64 (/.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 F))) (log.f64 (sqrt.f64 2)))) (sqrt.f64 C)))
	62.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.3b	(/.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)))
	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)))
	56.5b	(/.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)))))))
	48.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (+.f64 (/.f64 (.f64 B B) C) (/.f64 (.f64 A (.f64 B B)) (.f64 C C)))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	42.5b	(neg.f64 (/.f64 (sqrt.f64 (*.f64 -1/2 F)) (/.f64 (sqrt.f64 C) (sqrt.f64 2))))
	52.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	49.4b	(.f64 (sqrt.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 (neg.f64 (sqrt.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))))
	42.8b	(neg.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -1/2 F))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 F)))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 -1/2 F))) (sqrt.f64 2))) (sqrt.f64 C)))
	60.5b	(/.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)))
	60.5b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 B C)))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B) (fma.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (-.f64 C (hypot.f64 B C)))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))) (.f64 1/2 (.f64 (/.f64 (*.f64 A (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))))))))
	43.8b	(neg.f64 (/.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -1/2 F)))) (sqrt.f64 2)) (sqrt.f64 C)))
	59.9b	(/.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)))
	53.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	46.7b	(neg.f64 (sqrt.f64 (neg.f64 (/.f64 F C))))
	47.8b	(neg.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C)))) (log.f64 (sqrt.f64 2)))))
	49.7b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 A C) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (.f64 (.f64 (.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.8b	(neg.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	61.8b	(neg.f64 (/.f64 (.f64 (log.f64 (exp.f64 (sqrt.f64 (.f64 -1/2 F)))) (sqrt.f64 2)) (sqrt.f64 C)))
	50.1b	(/.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) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.3b	(/.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)))))))))
✓	42.5b	(neg.f64 (/.f64 (sqrt.f64 (neg.f64 F)) (sqrt.f64 C)))
	42.8b	(neg.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (sqrt.f64 (neg.f64 F))) (cbrt.f64 (sqrt.f64 (neg.f64 F)))) (fabs.f64 (cbrt.f64 C))) (/.f64 (cbrt.f64 (sqrt.f64 (neg.f64 F))) (sqrt.f64 (cbrt.f64 C)))))
	59.8b	(/.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)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	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)))))
	47.2b	(/.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)))
	49.3b	(/.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)))
	43.0b	(neg.f64 (/.f64 (.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 -1/2 F)))) (sqrt.f64 2)) (sqrt.f64 C)))
	47.1b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C)))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	44.2b	(neg.f64 (exp.f64 (-.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 F))) (log.f64 (sqrt.f64 2))) (log.f64 (sqrt.f64 C)))))

Compiler

Compiled 2916 to 1200 computations (58.8% saved)

regimes7.2s (19%)

Accuracy

Total 15.5b remaining (46.1%)

Threshold costs 0b (0%)

Counts

261 → 5

Compiler

Compiled 61036 to 38602 computations (36.8% saved)

bsearch21.0ms (0.1%)

Compiler: Compiled 44 to 32 computations (27.3% saved)

simplify52.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

129×	`distribute-rgt-neg-in_binary64`
93×	`cancel-sign-sub-inv_binary64`
91×	`distribute-lft-neg-in_binary64`
84×	`neg-sub0_binary64`
84×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	401
1	128	401
2	197	401
3	250	401
4	295	401
5	331	401
6	366	401
7	387	401
8	410	401
9	440	401
10	476	401
11	510	401
12	545	401
13	580	401
14	617	401
15	650	401
16	669	401
17	685	401
18	689	401
19	678	401

end19.0ms (0.1%)

Compiler: Compiled 795 to 540 computations (32.1% saved)

sample6.4s (16.8%)

Algorithm

1×

intervals

Results

1.1s	5547×	body	128	valid
798.0ms	636×	body	2048	valid
689.0ms	931×	body	1024	valid
594.0ms	818×	body	1024	nan
508.0ms	542×	body	2048	nan
443.0ms	2427×	body	128	nan
325.0ms	595×	body	512	nan
315.0ms	559×	body	512	valid
122.0ms	342×	body	256	nan
117.0ms	327×	body	256	valid

Compiler

Compiled 1434 to 924 computations (35.6% saved)

Iter	Nodes	Cost
0	70	401
1	128	401
2	197	401
3	250	401
4	295	401
5	331	401
6	366	401
7	387	401
8	410	401
9	440	401
10	476	401
11	510	401
12	545	401
13	580	401
14	617	401
15	650	401
16	669	401
17	685	401
18	689	401
19	678	401

Iter	Nodes	Cost
0	70	401
1	128	401
2	197	401
3	250	401
4	295	401
5	331	401
6	366	401
7	387	401
8	410	401
9	440	401
10	476	401
11	510	401
12	545	401
13	580	401
14	617	401
15	650	401
16	669	401
17	685	401
18	689	401
19	678	401

Details

analyze3.3s (8.7%)

sample253.0ms (0.7%)

simplify53.0ms (0.1%)

prune6.0ms (0%)

localize18.0ms (0%)

series17.5s (46.1%)

rewrite126.0ms (0.3%)

simplify673.0ms (1.8%)

prune1.3s (3.4%)

localize7.0ms (0%)

series53.0ms (0.1%)

rewrite12.0ms (0%)

simplify91.0ms (0.2%)

prune88.0ms (0.2%)

localize9.0ms (0%)

series102.0ms (0.3%)

rewrite20.0ms (0.1%)

simplify105.0ms (0.3%)

prune143.0ms (0.4%)

localize6.0ms (0%)

series29.0ms (0.1%)

rewrite18.0ms (0%)

simplify220.0ms (0.6%)

prune113.0ms (0.3%)

regimes7.2s (19%)

bsearch21.0ms (0.1%)

simplify52.0ms (0.1%)

end19.0ms (0.1%)

sample6.4s (16.8%)

Profiling

Iter	Nodes	Cost
0	70	401
1	128	401
2	197	401
3	250	401
4	295	401
5	331	401
6	366	401
7	387	401
8	410	401
9	440	401
10	476	401
11	510	401
12	545	401
13	580	401
14	617	401
15	650	401
16	669	401
17	685	401
18	689	401
19	678	401