Details

analyze3.4s (2.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	98.2%	1.8%	8
0%	94.3%	5.7%	9
0.4%	93%	6.6%	10
7.4%	83.3%	9.3%	11
12.4%	75.2%	12.4%	12
14.4%	68.9%	16.7%	13
16.8%	65.4%	17.8%	14

Compiler

Compiled 45 to 33 computations (26.7% saved)

sample177.0ms (0.1%)

Algorithm

1×

intervals

Results

30.0ms	174×	body	128	valid
23.0ms	30×	body	1024	nan
22.0ms	32×	body	1024	valid
21.0ms	19×	body	2048	valid
17.0ms	21×	body	2048	nan
17.0ms	79×	body	128	nan
9.0ms	18×	body	512	valid
8.0ms	15×	body	512	nan
5.0ms	13×	body	256	valid
5.0ms	14×	body	256	nan

Compiler

Compiled 93 to 69 computations (25.8% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

560×	`associate-l_binary64`
528×	`associate-r_binary64`
455×	`distribute-rgt-in_binary64`
450×	`fma-def_binary64`
449×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	66	49
2	202	49
3	721	49
4	2973	49
5	4968	49
6	4966	49
7	4969	49
8	4939	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

48.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	52.5b	(/.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)))
▶	48.6b	(/.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)))

Status

Error

Program

52.5b

(/.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)))

▶

48.6b

(/.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)))

Compiler

Compiled 239 to 156 computations (34.7% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.8b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	3.5b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	17.1b	(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)))))))
✓	18.9b	(/.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)))

series17.3s (11.5%)

Counts

4 → 124

Calls

4 calls:

9.6s	(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)))))))
7.4s	(/.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)))
223.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
63.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite52.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
31×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
23×	`pow1_binary64`

Counts

4 → 140

Calls

4 calls:

10.0ms	(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)))))))
10.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
9.0ms	(.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)))

simplify416.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-def_binary64`
274×	`associate-/l*_binary64`
213×	`associate-*l/_binary64`
183×	`associate-/r*_binary64`
149×	`times-frac_binary64`

Counts

264 → 361

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2448	45159
1	5052	45159

prune1.3s (0.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	335	26	361
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	337	26	363

Error

21.3b

Counts

363 → 26

Alt Table

Status	Error	Program
	48.7b	(/.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)))))))))
	59.4b	(/.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)))
	54.4b	(/.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 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.8b	(/.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)))
	57.9b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	55.2b	(/.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)))
	56.8b	(/.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)))
	56.1b	(/.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 (+.f64 (.f64 (+.f64 A C) (+.f64 A C)) (-.f64 (.f64 (hypot.f64 B (-.f64 A C)) (hypot.f64 B (-.f64 A C))) (*.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))
	55.6b	(/.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)))
	58.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
▶	47.9b	(.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)))))
	60.9b	(/.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))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(/.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)))
	55.3b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	48.7b	(.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))))
	54.8b	(/.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)))
	53.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	54.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.3b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))))) (.f64 A C))))))
	48.7b	(.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))))
	58.7b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.9b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

Compiler

Compiled 61950 to 33914 computations (45.3% saved)

localize20.0ms (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))))
	1.8b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	10.2b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	16.9b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series6.2s (4.1%)

Counts

3 → 60

Calls

3 calls:

4.9s

(/.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))))

1.2s

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

45.0ms

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

rewrite51.0ms (0%)

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:

18.0ms

(/.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))))

15.0ms

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

2.0ms

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

simplify453.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

657×	`*-commutative_binary64`
324×	`fma-def_binary64`
297×	`associate-r_binary64`
284×	`associate-+r+_binary64`
170×	`associate-/l*_binary64`

Counts

142 → 189

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1519	26044
1	5201	26044

prune1.2s (0.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	260	11	271
Fresh	8	17	25
Picked	1	0	1
Done	0	0	0
Total	269	28	297

Error

14.4b

Counts

297 → 28

Alt Table

Status	Error	Program
	48.7b	(/.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)))))))))
	59.4b	(/.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)))
	54.4b	(/.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 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.8b	(/.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)))
	55.2b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	56.1b	(/.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 (+.f64 (.f64 (+.f64 A C) (+.f64 A C)) (-.f64 (.f64 (hypot.f64 B (-.f64 A C)) (hypot.f64 B (-.f64 A C))) (*.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))
	57.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	60.3b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))))) (.f64 A C))))))
	54.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	54.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
▶	48.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	60.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.2b	(.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)))))
	60.9b	(/.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))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.0b	(.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)))))
	55.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (.f64 B B) A)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	53.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	58.0b	(/.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)))
	55.3b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.8b	(/.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)))
	53.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	53.5b	(.f64 -1 (/.f64 (-.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C))) (.f64 A (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (sqrt.f64 2))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 B B) (.f64 C C)) (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C)))) (.f64 A (.f64 C (sqrt.f64 2)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	55.2b	(/.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)))
	48.7b	(.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))))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))))
	54.5b	(.f64 -1 (/.f64 (-.f64 (fma.f64 1/2 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))))) (.f64 1/2 (.f64 (.f64 A (.f64 C (sqrt.f64 2))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))

Compiler

Compiled 40627 to 22895 computations (43.6% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))
	1.8b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	9.9b	(sqrt.f64 (.f64 2 (.f64 F (*.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))
	16.9b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series1.1s (0.7%)

Counts

2 → 56

Calls

2 calls:

1.1s

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

53.0ms

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

rewrite47.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
39×	`sqrt-prod_binary64`
32×	`sqrt-div_binary64`
27×	`pow1_binary64`
26×	`add-sqr-sqrt_binary64`

Counts

2 → 96

Calls

2 calls:

18.0ms

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

13.0ms

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

simplify153.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-def_binary64`
267×	`associate-/r*_binary64`
254×	`*-commutative_binary64`
208×	`associate-/l*_binary64`
183×	`times-frac_binary64`

Counts

152 → 214

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	716	9010
1	2193	7617
2	4975	7617

prune504.0ms (0.3%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	406	9	415
Fresh	4	23	27
Picked	1	0	1
Done	0	0	0
Total	411	32	443

Error

14.4b

Counts

443 → 32

Alt Table

Status	Error	Program
▶	48.7b	(/.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)))))))))
	59.4b	(/.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)))
	54.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (-.f64 (.f64 2 (/.f64 (.f64 A C) B)) B)))
	54.4b	(/.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 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.8b	(/.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)))
	55.2b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	53.6b	(.f64 -1 (/.f64 (fma.f64 1/2 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (/.f64 F (+.f64 A (hypot.f64 B A))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A)))) (.f64 (.f64 (.f64 A (.f64 C (sqrt.f64 2))) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 A A)) (+.f64 A (hypot.f64 B A)))))) -1/2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	56.1b	(/.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 (+.f64 (.f64 (+.f64 A C) (+.f64 A C)) (-.f64 (.f64 (hypot.f64 B (-.f64 A C)) (hypot.f64 B (-.f64 A C))) (*.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))
	51.9b	(.f64 -1 (/.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (+.f64 C (hypot.f64 B C)))) (.f64 (sqrt.f64 2) A)) (fma.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (+.f64 C (hypot.f64 B C))))) (.f64 A (.f64 C (sqrt.f64 2)))) -1/2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	60.3b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))))) (.f64 A C))))))
	54.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	60.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	49.2b	(.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)))))
	58.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 B))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	60.9b	(/.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))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (.f64 2 A)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	59.0b	(.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)))))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (.f64 2 C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	58.0b	(/.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)))
	55.3b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) B))
	52.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (cbrt.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))))
	57.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 A (.f64 (/.f64 (.f64 B B) C) -1/2))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	54.8b	(/.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)))
	53.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	55.2b	(/.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)))
	48.7b	(.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))))
	53.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	55.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 C (.f64 (/.f64 (.f64 B B) A) -1/2))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))

Compiler

Compiled 29243 to 14311 computations (51.1% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.8b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	3.5b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
	17.1b	(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)))))))
✓	18.5b	(/.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))))))))

series1.6min (64.7%)

Counts

1 → 20

Calls

1 calls:

1.6min

(/.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))))))))

rewrite13.0ms (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`
6×	`associate-*r/_binary64`

Counts

1 → 35

Calls

1 calls:

9.0ms

(/.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 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))))

simplify188.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

996×	`fma-def_binary64`
460×	`*-commutative_binary64`
229×	`associate-r_binary64`
189×	`+-commutative_binary64`
185×	`distribute-rgt-in_binary64`

Counts

55 → 102

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1037	16452
1	3442	13557
2	5080	13557

prune837.0ms (0.6%)

Pruning

35 alts after pruning (34 fresh and 1 done)

	Pruned	Kept	Total
New	331	10	341
Fresh	7	24	31
Picked	0	1	1
Done	0	0	0
Total	338	35	373

Error

14.3b

Counts

373 → 35

Alt Table

Status	Error	Program
✓	48.7b	(/.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)))))))))
	59.4b	(/.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)))
	54.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (-.f64 (.f64 2 (/.f64 (.f64 A C) B)) B)))
	54.4b	(/.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 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.8b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.5b	(/.f64 -1 (/.f64 (sqrt.f64 (.f64 -4 (/.f64 (.f64 A C) (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (pow.f64 A 2) (pow.f64 C 2)) (.f64 2 (*.f64 A C)))))))))) (sqrt.f64 2)))
	55.2b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	53.6b	(.f64 -1 (/.f64 (fma.f64 1/2 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (/.f64 F (+.f64 A (hypot.f64 B A))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A)))) (.f64 (.f64 (.f64 A (.f64 C (sqrt.f64 2))) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 A A)) (+.f64 A (hypot.f64 B A)))))) -1/2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	56.8b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (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)))))))
	61.4b	(/.f64 -1 (-.f64 (fma.f64 1/4 (fma.f64 (/.f64 A (.f64 C C)) (/.f64 (.f64 B B) (.f64 F (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -2 (/.f64 A F)))))) (/.f64 (.f64 B B) (.f64 C (.f64 F (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -2 (/.f64 A F)))))))) (/.f64 (sqrt.f64 (.f64 -2 (/.f64 A F))) (sqrt.f64 2))) (.f64 1/32 (/.f64 (pow.f64 B 4) (.f64 (.f64 C C) (.f64 (.f64 F F) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (.f64 -2 (/.f64 A F))) 3))))))))
	54.2b	(/.f64 -1 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 A F))) (sqrt.f64 2)))
	51.9b	(.f64 -1 (/.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 F (+.f64 C (hypot.f64 B C)))) (.f64 (sqrt.f64 2) A)) (fma.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (+.f64 C (hypot.f64 B C))))) (.f64 A (.f64 C (sqrt.f64 2)))) -1/2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	54.4b	(/.f64 -1 (.f64 (/.f64 B (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 F (+.f64 A (hypot.f64 B A)))))))
	54.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	48.7b	(.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))))
	55.3b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))))
	58.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 B))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	54.1b	(/.f64 -1 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 C F))) (sqrt.f64 2)))
	60.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	49.2b	(.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)))))
	59.0b	(.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)))))
	54.2b	(/.f64 -1 (.f64 (sqrt.f64 (/.f64 1 (.f64 F (+.f64 C (hypot.f64 C B))))) (/.f64 B (sqrt.f64 2))))
	60.9b	(/.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))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (.f64 2 A)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	54.4b	(/.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 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))))))
	58.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (.f64 2 C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	58.0b	(/.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)))
	52.8b	(/.f64 -1 (.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (/.f64 (sqrt.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 C A) (hypot.f64 B (-.f64 A C))))))))))
	53.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) B))
	54.8b	(/.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)))
	53.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	55.2b	(/.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)))
	57.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 A (.f64 (/.f64 (.f64 B B) C) -1/2))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 C (.f64 (/.f64 (.f64 B B) A) -1/2))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))

Compiler

Compiled 53969 to 30612 computations (43.3% saved)

regimes5.6s (3.8%)

Accuracy

Total 23.5b remaining (59.3%)

Threshold costs 0b (0%)

Counts

260 → 7

Compiler

Compiled 69896 to 43562 computations (37.7% saved)

bsearch755.0ms (0.5%)

Steps

Iters	Range		Point
5	6.088582401381689e-12	1.482793704034907e-11	6.4709542352011415e-12
9	4.750068690566693e-170	3.1279486243144705e-163	7.188285169875155e-169
10	-4.2377671794310114e-226	-1.1582273180771168e-237	-5.421061115337358e-229
8	-1.9264398386291934e-104	-1.5074797070138038e-107	-1.1148721127505119e-104
8	-2.7023173519515316e-84	-2.2140627483863102e-88	-2.3644555656536877e-87
6	-3.328319398720565e+84	-5.970423337538486e+83	-6.441662385210033e+83

Compiler

Compiled 5 to 4 computations (20% saved)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Rules

33×	`*-commutative_binary64`
24×	`+-commutative_binary64`
19×	`sub-neg_binary64`
17×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	320
1	130	320
2	165	320
3	192	320
4	209	320
5	214	320
6	215	320
7	214	320

end4.0ms (0%)

Compiler: Compiled 215 to 110 computations (48.8% saved)

sample13.2s (8.8%)

Algorithm

1×

intervals

Results

956.0ms	5538×	body	128	valid
613.0ms	897×	body	1024	valid
557.0ms	637×	body	2048	valid
536.0ms	771×	body	1024	nan
512.0ms	587×	body	2048	nan
507.0ms	2865×	body	128	nan
306.0ms	598×	body	512	valid
285.0ms	567×	body	512	nan
124.0ms	330×	body	256	valid
105.0ms	319×	body	256	nan

Compiler

Compiled 1826 to 1132 computations (38% saved)

Details

analyze3.4s (2.2%)

sample177.0ms (0.1%)

simplify81.0ms (0.1%)

prune6.0ms (0%)

localize18.0ms (0%)

series17.3s (11.5%)

rewrite52.0ms (0%)

simplify416.0ms (0.3%)

prune1.3s (0.8%)

localize20.0ms (0%)

series6.2s (4.1%)

rewrite51.0ms (0%)

simplify453.0ms (0.3%)

prune1.2s (0.8%)

localize21.0ms (0%)

series1.1s (0.7%)

rewrite47.0ms (0%)

simplify153.0ms (0.1%)

prune504.0ms (0.3%)

localize17.0ms (0%)

series1.6min (64.7%)

rewrite13.0ms (0%)

simplify188.0ms (0.1%)

prune837.0ms (0.6%)

regimes5.6s (3.8%)

bsearch755.0ms (0.5%)

simplify12.0ms (0%)

end4.0ms (0%)

sample13.2s (8.8%)

Profiling