Details

analyze3.3s (9.1%)

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)

sample6.5s (18.1%)

Results

1.5s	5718×	body	128	valid
825.0ms	702×	body	2048	valid
812.0ms	861×	body	1024	invalid
799.0ms	895×	body	1024	valid
706.0ms	2978×	body	128	invalid
668.0ms	598×	body	2048	invalid
404.0ms	580×	body	512	invalid
402.0ms	604×	body	512	valid
157.0ms	337×	body	256	valid
145.0ms	337×	body	256	invalid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify76.0ms (0.2%)

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

47.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	51.8b	(/.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)))
▶	47.3b	(/.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)))

Status

Error

Program

51.8b

(/.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)))

▶

47.3b

(/.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)))

Compiler

Compiled 239 to 156 computations (34.7% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(+.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))))))
✓	13.5b	(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)))

series16.0s (44.5%)

Counts

4 → 124

Calls

4 calls:

8.3s	(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)))
195.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
57.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite44.0ms (0.1%)

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:

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))))))
8.0ms	(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)))))))
5.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
5.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

simplify417.0ms (1.2%)

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

prune1.0s (2.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	336	25	361
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	338	25	363

Error

21.6b

Counts

363 → 25

Alt Table

Status	Error	Program
	47.3b	(.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)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	59.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.0b	(/.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)))
	57.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	47.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))))))) (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 (neg.f64 B)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.8b	(/.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)))
	52.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	59.0b	(/.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)))
	59.0b	(/.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)))
	57.2b	(/.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
▶	45.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (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)))
	58.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	53.8b	(/.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 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.2b	(/.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)))))))))
	61.4b	(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))))))
	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)))))))
	47.3b	(.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))))
	61.8b	(/.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) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.2b	(/.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)))
	58.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

Compiler

Compiled 61674 to 33784 computations (45.2% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 A (.f64 C -4) (.f64 B B))
	0.7b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	10.9b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	17.1b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series1.0s (2.9%)

Counts

3 → 76

Calls

3 calls:

979.0ms	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
43.0ms	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))
9.0ms	(fma.f64 A (.f64 C -4) (.f64 B B))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-*r/_binary64`
4×	`*-un-lft-identity_binary64`
4×	`sqrt-prod_binary64`

Counts

3 → 41

Calls

3 calls:

7.0ms	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
1.0ms	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))
0.0ms	(fma.f64 A (.f64 C -4) (.f64 B B))

simplify121.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
457×	`associate-l_binary64`
213×	`associate-/r*_binary64`
195×	`*-commutative_binary64`
163×	`associate-*r/_binary64`

Counts

117 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	525	6271
1	1642	5185
2	4962	5170
3	4981	5170

prune336.0ms (0.9%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	189	11	200
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	192	33	225

Error

13.9b

Counts

225 → 33

Alt Table

Status	Error	Program
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	47.3b	(.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)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	59.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.0b	(/.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)))
	57.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	58.3b	(.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)))))
	55.6b	(.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)))))
	60.3b	(/.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)))
	45.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))))
	47.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.6b	(.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 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	59.0b	(/.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)))
	46.7b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	59.0b	(/.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)))
	57.2b	(/.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)))
	52.2b	(/.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)))
▶	43.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	55.4b	(/.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)))
	45.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (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 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	58.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.4b	(.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)))))
	58.1b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	54.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 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)))))))
	47.3b	(.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))))
	61.8b	(/.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) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.4b	(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))))))

Compiler

Compiled 15007 to 8686 computations (42.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))
	0.7b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	10.1b	(sqrt.f64 (.f64 A (.f64 C -4)))
	10.9b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

series120.0ms (0.3%)

Counts

2 → 14

Calls

2 calls:

102.0ms	(.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))
18.0ms	(sqrt.f64 (.f64 A (.f64 C -4)))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
23×	`pow1_binary64`
19×	`sqrt-prod_binary64`
11×	`sqrt-pow1_binary64`
10×	`*-un-lft-identity_binary64`

Counts

2 → 67

Calls

2 calls:

5.0ms	(.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))
2.0ms	(sqrt.f64 (.f64 A (.f64 C -4)))

simplify84.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
542×	`times-frac_binary64`
416×	`fma-neg_binary64`
389×	`associate-r_binary64`
366×	`associate-l_binary64`

Counts

81 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1605
1	231	1417
2	677	1333
3	3847	1293
4	4987	1293
5	4969	1293

prune396.0ms (1.1%)

Pruning

37 alts after pruning (37 fresh and 0 done)

	Pruned	Kept	Total
New	258	5	263
Fresh	0	32	32
Picked	1	0	1
Done	0	0	0
Total	259	37	296

Error

13.8b

Counts

296 → 37

Alt Table

Status	Error	Program
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	47.3b	(.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)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	59.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.0b	(/.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)))
	57.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
▶	44.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))))) (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))))))
	58.3b	(.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)))))
	55.6b	(.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)))))
	60.3b	(/.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)))
	45.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))))
	47.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.6b	(.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 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	59.0b	(/.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)))
	46.7b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	59.0b	(/.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)))
	57.2b	(/.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)))
	48.5b	(.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))) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	52.2b	(/.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)))
	55.4b	(/.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)))
	45.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (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 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	58.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.4b	(.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)))))
	58.1b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	54.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 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)))))))
	47.3b	(.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))))
	61.8b	(/.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) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	48.9b	(.f64 -1 (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) 3)) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	57.9b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	59.8b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (fma.f64 A A (.f64 C (-.f64 C (.f64 2 A)))))))))) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	61.4b	(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))))))

Compiler

Compiled 19840 to 12040 computations (39.3% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))
	0.7b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	10.1b	(sqrt.f64 (.f64 A (.f64 C -4)))
	10.9b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

series252.0ms (0.7%)

Counts

1 → 14

Calls

1 calls:

252.0ms

(cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (*.f64 A (*.f64 C -4))) B)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 16

Calls

1 calls:

1.0ms

(cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (*.f64 A (*.f64 C -4))) B)))

simplify79.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

536×	`unswap-sqr_binary64`
535×	`fma-neg_binary64`
499×	`associate-r_binary64`
451×	`associate-l_binary64`
441×	`distribute-rgt-neg-in_binary64`

Counts

30 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	980
1	263	940
2	691	906
3	2856	902
4	4913	902
5	5064	902

prune738.0ms (2.1%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	359	3	362
Fresh	3	33	36
Picked	1	0	1
Done	0	0	0
Total	363	36	399

Error

13.8b

Counts

399 → 36

Alt Table

Status	Error	Program
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	47.3b	(.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)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	59.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	48.9b	(.f64 -1 (/.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) 3)) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	56.1b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))))) (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))))))
	57.0b	(/.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)))
	57.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	58.3b	(.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)))))
	55.6b	(.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)))))
	60.3b	(/.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)))
	45.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))))
	47.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.6b	(.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 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	59.0b	(/.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)))
	57.2b	(/.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)))
	48.5b	(.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))) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	52.2b	(/.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)))
	55.4b	(/.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)))
	45.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (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 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	58.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.4b	(.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)))))
	58.1b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.9b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))))) (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))))))
	58.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	54.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 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)))))))
	47.3b	(.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))))
	61.8b	(/.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) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F B))) (.f64 (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))))) (cbrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))))))
	56.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	57.9b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	61.4b	(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))))))

Compiler

Compiled 32423 to 20772 computations (35.9% saved)

regimes4.1s (11.5%)

Accuracy

Total 26.0b remaining (61.8%)

Threshold costs 0b (0%)

Counts

210 → 6

Compiler

Compiled 61157 to 38553 computations (37% saved)

bsearch590.0ms (1.6%)

Steps

Iters	Range		Point
7	5.564714352415159e+152	1.2241584666825242e+155	1.5281556949108983e+153
5	9.518137252297709e-117	2.2981855726167303e-116	2.116237083777588e-116
10	-3.910669829016136e-24	-6.397618016122035e-34	-3.262389646343389e-33
6	-9.943154998055778e+32	-1.8306339176123615e+32	-3.402280393262435e+32
9	-3.1319364677254346e+104	-1.2679296176760101e+98	-8.822223828748478e+98

Compiler

Compiled 5 to 4 computations (20% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary64`
22×	`+-commutative_binary64`
17×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	244
1	123	244
2	162	244
3	187	244
4	201	244
5	204	244
6	203	244

end679.0ms (1.9%)

Compiler: Compiled 1707 to 1109 computations (35% saved)

Details

analyze3.3s (9.1%)

sample6.5s (18.1%)

simplify76.0ms (0.2%)

prune6.0ms (0%)

localize17.0ms (0%)

series16.0s (44.5%)

rewrite44.0ms (0.1%)

simplify417.0ms (1.2%)

prune1.0s (2.8%)

localize15.0ms (0%)

series1.0s (2.9%)

rewrite10.0ms (0%)

simplify121.0ms (0.3%)

prune336.0ms (0.9%)

localize18.0ms (0.1%)

series120.0ms (0.3%)

rewrite13.0ms (0%)

simplify84.0ms (0.2%)

prune396.0ms (1.1%)

localize24.0ms (0.1%)

series252.0ms (0.7%)

rewrite2.0ms (0%)

simplify79.0ms (0.2%)

prune738.0ms (2.1%)

regimes4.1s (11.5%)

bsearch590.0ms (1.6%)

simplify9.0ms (0%)

end679.0ms (1.9%)

Profiling