Details

analyze3.2s (8.8%)

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)

sample6.4s (17.6%)

Results

1.5s	5760×	body	128	valid
814.0ms	714×	body	2048	valid
783.0ms	871×	body	1024	invalid
772.0ms	838×	body	1024	valid
719.0ms	2913×	body	128	invalid
684.0ms	606×	body	2048	invalid
410.0ms	592×	body	512	valid
390.0ms	578×	body	512	invalid
165.0ms	351×	body	256	valid
158.0ms	333×	body	256	invalid
3.0ms	1×	body	4096	valid

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

50.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	54.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
▶	50.5b	(/.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

54.1b

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

▶

50.5b

(/.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
✓	2.2b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	3.3b	(.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	(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)))))))
✓	23.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

series16.3s (44.5%)

Counts

4 → 124

Calls

4 calls:

8.7s	(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)))))))
7.3s	(/.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)))
210.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
91.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite52.0ms (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:

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 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
9.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
6.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

simplify409.0ms (1.1%)

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

prune1.2s (3.2%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	334	27	361
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	335	28	363

Error

25.1b

Counts

363 → 28

Alt Table

Status	Error	Program
	62.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
▶	48.5b	(.f64 -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)))))
	55.1b	(/.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)))
	49.2b	(/.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)))))))))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 2 (.f64 C (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 2 (.f64 A (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 2 (.f64 F (pow.f64 B 3))) (+.f64 (.f64 (pow.f64 A 2) (.f64 F B)) (.f64 (pow.f64 C 2) (.f64 F B)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.7b	(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))))))
	50.8b	(/.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)))
	54.9b	(cbrt.f64 (.f64 (.f64 (/.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))) (/.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)))) (/.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)))))
	50.6b	(/.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (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)))))))))))
	54.1b	(/.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)))
	54.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	50.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (.f64 (cbrt.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)))
	56.6b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	57.9b	(/.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)))
	49.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))))) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	59.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	62.5b	(/.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)))
	55.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	57.2b	(/.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)))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.6b	(/.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)))
	61.8b	(/.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)))
	54.5b	(/.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)))
	63.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (log.f64 (.f64 (exp.f64 (+.f64 A C)) (exp.f64 (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.2b	(/.f64 (neg.f64 (sqrt.f64 (/.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 (+.f64 A C) (+.f64 A C)) (.f64 (hypot.f64 B (-.f64 A C)) (hypot.f64 B (-.f64 A C))))))) (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

Compiler

Compiled 62140 to 34044 computations (45.2% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 A (.f64 C -4) (.f64 B B))
	2.2b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	10.3b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	20.4b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series1.1s (3.1%)

Counts

3 → 76

Calls

3 calls:

1.1s	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
47.0ms	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))
11.0ms	(fma.f64 A (.f64 C -4) (.f64 B B))

rewrite11.0ms (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:

8.0ms	(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))

simplify126.0ms (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

prune324.0ms (0.9%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	187	13	200
Fresh	4	23	27
Picked	1	0	1
Done	0	0	0
Total	192	36	228

Error

15.0b

Counts

228 → 36

Alt Table

Status	Error	Program
	61.8b	(/.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)))
	57.0b	(.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)))))
	59.3b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 A F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	62.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.1b	(/.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)))
	59.1b	(.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)))))
	53.8b	(.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)))))
	60.7b	(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))))))
	48.5b	(.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)))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	56.1b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	50.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (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)))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 2 (.f64 C (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 2 (.f64 A (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 2 (.f64 F (pow.f64 B 3))) (+.f64 (.f64 (pow.f64 A 2) (.f64 F B)) (.f64 (pow.f64 C 2) (.f64 F B)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.9b	(cbrt.f64 (.f64 (.f64 (/.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))) (/.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)))) (/.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)))))
	55.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (/.f64 (-.f64 (.f64 (+.f64 A C) (+.f64 A C)) (.f64 (hypot.f64 B (-.f64 A C)) (hypot.f64 B (-.f64 A C)))) (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	50.6b	(/.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (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)))))))))))
	54.1b	(/.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)))
▶	48.3b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	59.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	54.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	50.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (.f64 (cbrt.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)))
	56.6b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	48.6b	(.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)))))))
	53.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	58.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	57.9b	(/.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)))
	59.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	48.4b	(.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)))))
	62.5b	(/.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)))
	55.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	57.2b	(/.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)))
	49.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	50.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.6b	(/.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)))
	54.5b	(/.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)))
	63.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (log.f64 (.f64 (exp.f64 (+.f64 A C)) (exp.f64 (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 15405 to 8902 computations (42.2% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2))
✓	1.5b	(+.f64 C (hypot.f64 B C))
✓	10.0b	(sqrt.f64 (*.f64 (+.f64 C (hypot.f64 B C)) F))
	20.4b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series446.0ms (1.2%)

Counts

3 → 40

Calls

3 calls:

251.0ms	(.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2))
183.0ms	(sqrt.f64 (*.f64 (+.f64 C (hypot.f64 B C)) F))
13.0ms	(+.f64 C (hypot.f64 B C))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-r_binary64`

Counts

3 → 63

Calls

3 calls:

8.0ms	(.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2))
3.0ms	(sqrt.f64 (*.f64 (+.f64 C (hypot.f64 B C)) F))
2.0ms	(+.f64 C (hypot.f64 B C))

simplify86.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-def_binary64`
415×	`times-frac_binary64`
396×	`associate-/l*_binary64`
395×	`cancel-sign-sub-inv_binary64`
332×	`fma-neg_binary64`

Counts

103 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	2294
1	621	2238
2	1865	2163
3	4828	2163
4	4951	2163

prune229.0ms (0.6%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	7	28	35
Picked	1	0	1
Done	0	0	0
Total	196	33	229

Error

12.5b

Counts

229 → 33

Alt Table

Status	Error	Program
	61.8b	(/.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)))
	57.0b	(.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)))))
▶	44.7b	(.f64 -1 (/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	60.7b	(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))))))
	50.8b	(/.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)))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 2 (.f64 C (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 2 (.f64 A (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 2 (.f64 F (pow.f64 B 3))) (+.f64 (.f64 (pow.f64 A 2) (.f64 F B)) (.f64 (pow.f64 C 2) (.f64 F B)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.9b	(cbrt.f64 (.f64 (.f64 (/.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))) (/.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)))) (/.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)))))
	50.6b	(/.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (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)))))))))))
	51.4b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (*.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) B))
	55.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (/.f64 (-.f64 (.f64 (+.f64 A C) (+.f64 A C)) (.f64 (hypot.f64 B (-.f64 A C)) (hypot.f64 B (-.f64 A C)))) (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	54.1b	(/.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)))
	44.7b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (.f64 (sqrt.f64 F) (sqrt.f64 2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	54.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	50.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (.f64 (cbrt.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)))
	53.7b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (*.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) (neg.f64 B)))
	56.6b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	48.6b	(.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)))))))
	53.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	58.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	57.9b	(/.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)))
	59.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	62.5b	(/.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)))
	55.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	57.2b	(/.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)))
	50.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.6b	(/.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)))
	54.5b	(/.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)))
	62.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	48.8b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	59.1b	(.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)))))
	63.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (log.f64 (.f64 (exp.f64 (+.f64 A C)) (exp.f64 (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.4b	(/.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 8996 to 5100 computations (43.3% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 A (.f64 C -4) (.f64 B B))
✓	0.3b	(.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 2))
	1.5b	(+.f64 C (hypot.f64 B C))
	20.4b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series203.0ms (0.6%)

Counts

1 → 8

Calls

1 calls:

202.0ms

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

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
7×	`pow-prod-down_binary64`
6×	`associate-r_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cbrt-cube_binary64`

Counts

1 → 29

Calls

1 calls:

9.0ms

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

simplify59.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

368×	`*-commutative_binary64`
353×	`distribute-rgt-in_binary64`
350×	`distribute-lft-in_binary64`
311×	`cancel-sign-sub-inv_binary64`
292×	`fma-def_binary64`

Counts

37 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1009
1	357	971
2	1137	941
3	2866	933
4	5047	933

prune187.0ms (0.5%)

Pruning

38 alts after pruning (38 fresh and 0 done)

	Pruned	Kept	Total
New	159	9	168
Fresh	3	29	32
Picked	1	0	1
Done	0	0	0
Total	163	38	201

Error

7.8b

Counts

201 → 38

Alt Table

Status	Error	Program
	61.8b	(/.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)))
	57.0b	(.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)))))
	49.4b	(.f64 -1 (/.f64 (.f64 (*.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 2)) (neg.f64 B)))
	59.1b	(.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)))))
	43.4b	(.f64 -1 (/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 2)) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	41.7b	(.f64 -1 (/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 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)))))
	50.8b	(/.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)))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 2 (.f64 C (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 2 (.f64 A (.f64 F (pow.f64 B 2)))) (+.f64 (.f64 2 (.f64 F (pow.f64 B 3))) (+.f64 (.f64 (pow.f64 A 2) (.f64 F B)) (.f64 (pow.f64 C 2) (.f64 F B)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.9b	(cbrt.f64 (.f64 (.f64 (/.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))) (/.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)))) (/.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)))))
	50.6b	(/.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (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)))))))))))
	51.4b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (*.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) B))
	55.2b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (/.f64 (-.f64 (.f64 (+.f64 A C) (+.f64 A C)) (.f64 (hypot.f64 B (-.f64 A C)) (hypot.f64 B (-.f64 A C)))) (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	44.8b	(.f64 -1 (/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 2)) (.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)))))))
	54.1b	(/.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)))
	44.7b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (.f64 (sqrt.f64 F) (sqrt.f64 2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	54.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	48.4b	(.f64 -1 (/.f64 (.f64 (*.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 2)) B))
	44.7b	(.f64 -1 (/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	50.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (.f64 (cbrt.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)))
	53.7b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (*.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) (neg.f64 B)))
	56.6b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	48.5b	(.f64 -1 (/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 2)) (-.f64 B (.f64 2 (/.f64 (*.f64 A C) B)))))
	53.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	58.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	57.9b	(/.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)))
	53.6b	(.f64 -1 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 C 2)) (sqrt.f64 F)) (sqrt.f64 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	59.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	62.5b	(/.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)))
	55.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	57.2b	(/.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)))
	50.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.6b	(/.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)))
	54.5b	(/.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)))
	62.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	63.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (log.f64 (.f64 (exp.f64 (+.f64 A C)) (exp.f64 (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	42.0b	(.f64 -1 (/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 C (hypot.f64 B C))) (sqrt.f64 F)) (sqrt.f64 2)) (.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	59.4b	(/.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 6927 to 3843 computations (44.5% saved)

regimes4.6s (12.6%)

Accuracy

Total 25.6b remaining (72.8%)

Threshold costs 0b (0%)

Counts

230 → 5

Compiler

Compiled 58530 to 36177 computations (38.2% saved)

bsearch763.0ms (2.1%)

Steps

Iters	Range		Point
6	7.35257931601469e+96	4.888433981408039e+97	8.87383987340921e+96
9	2.2872528385738317e-159	4.64585637503025e-151	3.1016763674985758e-152
7	1.7845640036940609e-208	9.830755338581716e-207	3.7629617721837925e-208
9	-2.2087195814052107e-151	-1.0031712438063459e-159	-2.1674256738196374e-151

Compiler

Compiled 5 to 4 computations (20% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary64`
20×	`+-commutative_binary64`
19×	`sub-neg_binary64`
19×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	168
1	94	168
2	127	168
3	159	168
4	188	168
5	201	168
6	209	168
7	212	168
8	212	168

end682.0ms (1.9%)

Compiler: Compiled 1569 to 1003 computations (36.1% saved)

Iter	Nodes	Cost
0	59	168
1	94	168
2	127	168
3	159	168
4	188	168
5	201	168
6	209	168
7	212	168
8	212	168

Iter	Nodes	Cost
0	59	168
1	94	168
2	127	168
3	159	168
4	188	168
5	201	168
6	209	168
7	212	168
8	212	168

Details

analyze3.2s (8.8%)

sample6.4s (17.6%)

simplify76.0ms (0.2%)

prune6.0ms (0%)

localize17.0ms (0%)

series16.3s (44.5%)

rewrite52.0ms (0.1%)

simplify409.0ms (1.1%)

prune1.2s (3.2%)

localize18.0ms (0%)

series1.1s (3.1%)

rewrite11.0ms (0%)

simplify126.0ms (0.3%)

prune324.0ms (0.9%)

localize16.0ms (0%)

series446.0ms (1.2%)

rewrite17.0ms (0%)

simplify86.0ms (0.2%)

prune229.0ms (0.6%)

localize17.0ms (0%)

series203.0ms (0.6%)

rewrite11.0ms (0%)

simplify59.0ms (0.2%)

prune187.0ms (0.5%)

regimes4.6s (12.6%)

bsearch763.0ms (2.1%)

simplify9.0ms (0%)

end682.0ms (1.9%)

Profiling

Iter	Nodes	Cost
0	59	168
1	94	168
2	127	168
3	159	168
4	188	168
5	201	168
6	209	168
7	212	168
8	212	168