Details

analyze3.7s (11.9%)

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)

sample7.4s (24%)

Results

1.8s	5724×	body	128	valid
982.0ms	825×	body	1024	invalid
938.0ms	713×	body	2048	valid
857.0ms	880×	body	1024	valid
766.0ms	2997×	body	128	invalid
719.0ms	587×	body	2048	invalid
471.0ms	601×	body	512	valid
428.0ms	576×	body	512	invalid
173.0ms	336×	body	256	valid
169.0ms	355×	body	256	invalid
6.0ms	2×	body	4096	valid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify75.0ms (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

45.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	49.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (+.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
▶	46.0b	(/.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

49.6b

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

▶

46.0b

(/.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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	4.2b	(.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)))))))
✓	22.3b	(/.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)))

series8.8s (28.7%)

Counts

4 → 124

Calls

4 calls:

4.7s	(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)))))))
3.9s	(/.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)))
169.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
42.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite51.0ms (0.2%)

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	(.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	(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)))))))
7.0ms	(+.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)))

simplify424.0ms (1.4%)

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

prune1.1s (3.7%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	338	23	361
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	340	23	363

Error

24.4b

Counts

363 → 23

Alt Table

Status	Error	Program
	54.8b	(/.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)))
	59.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	59.0b	(/.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)))
	54.5b	(/.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)))
	56.5b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	51.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2))))) (.f64 (.f64 A C) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 C 2) (pow.f64 B 2))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	46.0b	(/.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)))))))))
	58.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	46.0b	(.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))))
	50.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 F (-.f64 (fma.f64 2 (.f64 C (.f64 B B)) (.f64 2 (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (+.f64 (.f64 B B) (.f64 C C))) (.f64 2 (.f64 A C)))) (.f64 B B)) (.f64 A (.f64 B B))))) (fma.f64 8 (.f64 (.f64 A A) C) (.f64 8 (+.f64 (.f64 A (.f64 C C)) (.f64 (.f64 A C) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (+.f64 (.f64 B B) (.f64 C C))) (.f64 2 (.f64 A C)))))))))))) (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)))
	59.8b	(/.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)))
	60.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
▶	44.8b	(.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)))))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (.f64 2 (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))) (.f64 F (.f64 B B))) (.f64 A (.f64 F (.f64 B B)))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 4 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))) (fma.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (.f64 F (pow.f64 B 6))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 6)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 5)))) (.f64 8 (+.f64 (.f64 (.f64 A A) (.f64 C F)) (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(/.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)))
	55.8b	(/.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)))
	45.4b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (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)))
	58.6b	(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))))))
	57.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.1b	(/.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)))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 61936 to 33910 computations (45.2% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 A (.f64 C -4) (.f64 B B))
	1.6b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	9.5b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	18.7b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series710.0ms (2.3%)

Counts

3 → 76

Calls

3 calls:

665.0ms	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
33.0ms	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))
11.0ms	(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))

simplify124.0ms (0.4%)

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

prune340.0ms (1.1%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	187	13	200
Fresh	3	19	22
Picked	1	0	1
Done	0	0	0
Total	191	32	223

Error

16.3b

Counts

223 → 32

Alt Table

Status	Error	Program
	54.8b	(/.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)))
	59.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	45.4b	(.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)))))
	50.6b	(.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)))))
	55.8b	(/.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)))
	55.9b	(.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)))))
	59.0b	(/.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)))
	58.6b	(.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)))))
	54.5b	(/.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)))
	58.6b	(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)))
	56.5b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	52.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	51.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2))))) (.f64 (.f64 A C) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 C 2) (pow.f64 B 2))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	46.0b	(/.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)))))))))
	58.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	46.0b	(.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))))
	50.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 F (-.f64 (fma.f64 2 (.f64 C (.f64 B B)) (.f64 2 (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (+.f64 (.f64 B B) (.f64 C C))) (.f64 2 (.f64 A C)))) (.f64 B B)) (.f64 A (.f64 B B))))) (fma.f64 8 (.f64 (.f64 A A) C) (.f64 8 (+.f64 (.f64 A (.f64 C C)) (.f64 (.f64 A C) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (+.f64 (.f64 B B) (.f64 C C))) (.f64 2 (.f64 A C)))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	53.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	45.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.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)))))
	59.8b	(/.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)))
	50.3b	(.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)))))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (.f64 2 (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))) (.f64 F (.f64 B B))) (.f64 A (.f64 F (.f64 B B)))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 4 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))) (fma.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (.f64 F (pow.f64 B 6))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 6)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 5)))) (.f64 8 (+.f64 (.f64 (.f64 A A) (.f64 C F)) (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (neg.f64 B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	57.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
▶	45.1b	(.f64 -1 (/.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	57.1b	(/.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)))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.7b	(.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)))))

Compiler

Compiled 15403 to 8888 computations (42.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (+.f64 A C))
✓	10.9b	(sqrt.f64 (.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))))))
✓	15.9b	(fma.f64 (*.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))
	18.7b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series943.0ms (3.1%)

Counts

3 → 72

Calls

3 calls:

865.0ms

(sqrt.f64 (*.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))))))

59.0ms

(fma.f64 (*.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))

18.0ms

(cbrt.f64 (+.f64 A C))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`
4×	`cbrt-prod_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

3 → 40

Calls

3 calls:

3.0ms

(sqrt.f64 (*.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))))))

2.0ms

(cbrt.f64 (+.f64 A C))

0.0ms

(fma.f64 (*.f64 (cbrt.f64 (+.f64 A C)) (cbrt.f64 (+.f64 A C))) (cbrt.f64 (+.f64 A C)) (hypot.f64 B (-.f64 A C)))

simplify112.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-def_binary64`
498×	`associate-l_binary64`
216×	`*-commutative_binary64`
200×	`associate-/r*_binary64`
189×	`associate-/l*_binary64`

Counts

112 → 185

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	664	7236
1	2030	6037
2	5493	6037

prune510.0ms (1.7%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	340	1	341
Fresh	0	31	31
Picked	0	1	1
Done	0	0	0
Total	340	33	373

Error

16.3b

Counts

373 → 33

Alt Table

Status	Error	Program
	54.8b	(/.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)))
	59.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
▶	45.4b	(.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)))))
	50.6b	(.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)))))
	55.8b	(/.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)))
	55.9b	(.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)))))
	59.0b	(/.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)))
	58.6b	(.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)))))
	54.5b	(/.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)))
	58.6b	(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)))
	54.4b	(.f64 -1 (/.f64 (sqrt.f64 (.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)))))) (-.f64 (.f64 2 (/.f64 (.f64 A C) B)) B)))
	56.5b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	52.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	51.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2))))) (.f64 (.f64 A C) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 C 2) (pow.f64 B 2))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	46.0b	(/.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)))))))))
	58.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	46.0b	(.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))))
	50.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 F (-.f64 (fma.f64 2 (.f64 C (.f64 B B)) (.f64 2 (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (+.f64 (.f64 B B) (.f64 C C))) (.f64 2 (.f64 A C)))) (.f64 B B)) (.f64 A (.f64 B B))))) (fma.f64 8 (.f64 (.f64 A A) C) (.f64 8 (+.f64 (.f64 A (.f64 C C)) (.f64 (.f64 A C) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (+.f64 (.f64 B B) (.f64 C C))) (.f64 2 (.f64 A C)))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	53.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	45.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.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)))))
	59.8b	(/.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)))
	50.3b	(.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)))))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (.f64 2 (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))) (.f64 F (.f64 B B))) (.f64 A (.f64 F (.f64 B B)))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 4 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))) (fma.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (.f64 F (pow.f64 B 6))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 6)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 5)))) (.f64 8 (+.f64 (.f64 (.f64 A A) (.f64 C F)) (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (neg.f64 B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	57.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
✓	45.1b	(.f64 -1 (/.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	57.1b	(/.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)))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.7b	(.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)))))

Compiler

Compiled 23514 to 12641 computations (46.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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)))
	1.6b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	9.5b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	11.0b	(sqrt.f64 (.f64 A (.f64 C -4)))

series96.0ms (0.3%)

Counts

2 → 14

Calls

2 calls:

81.0ms	(.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)))
15.0ms	(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)))
3.0ms	(sqrt.f64 (.f64 A (.f64 C -4)))

simplify87.0ms (0.3%)

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

prune405.0ms (1.3%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	259	4	263
Fresh	2	29	31
Picked	1	0	1
Done	0	1	1
Total	262	34	296

Error

16.3b

Counts

296 → 34

Alt Table

Status	Error	Program
	54.8b	(/.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)))
	59.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	50.6b	(.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)))))
	55.8b	(/.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)))
	55.9b	(.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)))))
	59.0b	(/.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)))
	58.6b	(.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)))))
	54.5b	(/.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)))
	58.6b	(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)))
	45.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 A C))) B))) 4) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (.f64 A C))) B)))))
	54.4b	(.f64 -1 (/.f64 (sqrt.f64 (.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)))))) (-.f64 (.f64 2 (/.f64 (.f64 A C) B)) B)))
	56.5b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	52.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	58.5b	(.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)))))
	51.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2))))) (.f64 (.f64 A C) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 C 2) (pow.f64 B 2))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	46.0b	(/.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)))))))))
	58.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
✓	45.1b	(.f64 -1 (/.f64 (sqrt.f64 (.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)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	47.5b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B 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)))))
	55.4b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A 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)))))
	46.0b	(.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))))
	50.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 F (-.f64 (fma.f64 2 (.f64 C (.f64 B B)) (.f64 2 (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (+.f64 (.f64 B B) (.f64 C C))) (.f64 2 (.f64 A C)))) (.f64 B B)) (.f64 A (.f64 B B))))) (fma.f64 8 (.f64 (.f64 A A) C) (.f64 8 (+.f64 (.f64 A (.f64 C C)) (.f64 (.f64 A C) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (+.f64 (.f64 B B) (.f64 C C))) (.f64 2 (.f64 A C)))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	53.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	59.8b	(/.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)))
	50.3b	(.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)))))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 A (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3)))) (fma.f64 1/2 (/.f64 (.f64 B B) C) (.f64 1/2 (+.f64 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (/.f64 (.f64 A (.f64 B B)) (.f64 C C))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))) (.f64 F (pow.f64 B 4)) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 4)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (.f64 2 (+.f64 (.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))) (.f64 F (.f64 B B))) (.f64 A (.f64 F (.f64 B B)))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 4 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))) (fma.f64 1/4 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 3))) (.f64 F (pow.f64 B 6))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 F (pow.f64 B 6)))) (sqrt.f64 (/.f64 1 (pow.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))) 5)))) (.f64 8 (+.f64 (.f64 (.f64 A A) (.f64 C F)) (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C)))))))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (neg.f64 B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	57.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.1b	(/.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)))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 18515 to 11150 computations (39.8% saved)

regimes4.2s (13.6%)

Accuracy

Total 22.2b remaining (58.4%)

Threshold costs 0b (0%)

Counts

218 → 5

Compiler

Compiled 58439 to 36797 computations (37% saved)

bsearch655.0ms (2.1%)

Steps

Iters	Range		Point
7	4.913099090158398	1206.5034603853478	1174.7036553333758
9	2.127197010704103e-308	1.3613232018606078e-302	7.496348083330435e-303
10	-1.6403020875512916e-199	-4.247543712303229e-215	-3.883371458485761e-210
9	-7.795975313307718e+37	-1.5011763295620477e+32	-2.0715755995410293e+32

Compiler

Compiled 5 to 4 computations (20% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
14×	`+-commutative_binary64`
10×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	231
1	88	231
2	106	231
3	119	231
4	126	231
5	127	231
6	127	231

end854.0ms (2.8%)

Compiler: Compiled 1737 to 1046 computations (39.8% saved)

Details

analyze3.7s (11.9%)

sample7.4s (24%)

simplify75.0ms (0.2%)

prune6.0ms (0%)

localize19.0ms (0.1%)

series8.8s (28.7%)

rewrite51.0ms (0.2%)

simplify424.0ms (1.4%)

prune1.1s (3.7%)

localize32.0ms (0.1%)

series710.0ms (2.3%)

rewrite10.0ms (0%)

simplify124.0ms (0.4%)

prune340.0ms (1.1%)

localize22.0ms (0.1%)

series943.0ms (3.1%)

rewrite7.0ms (0%)

simplify112.0ms (0.4%)

prune510.0ms (1.7%)

localize19.0ms (0.1%)

series96.0ms (0.3%)

rewrite13.0ms (0%)

simplify87.0ms (0.3%)

prune405.0ms (1.3%)

regimes4.2s (13.6%)

bsearch655.0ms (2.1%)

simplify8.0ms (0%)

end854.0ms (2.8%)

Profiling