Details

analyze3.2s (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)

sample198.0ms (0.6%)

Algorithm

1×

intervals

Results

30.0ms	179×	body	128	valid
20.0ms	30×	body	1024	nan
18.0ms	26×	body	1024	valid
17.0ms	88×	body	128	nan
16.0ms	18×	body	2048	nan
15.0ms	17×	body	2048	valid
11.0ms	20×	body	512	valid
7.0ms	14×	body	512	nan
5.0ms	14×	body	256	valid
4.0ms	10×	body	256	nan

Compiler

Compiled 93 to 69 computations (25.8% 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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

48.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	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)))
▶	48.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

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)))

▶

48.9b

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

Compiler

Compiled 239 to 156 computations (34.7% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	3.7b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	12.7b	(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)))))))
✓	23.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

series16.8s (47.4%)

Counts

4 → 124

Calls

4 calls:

8.9s	(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)))))))
7.7s	(/.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)))
208.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
52.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite46.0ms (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)))))))
9.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
5.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
4.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

simplify388.0ms (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

prune1.0s (2.9%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	337	24	361
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	339	24	363

Error

24.3b

Counts

363 → 24

Alt Table

Status	Error	Program
▶	48.8b	(.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)))))
	52.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	58.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 C (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 A 3)))) (fma.f64 1/2 (/.f64 (.f64 (.f64 C C) (.f64 B B)) (pow.f64 A 3)) (.f64 1/2 (+.f64 (/.f64 (.f64 C (.f64 B B)) (.f64 A A)) (/.f64 (.f64 B B) A)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.1b	(/.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)))
	52.1b	(/.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)))
	60.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	48.9b	(.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))))
	53.2b	(/.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)))
	54.4b	(/.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)))
	58.1b	(/.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)))
	57.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.1b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 A C) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (.f64 (.f64 (hypot.f64 B (-.f64 A C)) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.6b	(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))))))
	56.2b	(/.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)))))))
	61.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.3b	(/.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)))
	56.7b	(/.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)))
	55.8b	(/.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)))
	49.7b	(.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)))))
	56.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.8b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	56.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 A A) (.f64 F (.f64 B B))) C) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 62020 to 33882 computations (45.4% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 A (.f64 C -4) (.f64 B B))
	2.9b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	9.8b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	20.6b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series1.1s (3.1%)

Counts

3 → 76

Calls

3 calls:

1.0s	(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)))
11.0ms	(fma.f64 A (.f64 C -4) (.f64 B B))

rewrite9.0ms (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:

6.0ms	(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))

simplify154.0ms (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

prune353.0ms (1%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	188	12	200
Fresh	5	18	23
Picked	1	0	1
Done	0	0	0
Total	194	30	224

Error

14.0b

Counts

224 → 30

Alt Table

Status	Error	Program
	48.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (expm1.f64 (log1p.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	61.3b	(/.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)))
	59.5b	(.f64 -1 (/.f64 (fma.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 1/4 (.f64 (sqrt.f64 (/.f64 F (.f64 (fma.f64 A A (.f64 C (-.f64 C (.f64 2 A)))) (+.f64 A (+.f64 C (sqrt.f64 (fma.f64 A A (.f64 C (-.f64 C (.f64 2 A)))))))))) (.f64 (.f64 B B) (sqrt.f64 2))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	52.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	58.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 C (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 A 3)))) (fma.f64 1/2 (/.f64 (.f64 (.f64 C C) (.f64 B B)) (pow.f64 A 3)) (.f64 1/2 (+.f64 (/.f64 (.f64 C (.f64 B B)) (.f64 A A)) (/.f64 (.f64 B B) A)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.1b	(/.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)))
	56.4b	(.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)))))
	52.1b	(/.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)))
	60.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	48.9b	(.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))))
	56.9b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	53.2b	(/.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)))
	54.4b	(/.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)))
	57.0b	(.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)))))
	57.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.1b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 A C) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (.f64 (.f64 (hypot.f64 B (-.f64 A C)) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (-.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))
	48.9b	(.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)))))))
	61.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	56.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	57.0b	(.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)))))
	54.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	56.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 A A) (.f64 F (.f64 B B))) C) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.7b	(/.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)))
	56.3b	(.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)))))
▶	47.4b	(.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)))))
	61.8b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	47.6b	(.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)))))

Compiler

Compiled 15201 to 8704 computations (42.7% saved)

localize17.0ms (0%)

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)))
	2.9b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	8.8b	(sqrt.f64 (.f64 A (.f64 C -4)))
	9.8b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

series132.0ms (0.4%)

Counts

2 → 14

Calls

2 calls:

111.0ms	(.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)))
21.0ms	(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 (0.2%)

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

prune476.0ms (1.3%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	258	5	263
Fresh	3	26	29
Picked	1	0	1
Done	0	0	0
Total	262	31	293

Error

13.9b

Counts

293 → 31

Alt Table

Status	Error	Program
▶	48.3b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (expm1.f64 (log1p.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	61.3b	(/.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)))
	59.5b	(.f64 -1 (/.f64 (fma.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 1/4 (.f64 (sqrt.f64 (/.f64 F (.f64 (fma.f64 A A (.f64 C (-.f64 C (.f64 2 A)))) (+.f64 A (+.f64 C (sqrt.f64 (fma.f64 A A (.f64 C (-.f64 C (.f64 2 A)))))))))) (.f64 (.f64 B B) (sqrt.f64 2))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	52.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	58.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 C (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 A 3)))) (fma.f64 1/2 (/.f64 (.f64 (.f64 C C) (.f64 B B)) (pow.f64 A 3)) (.f64 1/2 (+.f64 (/.f64 (.f64 C (.f64 B B)) (.f64 A A)) (/.f64 (.f64 B B) A)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.1b	(/.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)))
	56.4b	(.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)))))
	52.1b	(/.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)))
	48.9b	(.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))))
	53.2b	(/.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)))
	54.4b	(/.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)))
	57.0b	(.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)))))
	57.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.1b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 A C) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (.f64 (.f64 (hypot.f64 B (-.f64 A C)) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (-.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))
	48.9b	(.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)))))))
	61.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	56.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	49.1b	(.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)))))
	61.8b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	54.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	56.9b	(.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)))))
	50.7b	(.f64 -1 (/.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (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)))))
	57.0b	(.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)))))
	56.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 A A) (.f64 F (.f64 B B))) C) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.7b	(/.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)))
	56.3b	(.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)))))
	57.5b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (.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)))))
	52.4b	(.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)))))

Compiler

Compiled 19818 to 11882 computations (40% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.0b	(expm1.f64 (log1p.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))
	2.9b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	8.8b	(sqrt.f64 (.f64 A (.f64 C -4)))
	9.8b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

series108.0ms (0.3%)

Counts

1 → 14

Calls

1 calls:

108.0ms

(expm1.f64 (log1p.f64 (hypot.f64 (sqrt.f64 (*.f64 A (*.f64 C -4))) B)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (hypot.f64 (sqrt.f64 (*.f64 A (*.f64 C -4))) B)))

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
439×	`cancel-sign-sub-inv_binary64`
393×	`fma-neg_binary64`
343×	`neg-mul-1_binary64`
337×	`neg-sub0_binary64`

Counts

25 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	599
1	173	542
2	450	524
3	2305	518
4	4418	518
5	5187	518

prune277.0ms (0.8%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	1	29	30
Picked	1	0	1
Done	0	0	0
Total	198	32	230

Error

13.9b

Counts

230 → 32

Alt Table

Status	Error	Program
	59.5b	(.f64 -1 (/.f64 (fma.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 1/4 (.f64 (sqrt.f64 (/.f64 F (.f64 (fma.f64 A A (.f64 C (-.f64 C (.f64 2 A)))) (+.f64 A (+.f64 C (sqrt.f64 (fma.f64 A A (.f64 C (-.f64 C (.f64 2 A)))))))))) (.f64 (.f64 B B) (sqrt.f64 2))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	52.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	58.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 2 C (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 A 3)))) (fma.f64 1/2 (/.f64 (.f64 (.f64 C C) (.f64 B B)) (pow.f64 A 3)) (.f64 1/2 (+.f64 (/.f64 (.f64 C (.f64 B B)) (.f64 A A)) (/.f64 (.f64 B B) A)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.1b	(/.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)))
	56.4b	(.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)))))
	52.1b	(/.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)))
	48.9b	(.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))))
	53.2b	(/.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)))
	54.4b	(/.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)))
	57.0b	(.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)))))
	57.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	53.2b	(.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))) (expm1.f64 (log1p.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	49.1b	(/.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 A C) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (.f64 (.f64 (hypot.f64 B (-.f64 A C)) F) 2) (fma.f64 A (.f64 C -4) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.1b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (expm1.f64 (log1p.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	56.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (pow.f64 (+.f64 A C) 3) (pow.f64 (hypot.f64 B (-.f64 A C)) 3))))))) (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (fma.f64 (+.f64 A C) (+.f64 A C) (*.f64 (hypot.f64 B (-.f64 A C)) (-.f64 (hypot.f64 B (-.f64 A C)) (+.f64 A C)))))))
	48.9b	(.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)))))))
	61.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	56.7b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	57.5b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (.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)))))
	48.6b	(.f64 -1 (/.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (expm1.f64 (log1p.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))))
	49.1b	(.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)))))
	61.8b	(-.f64 (.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (/.f64 (.f64 C (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B) (.f64 2 (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (*.f64 B B))))))))))))
	54.1b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	56.9b	(.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)))))
	50.7b	(.f64 -1 (/.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (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)))))
	57.0b	(.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)))))
	56.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 A A) (.f64 F (.f64 B B))) C) (.f64 8 (.f64 A (.f64 F (.f64 B B))))) (fma.f64 16 (.f64 (.f64 A A) (.f64 C F)) (/.f64 (.f64 F (pow.f64 B 4)) C))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.3b	(/.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)))
	56.7b	(/.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)))
	56.3b	(.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 14266 to 8583 computations (39.8% saved)

regimes4.0s (11.3%)

Accuracy

Total 22.8b remaining (58.3%)

Threshold costs 0b (0%)

Counts

231 → 5

Compiler

Compiled 67415 to 42041 computations (37.6% saved)

bsearch518.0ms (1.5%)

Steps

Iters	Range		Point
9	3.6076875719492157e-9	0.0004511602013462611	5.520316977367989e-9
9	1.6759604689826267e-90	2.25176216702913e-85	3.197177902139795e-89
5	-3.1629937872823096e-258	-1.5693367925029076e-258	-1.61868603355462e-258
9	-1.6111893087845041e+94	-1.0614191217817518e+87	-1.0845989431502955e+87

Compiler

Compiled 5 to 4 computations (20% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
16×	`+-commutative_binary64`
12×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	222
1	93	222
2	114	222
3	130	222
4	140	222
5	142	222
6	142	222

end2.0ms (0%)

Compiler: Compiled 150 to 81 computations (46% saved)

sample6.3s (17.8%)

Algorithm

1×

intervals

Results

981.0ms	5499×	body	128	valid
777.0ms	857×	body	1024	valid
725.0ms	843×	body	1024	nan
697.0ms	668×	body	2048	valid
505.0ms	2810×	body	128	nan
474.0ms	526×	body	2048	nan
396.0ms	597×	body	512	valid
326.0ms	556×	body	512	nan
131.0ms	378×	body	256	valid
122.0ms	339×	body	256	nan
1.0ms	1×	body	4096	valid

Compiler

Compiled 1581 to 943 computations (40.4% saved)

Details

analyze3.2s (9.1%)

sample198.0ms (0.6%)

simplify76.0ms (0.2%)

prune5.0ms (0%)

localize17.0ms (0%)

series16.8s (47.4%)

rewrite46.0ms (0.1%)

simplify388.0ms (1.1%)

prune1.0s (2.9%)

localize17.0ms (0%)

series1.1s (3.1%)

rewrite9.0ms (0%)

simplify154.0ms (0.4%)

prune353.0ms (1%)

localize17.0ms (0%)

series132.0ms (0.4%)

rewrite13.0ms (0%)

simplify87.0ms (0.2%)

prune476.0ms (1.3%)

localize17.0ms (0%)

series108.0ms (0.3%)

rewrite2.0ms (0%)

simplify54.0ms (0.2%)

prune277.0ms (0.8%)

regimes4.0s (11.3%)

bsearch518.0ms (1.5%)

simplify8.0ms (0%)

end2.0ms (0%)

sample6.3s (17.8%)

Profiling