Details

analyze3.2s (8.6%)

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%	98.2%	1.8%	7
0%	92%	8%	8
0%	91.2%	8.8%	9
0.4%	89.3%	10.3%	10
7.1%	79.2%	13.6%	11
11.9%	70.2%	17.9%	12
13.8%	67.4%	18.7%	13
16.6%	63.3%	20.1%	14

Compiler

Compiled 45 to 33 computations (26.7% saved)

sample237.0ms (0.6%)

Algorithm

1×

intervals

Symmetry

(sort A C)

Results

29.0ms	173×	body	128	valid
29.0ms	35×	body	1024	valid
22.0ms	16×	body	2048	valid
15.0ms	15×	body	2048	nan
13.0ms	76×	body	128	nan
12.0ms	24×	body	512	valid
12.0ms	17×	body	1024	nan
11.0ms	21×	body	512	nan
3.0ms	9×	body	256	nan
3.0ms	8×	body	256	valid

Compiler

Compiled 93 to 69 computations (25.8% saved)

simplify50.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

759×	`neg-mul-1_binary64`
493×	`associate-l_binary64`
463×	`associate-r_binary64`
420×	`distribute-rgt-in_binary64`
410×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	61	49
2	176	49
3	648	49
4	2727	49
5	4869	49
6	5512	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

49.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	51.6b	(/.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)))
▶	49.0b	(/.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

51.6b

(/.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)))

▶

49.0b

(/.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)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.8b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	5.5b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	11.2b	(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)))))))
✓	21.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

series16.4s (43.3%)

Counts

4 → 124

Calls

4 calls:

9.1s	(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)))))))
7.0s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
195.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
55.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite113.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`distribute-lft-in_binary64`
204×	`distribute-rgt-in_binary64`
164×	`*-un-lft-identity_binary64`
108×	`prod-diff_binary64`
105×	`add-sqr-sqrt_binary64`

Counts

4 → 284

Calls

4 calls:

22.0ms	(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)))))))
17.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
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)))
5.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

simplify700.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

721×	`times-frac_binary64`
670×	`fma-def_binary64`
277×	`associate-/l*_binary64`
190×	`associate-/r*_binary64`
93×	`sub-neg_binary64`

Counts

408 → 499

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	2765	55201
1	4842	49427
2	5911	49427

prune1.2s (3.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	473	26	499
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	475	26	501

Error

20.0b

Counts

501 → 26

Alt Table

Status	Error	Program
	60.4b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 B C)))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B) (fma.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (-.f64 C (hypot.f64 B C)))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))) (.f64 1/2 (.f64 (/.f64 (*.f64 A (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))))))))
	49.0b	(/.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)))))))))
	52.2b	(/.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)))
	54.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	59.3b	(/.f64 (neg.f64 (sqrt.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
	46.4b	(/.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) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	63.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	60.1b	(/.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)))
	49.5b	(/.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)))
	49.2b	(.f64 (.f64 (cbrt.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)))))))) (cbrt.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 (cbrt.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))))
	60.1b	(/.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)))
	53.6b	(/.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)))
▶	43.4b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	49.3b	(/.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)) (neg.f64 (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.7b	(/.f64 (neg.f64 (cbrt.f64 (.f64 (.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))))))) (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)))))))) (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)))
	51.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (fma.f64 A A (.f64 B B))))) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 8 (.f64 (.f64 A (.f64 C F)) (hypot.f64 A B)))))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 2 (.f64 (.f64 F (.f64 B B)) (hypot.f64 A B))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	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)))))
	63.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.4b	(/.f64 (neg.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)))
	61.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (fma.f64 A A (.f64 C C)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.5b	(/.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)))))))))

Compiler

Compiled 69865 to 36882 computations (47.2% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2))
✓	11.0b	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

series48.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

27.0ms	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2))
21.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`sqrt-prod_binary64`
6×	`sqrt-pow1_binary64`

Counts

2 → 44

Calls

2 calls:

6.0ms	(.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2))
3.0ms	(sqrt.f64 (*.f64 -1/2 (/.f64 F C)))

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

408×	`associate-*l/_binary64`
404×	`associate-*r/_binary64`
396×	`fma-def_binary64`
390×	`associate-/l*_binary64`
328×	`*-commutative_binary64`

Counts

44 → 46

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	636
1	95	600
2	236	596
3	514	596
4	997	596
5	1905	596
6	2041	596
7	2369	596
8	3387	596
9	4728	596
10	4986	596

prune101.0ms (0.3%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	35	11	46
Fresh	1	24	25
Picked	1	0	1
Done	0	0	0
Total	37	35	72

Error

17.8b

Counts

72 → 35

Alt Table

Status	Error	Program
	43.4b	(neg.f64 (.f64 (.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C))) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	49.4b	(/.f64 (neg.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)))
	43.7b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C)))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (cbrt.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	43.4b	(neg.f64 (.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	60.4b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 B C)))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B) (fma.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (-.f64 C (hypot.f64 B C)))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))) (.f64 1/2 (.f64 (/.f64 (*.f64 A (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))))))))
	49.0b	(/.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)))))))))
	52.2b	(/.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)))
	44.6b	(neg.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	54.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
▶	39.1b	(neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (sqrt.f64 C)))
	59.3b	(/.f64 (neg.f64 (sqrt.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
	61.5b	(neg.f64 (.f64 (log.f64 (exp.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	61.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (fma.f64 A A (.f64 C C)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	43.3b	(neg.f64 (sqrt.f64 (neg.f64 (/.f64 F C))))
	62.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	63.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.6b	(neg.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.7b	(neg.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C)))) (log.f64 (sqrt.f64 2)))))
	53.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	60.1b	(/.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)))
	49.5b	(/.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)))
	49.2b	(.f64 (.f64 (cbrt.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)))))))) (cbrt.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 (cbrt.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))))
	60.1b	(/.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)))
	53.6b	(/.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)))
	53.7b	(/.f64 (neg.f64 (cbrt.f64 (.f64 (.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))))))) (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)))))))) (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)))
	51.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (fma.f64 A A (.f64 B B))))) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 8 (.f64 (.f64 A (.f64 C F)) (hypot.f64 A B)))))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 2 (.f64 (.f64 F (.f64 B B)) (hypot.f64 A B))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	39.1b	(neg.f64 (.f64 (/.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 C)) (sqrt.f64 2)))
	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)))))
	63.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	43.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2))) (cbrt.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))) (cbrt.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))))
	47.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.3b	(/.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)) (neg.f64 (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	50.5b	(/.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)))))))))

Compiler

Compiled 3276 to 2083 computations (36.4% saved)

localize9.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (sqrt.f64 C))
✓	0.4b	(.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))

series42.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

34.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (sqrt.f64 C))
8.0ms	(.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))

rewrite14.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
11×	`sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
9×	`add-cbrt-cube_binary64`

Counts

2 → 59

Calls

2 calls:

6.0ms	(/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (sqrt.f64 C))
5.0ms	(.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))

simplify336.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

935×	`div-sub_binary64`
607×	`times-frac_binary64`
551×	`associate-/l*_binary64`
461×	`fma-def_binary64`
242×	`neg-mul-1_binary64`

Counts

59 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	1029
1	175	903
2	612	898
3	2835	898
4	2948	898
5	3706	898
6	4534	898
7	5856	898

prune128.0ms (0.3%)

Pruning

38 alts after pruning (38 fresh and 0 done)

	Pruned	Kept	Total
New	60	9	69
Fresh	5	29	34
Picked	1	0	1
Done	0	0	0
Total	66	38	104

Error

17.8b

Counts

104 → 38

Alt Table

Status	Error	Program
	40.6b	(neg.f64 (/.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 F))) (log.f64 (sqrt.f64 2)))) (sqrt.f64 C)))
	60.4b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 B C)))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B) (fma.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (-.f64 C (hypot.f64 B C)))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))) (.f64 1/2 (.f64 (/.f64 (*.f64 A (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))))))))
	49.0b	(/.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)))))))))
	52.2b	(/.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)))
	44.6b	(neg.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	54.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	41.2b	(neg.f64 (exp.f64 (-.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 F))) (log.f64 (sqrt.f64 2))) (log.f64 (sqrt.f64 C)))))
	59.3b	(/.f64 (neg.f64 (sqrt.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
	39.4b	(neg.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (*.f64 (cbrt.f64 (sqrt.f64 C)) (cbrt.f64 (sqrt.f64 C)))) (cbrt.f64 (sqrt.f64 C))))
	39.8b	(neg.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))) (sqrt.f64 C)))
	61.5b	(neg.f64 (.f64 (log.f64 (exp.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	61.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (fma.f64 A A (.f64 C C)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	39.2b	(neg.f64 (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 -1/2 F))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 -1/2 F))) (sqrt.f64 2))) (sqrt.f64 C)))
	63.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
▶	39.1b	(neg.f64 (/.f64 1 (/.f64 (sqrt.f64 C) (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))))
	44.7b	(neg.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C)))) (log.f64 (sqrt.f64 2)))))
	53.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	60.1b	(/.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)))
	49.5b	(/.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)))
	49.2b	(.f64 (.f64 (cbrt.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)))))))) (cbrt.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 (cbrt.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))))
	60.1b	(/.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)))
	53.6b	(/.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)))
	44.6b	(neg.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) 3)) (sqrt.f64 C)))
	53.7b	(/.f64 (neg.f64 (cbrt.f64 (.f64 (.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))))))) (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)))))))) (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)))
	51.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (fma.f64 A A (.f64 B B))))) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 8 (.f64 (.f64 A (.f64 C F)) (hypot.f64 A B)))))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 2 (.f64 (.f64 F (.f64 B B)) (hypot.f64 A B))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	43.3b	(neg.f64 (sqrt.f64 (/.f64 (neg.f64 F) C)))
	39.1b	(neg.f64 (.f64 (/.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 C)) (sqrt.f64 2)))
	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)))))
	63.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.1b	(neg.f64 (/.f64 (log.f64 (exp.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))) (sqrt.f64 C)))
	50.5b	(/.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)))))))))
	49.4b	(/.f64 (neg.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)))
	62.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	43.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2))) (cbrt.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))) (cbrt.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))))
	47.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.3b	(/.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)) (neg.f64 (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 3811 to 2489 computations (34.7% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (sqrt.f64 C) (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))))
✓	0.3b	(/.f64 (sqrt.f64 C) (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))
	0.4b	(.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))

series93.0ms (0.2%)

Counts

2 → 0

Calls

2 calls:

59.0ms	(/.f64 (sqrt.f64 C) (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))
34.0ms	(/.f64 1 (/.f64 (sqrt.f64 C) (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`times-frac_binary64`
29×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
28×	`add-exp-log_binary64`

Counts

2 → 100

Calls

2 calls:

9.0ms	(/.f64 1 (/.f64 (sqrt.f64 C) (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2))))
6.0ms	(/.f64 (sqrt.f64 C) (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))

simplify119.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

883×	`times-frac_binary64`
601×	`fma-def_binary64`
442×	`associate-/l*_binary64`
399×	`associate-/r*_binary64`
307×	`div-sub_binary64`

Counts

100 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	2419
1	200	2057
2	702	2002
3	3296	2002
4	3544	2002
5	4877	2002
6	5319	2002

prune186.0ms (0.5%)

Pruning

39 alts after pruning (39 fresh and 0 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	1	36	37
Picked	1	0	1
Done	0	0	0
Total	151	39	190

Error

17.8b

Counts

190 → 39

Alt Table

Status	Error	Program
	40.6b	(neg.f64 (/.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 F))) (log.f64 (sqrt.f64 2)))) (sqrt.f64 C)))
	60.4b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 (.f64 (fma.f64 C C (.f64 B B)) F) (-.f64 C (hypot.f64 B C)))))) (fma.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B) (fma.f64 1/2 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 C C)) (-.f64 C (hypot.f64 B C)))))) (fma.f64 2 (.f64 (/.f64 (.f64 A (.f64 (.f64 C C) (sqrt.f64 2))) (pow.f64 B 3)) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))) (.f64 1/2 (.f64 (/.f64 (*.f64 A (sqrt.f64 2)) B) (sqrt.f64 (/.f64 F (-.f64 C (hypot.f64 B C))))))))))
	49.0b	(/.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)))))))))
	52.2b	(/.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)))
	44.6b	(neg.f64 (.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	54.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	41.2b	(neg.f64 (exp.f64 (-.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 F))) (log.f64 (sqrt.f64 2))) (log.f64 (sqrt.f64 C)))))
	59.3b	(/.f64 (neg.f64 (sqrt.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 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
	39.4b	(neg.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) (*.f64 (cbrt.f64 (sqrt.f64 C)) (cbrt.f64 (sqrt.f64 C)))) (cbrt.f64 (sqrt.f64 C))))
	39.8b	(neg.f64 (/.f64 (expm1.f64 (log1p.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))) (sqrt.f64 C)))
	61.5b	(neg.f64 (.f64 (log.f64 (exp.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))))) (sqrt.f64 2)))
	61.4b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (fma.f64 A A (.f64 C C)))))) (.f64 10 (.f64 A (.f64 C (.f64 F B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	39.2b	(neg.f64 (/.f64 (.f64 (sqrt.f64 (sqrt.f64 (.f64 -1/2 F))) (.f64 (sqrt.f64 (sqrt.f64 (.f64 -1/2 F))) (sqrt.f64 2))) (sqrt.f64 C)))
	63.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	61.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.7b	(neg.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C)))) (log.f64 (sqrt.f64 2)))))
	53.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	60.1b	(/.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)))
	49.5b	(/.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)))
	49.2b	(.f64 (.f64 (cbrt.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)))))))) (cbrt.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 (cbrt.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))))
	60.1b	(/.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)))
	53.6b	(/.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)))
	44.6b	(neg.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)) 3)) (sqrt.f64 C)))
	40.6b	(neg.f64 (/.f64 1 (/.f64 (sqrt.f64 C) (exp.f64 (log.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))))))
	53.7b	(/.f64 (neg.f64 (cbrt.f64 (.f64 (.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))))))) (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)))))))) (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)))
	51.0b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (fma.f64 A A (.f64 B B))))) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 8 (.f64 (.f64 A (.f64 C F)) (hypot.f64 A B)))))) (fma.f64 8 (.f64 (.f64 A A) (.f64 C F)) (.f64 2 (.f64 (.f64 F (.f64 B B)) (hypot.f64 A B))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	43.3b	(neg.f64 (sqrt.f64 (/.f64 (neg.f64 F) C)))
	39.0b	(neg.f64 (/.f64 1 (/.f64 (sqrt.f64 C) (sqrt.f64 (neg.f64 F)))))
	43.6b	(neg.f64 (/.f64 1 (sqrt.f64 (/.f64 C (neg.f64 F)))))
	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)))))
	63.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 C)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.1b	(neg.f64 (/.f64 (log.f64 (exp.f64 (.f64 (sqrt.f64 (.f64 -1/2 F)) (sqrt.f64 2)))) (sqrt.f64 C)))
	50.5b	(/.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)))))))))
	49.4b	(/.f64 (neg.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)))
	62.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	43.7b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2))) (cbrt.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))) (cbrt.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))))
	47.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 A (-.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.3b	(/.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)) (neg.f64 (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 4368 to 3105 computations (28.9% saved)

regimes6.9s (18.3%)

Accuracy

Total 19.7b remaining (52.7%)

Threshold costs 0b (0%)

Counts

217 → 9

Compiler

Compiled 60712 to 38517 computations (36.6% saved)

bsearch898.0ms (2.4%)

Steps

Iters	Range		Point
8	1.8022595749629064e+25	3.8923631686048038e+28	1.8232299960392075e+25
7	5.64629812899529e-126	4.687027250864733e-124	1.0293379345528187e-124
8	3.813841930178294e-137	2.3698769330425035e-132	1.6492372060764243e-136
8	5.78560589821425e-249	6.892128875765963e-246	4.975272536947154e-246
8	5.710630143211127e-267	1.8047481032381059e-264	1.0618671080824585e-266
8	2.2593005080985367e-281	1.0626257412418848e-278	7.250586550384806e-280
8	-7.696731405548723e-25	-7.970215291687241e-29	-8.101188799698452e-29
9	-2.9743495255337486e+102	-2.3773675896696645e+95	-2.9228459489893423e+102

Compiler

Compiled 5 to 4 computations (20% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

43×	`*-commutative_binary64`
42×	`distribute-rgt-neg-in_binary64`
40×	`neg-sub0_binary64`
39×	`neg-mul-1_binary64`
35×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	97	319
1	159	317
2	226	317
3	283	317
4	326	317
5	352	317
6	375	317
7	391	317
8	397	317
9	399	317
10	395	317

end15.0ms (0%)

Compiler: Compiled 636 to 369 computations (42% saved)

sample6.8s (18.1%)

Algorithm

1×

intervals

Results

1.1s	5516×	body	128	valid
722.0ms	905×	body	1024	valid
687.0ms	643×	body	2048	valid
606.0ms	801×	body	1024	nan
562.0ms	559×	body	2048	nan
533.0ms	2482×	body	128	nan
350.0ms	606×	body	512	valid
309.0ms	552×	body	512	nan
136.0ms	352×	body	256	nan
133.0ms	330×	body	256	valid

Compiler

Compiled 1614 to 1001 computations (38% saved)

Iter	Nodes	Cost
0	97	319
1	159	317
2	226	317
3	283	317
4	326	317
5	352	317
6	375	317
7	391	317
8	397	317
9	399	317
10	395	317

Iter	Nodes	Cost
0	97	319
1	159	317
2	226	317
3	283	317
4	326	317
5	352	317
6	375	317
7	391	317
8	397	317
9	399	317
10	395	317

Details

analyze3.2s (8.6%)

sample237.0ms (0.6%)

simplify50.0ms (0.1%)

prune5.0ms (0%)

localize16.0ms (0%)

series16.4s (43.3%)

rewrite113.0ms (0.3%)

simplify700.0ms (1.8%)

prune1.2s (3.2%)

localize7.0ms (0%)

series48.0ms (0.1%)

rewrite11.0ms (0%)

simplify82.0ms (0.2%)

prune101.0ms (0.3%)

localize9.0ms (0%)

series42.0ms (0.1%)

rewrite14.0ms (0%)

simplify336.0ms (0.9%)

prune128.0ms (0.3%)

localize9.0ms (0%)

series93.0ms (0.2%)

rewrite22.0ms (0.1%)

simplify119.0ms (0.3%)

prune186.0ms (0.5%)

regimes6.9s (18.3%)

bsearch898.0ms (2.4%)

simplify22.0ms (0.1%)

end15.0ms (0%)

sample6.8s (18.1%)

Profiling

Iter	Nodes	Cost
0	97	319
1	159	317
2	226	317
3	283	317
4	326	317
5	352	317
6	375	317
7	391	317
8	397	317
9	399	317
10	395	317