Details

analyze3.4s (8.1%)

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%	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)

sample6.8s (16%)

Symmetry

(sort A C)

Results

1.6s	5767×	body	128	valid
857.0ms	896×	body	1024	invalid
837.0ms	872×	body	1024	valid
784.0ms	671×	body	2048	valid
716.0ms	624×	body	2048	invalid
659.0ms	2614×	body	128	invalid
419.0ms	601×	body	512	valid
396.0ms	578×	body	512	invalid
175.0ms	326×	body	256	invalid
171.0ms	345×	body	256	valid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify49.0ms (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

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

45.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	48.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
▶	45.6b	(/.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)))

Status

Error

Program

48.1b

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

▶

45.6b

(/.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)))

Compiler

Compiled 239 to 156 computations (34.7% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.3b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	2.3b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	16.4b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
✓	19.4b	(/.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)))

series16.6s (39.4%)

Counts

4 → 124

Calls

4 calls:

9.7s	(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)))))))
6.7s	(/.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)))
205.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
57.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite117.0ms (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:

25.0ms	(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)))

simplify681.0ms (1.6%)

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 (2.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	478	21	499
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	480	21	501

Error

15.5b

Counts

501 → 21

Alt Table

Status	Error	Program
	57.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 C (hypot.f64 C B))))))) (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)))))
	45.6b	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))))
	55.5b	(/.f64 (neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -4 (.f64 A (.f64 C (.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (fma.f64 A A (.f64 C C)) (.f64 2 (.f64 A C)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	55.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (-.f64 A (hypot.f64 A B)) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	45.9b	(/.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 (.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.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)))
▶	43.7b	(.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)))))
	47.7b	(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 C B)))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	44.6b	(.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)))))
	50.9b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 A (.f64 F (.f64 B B))) (.f64 -16 (.f64 (.f64 A A) (.f64 C F)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	44.6b	(/.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)))))))))
	45.6b	(.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)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	53.9b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	44.5b	(.f64 (sqrt.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))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	43.9b	(/.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)))

Compiler

Compiled 69037 to 36494 computations (47.1% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 A (.f64 C -4) (.f64 B B))
	2.3b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	10.1b	(sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	17.7b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series971.0ms (2.3%)

Counts

3 → 76

Calls

3 calls:

916.0ms	(sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
43.0ms	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))
11.0ms	(fma.f64 A (.f64 C -4) (.f64 B B))

rewrite18.0ms (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:

15.0ms	(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))

simplify94.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

478×	`fma-def_binary64`
453×	`associate-l_binary64`
440×	`associate-r_binary64`
214×	`associate-/r*_binary64`
193×	`*-commutative_binary64`

Counts

117 → 110

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	521	6268
1	1551	5217
2	5251	5217

prune349.0ms (0.8%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	199	9	208
Fresh	6	14	20
Picked	1	0	1
Done	0	0	0
Total	206	23	229

Error

12.1b

Counts

229 → 23

Alt Table

Status	Error	Program
	52.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	59.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (neg.f64 B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	57.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 C (hypot.f64 C B))))))) (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)))))
	45.6b	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))))
▶	43.8b	(.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)))))))
	49.2b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 A F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	51.4b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	55.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (-.f64 A (hypot.f64 A B)) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	45.9b	(/.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 (.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.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)))
	47.7b	(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))))
	63.4b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	45.6b	(.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)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	53.9b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	49.4b	(.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)))))
	44.5b	(.f64 (sqrt.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))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	62.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (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)))
	50.9b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 A (.f64 F (.f64 B B))) (.f64 -16 (.f64 (.f64 A A) (.f64 C F)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

Compiler

Compiled 14720 to 8243 computations (44% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 A (.f64 C -4) (.f64 B B))
	2.3b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	10.1b	(sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	19.8b	(cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series59.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

59.0ms

(cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

(cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))

simplify83.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary64`
374×	`fma-neg_binary64`
373×	`cancel-sign-sub-inv_binary64`
245×	`distribute-rgt-neg-in_binary64`
239×	`distribute-lft-neg-in_binary64`

Counts

49 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2243
1	564	2203
2	2065	2145
3	4785	2145
4	5041	2145

prune514.0ms (1.2%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	328	2	330
Fresh	1	21	22
Picked	0	1	1
Done	0	0	0
Total	329	24	353

Error

12.1b

Counts

353 → 24

Alt Table

Status	Error	Program
	52.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	59.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (neg.f64 B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	57.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 C (hypot.f64 C B))))))) (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)))))
	45.6b	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))))
✓	43.8b	(.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)))))))
	49.2b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 A F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	51.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) 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)))))))
	55.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (-.f64 A (hypot.f64 A B)) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	45.9b	(/.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 (.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.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)))
	47.7b	(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (exp.f64 (log.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))))
	50.9b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 A (.f64 F (.f64 B B))) (.f64 -16 (.f64 (.f64 A A) (.f64 C F)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.5b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))))
	63.4b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	45.6b	(.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)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	53.9b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	49.4b	(.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)))))
▶	44.5b	(.f64 (sqrt.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))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	62.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (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)))

Compiler

Compiled 25032 to 14233 computations (43.1% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.5b	(/.f64 (neg.f64 (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)))
	10.1b	(sqrt.f64 (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	11.0b	(.f64 (sqrt.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))))))) (fma.f64 A (.f64 C -4) (*.f64 B B))))
	17.7b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series5.7s (13.5%)

Counts

2 → 40

Calls

2 calls:

3.4s

(*.f64 (sqrt.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))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))

2.3s

(/.f64 (neg.f64 (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)))

rewrite44.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`times-frac_binary64`
61×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`
40×	`associate-r_binary64`

Counts

2 → 136

Calls

2 calls:

15.0ms

(*.f64 (sqrt.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))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))

5.0ms

(/.f64 (neg.f64 (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)))

simplify307.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

390×	`fma-def_binary64`
348×	`associate-r_binary64`
344×	`associate-+r+_binary64`
239×	`associate-*l/_binary64`
223×	`associate-/l*_binary64`

Counts

176 → 231

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1843	33562
1	5451	33562

prune899.0ms (2.1%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	322	2	324
Fresh	1	21	22
Picked	0	1	1
Done	0	1	1
Total	323	25	348

Error

12.1b

Counts

348 → 25

Alt Table

Status	Error	Program
	52.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	59.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (neg.f64 B)))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	57.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 C (hypot.f64 C B))))))) (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)))))
	45.6b	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (neg.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))))
✓	43.8b	(.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)))))))
	49.2b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 A F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	51.5b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) 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)))))))
	55.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (.f64 (-.f64 A (hypot.f64 A B)) (.f64 B B)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 -1/2 (/.f64 (.f64 B B) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	49.6b	(.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) 3)) (/.f64 (neg.f64 (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))))
	45.9b	(/.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 (.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.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)))
	47.7b	(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F))))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (pow.f64 B 2))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	44.6b	(.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (.f64 (sqrt.f64 2) (/.f64 (neg.f64 (sqrt.f64 (.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	62.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	50.9b	(/.f64 (neg.f64 (sqrt.f64 (fma.f64 8 (.f64 A (.f64 F (.f64 B B))) (.f64 -16 (.f64 (.f64 A A) (.f64 C F)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.5b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (sqrt.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))))
	63.4b	(.f64 -1 (/.f64 (.f64 2 (sqrt.f64 (.f64 C F))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	45.6b	(.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)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	53.9b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	49.4b	(.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)))))
✓	44.5b	(.f64 (sqrt.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))))))) (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)))

Compiler

Compiled 52521 to 28800 computations (45.2% saved)

regimes3.3s (7.8%)

Accuracy

Total 18.8b remaining (54.8%)

Threshold costs 0b (0%)

Counts

168 → 5

Compiler

Compiled 44818 to 27322 computations (39% saved)

bsearch324.0ms (0.8%)

Steps

Iters	Range		Point
6	1.0361390598745263e+66	1.3251135232729845e+67	1.0607308399078237e+66
5	-1.2229021616598468e-83	-3.801473491122653e-84	-9.066057881034669e-84
2	-1.5869722779207276e+41	-1.3857509824170218e+41	-1.5618196159827645e+41
8	-5.607015244516072e+64	-1.480650449626811e+60	-1.5045379819184283e+60

Compiler

Compiled 5 to 4 computations (20% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	181
1	102	181
2	142	181
3	170	181
4	186	181
5	190	181
6	191	181
7	191	181

end596.0ms (1.4%)

Compiler: Compiled 1301 to 815 computations (37.4% saved)

Details

analyze3.4s (8.1%)

sample6.8s (16%)

simplify49.0ms (0.1%)

prune6.0ms (0%)

localize19.0ms (0%)

series16.6s (39.4%)

rewrite117.0ms (0.3%)

simplify681.0ms (1.6%)

prune1.2s (2.9%)

localize19.0ms (0%)

series971.0ms (2.3%)

rewrite18.0ms (0%)

simplify94.0ms (0.2%)

prune349.0ms (0.8%)

localize23.0ms (0.1%)

series59.0ms (0.1%)

rewrite1.0ms (0%)

simplify83.0ms (0.2%)

prune514.0ms (1.2%)

localize18.0ms (0%)

series5.7s (13.5%)

rewrite44.0ms (0.1%)

simplify307.0ms (0.7%)

prune899.0ms (2.1%)

regimes3.3s (7.8%)

bsearch324.0ms (0.8%)

simplify9.0ms (0%)

end596.0ms (1.4%)

Profiling