Details

analyze3.4s (12.1%)

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)

sample6.9s (24.2%)

Symmetry

(sort A C)

Results

1.6s	5677×	body	128	valid
890.0ms	918×	body	1024	valid
840.0ms	682×	body	2048	valid
817.0ms	888×	body	1024	invalid
705.0ms	612×	body	2048	invalid
680.0ms	2558×	body	128	invalid
458.0ms	614×	body	512	valid
432.0ms	575×	body	512	invalid
180.0ms	365×	body	256	valid
162.0ms	341×	body	256	invalid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify52.0ms (0.2%)

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

46.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	51.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 (-.f64 (pow.f64 B 2) (.f64 (.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (.f64 (*.f64 4 A) C)))
▶	46.4b	(/.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)))

Status

Error

Program

51.5b

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

▶

46.4b

(/.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)))

Compiler

Compiled 239 to 156 computations (34.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.0b	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	5.7b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	14.3b	(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)))))))
✓	16.9b	(/.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)))

series7.8s (27.5%)

Counts

4 → 124

Calls

4 calls:

4.4s	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
3.2s	(/.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)))
161.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
44.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite109.0ms (0.4%)

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:

23.0ms	(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)))))))
16.0ms	(.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)))
5.0ms	(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

simplify714.0ms (2.5%)

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

prune1.8s (6.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	477	22	499
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	479	22	501

Error

15.0b

Counts

501 → 22

Alt Table

Status	Error	Program
	51.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	46.4b	(.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))))
	55.1b	(/.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)))
	47.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	62.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.5b	(/.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)))
	45.8b	(.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)))))
	44.1b	(/.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)))
	45.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 2 A (.f64 1/2 (/.f64 (.f64 B B) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	46.4b	(/.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)))))))))
	60.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (+.f64 C (/.f64 (.f64 A C) B))) (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) B)))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	51.9b	(/.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)))
	46.6b	(.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)))))
	53.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	52.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.4b	(.f64 -1 (.f64 (sqrt.f64 (*.f64 F (-.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (/.f64 (sqrt.f64 2) B)))
	46.9b	(/.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)))
	47.1b	(.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))))
	48.7b	(/.f64 (neg.f64 (neg.f64 (fma.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 C F))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
▶	43.0b	(/.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)))
	63.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))

Compiler

Compiled 69131 to 36552 computations (47.1% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 A (.f64 C -4) (.f64 B B))
✓	6.1b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A))))
✓	17.4b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A)))))
✓	18.6b	(/.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)))

series297.0ms (1%)

Counts

4 → 132

Calls

4 calls:

124.0ms	(/.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)))
112.0ms	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A)))))
51.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A))))
9.0ms	(fma.f64 A (.f64 C -4) (.f64 B B))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
33×	`pow1_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`

Counts

4 → 119

Calls

4 calls:

8.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A))))
6.0ms	(/.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)))
5.0ms	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A)))))
0.0ms	(fma.f64 A (.f64 C -4) (.f64 B B))

simplify137.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

524×	`associate-r_binary64`
408×	`associate-l_binary64`
346×	`times-frac_binary64`
278×	`associate-/r*_binary64`
278×	`associate-/l*_binary64`

Counts

251 → 269

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	451	10270
1	1304	9211
2	5254	9211

prune313.0ms (1.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	276	11	287
Fresh	12	9	21
Picked	1	0	1
Done	0	0	0
Total	289	20	309

Error

9.0b

Counts

309 → 20

Alt Table

Status	Error	Program
	51.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	43.1b	(/.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 F (*.f64 A 4))))))
	47.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	43.1b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A)))))) (/.f64 1 (fma.f64 A (.f64 C -4) (*.f64 B B))))
	46.9b	(.f64 -2 (sqrt.f64 (.f64 -1/4 (/.f64 F C))))
	59.5b	(/.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)))
	45.8b	(.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)))))
	48.5b	(/.f64 (neg.f64 (neg.f64 (.f64 A (sqrt.f64 (.f64 -16 (.f64 F C)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	51.9b	(/.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)))
	46.6b	(.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)))))
	56.9b	(/.f64 (neg.f64 (.f64 2 (.f64 A (sqrt.f64 (.f64 -4 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.7b	(.f64 -2 (/.f64 (sqrt.f64 (.f64 F A)) B))
▶	40.3b	(.f64 -1/4 (/.f64 (sqrt.f64 (.f64 -16 (*.f64 C F))) C))
	46.9b	(/.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)))
	50.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (expm1.f64 (log1p.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)))
	43.3b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 F (.f64 A 4))))) (.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 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 F (.f64 A 4)))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	61.1b	(.f64 2 (/.f64 (sqrt.f64 (.f64 F A)) B))
	61.1b	(.f64 2 (.f64 (sqrt.f64 (*.f64 A F)) (/.f64 1 B)))

Compiler

Compiled 13624 to 8001 computations (41.3% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -16 (.f64 C F))
✓	0.3b	(/.f64 (sqrt.f64 (.f64 -16 (.f64 C F))) C)
✓	15.8b	(sqrt.f64 (.f64 -16 (.f64 C F)))

series32.0ms (0.1%)

Counts

3 → 0

Calls

3 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 -16 (.f64 C F))) C)
12.0ms	(sqrt.f64 (.f64 -16 (.f64 C F)))
4.0ms	(.f64 -16 (.f64 C F))

rewrite14.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`

Counts

3 → 67

Calls

3 calls:

5.0ms	(/.f64 (sqrt.f64 (.f64 -16 (.f64 C F))) C)
4.0ms	(.f64 -16 (.f64 C F))
2.0ms	(sqrt.f64 (.f64 -16 (.f64 C F)))

simplify91.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

731×	`times-frac_binary64`
440×	`*-commutative_binary64`
438×	`associate-/l/_binary64`
416×	`associate-l_binary64`
408×	`associate-*l/_binary64`

Counts

67 → 70

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	100	1024
1	182	932
2	483	932
3	1454	932
4	3154	932
5	3533	932
6	4954	932
7	5014	932

prune84.0ms (0.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	19	19
Picked	1	0	1
Done	0	0	0
Total	64	26	90

Error

9.0b

Counts

90 → 26

Alt Table

Status	Error	Program
	52.7b	(.f64 -1/4 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (.f64 -16 (*.f64 C F))) C) 3)))
	51.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	43.1b	(/.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 F (*.f64 A 4))))))
	50.0b	(.f64 -1/4 (exp.f64 (-.f64 (log.f64 (sqrt.f64 (.f64 -16 (*.f64 C F)))) (log.f64 C))))
	47.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	43.1b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A)))))) (/.f64 1 (fma.f64 A (.f64 C -4) (*.f64 B B))))
	46.9b	(.f64 -2 (sqrt.f64 (.f64 -1/4 (/.f64 F C))))
	59.5b	(/.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)))
	45.8b	(.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)))))
▶	40.3b	(.f64 -1/4 (.f64 (sqrt.f64 (.f64 -16 (.f64 C F))) (/.f64 1 C)))
	41.8b	(.f64 -1/4 (/.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -16 (*.f64 C F))))) C))
	48.5b	(/.f64 (neg.f64 (neg.f64 (.f64 A (sqrt.f64 (.f64 -16 (.f64 F C)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	40.7b	(.f64 -1/4 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -16 (.f64 C F)))) (cbrt.f64 (sqrt.f64 (.f64 -16 (.f64 C F))))) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 -16 (*.f64 C F)))) C)))
	51.9b	(/.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)))
	46.6b	(.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)))))
	56.9b	(/.f64 (neg.f64 (.f64 2 (.f64 A (sqrt.f64 (.f64 -4 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.1b	(.f64 2 (/.f64 (sqrt.f64 (.f64 F A)) B))
	48.7b	(.f64 -1/4 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 -16 (.f64 C F))) C)) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 -16 (.f64 C F))) C))))
	59.7b	(.f64 -2 (/.f64 (sqrt.f64 (.f64 F A)) B))
	46.9b	(/.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)))
	50.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (expm1.f64 (log1p.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)))
	40.3b	(.f64 -1/4 (/.f64 1 (/.f64 C (sqrt.f64 (.f64 -16 (*.f64 C F))))))
	43.3b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 F (.f64 A 4))))) (.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 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 F (.f64 A 4)))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	61.1b	(.f64 2 (.f64 (sqrt.f64 (*.f64 A F)) (/.f64 1 B)))

Compiler

Compiled 2589 to 1683 computations (35% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(.f64 -16 (.f64 C F))
✓	0.3b	(.f64 (sqrt.f64 (.f64 -16 (*.f64 C F))) (/.f64 1 C))
	15.8b	(sqrt.f64 (.f64 -16 (.f64 C F)))

series16.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

16.0ms

(*.f64 (sqrt.f64 (*.f64 -16 (*.f64 C F))) (/.f64 1 C))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 39

Calls

1 calls:

9.0ms

(*.f64 (sqrt.f64 (*.f64 -16 (*.f64 C F))) (/.f64 1 C))

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-neg_binary64`
547×	`times-frac_binary64`
465×	`associate-/l*_binary64`
274×	`sqr-pow_binary64`
247×	`*-commutative_binary64`

Counts

39 → 58

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	662
1	129	587
2	311	587
3	814	587
4	1766	587
5	1800	587
6	2135	587
7	2953	587
8	4246	587
9	4974	587

prune84.0ms (0.3%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	24	25
Picked	0	1	1
Done	0	0	0
Total	91	26	117

Error

9.0b

Counts

117 → 26

Alt Table

Status	Error	Program
	52.7b	(.f64 -1/4 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (.f64 -16 (*.f64 C F))) C) 3)))
	51.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
	43.1b	(/.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 F (*.f64 A 4))))))
	41.8b	(.f64 -1/4 (.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 -16 (.f64 C F))))) (/.f64 1 C)))
	50.0b	(.f64 -1/4 (exp.f64 (-.f64 (log.f64 (sqrt.f64 (.f64 -16 (*.f64 C F)))) (log.f64 C))))
	47.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	43.1b	(.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 2 A)))))) (/.f64 1 (fma.f64 A (.f64 C -4) (*.f64 B B))))
	46.9b	(.f64 -2 (sqrt.f64 (.f64 -1/4 (/.f64 F C))))
	59.5b	(/.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)))
	45.8b	(.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)))))
	48.5b	(/.f64 (neg.f64 (neg.f64 (.f64 A (sqrt.f64 (.f64 -16 (.f64 F C)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	40.7b	(.f64 -1/4 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 -16 (.f64 C F)))) (cbrt.f64 (sqrt.f64 (.f64 -16 (.f64 C F))))) (/.f64 (cbrt.f64 (sqrt.f64 (.f64 -16 (*.f64 C F)))) C)))
	51.9b	(/.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)))
	46.6b	(.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)))))
	56.9b	(/.f64 (neg.f64 (.f64 2 (.f64 A (sqrt.f64 (.f64 -4 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
	61.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.1b	(.f64 2 (/.f64 (sqrt.f64 (.f64 F A)) B))
	48.7b	(.f64 -1/4 (.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 -16 (.f64 C F))) C)) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 -16 (.f64 C F))) C))))
	59.7b	(.f64 -2 (/.f64 (sqrt.f64 (.f64 F A)) B))
	46.9b	(/.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)))
	50.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (expm1.f64 (log1p.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)))
✓	40.3b	(.f64 -1/4 (.f64 (sqrt.f64 (.f64 -16 (.f64 C F))) (/.f64 1 C)))
	40.3b	(.f64 -1/4 (/.f64 1 (/.f64 C (sqrt.f64 (.f64 -16 (*.f64 C F))))))
	43.3b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 F (.f64 A 4))))) (.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 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 F (.f64 A 4)))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	61.1b	(.f64 2 (.f64 (sqrt.f64 (*.f64 A F)) (/.f64 1 B)))

Compiler

Compiled 2374 to 1592 computations (32.9% saved)

regimes5.7s (20.2%)

Accuracy

Total 23.2b remaining (61.5%)

Threshold costs 0b (0%)

Counts

276 → 8

Compiler

Compiled 67390 to 42765 computations (36.5% saved)

bsearch17.0ms (0.1%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary64`
17×	`+-commutative_binary64`
16×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	327
1	125	327
2	155	327
3	177	327
4	189	327
5	191	327
6	190	327

end592.0ms (2.1%)

Compiler: Compiled 1595 to 1002 computations (37.2% saved)

Details

analyze3.4s (12.1%)

sample6.9s (24.2%)

simplify52.0ms (0.2%)

prune6.0ms (0%)

localize18.0ms (0.1%)

series7.8s (27.5%)

rewrite109.0ms (0.4%)

simplify714.0ms (2.5%)

prune1.8s (6.4%)

localize14.0ms (0%)

series297.0ms (1%)

rewrite30.0ms (0.1%)

simplify137.0ms (0.5%)

prune313.0ms (1.1%)

localize7.0ms (0%)

series32.0ms (0.1%)

rewrite14.0ms (0%)

simplify91.0ms (0.3%)

prune84.0ms (0.3%)

localize7.0ms (0%)

series16.0ms (0.1%)

rewrite12.0ms (0%)

simplify83.0ms (0.3%)

prune84.0ms (0.3%)

regimes5.7s (20.2%)

bsearch17.0ms (0.1%)

simplify12.0ms (0%)

end592.0ms (2.1%)

Profiling