Details

analyze5.0s (8.2%)

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)

sample12.5s (20.5%)

Results

2.8s	5675×	body	128	valid
1.7s	924×	body	1024	valid
1.5s	3001×	body	128	invalid
1.5s	676×	body	2048	valid
1.4s	832×	body	1024	invalid
1.3s	607×	body	2048	invalid
821.0ms	624×	body	512	valid
796.0ms	613×	body	512	invalid
314.0ms	357×	body	256	valid
288.0ms	324×	body	256	invalid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify128.0ms (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

prune10.0ms (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

47.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	52.3b	(/.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)))
▶	47.9b	(/.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

52.3b

(/.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)))

▶

47.9b

(/.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)

localize27.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.7b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	5.4b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	13.6b	(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)))))))
✓	21.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

series29.0s (47.6%)

Counts

4 → 124

Calls

4 calls:

14.4s	(/.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)))
14.2s	(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)))))))
293.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
56.0ms	(+.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	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
8.0ms	(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)))))))
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)))

simplify815.0ms (1.3%)

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

prune1.4s (2.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	339	22	361
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	341	22	363

Error

23.3b

Counts

363 → 22

Alt Table

Status	Error	Program
	54.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	48.1b	(.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))))
	53.7b	(/.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)))
	48.1b	(/.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)))))))))
	55.8b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	47.9b	(/.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)))))))))
	53.3b	(/.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)))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.9b	(/.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)))))))
	60.1b	(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))))))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	55.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	59.8b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	58.9b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	59.2b	(/.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)))
▶	47.5b	(.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)))))
	56.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.3b	(/.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)))

Compiler

Compiled 61470 to 33658 computations (45.2% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 A (.f64 C -4) (.f64 B B))
	1.7b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	11.7b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	20.8b	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))

series1.7s (2.8%)

Counts

3 → 76

Calls

3 calls:

1.7s	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
58.0ms	(sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))
10.0ms	(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))

simplify186.0ms (0.3%)

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

prune561.0ms (0.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	191	9	200
Fresh	5	16	21
Picked	1	0	1
Done	0	0	0
Total	197	25	222

Error

14.6b

Counts

222 → 25

Alt Table

Status	Error	Program
	54.8b	(.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)))))
	58.3b	(.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)))))
	59.2b	(/.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)))
	51.3b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	54.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	51.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	56.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	48.1b	(.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))))
	54.7b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	48.1b	(/.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)))))))))
	55.8b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	52.6b	(.f64 -1 (/.f64 (fma.f64 1/2 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (/.f64 F (+.f64 A (hypot.f64 B A))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A)))) (.f64 (.f64 (.f64 A (.f64 C (sqrt.f64 2))) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 A A)) (+.f64 A (hypot.f64 B A)))))) -1/2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	47.9b	(/.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)))))))))
	53.3b	(/.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)))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.9b	(/.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)))))))
	60.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (-.f64 (+.f64 (.f64 A A) (.f64 C C)) (.f64 2 (.f64 A C))))))) (.f64 A C))))))
	57.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
▶	45.6b	(.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)))))
	56.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 A (.f64 1/2 (/.f64 (.f64 B B) A)))))) (sqrt.f64 (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)))
	55.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))

Compiler

Compiled 14505 to 8356 computations (42.4% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B)))
	1.7b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	10.7b	(sqrt.f64 (.f64 A (.f64 C -4)))
	11.7b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

series216.0ms (0.4%)

Counts

2 → 14

Calls

2 calls:

176.0ms	(.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)))
40.0ms	(sqrt.f64 (.f64 A (.f64 C -4)))

rewrite16.0ms (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)))

simplify98.0ms (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

prune463.0ms (0.8%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	259	4	263
Fresh	0	24	24
Picked	0	1	1
Done	0	0	0
Total	259	29	288

Error

14.6b

Counts

288 → 29

Alt Table

Status	Error	Program
	54.8b	(.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)))))
	58.3b	(.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)))))
	59.2b	(/.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)))
	51.3b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	54.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	51.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	56.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	54.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	48.1b	(.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))))
	54.7b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	48.1b	(/.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)))))))))
	55.8b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	52.6b	(.f64 -1 (/.f64 (fma.f64 1/2 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (/.f64 F (+.f64 A (hypot.f64 B A))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A)))) (.f64 (.f64 (.f64 A (.f64 C (sqrt.f64 2))) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 A A)) (+.f64 A (hypot.f64 B A)))))) -1/2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	47.9b	(/.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)))))))))
	53.3b	(/.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)))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.9b	(/.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)))))))
	60.1b	(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))))))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
▶	45.7b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (*.f64 C -4))) B))))))
	55.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	45.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (.f64 (sqrt.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)))) (sqrt.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))))) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (sqrt.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))))
	59.0b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	55.2b	(.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)))))
	57.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
✓	45.6b	(.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)))))
	56.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 A (.f64 1/2 (/.f64 (.f64 B B) A)))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))

Compiler

Compiled 19262 to 11674 computations (39.4% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))))
	1.7b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
	10.7b	(sqrt.f64 (.f64 A (.f64 C -4)))
	11.7b	(sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))

series109.0ms (0.2%)

Counts

1 → 14

Calls

1 calls:

109.0ms

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

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`sqrt-pow1_binary64`
35×	`pow1_binary64`
30×	`pow-prod-up_binary64`
23×	`pow1/2_binary64`
18×	`add-sqr-sqrt_binary64`

Counts

1 → 51

Calls

1 calls:

11.0ms

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

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-def_binary64`
439×	`cancel-sign-sub-inv_binary64`
359×	`fma-neg_binary64`
289×	`distribute-rgt-neg-in_binary64`
268×	`times-frac_binary64`

Counts

65 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	1221
1	246	1036
2	603	991
3	2486	985
4	4846	985
5	4999	985

prune582.0ms (1%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	278	3	281
Fresh	2	25	27
Picked	1	0	1
Done	0	1	1
Total	281	29	310

Error

14.6b

Counts

310 → 29

Alt Table

Status	Error	Program
	54.8b	(.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)))))
	58.3b	(.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)))))
	51.3b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (sqrt.f64 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	54.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (pow.f64 B 2) C)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	51.6b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (neg.f64 B)))
	56.5b	(/.f64 (neg.f64 (fma.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)) (/.f64 (.f64 F (.f64 (sqrt.f64 2) (.f64 B B))) (sqrt.f64 (.f64 -8 (.f64 A F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	46.4b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A))))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (.f64 (sqrt.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))))))
	57.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (pow.f64 B 2) A)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
✓	45.6b	(.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)))))
	55.2b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (.f64 (sqrt.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))))))
	54.8b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) B))
	48.1b	(.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))))
	54.7b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 A F)) (pow.f64 (sqrt.f64 2) 2)) (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)))))
	48.1b	(/.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)))))))))
	55.8b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	52.6b	(.f64 -1 (/.f64 (fma.f64 1/2 (.f64 (.f64 C (sqrt.f64 2)) (sqrt.f64 (/.f64 F (+.f64 A (hypot.f64 B A))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A)))) (.f64 (.f64 (.f64 A (.f64 C (sqrt.f64 2))) (sqrt.f64 (/.f64 F (.f64 (fma.f64 B B (.f64 A A)) (+.f64 A (hypot.f64 B A)))))) -1/2))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	47.9b	(/.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)))))))))
	53.3b	(/.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)))
	59.7b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.9b	(/.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)))))))
	60.1b	(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))))))
	55.1b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	45.9b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))) (.f64 (.f64 (sqrt.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)))) (sqrt.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))))) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (sqrt.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))))
	59.0b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)) (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B)))))
	59.0b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 (.f64 C F)) (pow.f64 (sqrt.f64 2) 2)) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (.f64 A (.f64 C -4))) B))) (.f64 (sqrt.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))))))
	56.0b	(.f64 -1 (/.f64 (sqrt.f64 (.f64 2 (.f64 F (fma.f64 2 A (.f64 1/2 (/.f64 (.f64 B B) A)))))) (sqrt.f64 (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)))

Compiler

Compiled 21692 to 13511 computations (37.7% saved)

regimes6.1s (10%)

Accuracy

Total 26.0b remaining (61.9%)

Threshold costs 0b (0%)

Counts

187 → 5

Compiler

Compiled 52223 to 33065 computations (36.7% saved)

bsearch629.0ms (1%)

Steps

Iters	Range		Point
9	1.8990648746020043e+205	2.2530053648905708e+210	1.20576307541013e+208
7	5.827598448476204e-197	4.042480915569983e-195	1.0029344104796189e-196
7	-8.619671994884689e-75	-5.1431321055870935e-76	-7.136749298156744e-75
8	-0.19139445767367044	-4.0913133510444114e-5	-0.03519957118389417

Compiler

Compiled 5 to 4 computations (20% saved)

simplify24.0ms (0%)

Algorithm

1×	egg-herbie

Rules

33×	`*-commutative_binary64`
25×	`+-commutative_binary64`
19×	`sub-neg_binary64`
17×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	233
1	125	233
2	166	233
3	198	233
4	217	233
5	223	233
6	224	233
7	223	233

end1.1s (1.9%)

Compiler: Compiled 1419 to 941 computations (33.7% saved)

Details

analyze5.0s (8.2%)

sample12.5s (20.5%)

simplify128.0ms (0.2%)

prune10.0ms (0%)

localize27.0ms (0%)

series29.0s (47.6%)

rewrite46.0ms (0.1%)

simplify815.0ms (1.3%)

prune1.4s (2.3%)

localize16.0ms (0%)

series1.7s (2.8%)

rewrite9.0ms (0%)

simplify186.0ms (0.3%)

prune561.0ms (0.9%)

localize36.0ms (0.1%)

series216.0ms (0.4%)

rewrite16.0ms (0%)

simplify98.0ms (0.2%)

prune463.0ms (0.8%)

localize20.0ms (0%)

series109.0ms (0.2%)

rewrite19.0ms (0%)

simplify78.0ms (0.1%)

prune582.0ms (1%)

regimes6.1s (10%)

bsearch629.0ms (1%)

simplify24.0ms (0%)

end1.1s (1.9%)

Profiling