Details

analyze3.3s (2.2%)

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)

sample143.0ms (0.1%)

Algorithm

1×

intervals

Results

35.0ms	192×	body	128	valid
17.0ms	24×	body	1024	valid
15.0ms	22×	body	1024	nan
13.0ms	67×	body	128	nan
12.0ms	14×	body	2048	nan
10.0ms	12×	body	2048	valid
9.0ms	19×	body	512	valid
6.0ms	11×	body	512	nan
3.0ms	8×	body	256	valid
3.0ms	8×	body	256	nan
1.0ms	1×	body	4096	valid

Compiler

Compiled 93 to 69 computations (25.8% saved)

simplify89.0ms (0.1%)

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

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
	51.9b	(/.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)))
▶	47.1b	(/.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

51.9b

(/.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)))

▶

47.1b

(/.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%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.3b	(+.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))))))
✓	15.9b	(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)))))))
✓	21.2b	(/.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)))

rewrite41.0ms (0%)

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:

11.0ms	(.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)))))))
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)))

series20.1s (13.4%)

Counts

4 → 124

Calls

4 calls:

11.0s	(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)))))))
8.8s	(/.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)))
219.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
48.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

simplify478.0ms (0.3%)

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 → 417

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2448	45159
1	5052	45159

prune1.0s (0.7%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	393	24	417
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	395	24	419

Error

24.1b

Counts

419 → 24

Alt Table

Status	Error	Program
	47.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.6b	(/.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)))
	54.3b	(/.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)))
▶	47.2b	(/.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)))))))))
	48.6b	(.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)))))
	60.7b	(/.f64 (neg.f64 (-.f64 (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (.f64 (sqrt.f64 2) B) (.f64 1/2 (.f64 (.f64 C (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))))) (.f64 2 (+.f64 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 1/2 (/.f64 (.f64 B B) C) (fma.f64 1/2 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (fma.f64 2 C (.f64 1/2 (/.f64 (.f64 A (.f64 B B)) (.f64 C C)))))) (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.3b	(/.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)))
	60.8b	(/.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)))
	60.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.7b	(/.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)))
	57.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	54.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	59.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	49.8b	(/.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)))))))))
	59.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	47.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (.f64 (cbrt.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)))
	47.2b	(.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))))
	61.2b	(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))))))
	60.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	55.1b	(/.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)))
	58.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

Compiler

Compiled 61778 to 33818 computations (45.3% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.3b	(+.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))))))
	15.9b	(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)))))))
✓	20.9b	(/.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))))))))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
6×	`associate-*r/_binary64`

Counts

1 → 35

Calls

1 calls:

10.0ms

(/.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))))))))

series1.8min (72.6%)

Counts

1 → 20

Calls

1 calls:

1.8min

(/.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))))))))

simplify245.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

996×	`fma-def_binary64`
460×	`*-commutative_binary64`
229×	`associate-r_binary64`
189×	`+-commutative_binary64`
185×	`distribute-rgt-in_binary64`

Counts

55 → 105

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1037	16452
1	3442	13557
2	5080	13557

prune1.0s (0.7%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	375	14	389
Fresh	7	16	23
Picked	1	0	1
Done	0	0	0
Total	383	30	413

Error

19.9b

Counts

413 → 30

Alt Table

Status	Error	Program
	47.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.9b	(/.f64 -1 (fma.f64 1/4 (/.f64 (.f64 B B) (.f64 C (.f64 F (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -2 (/.f64 A F))))))) (/.f64 (sqrt.f64 (.f64 -2 (/.f64 A F))) (sqrt.f64 2))))
	48.6b	(.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)))))
	60.7b	(/.f64 (neg.f64 (-.f64 (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (.f64 (sqrt.f64 2) B) (.f64 1/2 (.f64 (.f64 C (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))))) (.f64 2 (+.f64 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.5b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (.f64 -16 (.f64 A (.f64 (.f64 C C) F))))))
	59.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 1/2 (/.f64 (.f64 B B) C) (fma.f64 1/2 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (fma.f64 2 C (.f64 1/2 (/.f64 (.f64 A (.f64 B B)) (.f64 C C)))))) (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.1b	(/.f64 -1 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 A F))) (sqrt.f64 2)))
	55.3b	(/.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)))
	60.8b	(/.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)))
	47.2b	(/.f64 -1 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (/.f64 1 (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))))))))))
	58.6b	(/.f64 -1 (fma.f64 1/4 (/.f64 (.f64 B B) (.f64 A (.f64 F (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -2 (/.f64 C F))))))) (/.f64 (sqrt.f64 (.f64 -2 (/.f64 C F))) (sqrt.f64 2))))
	60.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.5b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))))
	56.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	55.1b	(/.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)))
	53.7b	(/.f64 -1 (.f64 (sqrt.f64 (/.f64 1 (.f64 F (+.f64 C (hypot.f64 C B))))) (/.f64 B (sqrt.f64 2))))
	54.7b	(/.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 2 C)))))))
	54.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	59.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (/.f64 (sqrt.f64 2) B)))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	53.6b	(/.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 2 A)))))))
	61.4b	(/.f64 -1 (/.f64 (sqrt.f64 (.f64 -4 (/.f64 (.f64 C A) (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (fma.f64 A A (.f64 C (-.f64 C (*.f64 2 A))))))))))) (sqrt.f64 2)))
▶	47.2b	(.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))))
	61.2b	(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))))))
	54.4b	(/.f64 -1 (.f64 (/.f64 B (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 F (+.f64 A (hypot.f64 B A)))))))
	56.9b	(/.f64 -1 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 C F))) (sqrt.f64 2)))
	58.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	55.4b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))))
	54.3b	(/.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 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))))))

Compiler

Compiled 54762 to 31103 computations (43.2% saved)

localize29.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.3b	(+.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))))))
	15.9b	(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)))))))
✓	20.5b	(.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))))

rewrite15.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
13×	`associate-*r/_binary64`
12×	`associate-l_binary64`
12×	`*-un-lft-identity_binary64`

Counts

1 → 52

Calls

1 calls:

9.0ms

(*.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)))))))) (/.f64 1 (fma.f64 A (*.f64 C -4) (*.f64 B B))))

series7.3s (4.9%)

Counts

1 → 20

Calls

1 calls:

7.3s	(.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))))

simplify436.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

541×	`*-commutative_binary64`
264×	`+-commutative_binary64`
250×	`fma-def_binary64`
243×	`associate-r_binary64`
232×	`associate-+r+_binary64`

Counts

72 → 140

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1211	20662
1	4434	18480
2	4958	18480
3	5000	18480
4	4937	18480

prune933.0ms (0.6%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	703	5	708
Fresh	5	24	29
Picked	0	1	1
Done	0	0	0
Total	708	30	738

Error

19.9b

Counts

738 → 30

Alt Table

Status	Error	Program
	47.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (.f64 (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.9b	(/.f64 -1 (fma.f64 1/4 (/.f64 (.f64 B B) (.f64 C (.f64 F (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -2 (/.f64 A F))))))) (/.f64 (sqrt.f64 (.f64 -2 (/.f64 A F))) (sqrt.f64 2))))
	48.6b	(.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)))))
	60.7b	(/.f64 (neg.f64 (-.f64 (fma.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))) (.f64 (sqrt.f64 2) B) (.f64 1/2 (.f64 (.f64 C (.f64 (sqrt.f64 2) B)) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))))) (fma.f64 1/2 (.f64 (.f64 A (.f64 C (.f64 (sqrt.f64 2) B))) (sqrt.f64 (/.f64 F (.f64 (+.f64 (.f64 A A) (.f64 B B)) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))))) (.f64 2 (+.f64 (.f64 (/.f64 (.f64 A (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 (.f64 F (+.f64 (.f64 A A) (.f64 B B))) (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B))))))) (.f64 (/.f64 (.f64 (.f64 A A) (.f64 C (sqrt.f64 2))) B) (sqrt.f64 (/.f64 F (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.0b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (fma.f64 1/2 (/.f64 (.f64 B B) C) (fma.f64 1/2 (/.f64 (.f64 (.f64 A A) (.f64 B B)) (pow.f64 C 3)) (fma.f64 2 C (.f64 1/2 (/.f64 (.f64 A (.f64 B B)) (.f64 C C)))))) (.f64 1/8 (/.f64 (pow.f64 B 4) (pow.f64 C 3))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	55.1b	(/.f64 -1 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 A F))) (sqrt.f64 2)))
	55.3b	(/.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)))
▶	47.2b	(/.f64 -1 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (/.f64 1 (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))))))))))
	58.6b	(/.f64 -1 (fma.f64 1/4 (/.f64 (.f64 B B) (.f64 A (.f64 F (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -2 (/.f64 C F))))))) (/.f64 (sqrt.f64 (.f64 -2 (/.f64 C F))) (sqrt.f64 2))))
	60.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.5b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))))
	56.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	55.4b	(.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (/.f64 1 (fma.f64 A (.f64 C -4) (*.f64 B B))))
	54.3b	(neg.f64 (.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A))))))
	58.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.5b	(.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (/.f64 1 (fma.f64 A (.f64 C -4) (.f64 B B))))
	53.6b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (/.f64 (sqrt.f64 2) B)))
	54.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	59.0b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	60.8b	(.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)))))))) (/.f64 1 (fma.f64 A (.f64 C -4) (*.f64 B B))))
	60.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	53.6b	(/.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 2 A)))))))
	61.4b	(/.f64 -1 (/.f64 (sqrt.f64 (.f64 -4 (/.f64 (.f64 C A) (.f64 F (+.f64 A (+.f64 C (sqrt.f64 (fma.f64 A A (.f64 C (-.f64 C (*.f64 2 A))))))))))) (sqrt.f64 2)))
✓	47.2b	(.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))))
	61.2b	(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))))))
	54.4b	(/.f64 -1 (.f64 (/.f64 B (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 F (+.f64 A (hypot.f64 B A)))))))
	56.9b	(/.f64 -1 (/.f64 (sqrt.f64 (*.f64 -2 (/.f64 C F))) (sqrt.f64 2)))
	55.1b	(/.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)))
	55.4b	(/.f64 -1 (/.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))))
	54.3b	(/.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 2 A) (.f64 1/2 (/.f64 (.f64 B B) C)))))))))

Compiler

Compiled 61058 to 34482 computations (43.5% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.3b	(+.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))))))
	15.9b	(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)))))))
✓	21.0b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (/.f64 1 (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)))))))))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-r_binary64`
17×	`add-sqr-sqrt_binary64`
14×	`times-frac_binary64`
11×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 43

Calls

1 calls:

16.0ms

(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (/.f64 1 (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)))))))))

Details

analyze3.3s (2.2%)

sample143.0ms (0.1%)

simplify89.0ms (0.1%)

prune6.0ms (0%)

localize18.0ms (0%)

rewrite41.0ms (0%)

series20.1s (13.4%)

simplify478.0ms (0.3%)

prune1.0s (0.7%)

localize21.0ms (0%)

rewrite13.0ms (0%)

series1.8min (72.6%)

simplify245.0ms (0.2%)

prune1.0s (0.7%)

localize29.0ms (0%)

rewrite15.0ms (0%)

series7.3s (4.9%)

simplify436.0ms (0.3%)

prune933.0ms (0.6%)

localize20.0ms (0%)

rewrite21.0ms (0%)

series5.8s (3.9%)

Profiling