Details

analyze3.3s (4.1%)

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%	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)

sample6.6s (8%)

Results

1.6s	5729×	body	128	valid
845.0ms	884×	body	1024	valid
770.0ms	697×	body	2048	valid
744.0ms	3069×	body	128	invalid
721.0ms	824×	body	1024	invalid
661.0ms	610×	body	2048	invalid
424.0ms	582×	body	512	invalid
414.0ms	606×	body	512	valid
155.0ms	338×	body	256	valid
153.0ms	347×	body	256	invalid
4.0ms	2×	body	4096	valid

Compiler

Compiled 134 to 98 computations (26.9% saved)

simplify76.0ms (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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

49.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	49.9b	(/.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)))
	52.7b	(/.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)))

Status

Error

Program

▶

49.9b

(/.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)))

52.7b

(/.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)))

Compiler

Compiled 239 to 156 computations (34.7% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	3.8b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
✓	11.7b	(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)))))))
✓	22.3b	(/.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)))

series16.7s (20.4%)

Counts

4 → 124

Calls

4 calls:

9.0s	(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)))))))
7.4s	(/.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)))
209.0ms	(.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)))

rewrite85.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

225×	`add-sqr-sqrt_binary64`
215×	`log1p-expm1-u_binary64`
215×	`expm1-log1p-u_binary64`
210×	`add-cbrt-cube_binary64`
210×	`add-exp-log_binary64`

Counts

4 → 112

Calls

4 calls:

82.0ms	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
82.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
82.0ms	(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)))))))
82.0ms	(/.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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	128
1	448	126
2	4697	126
3	4938	126
0	0	0
1	0	0

simplify378.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
267×	`associate-/l*_binary64`
212×	`associate-*l/_binary64`
171×	`associate-/r*_binary64`
146×	`times-frac_binary64`

Counts

236 → 323

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2221	37666
1	5018	37666

prune997.0ms (1.2%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	294	29	323
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	296	29	325

Error

27.9b

Counts

325 → 29

Alt Table

Status	Error	Program
	50.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (+.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.9b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 -8 (.f64 A F))) (.f64 C (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	56.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) (.f64 F (pow.f64 B 2)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	50.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) 2) (cbrt.f64 (hypot.f64 B (-.f64 A C))) (+.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.6b	(/.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)))
	60.8b	(/.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)))
	60.9b	(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))))))
	59.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
▶	49.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	49.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (sqrt.f64 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.1b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.6b	(sqrt.f64 (/.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)))))) (pow.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)) 2)))
	52.3b	(.f64 (/.f64 -1 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (/.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (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)))
	60.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) (+.f64 C B)))) (/.f64 (.f64 A C) B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 10 (.f64 A (.f64 C (.f64 F B)))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	54.5b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 (.f64 F (.f64 B B)) (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 8 (.f64 (.f64 (.f64 A A) (.f64 (.f64 C C) F)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B)))))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 8 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 (.f64 (.f64 A A) (.f64 (.f64 C C) (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (.f64 A A) (.f64 B B)) 3))) (fma.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B))))) (.f64 8 (.f64 (.f64 A A) (.f64 C F)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 A (.f64 (pow.f64 C 2) F))))) (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 (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)))
	57.5b	(/.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	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	50.1b	(.f64 (/.f64 -1 (pow.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) 2)) (/.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	59.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 (.f64 B B) (.f64 C C))) C) F)) (/.f64 (sqrt.f64 2) B)))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	58.6b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	61.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	57.4b	(/.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)))
	53.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))

Compiler

Compiled 58748 to 32838 computations (44.1% saved)

localize65.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.1b	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C)))))))
✓	9.5b	(fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))
✓	17.2b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))
✓	24.8b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

series27.0s (33%)

Counts

4 → 132

Calls

4 calls:

17.9s	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))
7.7s	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
1.3s	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C)))))))
115.0ms	(fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))

rewrite160.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

392×	`log1p-udef_binary64`
234×	`add-sqr-sqrt_binary64`
223×	`log1p-expm1-u_binary64`
223×	`expm1-log1p-u_binary64`
219×	`add-cbrt-cube_binary64`

Counts

4 → 95

Calls

4 calls:

153.0ms	(.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C)))))))
153.0ms	(fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))
153.0ms	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (*.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))
153.0ms	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	128
1	474	126
2	4498	126
3	5167	126
0	0	0
1	0	0

simplify817.0ms (1%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-def_binary64`
280×	`associate-/l*_binary64`
214×	`associate-*l/_binary64`
179×	`associate-*r/_binary64`
174×	`associate-/r*_binary64`

Counts

227 → 323

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2427	41113
1	5269	41113

prune2.7s (3.2%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	316	7	323
Fresh	5	23	28
Picked	0	1	1
Done	0	0	0
Total	321	31	352

Error

27.7b

Counts

352 → 31

Alt Table

Status	Error	Program
	63.5b	(/.f64 (neg.f64 (-.f64 (fma.f64 2 (.f64 (sqrt.f64 (.f64 (pow.f64 C 3) F)) (sqrt.f64 2)) (.f64 1/4 (.f64 (sqrt.f64 (/.f64 F C)) (.f64 (sqrt.f64 2) (.f64 B B))))) (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) (.f64 F (pow.f64 B 2)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	50.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (+.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	50.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) 2) (cbrt.f64 (hypot.f64 B (-.f64 A C))) (+.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.6b	(/.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)))
	60.8b	(/.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)))
	62.8b	(/.f64 (neg.f64 (.f64 -2 (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 C F))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
✓	49.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
▶	49.8b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (sqrt.f64 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	63.7b	(-.f64 (.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) A) (sqrt.f64 (.f64 C F)))) (fma.f64 1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 B B)) A) (sqrt.f64 (/.f64 F (pow.f64 C 3)))) (.f64 1/4 (.f64 (sqrt.f64 (/.f64 F C)) (sqrt.f64 2)))))
	58.6b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.1b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.6b	(sqrt.f64 (/.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)))))) (pow.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)) 2)))
	62.7b	(/.f64 (neg.f64 (sqrt.f64 (.f64 8 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	62.4b	(.f64 -1/2 (.f64 (sqrt.f64 (/.f64 F C)) (sqrt.f64 2)))
	61.1b	(/.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 (/.f64 -1 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (/.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 F C)))))
	60.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) (+.f64 C B)))) (/.f64 (.f64 A C) B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 10 (.f64 A (.f64 C (.f64 F B)))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	53.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	63.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 A)))))) (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 (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)))
	57.5b	(/.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	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	50.1b	(.f64 (/.f64 -1 (pow.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) 2)) (/.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.4b	(/.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)))
	54.5b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 (.f64 F (.f64 B B)) (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 8 (.f64 (.f64 (.f64 A A) (.f64 (.f64 C C) F)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B)))))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 8 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 (.f64 (.f64 A A) (.f64 (.f64 C C) (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (.f64 A A) (.f64 B B)) 3))) (fma.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B))))) (.f64 8 (.f64 (.f64 A A) (.f64 C F)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 62663 to 35249 computations (43.7% saved)

localize33.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.4b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	9.5b	(sqrt.f64 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))
✓	18.4b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (sqrt.f64 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
✓	18.5b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)) 2))

series8.5s (10.4%)

Counts

3 → 60

Calls

3 calls:

6.8s

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

1.6s

(sqrt.f64 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))

127.0ms

(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) 2))

rewrite119.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

395×	`log1p-udef_binary64`
233×	`add-sqr-sqrt_binary64`
223×	`log1p-expm1-u_binary64`
223×	`expm1-log1p-u_binary64`
218×	`add-cbrt-cube_binary64`

Counts

3 → 88

Calls

3 calls:

114.0ms

(sqrt.f64 (*.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))

114.0ms

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

113.0ms

(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	83
1	469	81
2	4618	81
3	5323	81
0	0	0
1	0	0

simplify406.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

657×	`*-commutative_binary64`
317×	`fma-def_binary64`
294×	`associate-r_binary64`
285×	`associate-+r+_binary64`
171×	`associate-/l*_binary64`

Counts

148 → 191

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1428	22547
1	5077	22547

prune1.5s (1.8%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	280	6	286
Fresh	2	27	29
Picked	1	0	1
Done	0	1	1
Total	283	34	317

Error

26.3b

Counts

317 → 34

Alt Table

Status	Error	Program
	50.2b	(.f64 (/.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) 1) (/.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))))
	50.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (+.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	63.5b	(/.f64 (neg.f64 (-.f64 (fma.f64 2 (.f64 (sqrt.f64 (.f64 (pow.f64 C 3) F)) (sqrt.f64 2)) (.f64 1/4 (.f64 (sqrt.f64 (/.f64 F C)) (.f64 (sqrt.f64 2) (.f64 B B))))) (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) (.f64 F (pow.f64 B 2)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	50.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) 2) (cbrt.f64 (hypot.f64 B (-.f64 A C))) (+.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.6b	(/.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)))
	60.8b	(/.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)))
	55.9b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (sqrt.f64 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (.f64 B B) C))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.8b	(/.f64 (neg.f64 (.f64 -2 (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 C F))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
✓	49.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	63.7b	(-.f64 (.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) A) (sqrt.f64 (.f64 C F)))) (fma.f64 1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 B B)) A) (sqrt.f64 (/.f64 F (pow.f64 C 3)))) (.f64 1/4 (.f64 (sqrt.f64 (/.f64 F C)) (sqrt.f64 2)))))
	55.5b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (.f64 (sqrt.f64 (.f64 A F)) (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.6b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.1b	(/.f64 (neg.f64 (.f64 A (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -8 (.f64 C F)))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.6b	(sqrt.f64 (/.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)))))) (pow.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)) 2)))
	62.4b	(.f64 -1/2 (.f64 (sqrt.f64 (/.f64 F C)) (sqrt.f64 2)))
	61.1b	(/.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 (/.f64 -1 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (/.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 F C)))))
	57.4b	(/.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)))
	53.1b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) (+.f64 C B)))) (/.f64 (.f64 A C) B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	61.6b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 10 (.f64 A (.f64 C (.f64 F B)))))) (fma.f64 2 (.f64 F (pow.f64 B 3)) (.f64 (.f64 F B) (+.f64 (.f64 A A) (.f64 C C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	53.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	63.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 A)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.9b	(/.f64 (neg.f64 (.f64 (neg.f64 (.f64 (sqrt.f64 2) B)) (sqrt.f64 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (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 (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)))
	57.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 -16 (.f64 (pow.f64 A 2) (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
▶	47.3b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (.f64 (sqrt.f64 F) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.4b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	54.5b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 (.f64 F (.f64 B B)) (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 8 (.f64 (.f64 (.f64 A A) (.f64 (.f64 C C) F)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B)))))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 8 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 (.f64 (.f64 A A) (.f64 (.f64 C C) (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (.f64 A A) (.f64 B B)) 3))) (fma.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B))))) (.f64 8 (.f64 (.f64 A A) (.f64 C F)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 42462 to 23551 computations (44.5% saved)

localize35.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(fma.f64 A (.f64 C -4) (.f64 B B))
	1.4b	(+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
✓	18.4b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (.f64 (sqrt.f64 F) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	18.5b	(sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)) 2))

series6.0s (7.3%)

Counts

2 → 56

Calls

2 calls:

6.0s

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

20.0ms

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

rewrite120.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

401×	`log1p-udef_binary64`
237×	`add-sqr-sqrt_binary64`
227×	`log1p-expm1-u_binary64`
227×	`expm1-log1p-u_binary64`
222×	`add-cbrt-cube_binary64`

Counts

2 → 37

Calls

2 calls:

117.0ms

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

117.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	62
1	482	58
2	4555	58
3	5273	58
0	0	0
1	0	0

simplify424.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

507×	`*-commutative_binary64`
257×	`+-commutative_binary64`
249×	`fma-def_binary64`
235×	`associate-r_binary64`
232×	`associate-+r+_binary64`

Counts

93 → 83

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1108	17937
1	4142	15285
2	5036	15285

prune1.2s (1.4%)

Pruning

39 alts after pruning (38 fresh and 1 done)

	Pruned	Kept	Total
New	239	8	247
Fresh	2	30	32
Picked	1	0	1
Done	0	1	1
Total	242	39	281

Error

22.2b

Counts

281 → 39

Alt Table

Status	Error	Program
	50.2b	(.f64 (/.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) 1) (/.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))))
	50.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (+.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	63.5b	(/.f64 (neg.f64 (-.f64 (fma.f64 2 (.f64 (sqrt.f64 (.f64 (pow.f64 C 3) F)) (sqrt.f64 2)) (.f64 1/4 (.f64 (sqrt.f64 (/.f64 F C)) (.f64 (sqrt.f64 2) (.f64 B B))))) (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 C F))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.6b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (+.f64 (sqrt.f64 (+.f64 (pow.f64 B 2) (pow.f64 C 2))) C) (.f64 F (pow.f64 B 2)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	50.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 B (-.f64 A C))) 2) (cbrt.f64 (hypot.f64 B (-.f64 A C))) (+.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.6b	(/.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)))
	60.8b	(/.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)))
	55.9b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (sqrt.f64 (.f64 F (-.f64 (.f64 2 A) (.f64 1/2 (/.f64 (.f64 B B) C))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	62.8b	(/.f64 (neg.f64 (.f64 -2 (.f64 (.f64 A (sqrt.f64 2)) (sqrt.f64 (.f64 C F))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	59.4b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F B))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
✓	49.3b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (fma.f64 (pow.f64 (cbrt.f64 A) 2) (cbrt.f64 A) (+.f64 C (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.0b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (.f64 (sqrt.f64 F) (sqrt.f64 (-.f64 (.f64 2 C) (.f64 1/2 (/.f64 (.f64 B B) A))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	63.7b	(-.f64 (.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) A) (sqrt.f64 (.f64 C F)))) (fma.f64 1/16 (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 B B)) A) (sqrt.f64 (/.f64 F (pow.f64 C 3)))) (.f64 1/4 (.f64 (sqrt.f64 (/.f64 F C)) (sqrt.f64 2)))))
	55.5b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (.f64 (sqrt.f64 (.f64 A F)) (sqrt.f64 2)))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	58.6b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 F (+.f64 A (sqrt.f64 (+.f64 (pow.f64 A 2) (pow.f64 B 2)))))) (.f64 (sqrt.f64 2) B))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	56.1b	(/.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)))
	47.3b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (.f64 (sqrt.f64 F) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (pow.f64 (sqrt.f64 (fma.f64 A (.f64 C -4) (*.f64 B B))) 2))
	54.4b	(neg.f64 (.f64 (/.f64 (sqrt.f64 2) B) (sqrt.f64 (.f64 F (+.f64 A (hypot.f64 B A))))))
	61.6b	(sqrt.f64 (/.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)))))) (pow.f64 (fma.f64 A (.f64 C -4) (*.f64 B B)) 2)))
	62.4b	(.f64 -1/2 (.f64 (sqrt.f64 (/.f64 F C)) (sqrt.f64 2)))
	50.1b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (.f64 (sqrt.f64 F) (sqrt.f64 (+.f64 A (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	54.2b	(neg.f64 (.f64 (sqrt.f64 (.f64 (+.f64 C (hypot.f64 B C)) F)) (/.f64 (sqrt.f64 2) B)))
	61.1b	(/.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 (/.f64 -1 (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))) (/.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (sqrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	59.5b	(/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 F (pow.f64 B 3))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	60.8b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/4 (/.f64 F C)))))
	56.6b	(/.f64 (neg.f64 (.f64 (neg.f64 (.f64 (sqrt.f64 2) B)) (.f64 (sqrt.f64 F) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	57.4b	(/.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)))
	53.1b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (sqrt.f64 (.f64 F (+.f64 C (sqrt.f64 (+.f64 (pow.f64 C 2) (pow.f64 B 2)))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	53.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
	63.1b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (neg.f64 A)))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	47.6b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2)) (.f64 (sqrt.f64 F) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (.f64 (pow.f64 (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B))) 2) (cbrt.f64 (fma.f64 A (.f64 C -4) (.f64 B B)))))
	54.5b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 2 (.f64 C (.f64 F (.f64 B B))) (fma.f64 2 (.f64 (.f64 F (.f64 B B)) (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 2 (.f64 A (.f64 F (.f64 B B))) (.f64 8 (.f64 (.f64 (.f64 A A) (.f64 (.f64 C C) F)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B)))))))))) (fma.f64 8 (.f64 A (.f64 (.f64 C C) F)) (fma.f64 8 (.f64 (.f64 A (.f64 C F)) (sqrt.f64 (+.f64 (.f64 A A) (.f64 B B)))) (fma.f64 (.f64 (.f64 A A) (.f64 (.f64 C C) (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (.f64 A A) (.f64 B B)) 3))) (fma.f64 2 (.f64 (.f64 A (.f64 C (.f64 F (.f64 B B)))) (sqrt.f64 (/.f64 1 (+.f64 (.f64 A A) (.f64 B B))))) (.f64 8 (.f64 (.f64 A A) (.f64 C F)))))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))
	51.4b	(/.f64 (neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) 2) 3/2)) (.f64 (sqrt.f64 F) (sqrt.f64 (+.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (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 (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)))
	57.5b	(/.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	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 -1/2 (/.f64 F A)))))
	60.1b	(/.f64 (neg.f64 (sqrt.f64 (-.f64 (fma.f64 4 (/.f64 (.f64 (.f64 C C) (.f64 F (.f64 B B))) A) (.f64 8 (.f64 C (.f64 F (.f64 B B))))) (+.f64 (/.f64 (.f64 F (pow.f64 B 4)) A) (.f64 16 (.f64 A (.f64 (.f64 C C) F))))))) (fma.f64 A (.f64 C -4) (*.f64 B B)))
	60.2b	(/.f64 (neg.f64 (sqrt.f64 (.f64 (fma.f64 A (.f64 C -4) (.f64 B B)) (.f64 2 (.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (.f64 A A) B) (fma.f64 1/2 (/.f64 (.f64 C C) B) (+.f64 C B)))) (/.f64 (.f64 A C) B))))))) (fma.f64 A (.f64 C -4) (.f64 B B)))

Compiler

Compiled 33076 to 19445 computations (41.2% saved)

regimes3.7s (4.5%)

Accuracy

Total 22.0b remaining (53.2%)

Threshold costs 0b (0%)

Counts

209 → 4

Compiler

Compiled 55800 to 35247 computations (36.8% saved)

bsearch288.0ms (0.4%)

Steps

Iters	Range		Point
3	5.253076716964708e+48	7.068835606170797e+48	6.316120380681736e+48
10	5.627970350040218e-126	2.7553854351036366e-116	2.0318267948283777e-124
8	-8.927548187230698e-34	-1.3313429753760538e-37	-5.535441828491868e-34

Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

27×	`*-commutative_binary64`
22×	`+-commutative_binary64`
18×	`sub-neg_binary64`
17×	`neg-sub0_binary64`
17×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	195
1	104	195
2	152	195
3	182	195
4	198	195
5	201	195
6	200	195

end713.0ms (0.9%)

Compiler: Compiled 1763 to 1080 computations (38.7% saved)

Details

analyze3.3s (4.1%)

sample6.6s (8%)

simplify76.0ms (0.1%)

prune5.0ms (0%)

localize16.0ms (0%)

series16.7s (20.4%)

rewrite85.0ms (0.1%)

simplify378.0ms (0.5%)

prune997.0ms (1.2%)

localize65.0ms (0.1%)

series27.0s (33%)

rewrite160.0ms (0.2%)

simplify817.0ms (1%)

prune2.7s (3.2%)

localize33.0ms (0%)

series8.5s (10.4%)

rewrite119.0ms (0.1%)

simplify406.0ms (0.5%)

prune1.5s (1.8%)

localize35.0ms (0%)

series6.0s (7.3%)

rewrite120.0ms (0.1%)

simplify424.0ms (0.5%)

prune1.2s (1.4%)

regimes3.7s (4.5%)

bsearch288.0ms (0.4%)

simplify7.0ms (0%)

end713.0ms (0.9%)

Profiling