Details

analyze713.0ms (9.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
34.7%	55.4%	9.9%	9
36.1%	51.1%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.0s (26.7%)

Results

658.0ms	5389×	body	128	valid
515.0ms	1139×	body	2048	valid
276.0ms	757×	body	1024	valid
232.0ms	420×	body	4096	valid
119.0ms	1050×	body	128	invalid
107.0ms	381×	body	512	valid
35.0ms	170×	body	256	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess42.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

508×	`times-frac_binary64`
390×	`div-sub_binary64`
354×	`fma-def_binary64`
351×	`fma-neg_binary64`
312×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	80
1	65	72
2	112	72
3	222	72
4	365	72
5	620	72
6	1057	72
7	1768	72
8	4025	72
0	3	3

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
(/.f64 (+.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 b_2 c)))) b_2)
(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) c)
(/.f64 (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 a b_2)))) a)

Outputs
(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
(/.f64 (-.f64 (sqrt.f64 (fma.f64 c (neg.f64 a) (*.f64 b_2 b_2))) b_2) a)
(/.f64 (+.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 b_2 c)))) b_2)
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b_2 c))) a) b_2)
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 (neg.f64 c) (*.f64 a a))) a) b_2)
(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 c a)))) c)
(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) c)
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c)
(/.f64 (-.f64 (sqrt.f64 (fma.f64 c (neg.f64 a) (*.f64 b_2 b_2))) b_2) c)
(/.f64 (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 a b_2)))) a)
(/.f64 (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 b_2 a)))) a)
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 c c) (.f64 b_2 a))) c) a)
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 (neg.f64 a) (*.f64 c c))) c) a)

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify109.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
361×	`div-sub_binary64`
341×	`fma-def_binary64`
313×	`associate-/l*_binary64`
224×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	23	18
2	42	18
3	77	18
4	123	18
5	218	18
6	370	18
7	586	18
8	948	18
9	1471	18
10	2000	18
11	3220	18
12	4095	18
13	4427	18
14	4435	18
15	4443	18
16	4469	18
17	4485	18
18	4521	18
19	4553	18
20	4565	18

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Outputs
(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 58 to 30 computations (48.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	21.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series33.0ms (0.4%)

Counts

4 → 96

Calls

36 calls:

Time	Variable		Point	Expression
3.0ms	a	@	inf	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.0ms	a	@	inf	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
2.0ms	c	@	inf	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
2.0ms	a	@	inf	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
2.0ms	c	@	inf	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite91.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
338×	`fma-neg_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
159×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	55
1	239	55
2	3653	55

Stop Event

1×	node limit

Counts

4 → 313

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
(-.f64 (.f64 b_2 b_2) (.f64 a c))
(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 2))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 2)) 1/2) (pow.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 b_2 4) (pow.f64 (.f64 a c) 2))) (sqrt.f64 (fma.f64 b_2 b_2 (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 b_2 6) (pow.f64 (.f64 a c) 3))) (sqrt.f64 (fma.f64 (.f64 a c) (fma.f64 b_2 b_2 (.f64 a c)) (pow.f64 b_2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 b_2 b_2) (neg.f64 (.f64 a c)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 b_2 b_2) (.f64 (neg.f64 (.f64 a c)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 b_2 b_2) (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) (fma.f64 a (neg.f64 c) (.f64 a c)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) (fma.f64 (neg.f64 (.f64 a c)) 1 (.f64 a c)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 a c))) (pow.f64 (cbrt.f64 (.f64 a c)) 2) (.f64 a c)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) (.f64 (fma.f64 a (neg.f64 c) (.f64 a c)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) (+.f64 (fma.f64 a (neg.f64 c) (.f64 a c)) (fma.f64 a (neg.f64 c) (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 a (neg.f64 c) (.f64 a c)) (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (.f64 a c)) (.f64 b_2 b_2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 2)) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) (.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 b_2 6) (pow.f64 (.f64 a c) 3)) (/.f64 1 (fma.f64 (.f64 a c) (fma.f64 b_2 b_2 (.f64 a c)) (pow.f64 b_2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 b_2 4) (pow.f64 (.f64 a c) 2)) (/.f64 1 (fma.f64 b_2 b_2 (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4)) (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 b_2 (sqrt.f64 (.f64 a c))) (-.f64 b_2 (sqrt.f64 (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 a c) (fma.f64 b_2 b_2 (.f64 a c)) (pow.f64 b_2 4)) (-.f64 (pow.f64 b_2 6) (pow.f64 (.f64 a c) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 b_2 b_2 (.f64 a c)) (-.f64 (pow.f64 b_2 4) (pow.f64 (.f64 a c) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 b_2 6) (pow.f64 (.f64 a c) 3)) (fma.f64 (.f64 a c) (fma.f64 b_2 b_2 (.f64 a c)) (pow.f64 b_2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 b_2 4) (pow.f64 (.f64 a c) 2)) (fma.f64 b_2 b_2 (.f64 a c)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 b_2 6) (pow.f64 (.f64 a c) 3))) (neg.f64 (fma.f64 (.f64 a c) (fma.f64 b_2 b_2 (.f64 a c)) (pow.f64 b_2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 b_2 4) (pow.f64 (.f64 a c) 2))) (neg.f64 (fma.f64 b_2 b_2 (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 b_2 6) (pow.f64 (neg.f64 (.f64 a c)) 3)) (+.f64 (pow.f64 b_2 4) (-.f64 (.f64 (neg.f64 (.f64 a c)) (neg.f64 (.f64 a c))) (.f64 (.f64 b_2 b_2) (neg.f64 (.f64 a c))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3) (pow.f64 (fma.f64 a (neg.f64 c) (.f64 a c)) 3)) (+.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 2) (-.f64 (.f64 (fma.f64 a (neg.f64 c) (.f64 a c)) (fma.f64 a (neg.f64 c) (.f64 a c))) (.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) (fma.f64 a (neg.f64 c) (.f64 a c))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 b_2 4) (.f64 (neg.f64 (.f64 a c)) (neg.f64 (.f64 a c)))) (-.f64 (.f64 b_2 b_2) (neg.f64 (.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 2) (.f64 (fma.f64 a (neg.f64 c) (.f64 a c)) (fma.f64 a (neg.f64 c) (.f64 a c)))) (-.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) (fma.f64 a 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log1p.f64 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (/.f64 1 a) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (.f64 a a))) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 a)) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 a)) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 1) (/.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) a) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (cbrt.f64 (.f64 a a))) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (cbrt.f64 a)) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) (cbrt.f64 (.f64 a a))) (/.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) (cbrt.f64 a)) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 a)) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 a)) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) (sqrt.f64 a)) (/.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) (sqrt.f64 a)) (neg.f64 (/.f64 b_2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) a)) 1))))))

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

738×	`times-frac_binary64`
492×	`associate-/l*_binary64`
401×	`associate-/r*_binary64`
360×	`fma-def_binary64`
133×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2203
1	392	2175
2	1383	2133

Stop Event

1×	node limit

Counts

409 → 388

Calls

Call 1

Inputs
(sqrt.f64 (neg.f64 (*.f64 c a)))
(+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (*.f64 c a))))))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a)))))) (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 b_2 6) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 5))) (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a))))))) (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3))))
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(*.f64 -1 b_2)
(-.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) b_2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))) b_2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))) b_2)
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(pow.f64 b_2 2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(pow.f64 b_2 2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(pow.f64 b_2 2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(pow.f64 b_2 2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(sqrt.f64 (neg.f64 (*.f64 c a)))
(-.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (*.f64 c a)))))) b_2)
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a)))))) (+.f64 b_2 (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3)))))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))
(*.f64 -2 b_2)
(-.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (*.f64 2 b_2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))) (*.f64 2 b_2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))) (*.f64 2 b_2))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) a)
(-.f64 (/.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) a) (/.f64 b_2 a))
(-.f64 (+.f64 (/.f64 (sqrt.f64 (neg.f64 (.f64 c a))) a) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (.f64 a (sqrt.f64 (neg.f64 (.f64 c a))))))) (/.f64 b_2 a))
(-.f64 (+.f64 (/.f64 (sqrt.f64 (neg.f64 (.f64 c a))) a) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (.f64 a (sqrt.f64 (neg.f64 (.f64 c a))))))) (+.f64 (/.f64 b_2 a) (.f64 1/8 (/.f64 (pow.f64 b_2 4) (.f64 a (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3))))))
(*.f64 -1/2 (/.f64 c b_2))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3))))))
(neg.f64 (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b_2 7))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))))))
(*.f64 -2 (/.f64 b_2 a))
(-.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 2 (/.f64 b_2 a)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))) (.f64 2 (/.f64 b_2 a)))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) a) (pow.f64 b_2 3))))) (.f64 2 (/.f64 b_2 a)))
(*.f64 -1/2 (/.f64 c b_2))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3))))))
(neg.f64 (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b_2 7))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))))))
(*.f64 -1/2 (/.f64 c b_2))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3))))))
(neg.f64 (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b_2 7))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))))))

Outputs
(sqrt.f64 (neg.f64 (*.f64 c a)))
(sqrt.f64 (*.f64 c (neg.f64 a)))
(+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (*.f64 c a))))))
(+.f64 (sqrt.f64 (.f64 c (neg.f64 a))) (/.f64 (.f64 1/2 (.f64 b_2 b_2)) (sqrt.f64 (.f64 c (neg.f64 a)))))
(fma.f64 1/2 (/.f64 (.f64 b_2 b_2) (sqrt.f64 (.f64 c (neg.f64 a)))) (sqrt.f64 (*.f64 c (neg.f64 a))))
(fma.f64 1/2 (/.f64 b_2 (/.f64 (sqrt.f64 (.f64 c (neg.f64 a))) b_2)) (sqrt.f64 (.f64 c (neg.f64 a))))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a)))))) (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3))))
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(fma.f64 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) -1/8 (fma.f64 1/2 (/.f64 b_2 (/.f64 (sqrt.f64 (.f64 c (neg.f64 a))) b_2)) (fma.f64 1/16 (/.f64 (pow.f64 b_2 6) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 5)) (sqrt.f64 (.f64 c (neg.f64 a))))))
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(-.f64 b_2 (/.f64 (.f64 1/2 (.f64 c a)) b_2))
(+.f64 b_2 (*.f64 (/.f64 c (/.f64 b_2 a)) -1/2))
(fma.f64 (*.f64 (/.f64 c b_2) a) -1/2 b_2)
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) (*.f64 a a))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (/.f64 (.f64 (.f64 1/8 (.f64 a a)) (.f64 c c)) (pow.f64 b_2 3))))
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(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (pow.f64 a 3) (/.f64 (pow.f64 b_2 5) (pow.f64 c 3))) (/.f64 (.f64 (.f64 1/8 (.f64 a a)) (.f64 c c)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (fma.f64 1/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b_2 3)) a) a) (/.f64 (pow.f64 c 3) (/.f64 (/.f64 (pow.f64 b_2 5) (pow.f64 a 3)) 1/16)))))
(*.f64 -1 b_2)
(neg.f64 b_2)
(-.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) b_2)
(-.f64 (/.f64 (.f64 1/2 (.f64 c a)) b_2) b_2)
(fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (neg.f64 b_2))
(-.f64 (*.f64 (/.f64 1/2 (/.f64 b_2 c)) a) b_2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))) b_2)
(-.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) (*.f64 a a))))) b_2)
(fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (-.f64 (/.f64 (.f64 (.f64 1/8 (.f64 a a)) (.f64 c c)) (pow.f64 b_2 3)) b_2))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (.f64 (/.f64 (.f64 1/8 (.f64 c c)) (/.f64 (pow.f64 b_2 3) a)) a)) b_2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))) b_2)
(-.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) (.f64 a a)))))) b_2)
(-.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (pow.f64 a 3) (/.f64 (pow.f64 b_2 5) (pow.f64 c 3))) (/.f64 (.f64 (.f64 1/8 (.f64 a a)) (.f64 c c)) (pow.f64 b_2 3)))) b_2)
(-.f64 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (fma.f64 1/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b_2 3)) a) a) (/.f64 (pow.f64 c 3) (/.f64 (/.f64 (pow.f64 b_2 5) (pow.f64 a 3)) 1/16)))) b_2)
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(-.f64 b_2 (/.f64 (.f64 1/2 (.f64 c a)) b_2))
(+.f64 b_2 (*.f64 (/.f64 c (/.f64 b_2 a)) -1/2))
(fma.f64 (*.f64 (/.f64 c b_2) a) -1/2 b_2)
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) (*.f64 a a))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (/.f64 (.f64 (.f64 1/8 (.f64 a a)) (.f64 c c)) (pow.f64 b_2 3))))
(+.f64 b_2 (fma.f64 (.f64 (/.f64 c b_2) a) -1/2 (.f64 (.f64 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 3)) a) a) -1/8)))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) (.f64 a a)))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (pow.f64 a 3) (/.f64 (pow.f64 b_2 5) (pow.f64 c 3))) (/.f64 (.f64 (.f64 1/8 (.f64 a a)) (.f64 c c)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (fma.f64 1/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b_2 3)) a) a) (/.f64 (pow.f64 c 3) (/.f64 (/.f64 (pow.f64 b_2 5) (pow.f64 a 3)) 1/16)))))
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(-.f64 b_2 (/.f64 (.f64 1/2 (.f64 c a)) b_2))
(+.f64 b_2 (*.f64 (/.f64 c (/.f64 b_2 a)) -1/2))
(fma.f64 (*.f64 (/.f64 c b_2) a) -1/2 b_2)
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) (*.f64 a a))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (/.f64 (.f64 (.f64 1/8 (.f64 a a)) (.f64 c c)) (pow.f64 b_2 3))))
(+.f64 b_2 (fma.f64 (.f64 (/.f64 c b_2) a) -1/2 (.f64 (.f64 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 3)) a) a) -1/8)))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) (.f64 a a)))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (pow.f64 a 3) (/.f64 (pow.f64 b_2 5) (pow.f64 c 3))) (/.f64 (.f64 (.f64 1/8 (.f64 a a)) (.f64 c c)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (.f64 (/.f64 c b_2) a) (fma.f64 1/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b_2 3)) a) a) (/.f64 (pow.f64 c 3) (/.f64 (/.f64 (pow.f64 b_2 5) (pow.f64 a 3)) 1/16)))))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(pow.f64 b_2 2)
(*.f64 b_2 b_2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(pow.f64 b_2 2)
(*.f64 b_2 b_2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(pow.f64 b_2 2)
(*.f64 b_2 b_2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(pow.f64 b_2 2)
(*.f64 b_2 b_2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(sqrt.f64 (neg.f64 (*.f64 c a)))
(sqrt.f64 (*.f64 c (neg.f64 a)))
(-.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
(-.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) b_2)
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (*.f64 c a)))))) b_2)
(+.f64 (sqrt.f64 (.f64 c (neg.f64 a))) (-.f64 (/.f64 (.f64 1/2 (.f64 b_2 b_2)) (sqrt.f64 (.f64 c (neg.f64 a)))) b_2))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 b_2 b_2) (sqrt.f64 (.f64 c (neg.f64 a)))) (sqrt.f64 (*.f64 c (neg.f64 a)))) b_2)
(fma.f64 1/2 (/.f64 b_2 (/.f64 (sqrt.f64 (.f64 c (neg.f64 a))) b_2)) (-.f64 (sqrt.f64 (.f64 c (neg.f64 a))) b_2))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a)))))) (+.f64 b_2 (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3)))))
(-.f64 (+.f64 (sqrt.f64 (.f64 c (neg.f64 a))) (/.f64 (.f64 1/2 (.f64 b_2 b_2)) (sqrt.f64 (.f64 c (neg.f64 a))))) (+.f64 b_2 (/.f64 (.f64 1/8 (pow.f64 b_2 4)) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 b_2 b_2) (sqrt.f64 (.f64 c (neg.f64 a)))) (sqrt.f64 (.f64 c (neg.f64 a)))) (fma.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) b_2))
(-.f64 (fma.f64 1/2 (/.f64 b_2 (/.f64 (sqrt.f64 (.f64 c (neg.f64 a))) b_2)) (sqrt.f64 (.f64 c (neg.f64 a)))) (fma.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) 3)) b_2))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(*.f64 (/.f64 c (/.f64 b_2 a)) -1/2)
(.f64 (/.f64 (.f64 c -1/2) b_2) a)
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) (*.f64 a a))))))
(+.f64 (.f64 (/.f64 c (/.f64 b_2 a)) -1/2) (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b_2 3)) (*.f64 a a)) -1/8))
(fma.f64 (.f64 (/.f64 c b_2) a) -1/2 (.f64 (.f64 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 3)) a) a) -1/8))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) (.f64 a a)))))))
(-.f64 (.f64 (/.f64 (pow.f64 a 3) (/.f64 (pow.f64 b_2 5) (pow.f64 c 3))) -1/16) (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (/.f64 (.f64 (.f64 1/8 (.f64 a a)) (*.f64 c c)) (pow.f64 b_2 3))))
(fma.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (pow.f64 a 3)) -1/16 (fma.f64 (.f64 (/.f64 c b_2) a) -1/2 (.f64 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b_2 3)) a) a) -1/8)))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))
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(fma.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (.f64 a a)) -1/16 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 3)) a) -1/8)))
(neg.f64 (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b_2 7))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))))))
(neg.f64 (fma.f64 5/128 (/.f64 (pow.f64 c 4) (/.f64 (pow.f64 b_2 7) (pow.f64 a 3))) (fma.f64 1/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b_2 5) (.f64 a a))) (fma.f64 1/2 (/.f64 c b_2) (.f64 1/8 (/.f64 (*.f64 c c) (/.f64 (pow.f64 b_2 3) a)))))))
(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b_2 7)) (pow.f64 a 3)) -5/128) (fma.f64 1/16 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (.f64 a a)) (fma.f64 1/2 (/.f64 c b_2) (/.f64 (.f64 1/8 (.f64 c c)) (/.f64 (pow.f64 b_2 3) a)))))
(fma.f64 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b_2 7)) (pow.f64 a 3)) -5/128 (fma.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (.f64 a a)) -1/16 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b_2 3)) a) -1/8))))
(*.f64 -1/2 (/.f64 c b_2))
(/.f64 -1/2 (/.f64 b_2 c))
(/.f64 (*.f64 c -1/2) b_2)
(neg.f64 (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))))
(neg.f64 (fma.f64 1/2 (/.f64 c b_2) (.f64 1/8 (/.f64 (.f64 c c) (/.f64 (pow.f64 b_2 3) a)))))
(-.f64 (/.f64 -1/2 (/.f64 b_2 c)) (/.f64 (.f64 1/8 (.f64 c c)) (/.f64 (pow.f64 b_2 3) a)))
(fma.f64 -1/2 (/.f64 c b_2) (.f64 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 3)) a) -1/8))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3))))))
(neg.f64 (fma.f64 1/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b_2 5) (.f64 a a))) (fma.f64 1/2 (/.f64 c b_2) (.f64 1/8 (/.f64 (*.f64 c c) (/.f64 (pow.f64 b_2 3) a))))))
(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (.f64 a a)) -1/16) (fma.f64 1/2 (/.f64 c b_2) (/.f64 (.f64 1/8 (*.f64 c c)) (/.f64 (pow.f64 b_2 3) a))))
(fma.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (.f64 a a)) -1/16 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 3)) a) -1/8)))
(neg.f64 (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b_2 7))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 c b_2)) (.f64 1/8 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b_2 3)))))))
(neg.f64 (fma.f64 5/128 (/.f64 (pow.f64 c 4) (/.f64 (pow.f64 b_2 7) (pow.f64 a 3))) (fma.f64 1/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b_2 5) (.f64 a a))) (fma.f64 1/2 (/.f64 c b_2) (.f64 1/8 (/.f64 (*.f64 c c) (/.f64 (pow.f64 b_2 3) a)))))))
(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b_2 7)) (pow.f64 a 3)) -5/128) (fma.f64 1/16 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (.f64 a a)) (fma.f64 1/2 (/.f64 c b_2) (/.f64 (.f64 1/8 (.f64 c c)) (/.f64 (pow.f64 b_2 3) a)))))
(fma.f64 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b_2 7)) (pow.f64 a 3)) -5/128 (fma.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (.f64 a a)) -1/16 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b_2 3)) a) -1/8))))

prune260.0ms (3.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	376	12	388
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	376	13	389

Error

4.8b

Counts

389 → 13

Alt Table

Status	Error	Program
	49.2b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (sqrt.f64 a)))
	43.9b	(/.f64 (fma.f64 b_2 -2 (*.f64 (/.f64 1/2 (/.f64 b_2 c)) a)) a)
	42.8b	(.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)) (cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) a) 2)))
	40.6b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3/2)) b_2) a)
	50.7b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b_2)) a)
▶	30.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2) a)
	43.4b	(*.f64 -2 (/.f64 b_2 a))
	30.5b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
✓	30.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	30.8b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 1 a)))
	32.3b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) a)) (neg.f64 (/.f64 b_2 a)))
	44.3b	(*.f64 -1/2 (/.f64 c b_2))
	47.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)) 2)

Compiler

Compiled 9736 to 3005 computations (69.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)
✓	1.5b	(fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))
✓	21.9b	(sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c)))))
✓	51.6b	(fma.f64 a (neg.f64 c) (*.f64 a c))

series28.0ms (0.4%)

Counts

4 → 100

Calls

33 calls:

Time	Variable		Point	Expression
10.0ms	b_2	@	inf	(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)
1.0ms	a	@	-inf	(fma.f64 a (neg.f64 c) (*.f64 a c))
1.0ms	c	@	inf	(fma.f64 a (neg.f64 c) (*.f64 a c))
1.0ms	a	@	inf	(fma.f64 a (neg.f64 c) (*.f64 a c))
1.0ms	c	@	0	(fma.f64 a (neg.f64 c) (*.f64 a c))

rewrite70.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

514×	`log-prod_binary64`
367×	`fma-def_binary64`
217×	`fma-neg_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	77
1	233	57
2	3104	57

Stop Event

1×	node limit

Counts

4 → 191

Calls

Call 1

Inputs
(fma.f64 a (neg.f64 c) (*.f64 a c))
(sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c)))))
(fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))
(-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a c) (.f64 a c))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 a (+.f64 c c)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 a (+.f64 c c)))) (cbrt.f64 (exp.f64 (.f64 a (+.f64 c c)))))) (log.f64 (cbrt.f64 (exp.f64 (.f64 a (+.f64 c c))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 a (+.f64 c c))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 a (+.f64 c c))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 a c) (.f64 a c))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 a (+.f64 c c)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 a (+.f64 c c))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 a (+.f64 c c)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 a (+.f64 c c)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 a (+.f64 c c))) (cbrt.f64 (pow.f64 (.f64 a (+.f64 c c)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 a (+.f64 c c)) 2)) (cbrt.f64 (.f64 a (+.f64 c c))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 a (+.f64 c c))) (sqrt.f64 (.f64 a (+.f64 c c))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 a c) 3) (pow.f64 (.f64 a c) 3)) (+.f64 (pow.f64 (.f64 a c) 2) (-.f64 (pow.f64 (.f64 a c) 2) (pow.f64 (.f64 a c) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 a c) 2) (pow.f64 (.f64 a c) 2)) (.f64 a (+.f64 c c)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 a (+.f64 c c)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 a (+.f64 c c)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 a (+.f64 c c))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 a (+.f64 c c))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 a (+.f64 c c)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 a (+.f64 c c))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 a (+.f64 c c)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (pow.f64 (exp.f64 c) a) (pow.f64 (exp.f64 c) a)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (.f64 a c))) (pow.f64 (exp.f64 c) a)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (pow.f64 (exp.f64 c) a) (+.f64 1 (expm1.f64 (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (.f64 a c))) (+.f64 1 (expm1.f64 (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 a c))) (pow.f64 (exp.f64 c) a)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 c) a) (+.f64 1 (expm1.f64 (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 a c))) (+.f64 1 (expm1.f64 (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 a (+.f64 c c)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 a (+.f64 c c))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 a (+.f64 c c))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 a (+.f64 c c))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 a (+.f64 c c))) 1))))))
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(fma.f64 b_2 b_2 (fma.f64 a c (.f64 a (+.f64 c c)))) 1/4) (sqrt.f64 b_2)) (fma.f64 (neg.f64 (cbrt.f64 b_2)) (pow.f64 (cbrt.f64 b_2) 2) b_2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 (fma.f64 b_2 b_2 (fma.f64 a c (.f64 a (+.f64 c c)))) 1/4) (sqrt.f64 b_2)) (-.f64 (pow.f64 (fma.f64 b_2 b_2 (fma.f64 a c (.f64 a (+.f64 c c)))) 1/4) (sqrt.f64 b_2)) (+.f64 (neg.f64 b_2) b_2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 b_2) 2)) (cbrt.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (fma.f64 a c (.f64 a (+.f64 c c))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (fma.f64 a c (.f64 a (+.f64 c c))))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (fma.f64 a c (.f64 a (+.f64 c c))))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (fma.f64 a c (*.f64 a (+.f64 c c))))) b_2)) 1))))))

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

416×	`times-frac_binary64`
278×	`associate-/l*_binary64`
263×	`associate-r_binary64`
234×	`associate-/r*_binary64`
223×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	1573
1	272	1557
2	879	1533
3	4610	1533

Stop Event

1×	node limit

Counts

291 → 243

Calls

Call 1

Inputs
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(sqrt.f64 (neg.f64 (*.f64 c a)))
(+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (*.f64 c a))))))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a)))))) (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 b_2 6) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 5))) (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a))))))) (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3))))
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(*.f64 -1 b_2)
(-.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) b_2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))) b_2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))) b_2)
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(pow.f64 b_2 2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(pow.f64 b_2 2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(pow.f64 b_2 2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(pow.f64 b_2 2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(.f64 -1 (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(sqrt.f64 (neg.f64 (*.f64 c a)))
(-.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (*.f64 c a)))))) b_2)
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a)))))) (+.f64 b_2 (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3)))))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))
(*.f64 -2 b_2)
(-.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (*.f64 2 b_2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))) (*.f64 2 b_2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))) (*.f64 2 b_2))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))

Outputs
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(sqrt.f64 (neg.f64 (*.f64 c a)))
(sqrt.f64 (*.f64 c (neg.f64 a)))
(+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (*.f64 c a))))))
(+.f64 (sqrt.f64 (.f64 c (neg.f64 a))) (/.f64 (.f64 1/2 (.f64 b_2 b_2)) (sqrt.f64 (.f64 c (neg.f64 a)))))
(fma.f64 1/2 (/.f64 (.f64 b_2 b_2) (sqrt.f64 (.f64 c (neg.f64 a)))) (sqrt.f64 (*.f64 c (neg.f64 a))))
(fma.f64 1/2 (.f64 (/.f64 b_2 (sqrt.f64 (.f64 c (neg.f64 a)))) b_2) (sqrt.f64 (*.f64 c (neg.f64 a))))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a)))))) (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3))))
(+.f64 (sqrt.f64 (.f64 c (neg.f64 a))) (-.f64 (/.f64 (.f64 1/2 (.f64 b_2 b_2)) (sqrt.f64 (.f64 c (neg.f64 a)))) (/.f64 (.f64 1/8 (pow.f64 b_2 4)) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3))))
(+.f64 (sqrt.f64 (.f64 c (neg.f64 a))) (fma.f64 1/2 (/.f64 (.f64 b_2 b_2) (sqrt.f64 (.f64 c (neg.f64 a)))) (.f64 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) 3)) -1/8)))
(fma.f64 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) -1/8 (fma.f64 1/2 (.f64 (/.f64 b_2 (sqrt.f64 (.f64 c (neg.f64 a)))) b_2) (sqrt.f64 (.f64 c (neg.f64 a)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 b_2 6) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 5))) (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a))))))) (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 b_2 6) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 5)) (+.f64 (sqrt.f64 (.f64 c (neg.f64 a))) (/.f64 (.f64 1/2 (.f64 b_2 b_2)) (sqrt.f64 (.f64 c (neg.f64 a)))))) (/.f64 (.f64 1/8 (pow.f64 b_2 4)) (pow.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) 3)))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 b_2 6) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 5)) (fma.f64 1/2 (/.f64 (.f64 b_2 b_2) (sqrt.f64 (.f64 c (neg.f64 a)))) (sqrt.f64 (.f64 c (neg.f64 a))))) (.f64 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) -1/8))
(fma.f64 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 b_2 6) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 5)) (fma.f64 1/2 (.f64 (/.f64 b_2 (sqrt.f64 (.f64 c (neg.f64 a)))) b_2) (sqrt.f64 (*.f64 c (neg.f64 a))))))
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(+.f64 b_2 (*.f64 (/.f64 c (/.f64 b_2 a)) -1/2))
(+.f64 b_2 (*.f64 (/.f64 a (/.f64 b_2 c)) -1/2))
(fma.f64 (*.f64 a (/.f64 c b_2)) -1/2 b_2)
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)))))
(+.f64 b_2 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a))))))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) (/.f64 (.f64 1/16 (pow.f64 c 3)) (/.f64 (pow.f64 b_2 5) (pow.f64 a 3))))))
(-.f64 b_2 (fma.f64 1/2 (.f64 a (/.f64 c b_2)) (fma.f64 1/8 (.f64 (.f64 a a) (/.f64 c (/.f64 (pow.f64 b_2 3) c))) (/.f64 (.f64 (pow.f64 a 3) (*.f64 1/16 (pow.f64 c 3))) (pow.f64 b_2 5)))))
(*.f64 -1 b_2)
(neg.f64 b_2)
(-.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) b_2)
(fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (neg.f64 b_2))
(-.f64 (*.f64 1/2 (/.f64 a (/.f64 b_2 c))) b_2)
(fma.f64 1/2 (*.f64 a (/.f64 c b_2)) (neg.f64 b_2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))) b_2)
(-.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b_2 3)))) b_2)
(-.f64 (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)))) b_2)
(-.f64 (/.f64 (.f64 (.f64 a (.f64 c a)) (.f64 c 1/8)) (pow.f64 b_2 3)) (fma.f64 (*.f64 a (/.f64 c b_2)) -1/2 b_2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))) b_2)
(-.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3))))) b_2)
(-.f64 (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) (/.f64 (.f64 1/16 (pow.f64 c 3)) (/.f64 (pow.f64 b_2 5) (pow.f64 a 3))))) b_2)
(-.f64 (fma.f64 1/8 (.f64 (.f64 a a) (/.f64 c (/.f64 (pow.f64 b_2 3) c))) (/.f64 (.f64 (pow.f64 a 3) (.f64 1/16 (pow.f64 c 3))) (pow.f64 b_2 5))) (fma.f64 (*.f64 a (/.f64 c b_2)) -1/2 b_2))
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(+.f64 b_2 (*.f64 (/.f64 c (/.f64 b_2 a)) -1/2))
(+.f64 b_2 (*.f64 (/.f64 a (/.f64 b_2 c)) -1/2))
(fma.f64 (*.f64 a (/.f64 c b_2)) -1/2 b_2)
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)))))
(+.f64 b_2 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a))))))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) (/.f64 (.f64 1/16 (pow.f64 c 3)) (/.f64 (pow.f64 b_2 5) (pow.f64 a 3))))))
(-.f64 b_2 (fma.f64 1/2 (.f64 a (/.f64 c b_2)) (fma.f64 1/8 (.f64 (.f64 a a) (/.f64 c (/.f64 (pow.f64 b_2 3) c))) (/.f64 (.f64 (pow.f64 a 3) (*.f64 1/16 (pow.f64 c 3))) (pow.f64 b_2 5)))))
b_2
(-.f64 b_2 (.f64 1/2 (/.f64 (.f64 c a) b_2)))
(+.f64 b_2 (*.f64 (/.f64 c (/.f64 b_2 a)) -1/2))
(+.f64 b_2 (*.f64 (/.f64 a (/.f64 b_2 c)) -1/2))
(fma.f64 (*.f64 a (/.f64 c b_2)) -1/2 b_2)
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b_2 3)))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)))))
(+.f64 b_2 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a))))))
(-.f64 b_2 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3))))))
(-.f64 b_2 (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) (/.f64 (.f64 1/16 (pow.f64 c 3)) (/.f64 (pow.f64 b_2 5) (pow.f64 a 3))))))
(-.f64 b_2 (fma.f64 1/2 (.f64 a (/.f64 c b_2)) (fma.f64 1/8 (.f64 (.f64 a a) (/.f64 c (/.f64 (pow.f64 b_2 3) c))) (/.f64 (.f64 (pow.f64 a 3) (*.f64 1/16 (pow.f64 c 3))) (pow.f64 b_2 5)))))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(pow.f64 b_2 2)
(*.f64 b_2 b_2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(pow.f64 b_2 2)
(*.f64 b_2 b_2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(pow.f64 b_2 2)
(*.f64 b_2 b_2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(pow.f64 b_2 2)
(*.f64 b_2 b_2)
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(.f64 -1 (.f64 c a))
(*.f64 c (neg.f64 a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(-.f64 (pow.f64 b_2 2) (*.f64 c a))
(-.f64 (.f64 b_2 b_2) (.f64 c a))
(sqrt.f64 (neg.f64 (*.f64 c a)))
(sqrt.f64 (*.f64 c (neg.f64 a)))
(-.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
(-.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) b_2)
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (*.f64 c a)))))) b_2)
(+.f64 (sqrt.f64 (.f64 c (neg.f64 a))) (-.f64 (/.f64 (.f64 1/2 (.f64 b_2 b_2)) (sqrt.f64 (.f64 c (neg.f64 a)))) b_2))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 b_2 b_2) (sqrt.f64 (.f64 c (neg.f64 a)))) (sqrt.f64 (*.f64 c (neg.f64 a)))) b_2)
(fma.f64 1/2 (.f64 (/.f64 b_2 (sqrt.f64 (.f64 c (neg.f64 a)))) b_2) (-.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) b_2))
(-.f64 (+.f64 (sqrt.f64 (neg.f64 (.f64 c a))) (.f64 1/2 (/.f64 (pow.f64 b_2 2) (sqrt.f64 (neg.f64 (.f64 c a)))))) (+.f64 b_2 (.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 3)))))
(-.f64 (+.f64 (sqrt.f64 (.f64 c (neg.f64 a))) (/.f64 (.f64 1/2 (.f64 b_2 b_2)) (sqrt.f64 (.f64 c (neg.f64 a))))) (+.f64 b_2 (/.f64 (.f64 1/8 (pow.f64 b_2 4)) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 b_2 b_2) (sqrt.f64 (.f64 c (neg.f64 a)))) (sqrt.f64 (.f64 c (neg.f64 a)))) (fma.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) b_2))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 b_2 (sqrt.f64 (.f64 c (neg.f64 a)))) b_2) (sqrt.f64 (.f64 c (neg.f64 a)))) (fma.f64 1/8 (/.f64 (pow.f64 b_2 4) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) b_2))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(*.f64 (/.f64 c (/.f64 b_2 a)) -1/2)
(*.f64 (/.f64 a (/.f64 b_2 c)) -1/2)
(.f64 (.f64 a (/.f64 c b_2)) -1/2)
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b_2 3)))))
(+.f64 (.f64 (/.f64 a (/.f64 b_2 c)) -1/2) (.f64 (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
(fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3))))))
(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (pow.f64 a 3)) -1/16) (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)))))
(fma.f64 (.f64 (pow.f64 a 3) (/.f64 (pow.f64 c 3) (pow.f64 b_2 5))) -1/16 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (*.f64 c a))))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))
(neg.f64 (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 5/128 (/.f64 (pow.f64 c 4) (/.f64 (pow.f64 b_2 7) (pow.f64 a 4))) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3)))))))
(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (pow.f64 a 3)) -1/16) (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) (/.f64 (.f64 (*.f64 5/128 (pow.f64 c 4)) (pow.f64 a 4)) (pow.f64 b_2 7)))))
(-.f64 (fma.f64 (.f64 (pow.f64 a 3) (/.f64 (pow.f64 c 3) (pow.f64 b_2 5))) -1/16 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a)))))) (.f64 5/128 (*.f64 (pow.f64 a 4) (/.f64 (pow.f64 c 4) (pow.f64 b_2 7)))))
(*.f64 -2 b_2)
(*.f64 b_2 -2)
(-.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (*.f64 2 b_2))
(+.f64 (.f64 1/2 (/.f64 c (/.f64 b_2 a))) (.f64 b_2 -2))
(fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (*.f64 b_2 -2))
(fma.f64 1/2 (.f64 a (/.f64 c b_2)) (.f64 b_2 -2))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))) (*.f64 2 b_2))
(+.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b_2 3)))) (*.f64 b_2 -2))
(fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) (.f64 b_2 -2)))
(fma.f64 b_2 -2 (fma.f64 1/2 (.f64 a (/.f64 c b_2)) (/.f64 (.f64 (.f64 a (.f64 c a)) (*.f64 c 1/8)) (pow.f64 b_2 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))) (*.f64 2 b_2))
(+.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b_2 3))))) (.f64 b_2 -2))
(+.f64 (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (/.f64 (.f64 1/16 (pow.f64 c 3)) (/.f64 (pow.f64 b_2 5) (pow.f64 a 3)))) (fma.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) (*.f64 b_2 -2)))
(fma.f64 b_2 -2 (fma.f64 1/2 (.f64 a (/.f64 c b_2)) (fma.f64 1/8 (.f64 (.f64 a a) (/.f64 c (/.f64 (pow.f64 b_2 3) c))) (/.f64 (.f64 (pow.f64 a 3) (*.f64 1/16 (pow.f64 c 3))) (pow.f64 b_2 5)))))
(fma.f64 1/2 (.f64 a (/.f64 c b_2)) (fma.f64 1/16 (.f64 (pow.f64 a 3) (/.f64 (pow.f64 c 3) (pow.f64 b_2 5))) (fma.f64 1/8 (.f64 (.f64 a a) (/.f64 c (/.f64 (pow.f64 b_2 3) c))) (*.f64 b_2 -2))))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(*.f64 (/.f64 c (/.f64 b_2 a)) -1/2)
(*.f64 (/.f64 a (/.f64 b_2 c)) -1/2)
(.f64 (.f64 a (/.f64 c b_2)) -1/2)
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b_2 3)))))
(+.f64 (.f64 (/.f64 a (/.f64 b_2 c)) -1/2) (.f64 (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
(fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3))))))
(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (pow.f64 a 3)) -1/16) (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)))))
(fma.f64 (.f64 (pow.f64 a 3) (/.f64 (pow.f64 c 3) (pow.f64 b_2 5))) -1/16 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (*.f64 c a))))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))
(neg.f64 (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 5/128 (/.f64 (pow.f64 c 4) (/.f64 (pow.f64 b_2 7) (pow.f64 a 4))) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3)))))))
(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (pow.f64 a 3)) -1/16) (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) (/.f64 (.f64 (*.f64 5/128 (pow.f64 c 4)) (pow.f64 a 4)) (pow.f64 b_2 7)))))
(-.f64 (fma.f64 (.f64 (pow.f64 a 3) (/.f64 (pow.f64 c 3) (pow.f64 b_2 5))) -1/16 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a)))))) (.f64 5/128 (*.f64 (pow.f64 a 4) (/.f64 (pow.f64 c 4) (pow.f64 b_2 7)))))
(.f64 -1/2 (/.f64 (.f64 c a) b_2))
(*.f64 (/.f64 c (/.f64 b_2 a)) -1/2)
(*.f64 (/.f64 a (/.f64 b_2 c)) -1/2)
(.f64 (.f64 a (/.f64 c b_2)) -1/2)
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))
(neg.f64 (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b_2 3)))))
(+.f64 (.f64 (/.f64 a (/.f64 b_2 c)) -1/2) (.f64 (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
(fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a)))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3))))))
(neg.f64 (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3))))))
(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (pow.f64 a 3)) -1/16) (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)))))
(fma.f64 (.f64 (pow.f64 a 3) (/.f64 (pow.f64 c 3) (pow.f64 b_2 5))) -1/16 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (*.f64 c a))))))
(neg.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 c a) b_2)) (+.f64 (.f64 5/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b_2 7))) (.f64 1/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b_2 3)))))))
(neg.f64 (fma.f64 1/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b_2 5)) (fma.f64 1/2 (/.f64 c (/.f64 b_2 a)) (fma.f64 5/128 (/.f64 (pow.f64 c 4) (/.f64 (pow.f64 b_2 7) (pow.f64 a 4))) (.f64 1/8 (/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b_2 3)))))))
(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b_2 5)) (pow.f64 a 3)) -1/16) (fma.f64 1/2 (/.f64 a (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) (/.f64 (.f64 (*.f64 5/128 (pow.f64 c 4)) (pow.f64 a 4)) (pow.f64 b_2 7)))))
(-.f64 (fma.f64 (.f64 (pow.f64 a 3) (/.f64 (pow.f64 c 3) (pow.f64 b_2 5))) -1/16 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a)))))) (.f64 5/128 (*.f64 (pow.f64 a 4) (/.f64 (pow.f64 c 4) (pow.f64 b_2 7)))))

prune173.0ms (2.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	242	1	243
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	243	13	256

Error

4.8b

Counts

256 → 13

Alt Table

Status	Error	Program
	49.2b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (sqrt.f64 a)))
	43.9b	(/.f64 (fma.f64 b_2 -2 (*.f64 (/.f64 1/2 (/.f64 b_2 c)) a)) a)
	42.8b	(.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)) (cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) a) 2)))
	40.6b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3/2)) b_2) a)
✓	30.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2) a)
	43.4b	(*.f64 -2 (/.f64 b_2 a))
▶	30.5b	(pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) -1)
✓	30.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	52.3b	(/.f64 (fma.f64 (.f64 a (/.f64 c b_2)) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a (.f64 c a))))) a)
	30.8b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 1 a)))
	32.3b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) a))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) a)) (neg.f64 (/.f64 b_2 a)))
	44.3b	(*.f64 -1/2 (/.f64 c b_2))
	47.8b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)) 2)

Compiler

Compiled 6605 to 1988 computations (69.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
	1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	21.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series26.0ms (0.4%)

Counts

1 → 20

Calls

9 calls:

Time	Variable		Point	Expression
10.0ms	c	@	inf	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
4.0ms	a	@	inf	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
3.0ms	a	@	-inf	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
3.0ms	b_2	@	0	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
2.0ms	c	@	-inf	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

rewrite56.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`fma-def_binary64`
317×	`fma-neg_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
125×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	236	18
2	3517	18

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 a) 2) (*.f64 (cbrt.f64 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (cbrt.f64 (pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 2)) (cbrt.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 a) (*.f64 (sqrt.f64 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (sqrt.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 a) (/.f64 1 (neg.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) a)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a) 2) 1) (/.f64 (cbrt.f64 a) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a) 1) (/.f64 (sqrt.f64 a) (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 2)) (/.f64 a (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a) 2) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 2)) (cbrt.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 2)) (/.f64 (sqrt.f64 a) (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a) 2) (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) (/.f64 (cbrt.f64 a) (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a (-.f64 (pow.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)) 3/2) (pow.f64 b_2 3))) (fma.f64 b_2 (+.f64 b_2 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (-.f64 (*.f64 b_2 b_2) (*.f64 a c))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a (-.f64 (*.f64 b_2 b_2) (fma.f64 a c (*.f64 b_2 b_2)))) (+.f64 b_2 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 a (neg.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 a 3) (pow.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2))) 1))))))

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-neg_binary64`
456×	`times-frac_binary64`
302×	`associate-/l*_binary64`
265×	`associate-/r*_binary64`
232×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	629
1	235	602
2	754	584
3	4187	582

Stop Event

1×	node limit

Counts

55 → 58

Calls

Call 1

Inputs
(*.f64 -2 (/.f64 b_2 c))
(-.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 2 (/.f64 b_2 c)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (.f64 1/2 (/.f64 a b_2))) (.f64 2 (/.f64 b_2 c)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))))) (.f64 2 (/.f64 b_2 c)))
(/.f64 a (sqrt.f64 (neg.f64 (*.f64 c a))))
(+.f64 (/.f64 a (sqrt.f64 (neg.f64 (.f64 c a)))) (/.f64 (.f64 a b_2) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 2)))
(+.f64 (.f64 1/2 (/.f64 (.f64 a (pow.f64 b_2 2)) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 3))) (+.f64 (/.f64 a (sqrt.f64 (neg.f64 (.f64 c a)))) (/.f64 (.f64 a b_2) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 2))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 a (pow.f64 b_2 2)) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 3))) (+.f64 (/.f64 a (sqrt.f64 (neg.f64 (.f64 c a)))) (/.f64 (.f64 a b_2) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 2)))) (.f64 1/8 (/.f64 (.f64 a (pow.f64 b_2 4)) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 5))))
(*.f64 -2 (/.f64 b_2 c))
(-.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 2 (/.f64 b_2 c)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (.f64 1/2 (/.f64 a b_2))) (.f64 2 (/.f64 b_2 c)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))))) (.f64 2 (/.f64 b_2 c)))
(*.f64 -1/2 (/.f64 a b_2))
(neg.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (*.f64 1/2 (/.f64 a b_2))))
(neg.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))) (*.f64 1/2 (/.f64 a b_2)))))
(neg.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 5/128 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 4)) (pow.f64 b_2 7)))))))
(*.f64 -2 (/.f64 b_2 c))
(-.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 2 (/.f64 b_2 c)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (.f64 1/2 (/.f64 a b_2))) (.f64 2 (/.f64 b_2 c)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))))) (.f64 2 (/.f64 b_2 c)))

Outputs
(*.f64 -2 (/.f64 b_2 c))
(-.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 2 (/.f64 b_2 c)))
(+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 -2 (/.f64 b_2 c)))
(fma.f64 1/2 (/.f64 a b_2) (*.f64 -2 (/.f64 b_2 c)))
(fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (.f64 1/2 (/.f64 a b_2))) (.f64 2 (/.f64 b_2 c)))
(+.f64 (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (.f64 1/2 (/.f64 a b_2))) (*.f64 -2 (/.f64 b_2 c)))
(fma.f64 1/8 (/.f64 (.f64 a a) (/.f64 (pow.f64 b_2 3) c)) (fma.f64 1/2 (/.f64 a b_2) (.f64 -2 (/.f64 b_2 c))))
(fma.f64 -2 (/.f64 b_2 c) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))))) (.f64 2 (/.f64 b_2 c)))
(+.f64 (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/16 (/.f64 (.f64 (pow.f64 a 3) (.f64 c c)) (pow.f64 b_2 5))))) (*.f64 -2 (/.f64 b_2 c)))
(+.f64 (.f64 -2 (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 a a) (/.f64 (pow.f64 b_2 3) c)) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/16 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 5)) (pow.f64 a 3))))))
(fma.f64 -2 (/.f64 b_2 c) (fma.f64 1/2 (/.f64 a b_2) (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (/.f64 (.f64 c 1/16) (/.f64 (/.f64 (pow.f64 b_2 5) (pow.f64 a 3)) c)))))
(fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (fma.f64 1/2 (/.f64 a b_2) (fma.f64 (/.f64 c (/.f64 (pow.f64 b_2 5) c)) (.f64 1/16 (pow.f64 a 3)) (*.f64 -2 (/.f64 b_2 c)))))
(/.f64 a (sqrt.f64 (neg.f64 (*.f64 c a))))
(/.f64 a (sqrt.f64 (*.f64 c (neg.f64 a))))
(+.f64 (/.f64 a (sqrt.f64 (neg.f64 (.f64 c a)))) (/.f64 (.f64 a b_2) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 2)))
(+.f64 (/.f64 a (sqrt.f64 (.f64 c (neg.f64 a)))) (/.f64 (.f64 b_2 a) (pow.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) 2)))
(+.f64 (/.f64 a (sqrt.f64 (.f64 c (neg.f64 a)))) (.f64 (/.f64 a (*.f64 c (neg.f64 a))) b_2))
(fma.f64 (/.f64 a (.f64 c (neg.f64 a))) b_2 (/.f64 a (sqrt.f64 (.f64 c (neg.f64 a)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 a (pow.f64 b_2 2)) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 3))) (+.f64 (/.f64 a (sqrt.f64 (neg.f64 (.f64 c a)))) (/.f64 (.f64 a b_2) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 2))))
(fma.f64 1/2 (/.f64 (.f64 a (.f64 b_2 b_2)) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) (+.f64 (/.f64 a (sqrt.f64 (.f64 c (neg.f64 a)))) (/.f64 (.f64 b_2 a) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 2))))
(+.f64 (.f64 (/.f64 a (.f64 c (neg.f64 a))) b_2) (fma.f64 1/2 (/.f64 (.f64 b_2 (.f64 b_2 a)) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) (/.f64 a (sqrt.f64 (.f64 c (neg.f64 a))))))
(fma.f64 1/2 (/.f64 (.f64 b_2 (.f64 b_2 a)) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) (fma.f64 (/.f64 a (.f64 c (neg.f64 a))) b_2 (/.f64 a (sqrt.f64 (*.f64 c (neg.f64 a))))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (.f64 a (pow.f64 b_2 2)) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 3))) (+.f64 (/.f64 a (sqrt.f64 (neg.f64 (.f64 c a)))) (/.f64 (.f64 a b_2) (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 2)))) (.f64 1/8 (/.f64 (.f64 a (pow.f64 b_2 4)) (pow.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) 5))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 a (.f64 b_2 b_2)) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) (+.f64 (/.f64 a (sqrt.f64 (.f64 c (neg.f64 a)))) (/.f64 (.f64 b_2 a) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 2)))) (/.f64 (.f64 1/8 (.f64 a (pow.f64 b_2 4))) (pow.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) 5)))
(+.f64 (+.f64 (.f64 (/.f64 a (.f64 c (neg.f64 a))) b_2) (fma.f64 1/2 (/.f64 (.f64 b_2 (.f64 b_2 a)) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) (/.f64 a (sqrt.f64 (.f64 c (neg.f64 a)))))) (.f64 (/.f64 (.f64 a (pow.f64 b_2 4)) (pow.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) 5)) -1/8))
(fma.f64 (.f64 (pow.f64 b_2 4) (/.f64 a (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 5))) -1/8 (fma.f64 1/2 (/.f64 (.f64 b_2 (.f64 b_2 a)) (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3)) (fma.f64 (/.f64 a (.f64 c (neg.f64 a))) b_2 (/.f64 a (sqrt.f64 (*.f64 c (neg.f64 a)))))))
(*.f64 -2 (/.f64 b_2 c))
(-.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 2 (/.f64 b_2 c)))
(+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 -2 (/.f64 b_2 c)))
(fma.f64 1/2 (/.f64 a b_2) (*.f64 -2 (/.f64 b_2 c)))
(fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (.f64 1/2 (/.f64 a b_2))) (.f64 2 (/.f64 b_2 c)))
(+.f64 (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (.f64 1/2 (/.f64 a b_2))) (*.f64 -2 (/.f64 b_2 c)))
(fma.f64 1/8 (/.f64 (.f64 a a) (/.f64 (pow.f64 b_2 3) c)) (fma.f64 1/2 (/.f64 a b_2) (.f64 -2 (/.f64 b_2 c))))
(fma.f64 -2 (/.f64 b_2 c) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))))) (.f64 2 (/.f64 b_2 c)))
(+.f64 (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/16 (/.f64 (.f64 (pow.f64 a 3) (.f64 c c)) (pow.f64 b_2 5))))) (*.f64 -2 (/.f64 b_2 c)))
(+.f64 (.f64 -2 (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 a a) (/.f64 (pow.f64 b_2 3) c)) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/16 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 5)) (pow.f64 a 3))))))
(fma.f64 -2 (/.f64 b_2 c) (fma.f64 1/2 (/.f64 a b_2) (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (/.f64 (.f64 c 1/16) (/.f64 (/.f64 (pow.f64 b_2 5) (pow.f64 a 3)) c)))))
(fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (fma.f64 1/2 (/.f64 a b_2) (fma.f64 (/.f64 c (/.f64 (pow.f64 b_2 5) c)) (.f64 1/16 (pow.f64 a 3)) (*.f64 -2 (/.f64 b_2 c)))))
(*.f64 -1/2 (/.f64 a b_2))
(*.f64 (/.f64 a b_2) -1/2)
(/.f64 -1/2 (/.f64 b_2 a))
(*.f64 (/.f64 -1/2 b_2) a)
(neg.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (*.f64 1/2 (/.f64 a b_2))))
(neg.f64 (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (.f64 1/2 (/.f64 a b_2))))
(-.f64 (/.f64 -1/2 (/.f64 b_2 a)) (.f64 1/8 (/.f64 (.f64 a a) (/.f64 (pow.f64 b_2 3) c))))
(fma.f64 (/.f64 a b_2) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a a))))
(neg.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))) (*.f64 1/2 (/.f64 a b_2)))))
(neg.f64 (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/16 (/.f64 (.f64 (pow.f64 a 3) (.f64 c c)) (pow.f64 b_2 5))))))
(-.f64 (.f64 (/.f64 (.f64 a a) (/.f64 (pow.f64 b_2 3) c)) -1/8) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/16 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 5)) (pow.f64 a 3)))))
(fma.f64 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) -1/8 (fma.f64 (/.f64 a b_2) -1/2 (.f64 (*.f64 (pow.f64 a 3) (/.f64 c (/.f64 (pow.f64 b_2 5) c))) -1/16)))
(fma.f64 (/.f64 a b_2) -1/2 (fma.f64 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) -1/8 (.f64 (*.f64 (pow.f64 a 3) (/.f64 c (/.f64 (pow.f64 b_2 5) c))) -1/16)))
(neg.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))) (+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 5/128 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 4)) (pow.f64 b_2 7)))))))
(neg.f64 (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (fma.f64 1/16 (/.f64 (.f64 (pow.f64 a 3) (.f64 c c)) (pow.f64 b_2 5)) (fma.f64 1/2 (/.f64 a b_2) (.f64 5/128 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b_2 7) (pow.f64 a 4))))))))
(-.f64 (.f64 (/.f64 (.f64 a a) (/.f64 (pow.f64 b_2 3) c)) -1/8) (fma.f64 1/16 (.f64 (/.f64 (.f64 c c) (pow.f64 b_2 5)) (pow.f64 a 3)) (fma.f64 1/2 (/.f64 a b_2) (*.f64 5/128 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b_2 7) (pow.f64 a 4)))))))
(-.f64 (fma.f64 (/.f64 a b_2) -1/2 (/.f64 (.f64 c -1/8) (/.f64 (pow.f64 b_2 3) (.f64 a a)))) (fma.f64 5/128 (.f64 (pow.f64 a 4) (/.f64 (pow.f64 c 3) (pow.f64 b_2 7))) (/.f64 (.f64 c 1/16) (/.f64 (/.f64 (pow.f64 b_2 5) (pow.f64 a 3)) c))))
(fma.f64 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) -1/8 (fma.f64 (.f64 (pow.f64 a 4) (/.f64 (pow.f64 c 3) (pow.f64 b_2 7))) -5/128 (fma.f64 (.f64 (pow.f64 a 3) (/.f64 c (/.f64 (pow.f64 b_2 5) c))) -1/16 (.f64 (/.f64 -1/2 b_2) a))))
(*.f64 -2 (/.f64 b_2 c))
(-.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 2 (/.f64 b_2 c)))
(+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 -2 (/.f64 b_2 c)))
(fma.f64 1/2 (/.f64 a b_2) (*.f64 -2 (/.f64 b_2 c)))
(fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (.f64 1/2 (/.f64 a b_2))) (.f64 2 (/.f64 b_2 c)))
(+.f64 (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (.f64 1/2 (/.f64 a b_2))) (*.f64 -2 (/.f64 b_2 c)))
(fma.f64 1/8 (/.f64 (.f64 a a) (/.f64 (pow.f64 b_2 3) c)) (fma.f64 1/2 (/.f64 a b_2) (.f64 -2 (/.f64 b_2 c))))
(fma.f64 -2 (/.f64 b_2 c) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 c (pow.f64 a 2)) (pow.f64 b_2 3))) (+.f64 (.f64 1/2 (/.f64 a b_2)) (.f64 1/16 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 3)) (pow.f64 b_2 5))))) (.f64 2 (/.f64 b_2 c)))
(+.f64 (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/16 (/.f64 (.f64 (pow.f64 a 3) (.f64 c c)) (pow.f64 b_2 5))))) (*.f64 -2 (/.f64 b_2 c)))
(+.f64 (.f64 -2 (/.f64 b_2 c)) (fma.f64 1/8 (/.f64 (.f64 a a) (/.f64 (pow.f64 b_2 3) c)) (fma.f64 1/2 (/.f64 a b_2) (.f64 1/16 (.f64 (/.f64 (*.f64 c c) (pow.f64 b_2 5)) (pow.f64 a 3))))))
(fma.f64 -2 (/.f64 b_2 c) (fma.f64 1/2 (/.f64 a b_2) (fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (/.f64 (.f64 c 1/16) (/.f64 (/.f64 (pow.f64 b_2 5) (pow.f64 a 3)) c)))))
(fma.f64 1/8 (/.f64 c (/.f64 (pow.f64 b_2 3) (.f64 a a))) (fma.f64 1/2 (/.f64 a b_2) (fma.f64 (/.f64 c (/.f64 (pow.f64 b_2 5) c)) (.f64 1/16 (pow.f64 a 3)) (*.f64 -2 (/.f64 b_2 c)))))

prune326.0ms (4.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	372	3	375
Fresh	5	5	10
Picked	1	0	1
Done	0	2	2
Total	378	10	388

Error

4.7b

Counts

388 → 10

Alt Table

Status	Error	Program
	49.2b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (sqrt.f64 a)))
	43.9b	(/.f64 (fma.f64 b_2 -2 (*.f64 (/.f64 1/2 (/.f64 b_2 c)) a)) a)
▶	30.8b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 1 a)))
	43.9b	(pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1)
	42.8b	(.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)) (cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) a) 2)))
	43.5b	(pow.f64 (*.f64 -1/2 (/.f64 a b_2)) -1)
✓	30.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2) a)
	44.3b	(*.f64 -1/2 (/.f64 c b_2))
✓	30.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	40.9b	(pow.f64 (.f64 (/.f64 a (-.f64 (.f64 b_2 b_2) (fma.f64 a c (.f64 b_2 b_2)))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) -1)

Compiler

Compiled 10081 to 3668 computations (63.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
	1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	21.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series29.0ms (0.4%)

Counts

1 → 4

Calls

9 calls:

Time	Variable		Point	Expression
7.0ms	c	@	inf	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
5.0ms	a	@	inf	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
3.0ms	b_2	@	0	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
3.0ms	b_2	@	-inf	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
3.0ms	c	@	0	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

rewrite45.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`fma-def_binary64`
311×	`fma-neg_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
120×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	230	17
2	3260	16

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)) (cbrt.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2))) (cbrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2) 1/4) (pow.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)) 2)) (sqrt.f64 (cbrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 a c (*.f64 b_2 b_2)))) (sqrt.f64 (+.f64 b_2 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)) 3/2) (pow.f64 b_2 3))) (sqrt.f64 (fma.f64 b_2 (+.f64 b_2 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c))))) (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (pow.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)) 1/4) (sqrt.f64 (neg.f64 b_2)))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 (neg.f64 b_2)) (pow.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2))) 1))))))

simplify33.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

434×	`fma-def_binary64`
414×	`cancel-sign-sub-inv_binary64`
382×	`fma-neg_binary64`
319×	`unswap-sqr_binary64`
289×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	180
1	98	178
2	237	172
3	705	172
4	2236	170
5	4554	170

Stop Event

1×	node limit

Counts

31 → 35

Calls

Call 1

Inputs
(sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))
(-.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 c a)))) (.f64 1/2 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 (.f64 c a))))))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (pow.f64 b_2 2) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 3))))) (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 c a))))) (.f64 1/2 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 (*.f64 c a))))))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (pow.f64 b_2 2) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 3))))) (+.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 c a)))) (.f64 1/16 (.f64 (pow.f64 b_2 3) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 5))))))) (.f64 1/2 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 (.f64 c a))))))))

Outputs
(sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))
(sqrt.f64 (sqrt.f64 (*.f64 (neg.f64 c) a)))
(sqrt.f64 (sqrt.f64 (*.f64 a (neg.f64 c))))
(sqrt.f64 (sqrt.f64 (*.f64 c (neg.f64 a))))
(-.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 c a)))) (.f64 1/2 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 (.f64 c a))))))))
(+.f64 (sqrt.f64 (sqrt.f64 (.f64 (neg.f64 c) a))) (.f64 -1/2 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 (neg.f64 c) a)))))))
(+.f64 (sqrt.f64 (sqrt.f64 (.f64 a (neg.f64 c)))) (.f64 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 a (neg.f64 c)))))) -1/2))
(fma.f64 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 a (neg.f64 c)))))) -1/2 (sqrt.f64 (sqrt.f64 (*.f64 a (neg.f64 c)))))
(fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 c (neg.f64 a))))) (.f64 b_2 -1/2) (sqrt.f64 (sqrt.f64 (*.f64 c (neg.f64 a)))))
(fma.f64 b_2 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 a (neg.f64 c))))) -1/2) (sqrt.f64 (sqrt.f64 (*.f64 a (neg.f64 c)))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (pow.f64 b_2 2) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 3))))) (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 c a))))) (.f64 1/2 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 (*.f64 c a))))))))
(+.f64 (fma.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 (neg.f64 c) a)) 3))) (.f64 b_2 b_2)) (sqrt.f64 (sqrt.f64 (.f64 (neg.f64 c) a)))) (.f64 -1/2 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (*.f64 (neg.f64 c) a)))))))
(+.f64 (fma.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 a (neg.f64 c))) 3))) (.f64 b_2 b_2)) (sqrt.f64 (sqrt.f64 (.f64 a (neg.f64 c))))) (.f64 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (*.f64 a (neg.f64 c)))))) -1/2))
(fma.f64 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 a (neg.f64 c)))))) -1/2 (fma.f64 1/8 (.f64 b_2 (.f64 b_2 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 a (neg.f64 c))) 3))))) (sqrt.f64 (sqrt.f64 (.f64 a (neg.f64 c))))))
(fma.f64 b_2 (.f64 b_2 (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3))))) (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 c (neg.f64 a))))) (.f64 b_2 -1/2) (sqrt.f64 (sqrt.f64 (.f64 c (neg.f64 a))))))
(+.f64 (sqrt.f64 (sqrt.f64 (.f64 a (neg.f64 c)))) (.f64 b_2 (fma.f64 b_2 (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 a (neg.f64 c))) 3)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 a (neg.f64 c))))) -1/2))))
(-.f64 (+.f64 (.f64 1/8 (.f64 (pow.f64 b_2 2) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 3))))) (+.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 c a)))) (.f64 1/16 (.f64 (pow.f64 b_2 3) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (neg.f64 (.f64 c a))) 5))))))) (.f64 1/2 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (neg.f64 (.f64 c a))))))))
(+.f64 (+.f64 (fma.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 (neg.f64 c) a)) 3))) (.f64 b_2 b_2)) (sqrt.f64 (sqrt.f64 (.f64 (neg.f64 c) a)))) (.f64 1/16 (.f64 (pow.f64 b_2 3) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 (neg.f64 c) a)) 5)))))) (.f64 -1/2 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 (neg.f64 c) a)))))))
(+.f64 (fma.f64 1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 a (neg.f64 c))) 3))) (.f64 b_2 b_2)) (fma.f64 1/16 (.f64 (pow.f64 b_2 3) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 a (neg.f64 c))) 5)))) (sqrt.f64 (sqrt.f64 (.f64 a (neg.f64 c)))))) (.f64 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (*.f64 a (neg.f64 c)))))) -1/2))
(fma.f64 (.f64 b_2 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 a (neg.f64 c)))))) -1/2 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 a (neg.f64 c))) 5))) (.f64 1/16 (pow.f64 b_2 3)) (fma.f64 1/8 (.f64 b_2 (.f64 b_2 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 a (neg.f64 c))) 3))))) (sqrt.f64 (sqrt.f64 (.f64 a (neg.f64 c)))))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 5))) (.f64 1/16 (pow.f64 b_2 3)) (fma.f64 b_2 (.f64 b_2 (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 c (neg.f64 a))) 3))))) (fma.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 c (neg.f64 a))))) (.f64 b_2 -1/2) (sqrt.f64 (sqrt.f64 (.f64 c (neg.f64 a)))))))
(+.f64 (sqrt.f64 (sqrt.f64 (.f64 a (neg.f64 c)))) (fma.f64 1/16 (.f64 (pow.f64 b_2 3) (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 a (neg.f64 c))) 5)))) (.f64 b_2 (fma.f64 b_2 (.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 (.f64 a (neg.f64 c))) 3)))) (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (.f64 a (neg.f64 c))))) -1/2)))))

prune448.0ms (6.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	702	2	704
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	703	11	714

Error

4.7b

Counts

714 → 11

Alt Table

Status	Error	Program
	49.2b	(.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (sqrt.f64 a)))
	43.9b	(/.f64 (fma.f64 b_2 -2 (*.f64 (/.f64 1/2 (/.f64 b_2 c)) a)) a)
✓	30.8b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 1 a)))
	43.9b	(pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1)
	35.4b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 b_2 (sqrt.f64 (*.f64 a (neg.f64 c)))) b_2) 3/2)) (/.f64 1 a)))
	43.5b	(pow.f64 (*.f64 -1/2 (/.f64 a b_2)) -1)
	52.7b	(.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (.f64 (sqrt.f64 (fma.f64 b_2 -2 (*.f64 (/.f64 1/2 (/.f64 b_2 c)) a))) (/.f64 1 a)))
✓	30.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b_2 b_2 (fma.f64 a (neg.f64 c) (fma.f64 a (neg.f64 c) (*.f64 a c))))) b_2) a)
	44.3b	(*.f64 -1/2 (/.f64 c b_2))
✓	30.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	40.9b	(pow.f64 (.f64 (/.f64 a (-.f64 (.f64 b_2 b_2) (fma.f64 a c (.f64 b_2 b_2)))) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) -1)

Compiler

Compiled 27652 to 7613 computations (72.5% saved)

regimes2.4s (32.9%)

Accuracy

Total 6.7b remaining (57.2%)

Threshold costs 0b (0%)

Counts

216 → 5

Compiler

Compiled 3974 to 1362 computations (65.7% saved)

bsearch127.0ms (1.7%)

Algorithm

4×	binary-search

Calls

4 calls:

49.0ms	b_2
40.0ms	b_2
30.0ms	b_2
6.0ms	b_2

Steps

Iters	Point		Range
1.55e+31	∈ [	1.5162485363423706e+31	,	4.911205930235825e+31	]
2e-46	∈ [	6.012697906501275e-50	,	2.6708987091530204e-46	]
3.9e-115	∈ [	1.0054262874350506e-126	,	3.2304035240840694e-113	]
-1e+98	∈ [	-2.0163042400047604e+98	,	-7.75667309475295e+91	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	94
1	51	94
2	63	94
3	70	94
4	74	94
5	75	94

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 b_2 -99999999999999999769037024514370800696612547992403838920556863966097586548129676477911932478685184) (*.f64 -2 (/.f64 b_2 a)) (if (<=.f64 b_2 4325364722828471/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a) (if (<=.f64 b_2 5142201741628769/25711008708143844408671393477458601640355247900524685364822016) (pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1) (if (<=.f64 b_2 15500000000000001011899126775808) (/.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) a) (pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1)))))

Outputs

(if (<=.f64 b_2 -99999999999999999769037024514370800696612547992403838920556863966097586548129676477911932478685184) (*.f64 -2 (/.f64 b_2 a)) (if (<=.f64 b_2 4325364722828471/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a) (if (<=.f64 b_2 5142201741628769/25711008708143844408671393477458601640355247900524685364822016) (pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1) (if (<=.f64 b_2 15500000000000001011899126775808) (/.f64 (sqrt.f64 (*.f64 c (neg.f64 a))) a) (pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1)))))

(if (<=.f64 b_2 -99999999999999999769037024514370800696612547992403838920556863966097586548129676477911932478685184) (*.f64 -2 (/.f64 b_2 a)) (if (<=.f64 b_2 4325364722828471/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a) (if (<=.f64 b_2 5142201741628769/25711008708143844408671393477458601640355247900524685364822016) (pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1) (if (<=.f64 b_2 15500000000000001011899126775808) (/.f64 (sqrt.f64 (neg.f64 (*.f64 a c))) a) (pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1)))))

(if (<=.f64 b_2 -99999999999999999769037024514370800696612547992403838920556863966097586548129676477911932478685184) (*.f64 -2 (/.f64 b_2 a)) (if (<=.f64 b_2 4325364722828471/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a) (if (<=.f64 b_2 5142201741628769/25711008708143844408671393477458601640355247900524685364822016) (pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1) (if (<=.f64 b_2 15500000000000001011899126775808) (/.f64 (sqrt.f64 (*.f64 a (neg.f64 c))) a) (pow.f64 (fma.f64 -2 (/.f64 b_2 c) (*.f64 1/2 (/.f64 a b_2))) -1)))))

end157.0ms (2.1%)

Stop Event

1×

fuel

Compiler

Compiled 359 to 220 computations (38.7% saved)

Details

analyze713.0ms (9.7%)

sample2.0s (26.7%)

preprocess42.0ms (0.6%)

simplify109.0ms (1.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series33.0ms (0.4%)

rewrite91.0ms (1.2%)

simplify53.0ms (0.7%)

prune260.0ms (3.5%)

localize13.0ms (0.2%)

series28.0ms (0.4%)

rewrite70.0ms (1%)

simplify62.0ms (0.8%)

prune173.0ms (2.4%)

localize9.0ms (0.1%)

series26.0ms (0.4%)

rewrite56.0ms (0.8%)

simplify41.0ms (0.6%)

prune326.0ms (4.4%)

localize11.0ms (0.1%)

series29.0ms (0.4%)

rewrite45.0ms (0.6%)

simplify33.0ms (0.4%)

prune448.0ms (6.1%)

regimes2.4s (32.9%)

bsearch127.0ms (1.7%)

simplify4.0ms (0.1%)

end157.0ms (2.1%)

Profiling