Details

analyze966.0ms (12.2%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	93.6%	6.4%	7
6.2%	87.4%	6.4%	8
10.1%	81.1%	8.7%	9
15.6%	71%	13.4%	10
22%	63%	15%	11
29.1%	52.9%	18.1%	12
33.8%	45.6%	20.5%	13
38.8%	38.9%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.2s (27.8%)

Results

738.0ms	5410×	body	128	valid
599.0ms	1134×	body	2048	valid
318.0ms	749×	body	1024	valid
227.0ms	383×	body	4096	valid
132.0ms	1091×	body	128	invalid
127.0ms	369×	body	512	valid
45.0ms	211×	body	256	valid

Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess50.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

807×	`fma-def_binary64`
679×	`div-sub_binary64`
295×	`fma-neg_binary64`
214×	`associate-/l*_binary64`
209×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	104
1	98	88
2	198	88
3	446	88
4	768	88
5	1261	88
6	2236	88
7	4458	88
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) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 4 (.f64 b c))))) (.f64 2 b))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (.f64 2 c))
(/.f64 (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 4 (.f64 a b))))) (.f64 2 a))

Outputs
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 -4 (.f64 a c))))) (.f64 a 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b) (*.f64 a 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4))))) (/.f64 -1/2 a))
(/.f64 (+.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 4 (.f64 b c))))) (.f64 2 b))
(/.f64 (+.f64 (neg.f64 a) (sqrt.f64 (+.f64 (.f64 a a) (.f64 -4 (.f64 b c))))) (.f64 b 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 a a (.f64 (.f64 b c) -4))) a) (*.f64 b 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 a a (.f64 b (.f64 c -4)))) a) (*.f64 b 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b (.f64 c -4) (.f64 a a))) a) (*.f64 b 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 c (.f64 b -4) (.f64 a a))) a) (*.f64 b 2))
(.f64 (-.f64 a (sqrt.f64 (fma.f64 (.f64 b c) -4 (*.f64 a a)))) (/.f64 -1/2 b))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 c a))))) (.f64 2 c))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 -4 (.f64 a c))))) (.f64 c 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b) (*.f64 c 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b) (*.f64 c 2))
(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4))))) (/.f64 -1/2 c))
(/.f64 (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 4 (.f64 a b))))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 4 (.f64 b a))))) (.f64 a 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 c c (.f64 (.f64 b a) -4))) c) (*.f64 a 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 b a) -4 (.f64 c c))) c) (*.f64 a 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b (.f64 a -4) (.f64 c c))) c) (*.f64 a 2))
(.f64 -1/2 (/.f64 (-.f64 c (sqrt.f64 (fma.f64 b (.f64 a -4) (*.f64 c c)))) a))

Compiler

Compiled 20 to 14 computations (30% saved)

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
619×	`times-frac_binary64`
338×	`fma-def_binary64`
314×	`associate-/l*_binary64`
262×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	69	22
3	161	22
4	259	22
5	417	22
6	734	22
7	1326	22
8	2618	22
9	3877	22

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Outputs
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (+.f64 (.f64 b b) (.f64 -4 (.f64 a c))))) (.f64 a 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b) (*.f64 a 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 (.f64 a c) -4 (.f64 b b))) b) (*.f64 a 2))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) b) (*.f64 a 2))
(.f64 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4))))) a) -1/2)
(.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4))))) (/.f64 -1/2 a))
(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

35.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	35.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	35.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 75 computations (32.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.6b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	24.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series35.0ms (0.4%)

Counts

4 → 96

Calls

36 calls:

Time	Variable		Point	Expression
5.0ms	c	@	inf	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
2.0ms	a	@	inf	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
2.0ms	a	@	-inf	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
2.0ms	a	@	inf	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
2.0ms	c	@	inf	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite77.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

277×	`log1p-udef_binary64`
173×	`add-sqr-sqrt_binary64`
166×	`*-un-lft-identity_binary64`
166×	`pow1_binary64`
162×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	343	62
2	4905	62

Stop Event

1×	node limit

Counts

4 → 158

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 b 4) (.f64 (pow.f64 (.f64 a c) 2) 16))) (sqrt.f64 (fma.f64 b b (.f64 4 (.f64 a c)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 b 6) (.f64 (pow.f64 (.f64 a c) 3) 64))) (sqrt.f64 (+.f64 (pow.f64 b 4) (.f64 (.f64 4 (.f64 a c)) (fma.f64 b b (.f64 4 (.f64 a c)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 b b) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (/.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 0) b)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) 2) (cbrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 b 3) (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2)) (/.f64 1 (fma.f64 b b (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4))) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 b b (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))) (+.f64 (pow.f64 b 3) (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 b 3) (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2)) (fma.f64 b b (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 b 3) (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2)) (+.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) (-.f64 (.f64 b b) (.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 b 3) (pow.f64 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b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (.f64 a -2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (/.f64 1/2 a)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) 3) (pow.f64 (.f64 a 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))))))))

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
432×	`fma-def_binary64`
422×	`associate-/r*_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	402	2164
2	1403	2078

Stop Event

1×	node limit

Counts

254 → 232

Calls

Call 1

Inputs
(sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))) (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 b 6) (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))) 3))))
b
(-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(*.f64 -1 b)
(-.f64 (.f64 2 (/.f64 (.f64 c a) b)) b)
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))) b)
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))) b)
b
(-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
b
(-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))
(-.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) b)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a))))) b)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) 3))) b))
(.f64 -2 (/.f64 (.f64 c a) b))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
(*.f64 -2 b)
(-.f64 (.f64 2 (/.f64 (.f64 c a) b)) (*.f64 2 b))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))) (*.f64 2 b))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))) (*.f64 2 b))
(.f64 -2 (/.f64 (.f64 c a) b))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
(.f64 -2 (/.f64 (.f64 c a) b))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(pow.f64 b 2)
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(pow.f64 b 2)
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(pow.f64 b 2)
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(pow.f64 b 2)
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))) a))
(-.f64 (.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) a)) (.f64 1/2 (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))))) (.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) a))) (.f64 1/2 (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))))) (.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) a))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 b 4) (.f64 a (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) 3)))) (.f64 1/2 (/.f64 b a))))
(*.f64 -1 (/.f64 c b))
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
(*.f64 -1 (/.f64 b a))
(-.f64 (/.f64 c b) (/.f64 b a))
(-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)) (/.f64 b a))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b))) (/.f64 b a))
(*.f64 -1 (/.f64 c b))
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
(*.f64 -1 (/.f64 c b))
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))

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

prune174.0ms (2.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	219	13	232
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	220	14	234

Error

5.2b

Counts

234 → 14

Alt Table

Status	Error	Program
▶	35.5b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b) (*.f64 2 a))
	40.7b	(/.f64 (neg.f64 c) b)
	47.2b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4))))) -1)
	35.7b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	47.4b	(.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a))) (pow.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 2))
	43.3b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.3b	(/.f64 (neg.f64 b) a)
	57.7b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	36.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) 2)))) (.f64 2 a))
	52.5b	(-.f64 (.f64 -2 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b 5)) (.f64 a a))) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
	45.9b	(neg.f64 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
	55.6b	(pow.f64 (sqrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 2)
	43.4b	(/.f64 (+.f64 (neg.f64 b) (-.f64 (.f64 2 (.f64 (/.f64 c b) a)) b)) (*.f64 2 a))
	35.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))

Compiler

Compiled 6332 to 3706 computations (41.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b) (*.f64 2 a))
✓	1.0b	(fma.f64 b b (.f64 (.f64 a c) -4))
✓	1.6b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b)
✓	24.1b	(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))

series15.0ms (0.2%)

Counts

4 → 96

Calls

36 calls:

Time	Variable		Point	Expression
1.0ms	b	@	0	(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))
1.0ms	a	@	inf	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b) (*.f64 2 a))
1.0ms	a	@	-inf	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b) (*.f64 2 a))
0.0ms	a	@	inf	(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))
0.0ms	c	@	inf	(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))

rewrite81.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

329×	`fma-def_binary64`
255×	`expm1-udef_binary64`
255×	`log1p-udef_binary64`
214×	`fma-neg_binary64`
145×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	284	59
2	3882	59

Stop Event

1×	node limit

Counts

4 → 194

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))
(-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b)
(fma.f64 b b (.f64 (.f64 a c) -4))
(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) b) (*.f64 2 a))

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

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
432×	`fma-def_binary64`
422×	`associate-/r*_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	402	2164
2	1403	2078

Stop Event

1×	node limit

Counts

290 → 268

Calls

Call 1

Inputs
(sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))) (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 b 6) (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))) 3))))
b
(-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(*.f64 -1 b)
(-.f64 (.f64 2 (/.f64 (.f64 c a) b)) b)
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))) b)
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))) b)
b
(-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
b
(-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(-.f64 b (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))
(-.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) b)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a))))) b)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))))) (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) 3))) b))
(.f64 -2 (/.f64 (.f64 c a) b))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
(*.f64 -2 b)
(-.f64 (.f64 2 (/.f64 (.f64 c a) b)) (*.f64 2 b))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))) (*.f64 2 b))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))) (*.f64 2 b))
(.f64 -2 (/.f64 (.f64 c a) b))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
(.f64 -2 (/.f64 (.f64 c a) b))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3)))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)))))))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(pow.f64 b 2)
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(pow.f64 b 2)
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(pow.f64 b 2)
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(pow.f64 b 2)
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 -4 (.f64 c a))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(-.f64 (pow.f64 b 2) (.f64 4 (.f64 c a)))
(.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (*.f64 c a)))) a))
(-.f64 (.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) a)) (.f64 1/2 (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))))) (.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) a))) (.f64 1/2 (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a))))))) (.f64 1/2 (/.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) a))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 b 4) (.f64 a (pow.f64 (sqrt.f64 (neg.f64 (.f64 4 (.f64 c a)))) 3)))) (.f64 1/2 (/.f64 b a))))
(*.f64 -1 (/.f64 c b))
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
(*.f64 -1 (/.f64 b a))
(-.f64 (/.f64 c b) (/.f64 b a))
(-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)) (/.f64 b a))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b))) (/.f64 b a))
(*.f64 -1 (/.f64 c b))
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))
(*.f64 -1 (/.f64 c b))
(neg.f64 (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b))))
(neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 2)) (pow.f64 b 5))) (+.f64 (.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7))) (+.f64 (/.f64 (*.f64 (pow.f64 c 2) a) (pow.f64 b 3)) (/.f64 c b)))))

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

prune195.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	260	8	268
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	269	13	282

Error

5.2b

Counts

282 → 13

Alt Table

Status	Error	Program
	36.5b	(/.f64 (-.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) (pow.f64 (cbrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) 2))) b) (.f64 2 a))
	35.7b	(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2) b) (*.f64 2 a))
	45.9b	(neg.f64 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
	40.7b	(/.f64 (neg.f64 c) b)
▶	32.2b	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) -1)
	47.1b	(pow.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 2)
	43.4b	(/.f64 (-.f64 (-.f64 (.f64 2 (.f64 (/.f64 c b) a)) b) b) (*.f64 2 a))
	57.7b	(/.f64 (-.f64 b b) (*.f64 2 a))
	32.7b	(.f64 (cbrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))) (pow.f64 (cbrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 2))
	32.3b	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	43.3b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.3b	(/.f64 (neg.f64 b) a)
	52.5b	(-.f64 (.f64 -2 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b 5)) (.f64 a a))) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))

Compiler

Compiled 6941 to 4361 computations (37.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))
✓	0.1b	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) -1)
✓	0.4b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
✓	12.7b	(sqrt.f64 (.f64 a (.f64 c -4)))

series199.0ms (2.5%)

Counts

4 → 36

Calls

33 calls:

Time	Variable		Point	Expression
75.0ms	c	@	inf	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) -1)
24.0ms	c	@	-inf	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) -1)
18.0ms	a	@	inf	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) -1)
16.0ms	a	@	-inf	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) -1)
11.0ms	a	@	-inf	(/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))

rewrite74.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

584×	`prod-diff_binary64`
163×	`add-sqr-sqrt_binary64`
156×	`pow1_binary64`
154×	`*-un-lft-identity_binary64`
152×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	66
1	327	63
2	4158	63

Stop Event

1×	node limit

Counts

4 → 137

Calls

Call 1

Inputs
(sqrt.f64 (.f64 a (.f64 c -4)))
(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) -1)
(/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))

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

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

597×	`associate-/l*_binary64`
582×	`associate-/r*_binary64`
383×	`fma-def_binary64`
224×	`cancel-sign-sub-inv_binary64`
215×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1533
1	443	1383
2	1516	1346

Stop Event

1×	node limit

Counts

173 → 209

Calls

Call 1

Inputs
(sqrt.f64 (.f64 -4 (.f64 c a)))
(-.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (sqrt.f64 (.f64 -4 (*.f64 c a)))) b)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (sqrt.f64 (.f64 -4 (.f64 c a)))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3))) b))
(.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2) b))
(-.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5))) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b))) (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 4) (pow.f64 b 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5))) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (.f64 5/128 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 8) (pow.f64 b 7)))))
(*.f64 -2 b)
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (.f64 2 b)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (*.f64 2 b)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5))) (.f64 2 b))))
(.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) a))
(-.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/2 (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (.f64 1/2 (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 b 4) (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)))) (.f64 1/2 (/.f64 b a))))
(.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))
(-.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(-.f64 (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(-.f64 (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (+.f64 (.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 8) (.f64 a (pow.f64 b 7)))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3))))))
(*.f64 -1 (/.f64 b a))
(neg.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a)))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a)))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a))))
(/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))
(+.f64 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (/.f64 a (sqrt.f64 (.f64 -4 (*.f64 c a)))))
(+.f64 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (+.f64 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a)))) (.f64 1/2 (/.f64 (.f64 a (pow.f64 b 2)) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 3)))))
(-.f64 (+.f64 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (+.f64 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a)))) (.f64 1/2 (/.f64 (.f64 a (pow.f64 b 2)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3))))) (.f64 1/8 (/.f64 (.f64 a (pow.f64 b 4)) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 5))))
(.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)))
(+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (*.f64 1/2 (/.f64 a b)))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (.f64 1/2 (/.f64 a b))) (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2)) (pow.f64 b 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (.f64 1/2 (/.f64 a b)))) (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2)) (pow.f64 b 3))))
(*.f64 -1/2 (/.f64 a b))
(-.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (*.f64 1/2 (/.f64 a b)))
(-.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (*.f64 1/2 (/.f64 a b))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (.f64 5/128 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6)) (pow.f64 b 7)))) (+.f64 (.f64 1/16 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (*.f64 1/2 (/.f64 a b))))

Outputs
(sqrt.f64 (.f64 -4 (.f64 c a)))
(sqrt.f64 (.f64 a (.f64 -4 c)))
(-.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) b)
(-.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) b)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (sqrt.f64 (.f64 -4 (*.f64 c a)))) b)
(-.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 -4 (.f64 c a)))) (sqrt.f64 (.f64 -4 (*.f64 c a)))) b)
(fma.f64 1/2 (/.f64 b (/.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) b)) (-.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) b))
(fma.f64 1/2 (.f64 (/.f64 b (sqrt.f64 (.f64 a (.f64 -4 c)))) b) (-.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) b))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (sqrt.f64 (.f64 -4 (.f64 c a)))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3))) b))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 -4 (.f64 c a)))) (sqrt.f64 (.f64 -4 (.f64 c a)))) (fma.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 3)) b))
(-.f64 (fma.f64 1/2 (/.f64 b (/.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) b)) (sqrt.f64 (.f64 a (.f64 -4 c)))) (fma.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 3)) b))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 b (sqrt.f64 (.f64 a (.f64 -4 c)))) b) (sqrt.f64 (.f64 a (.f64 -4 c)))) (fma.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) 3)) b))
(.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2) b))
(.f64 1/2 (/.f64 (.f64 a (*.f64 -4 c)) b))
(.f64 1/2 (/.f64 (.f64 c a) (/.f64 b -4)))
(-.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (.f64 -1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))))
(fma.f64 1/2 (/.f64 (.f64 a (.f64 -4 c)) b) (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) 4) (pow.f64 b 3)) -1/8))
(fma.f64 1/2 (/.f64 (.f64 c a) (/.f64 b -4)) (/.f64 -1/8 (/.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) 4))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5))) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b))) (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 4) (pow.f64 b 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5)) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b))) (.f64 -1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))))
(fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 6) (pow.f64 b 5)) (fma.f64 1/2 (/.f64 (.f64 a (.f64 -4 c)) b) (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) 4) (pow.f64 b 3)) -1/8)))
(fma.f64 1/2 (/.f64 (.f64 c a) (/.f64 b -4)) (fma.f64 1/16 (/.f64 (pow.f64 (.f64 a (.f64 -4 c)) 3) (pow.f64 b 5)) (/.f64 -1/8 (/.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) 4)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5))) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (.f64 5/128 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 8) (pow.f64 b 7)))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5)) (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b))) (fma.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3)) (.f64 5/128 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 8) (pow.f64 b 7)))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 6) (pow.f64 b 5)) (fma.f64 1/2 (/.f64 (.f64 a (.f64 -4 c)) b) (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4) (pow.f64 b 3)) -1/8))) (.f64 -5/128 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 8) (pow.f64 b 7))))
(fma.f64 1/2 (/.f64 (.f64 c a) (/.f64 b -4)) (fma.f64 1/16 (/.f64 (pow.f64 (.f64 a (.f64 -4 c)) 3) (pow.f64 b 5)) (fma.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4) (pow.f64 b 3)) -1/8 (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 8) (pow.f64 b 7)) -5/128))))
(*.f64 -2 b)
(*.f64 b -2)
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (.f64 2 b)))
(neg.f64 (fma.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b) (*.f64 b 2)))
(-.f64 (.f64 b -2) (.f64 1/2 (/.f64 (.f64 a (.f64 -4 c)) b)))
(fma.f64 (/.f64 (.f64 c a) (/.f64 b -4)) -1/2 (.f64 b -2))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (*.f64 2 b)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (fma.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b) (.f64 b 2)))
(fma.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4) (pow.f64 b 3)) (-.f64 (.f64 b -2) (.f64 1/2 (/.f64 (.f64 a (.f64 -4 c)) b))))
(fma.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4) (pow.f64 b 3)) (fma.f64 (/.f64 (.f64 c a) (/.f64 b -4)) -1/2 (.f64 b -2)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5))) (.f64 2 b))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (fma.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b) (fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5)) (.f64 b 2))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4) (pow.f64 b 3))) (fma.f64 1/2 (/.f64 (.f64 a (.f64 -4 c)) b) (fma.f64 b 2 (/.f64 (.f64 1/16 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 6)) (pow.f64 b 5)))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4) (pow.f64 b 3))) (fma.f64 b 2 (fma.f64 1/2 (/.f64 (.f64 c a) (/.f64 b -4)) (/.f64 (pow.f64 (.f64 a (.f64 -4 c)) 3) (/.f64 (pow.f64 b 5) 1/16)))))
(.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) a))
(.f64 1/2 (/.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) a))
(-.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/2 (/.f64 b a)))
(.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) a) (/.f64 b a)))
(.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) a) (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (.f64 1/2 (/.f64 b a)))
(+.f64 (fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a) (.f64 1/4 (/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (.f64 -1/2 (/.f64 b a)))
(fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) a) (fma.f64 1/4 (/.f64 (/.f64 b (/.f64 a b)) (sqrt.f64 (.f64 a (.f64 -4 c)))) (*.f64 (/.f64 b a) -1/2)))
(fma.f64 1/4 (/.f64 b (/.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) (/.f64 b a))) (.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) a) (/.f64 b a))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 b 4) (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)))) (.f64 1/2 (/.f64 b a))))
(-.f64 (fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a) (.f64 1/4 (/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (fma.f64 1/16 (/.f64 (/.f64 (pow.f64 b 4) a) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)) (.f64 1/2 (/.f64 b a))))
(-.f64 (fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) a) (fma.f64 1/4 (/.f64 (/.f64 b (/.f64 a b)) (sqrt.f64 (.f64 a (.f64 -4 c)))) (.f64 (/.f64 b a) -1/2))) (.f64 1/16 (/.f64 (/.f64 (pow.f64 b 4) a) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 3))))
(fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) a) (fma.f64 1/4 (/.f64 b (/.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) (/.f64 b a))) (fma.f64 (/.f64 b a) -1/2 (/.f64 -1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 3) (/.f64 (pow.f64 b 4) a))))))
(.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))
(/.f64 (.f64 (.f64 a (.f64 -4 c)) 1/4) (.f64 a b))
(.f64 1/4 (/.f64 a (/.f64 (.f64 a b) (*.f64 -4 c))))
(-.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (.f64 -1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(fma.f64 1/4 (/.f64 (.f64 a (.f64 -4 c)) (.f64 a b)) (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4) (*.f64 a (pow.f64 b 3))) -1/16))
(fma.f64 1/4 (/.f64 a (/.f64 (.f64 a b) (.f64 -4 c))) (/.f64 -1/16 (/.f64 (.f64 a (pow.f64 b 3)) (pow.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) 4))))
(-.f64 (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(+.f64 (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (.f64 -1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (*.f64 a (pow.f64 b 3)))))
(fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 6) (.f64 a (pow.f64 b 5))) (fma.f64 1/4 (/.f64 (.f64 a (.f64 -4 c)) (.f64 a b)) (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4) (.f64 a (pow.f64 b 3))) -1/16)))
(fma.f64 1/4 (/.f64 a (/.f64 (.f64 a b) (.f64 -4 c))) (fma.f64 1/32 (/.f64 (pow.f64 (.f64 a (.f64 -4 c)) 3) (.f64 a (pow.f64 b 5))) (/.f64 -1/16 (/.f64 (.f64 a (pow.f64 b 3)) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4)))))
(-.f64 (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (+.f64 (.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 8) (.f64 a (pow.f64 b 7)))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3))))))
(-.f64 (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (fma.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 8) (.f64 a (pow.f64 b 7))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3))))))
(-.f64 (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 6) (.f64 a (pow.f64 b 5))) (/.f64 (.f64 (.f64 a (.f64 -4 c)) 1/4) (.f64 a b))) (fma.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 8) (.f64 a (pow.f64 b 7))) (/.f64 1/16 (/.f64 (.f64 a (pow.f64 b 3)) (pow.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) 4)))))
(fma.f64 1/4 (/.f64 a (/.f64 (.f64 a b) (.f64 -4 c))) (fma.f64 1/32 (/.f64 (pow.f64 (.f64 a (.f64 -4 c)) 3) (.f64 a (pow.f64 b 5))) (fma.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4) (.f64 a (pow.f64 b 3))) -1/16 (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 8) (.f64 a (pow.f64 b 7))) -5/256))))
(*.f64 -1 (/.f64 b a))
(neg.f64 (/.f64 b a))
(/.f64 (neg.f64 b) a)
(neg.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a)))
(neg.f64 (fma.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (*.f64 a b)) (/.f64 b a)))
(-.f64 (.f64 (/.f64 (.f64 a (.f64 -4 c)) (.f64 a b)) -1/4) (/.f64 b a))
(-.f64 (.f64 (/.f64 a (/.f64 (.f64 a b) (*.f64 -4 c))) -1/4) (/.f64 b a))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a)))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (fma.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (*.f64 a b)) (/.f64 b a)))
(-.f64 (/.f64 1/16 (/.f64 (.f64 a (pow.f64 b 3)) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4))) (fma.f64 1/4 (/.f64 (.f64 a (.f64 -4 c)) (.f64 a b)) (/.f64 b a)))
(-.f64 (.f64 (/.f64 1/16 (.f64 a (pow.f64 b 3))) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4)) (fma.f64 1/4 (/.f64 a (/.f64 (.f64 a b) (.f64 -4 c))) (/.f64 b a)))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a))))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5))) (fma.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)) (/.f64 b a))))
(-.f64 (/.f64 1/16 (/.f64 (.f64 a (pow.f64 b 3)) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4))) (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 6) (.f64 a (pow.f64 b 5))) (fma.f64 1/4 (/.f64 (.f64 a (.f64 -4 c)) (*.f64 a b)) (/.f64 b a))))
(-.f64 (.f64 (/.f64 1/16 (.f64 a (pow.f64 b 3))) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4)) (fma.f64 1/4 (/.f64 a (/.f64 (.f64 a b) (.f64 -4 c))) (fma.f64 1/32 (/.f64 (pow.f64 (.f64 a (.f64 -4 c)) 3) (*.f64 a (pow.f64 b 5))) (/.f64 b a))))
(/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))
(/.f64 a (sqrt.f64 (.f64 a (.f64 -4 c))))
(+.f64 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (/.f64 a (sqrt.f64 (.f64 -4 (*.f64 c a)))))
(+.f64 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a)))) (/.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)))
(+.f64 (/.f64 a (sqrt.f64 (.f64 a (.f64 -4 c)))) (/.f64 (.f64 a b) (.f64 a (*.f64 -4 c))))
(fma.f64 (/.f64 a (.f64 a (.f64 -4 c))) b (/.f64 a (sqrt.f64 (.f64 a (.f64 -4 c)))))
(+.f64 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (+.f64 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a)))) (.f64 1/2 (/.f64 (.f64 a (pow.f64 b 2)) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 3)))))
(+.f64 (/.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (+.f64 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a)))) (.f64 1/2 (/.f64 (.f64 a (.f64 b b)) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 3)))))
(+.f64 (/.f64 (.f64 a b) (.f64 a (.f64 -4 c))) (fma.f64 1/2 (/.f64 (.f64 a (.f64 b b)) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 3)) (/.f64 a (sqrt.f64 (.f64 a (*.f64 -4 c))))))
(fma.f64 1/2 (.f64 (/.f64 b (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 3) b)) a) (fma.f64 (/.f64 a (.f64 a (.f64 -4 c))) b (/.f64 a (sqrt.f64 (.f64 a (*.f64 -4 c))))))
(-.f64 (+.f64 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (+.f64 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a)))) (.f64 1/2 (/.f64 (.f64 a (pow.f64 b 2)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3))))) (.f64 1/8 (/.f64 (.f64 a (pow.f64 b 4)) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 5))))
(+.f64 (/.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (-.f64 (+.f64 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a)))) (.f64 1/2 (/.f64 (.f64 a (.f64 b b)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)))) (.f64 1/8 (/.f64 (.f64 a (pow.f64 b 4)) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 5)))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 a (.f64 b b)) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 3)) (/.f64 a (sqrt.f64 (.f64 a (.f64 -4 c))))) (-.f64 (/.f64 (.f64 a b) (.f64 a (.f64 -4 c))) (/.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 5) (.f64 a (pow.f64 b 4))))))
(fma.f64 (.f64 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 5)) a) -1/8 (fma.f64 1/2 (.f64 (/.f64 b (/.f64 (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 3) b)) a) (fma.f64 (/.f64 a (.f64 a (.f64 -4 c))) b (/.f64 a (sqrt.f64 (.f64 a (.f64 -4 c)))))))
(.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)))
(/.f64 (.f64 2 (.f64 a b)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))
(/.f64 (.f64 2 (.f64 a b)) (.f64 a (.f64 -4 c)))
(.f64 (/.f64 2 (.f64 a (.f64 -4 c))) (.f64 a b))
(+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (*.f64 1/2 (/.f64 a b)))
(fma.f64 2 (/.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (*.f64 1/2 (/.f64 a b)))
(fma.f64 1/2 (/.f64 a b) (/.f64 (.f64 2 (.f64 a b)) (.f64 a (.f64 -4 c))))
(fma.f64 1/2 (/.f64 a b) (.f64 (/.f64 2 (.f64 a (.f64 -4 c))) (.f64 a b)))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (.f64 1/2 (/.f64 a b))) (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2)) (pow.f64 b 3))))
(+.f64 (fma.f64 2 (/.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (.f64 1/2 (/.f64 a b))) (.f64 -1/8 (/.f64 a (/.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)))))
(fma.f64 2 (/.f64 (.f64 a b) (.f64 a (.f64 -4 c))) (fma.f64 1/2 (/.f64 a b) (.f64 (.f64 (/.f64 a (pow.f64 b 3)) (.f64 a (*.f64 -4 c))) -1/8)))
(fma.f64 2 (.f64 (/.f64 a (.f64 a (.f64 -4 c))) b) (fma.f64 1/2 (/.f64 a b) (.f64 (.f64 (/.f64 a (pow.f64 b 3)) (.f64 a (*.f64 -4 c))) -1/8)))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (.f64 1/2 (/.f64 a b)))) (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2)) (pow.f64 b 3))))
(+.f64 (fma.f64 1/16 (/.f64 a (/.f64 (pow.f64 b 5) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4))) (fma.f64 2 (/.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (.f64 1/2 (/.f64 a b)))) (.f64 -1/8 (/.f64 a (/.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)))))
(fma.f64 1/16 (.f64 (/.f64 a (pow.f64 b 5)) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4)) (fma.f64 2 (/.f64 (.f64 a b) (.f64 a (.f64 -4 c))) (fma.f64 1/2 (/.f64 a b) (.f64 (.f64 (/.f64 a (pow.f64 b 3)) (.f64 a (.f64 -4 c))) -1/8))))
(fma.f64 1/16 (.f64 (/.f64 a (pow.f64 b 5)) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4)) (fma.f64 2 (.f64 (/.f64 a (.f64 a (.f64 -4 c))) b) (fma.f64 1/2 (/.f64 a b) (.f64 (.f64 (/.f64 a (pow.f64 b 3)) (.f64 a (.f64 -4 c))) -1/8))))
(*.f64 -1/2 (/.f64 a b))
(/.f64 (*.f64 -1/2 a) b)
(*.f64 (/.f64 a b) -1/2)
(-.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (*.f64 1/2 (/.f64 a b)))
(+.f64 (.f64 1/8 (/.f64 a (/.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)))) (/.f64 (.f64 -1/2 a) b))
(fma.f64 1/8 (.f64 (/.f64 a (pow.f64 b 3)) (.f64 a (.f64 -4 c))) (.f64 (/.f64 a b) -1/2))
(-.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (*.f64 1/2 (/.f64 a b))))
(-.f64 (.f64 1/8 (/.f64 a (/.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)))) (fma.f64 1/16 (/.f64 a (/.f64 (pow.f64 b 5) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4))) (.f64 1/2 (/.f64 a b))))
(-.f64 (fma.f64 1/8 (.f64 (/.f64 a (pow.f64 b 3)) (.f64 a (.f64 -4 c))) (.f64 (/.f64 a b) -1/2)) (/.f64 (.f64 (.f64 1/16 a) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4)) (pow.f64 b 5)))
(fma.f64 1/8 (.f64 (/.f64 a (pow.f64 b 3)) (.f64 a (.f64 -4 c))) (fma.f64 (/.f64 a b) -1/2 (/.f64 (.f64 -1/16 a) (/.f64 (pow.f64 b 5) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4)))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (.f64 5/128 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6)) (pow.f64 b 7)))) (+.f64 (.f64 1/16 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (*.f64 1/2 (/.f64 a b))))
(-.f64 (fma.f64 1/8 (/.f64 a (/.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (.f64 5/128 (/.f64 a (/.f64 (pow.f64 b 7) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6))))) (fma.f64 1/16 (/.f64 a (/.f64 (pow.f64 b 5) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4))) (.f64 1/2 (/.f64 a b))))
(-.f64 (fma.f64 1/8 (.f64 (/.f64 a (pow.f64 b 3)) (.f64 a (.f64 -4 c))) (/.f64 5/128 (/.f64 (pow.f64 b 7) (.f64 a (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 6))))) (fma.f64 1/2 (/.f64 a b) (/.f64 (.f64 (.f64 1/16 a) (pow.f64 (sqrt.f64 (.f64 a (.f64 -4 c))) 4)) (pow.f64 b 5))))
(fma.f64 1/8 (.f64 (/.f64 a (pow.f64 b 3)) (.f64 a (.f64 -4 c))) (fma.f64 5/128 (.f64 (/.f64 a (pow.f64 b 7)) (pow.f64 (.f64 a (.f64 -4 c)) 3)) (fma.f64 (/.f64 a b) -1/2 (/.f64 (.f64 -1/16 a) (/.f64 (pow.f64 b 5) (pow.f64 (sqrt.f64 (.f64 a (*.f64 -4 c))) 4))))))

prune178.0ms (2.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	206	3	209
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	208	14	222

Error

3.5b

Counts

222 → 14

Alt Table

Status	Error	Program
	36.5b	(/.f64 (-.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) (pow.f64 (cbrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) 2))) b) (.f64 2 a))
	35.7b	(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2) b) (*.f64 2 a))
	47.6b	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b))) -1)
	47.1b	(pow.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 2)
	45.4b	(pow.f64 (.f64 2 (fma.f64 1/2 (/.f64 a b) (.f64 (/.f64 2 (.f64 a (.f64 -4 c))) (*.f64 a b)))) -1)
▶	32.3b	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	45.9b	(neg.f64 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
	40.7b	(/.f64 (neg.f64 c) b)
✓	32.2b	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) -1)
	43.4b	(/.f64 (-.f64 (-.f64 (.f64 2 (.f64 (/.f64 c b) a)) b) b) (*.f64 2 a))
	32.7b	(.f64 (cbrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))) (pow.f64 (cbrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))) 2))
	47.2b	(.f64 1/4 (/.f64 a (/.f64 (.f64 a b) (*.f64 -4 c))))
	43.3b	(/.f64 (neg.f64 b) a)
	52.5b	(-.f64 (.f64 -2 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b 5)) (.f64 a a))) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))

Compiler

Compiled 5947 to 3878 computations (34.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))
✓	0.2b	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
	0.4b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
	12.7b	(sqrt.f64 (.f64 a (.f64 c -4)))

series26.0ms (0.3%)

Counts

2 → 26

Calls

18 calls:

Time	Variable		Point	Expression
5.0ms	c	@	inf	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
3.0ms	c	@	-inf	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
2.0ms	a	@	-inf	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
2.0ms	c	@	inf	(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))
2.0ms	a	@	inf	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))

rewrite58.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`prod-diff_binary64`
249×	`log1p-udef_binary64`
143×	`add-sqr-sqrt_binary64`
137×	`pow1_binary64`
136×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	283	33
2	3645	33

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

Inputs
(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))

Outputs

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

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

simplify29.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

746×	`times-frac_binary64`
398×	`associate-/l*_binary64`
369×	`associate-/r*_binary64`
289×	`associate-r_binary64`
252×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	958
1	315	885
2	1037	843

Stop Event

1×	node limit

Counts

87 → 108

Calls

Call 1

Inputs
(.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) a))
(-.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/2 (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (.f64 1/2 (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 b 4) (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)))) (.f64 1/2 (/.f64 b a))))
(.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))
(-.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(-.f64 (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(-.f64 (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (+.f64 (.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 8) (.f64 a (pow.f64 b 7)))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3))))))
(*.f64 -1 (/.f64 b a))
(neg.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a)))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a)))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a))))
(sqrt.f64 (.f64 -4 (.f64 c a)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (sqrt.f64 (.f64 -4 (*.f64 c a))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (sqrt.f64 (.f64 -4 (.f64 c a)))) (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (+.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) (.f64 1/16 (/.f64 (pow.f64 b 6) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 5))))) (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 3))))
b
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2) b)) b)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) b) (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5))) b)) (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 4) (pow.f64 b 3))))
(*.f64 -1 b)
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2) b)) b))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) b))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 6) (pow.f64 b 5))) b)))
b
b

Outputs
(.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) a))
(.f64 1/2 (/.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) a))
(.f64 (/.f64 1/2 a) (sqrt.f64 (.f64 c (*.f64 a -4))))
(-.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/2 (/.f64 b a)))
(.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) a) (/.f64 b a)))
(.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) a) (/.f64 b a)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (.f64 1/2 (/.f64 b a)))
(+.f64 (fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a) (.f64 1/4 (/.f64 (/.f64 (.f64 b b) a) (sqrt.f64 (.f64 -4 (.f64 c a)))))) (*.f64 -1/2 (/.f64 b a)))
(fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (fma.f64 1/4 (/.f64 (/.f64 (.f64 b b) (sqrt.f64 (.f64 c (.f64 a -4)))) a) (.f64 (/.f64 b a) -1/2)))
(fma.f64 1/4 (/.f64 b (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) (/.f64 b a))) (.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) a) (/.f64 b a))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/4 (/.f64 (pow.f64 b 2) (.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 b 4) (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)))) (.f64 1/2 (/.f64 b a))))
(-.f64 (fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a) (.f64 1/4 (/.f64 (/.f64 (.f64 b b) a) (sqrt.f64 (.f64 -4 (.f64 c a)))))) (fma.f64 1/16 (/.f64 (/.f64 (pow.f64 b 4) a) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)) (*.f64 1/2 (/.f64 b a))))
(-.f64 (fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (.f64 1/4 (/.f64 (/.f64 (.f64 b b) (sqrt.f64 (.f64 c (.f64 a -4)))) a))) (fma.f64 1/2 (/.f64 b a) (.f64 1/16 (/.f64 (pow.f64 b 4) (.f64 a (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 3))))))
(fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) a) (fma.f64 1/4 (/.f64 b (/.f64 (sqrt.f64 (.f64 c (.f64 a -4))) (/.f64 b a))) (fma.f64 (/.f64 b a) -1/2 (.f64 (/.f64 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) 3)) a) -1/16))))
(.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))
(.f64 1/4 (/.f64 (.f64 c (.f64 a -4)) (.f64 a b)))
(/.f64 (.f64 (.f64 c a) -1) (*.f64 a b))
(-.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (.f64 -1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(fma.f64 1/4 (/.f64 (.f64 c (.f64 a -4)) (.f64 a b)) (/.f64 (.f64 -1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) a)) (pow.f64 b 3)))
(fma.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (.f64 a (pow.f64 b 3))) -1/16 (/.f64 (.f64 (.f64 c a) -1) (.f64 a b)))
(-.f64 (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))))
(+.f64 (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (.f64 -1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (*.f64 a (pow.f64 b 3)))))
(fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 6) (.f64 a (pow.f64 b 5))) (fma.f64 1/4 (/.f64 (.f64 c (.f64 a -4)) (.f64 a b)) (/.f64 (.f64 -1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) 4) a)) (pow.f64 b 3))))
(fma.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (.f64 a (pow.f64 b 3))) -1/16 (fma.f64 1/32 (/.f64 (pow.f64 (.f64 c (.f64 a -4)) 3) (.f64 a (pow.f64 b 5))) (/.f64 (.f64 (.f64 c a) -1) (*.f64 a b))))
(-.f64 (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (+.f64 (.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 8) (.f64 a (pow.f64 b 7)))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3))))))
(-.f64 (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5))) (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))) (fma.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 8) (.f64 a (pow.f64 b 7))) (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3))))))
(-.f64 (fma.f64 1/4 (/.f64 (.f64 c (.f64 a -4)) (.f64 a b)) (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 6) (.f64 a (pow.f64 b 5))))) (fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (.f64 a (pow.f64 b 3))) (.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 8) (.f64 a (pow.f64 b 7))))))
(-.f64 (fma.f64 1/32 (/.f64 (pow.f64 (.f64 c (.f64 a -4)) 3) (.f64 a (pow.f64 b 5))) (/.f64 (.f64 (.f64 c a) -1) (.f64 a b))) (fma.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 8) (.f64 a (pow.f64 b 7))) (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (pow.f64 b 3)) (/.f64 1/16 a))))
(*.f64 -1 (/.f64 b a))
(/.f64 (neg.f64 b) a)
(neg.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a)))
(neg.f64 (fma.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (*.f64 a b)) (/.f64 b a)))
(-.f64 (.f64 (/.f64 (.f64 c (.f64 a -4)) (.f64 a b)) -1/4) (/.f64 b a))
(-.f64 (/.f64 (neg.f64 b) a) (/.f64 (.f64 (.f64 c a) -1) (*.f64 a b)))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a)))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (fma.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (*.f64 a b)) (/.f64 b a)))
(-.f64 (.f64 (/.f64 1/16 (pow.f64 b 3)) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) a)) (fma.f64 1/4 (/.f64 (.f64 c (.f64 a -4)) (.f64 a b)) (/.f64 b a)))
(-.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (pow.f64 b 3)) (/.f64 1/16 a)) (+.f64 (/.f64 b a) (/.f64 (.f64 (.f64 c a) -1) (.f64 a b))))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (+.f64 (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5)))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b))) (/.f64 b a))))
(-.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (.f64 a (pow.f64 b 3)))) (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (.f64 a (pow.f64 b 5))) (fma.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)) (/.f64 b a))))
(-.f64 (.f64 (/.f64 1/16 (pow.f64 b 3)) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) a)) (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 6) (.f64 a (pow.f64 b 5))) (fma.f64 1/4 (/.f64 (.f64 c (.f64 a -4)) (*.f64 a b)) (/.f64 b a))))
(-.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (pow.f64 b 3)) (/.f64 1/16 a)) (+.f64 (/.f64 b a) (fma.f64 1/32 (/.f64 (pow.f64 (.f64 c (.f64 a -4)) 3) (.f64 a (pow.f64 b 5))) (/.f64 (.f64 (.f64 c a) -1) (*.f64 a b)))))
(sqrt.f64 (.f64 -4 (.f64 c a)))
(sqrt.f64 (.f64 c (.f64 a -4)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (sqrt.f64 (.f64 -4 (*.f64 c a))))
(fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 -4 (.f64 c a)))) (sqrt.f64 (.f64 -4 (*.f64 c a))))
(fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 c (.f64 a -4)))) (sqrt.f64 (.f64 c (*.f64 a -4))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (sqrt.f64 (.f64 -4 (.f64 c a)))) (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 -4 (.f64 c a)))) (sqrt.f64 (.f64 -4 (.f64 c a)))) (.f64 -1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 c (.f64 a -4)))) (sqrt.f64 (.f64 c (.f64 a -4)))) (/.f64 (.f64 -1/8 (pow.f64 b 4)) (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 3)))
(fma.f64 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 3)) -1/8 (fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 c (.f64 a -4)))) (sqrt.f64 (.f64 c (*.f64 a -4)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (sqrt.f64 (.f64 -4 (.f64 c a))))) (+.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) (.f64 1/16 (/.f64 (pow.f64 b 6) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 5))))) (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 3))))
(-.f64 (+.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 -4 (.f64 c a)))) (sqrt.f64 (.f64 -4 (.f64 c a)))) (/.f64 (.f64 1/16 (pow.f64 b 6)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 5))) (.f64 1/8 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 3))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 c (.f64 a -4)))) (fma.f64 1/16 (/.f64 (pow.f64 b 6) (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 5)) (sqrt.f64 (.f64 c (.f64 a -4))))) (/.f64 (.f64 -1/8 (pow.f64 b 4)) (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 3)))
(fma.f64 (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 3)) -1/8 (fma.f64 1/2 (/.f64 (.f64 b b) (sqrt.f64 (.f64 c (.f64 a -4)))) (fma.f64 1/16 (/.f64 (pow.f64 b 6) (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 5)) (sqrt.f64 (.f64 c (*.f64 a -4))))))
b
(+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2) b)) b)
(fma.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b) b)
(fma.f64 1/2 (/.f64 (.f64 c (.f64 a -4)) b) b)
(+.f64 b (/.f64 (.f64 (.f64 c a) -2) b))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) b) (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b) b) (.f64 -1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 4) (pow.f64 b 3))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 c (.f64 a -4)) b) b) (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) 4) (pow.f64 b 3)) -1/8))
(fma.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (pow.f64 b 3)) -1/8 (+.f64 b (/.f64 (.f64 (.f64 c a) -2) b)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5))) b)) (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 4) (pow.f64 b 3))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b) (fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 5)) b)) (.f64 -1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 4) (pow.f64 b 3))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 c (.f64 a -4)) b) (fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 6) (pow.f64 b 5)) b)) (.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) 4) (pow.f64 b 3)) -1/8))
(fma.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (pow.f64 b 3)) -1/8 (+.f64 b (fma.f64 1/16 (/.f64 (pow.f64 (.f64 c (.f64 a -4)) 3) (pow.f64 b 5)) (/.f64 (.f64 (.f64 c a) -2) b))))
(*.f64 -1 b)
(neg.f64 b)
(neg.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2) b)) b))
(neg.f64 (fma.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b) b))
(-.f64 (.f64 (/.f64 (.f64 c (*.f64 a -4)) b) -1/2) b)
(-.f64 (neg.f64 b) (/.f64 (.f64 (.f64 c a) -2) b))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) b))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (fma.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2) b) b))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (pow.f64 b 3))) (fma.f64 1/2 (/.f64 (.f64 c (*.f64 a -4)) b) b))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (pow.f64 b 3))) (+.f64 b (/.f64 (.f64 (*.f64 c a) -2) b)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 6) (pow.f64 b 5))) b)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3))) (fma.f64 1/2 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) b) (fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 6) (pow.f64 b 5)) b)))
(-.f64 (fma.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (pow.f64 b 3)) (.f64 (/.f64 (.f64 c (.f64 a -4)) b) -1/2)) (fma.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) 6) (pow.f64 b 5)) b))
(-.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 4) (pow.f64 b 3))) (/.f64 (.f64 (.f64 c a) -2) b)) (fma.f64 1/16 (/.f64 (pow.f64 (.f64 c (*.f64 a -4)) 3) (pow.f64 b 5)) b))
b
b

prune183.0ms (2.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	206	2	208
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	209	13	222

Error

3.5b

Counts

222 → 13

Alt Table

Status	Error	Program
	47.6b	(.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4)))) b) (/.f64 1/2 a))
	36.5b	(/.f64 (-.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) (pow.f64 (cbrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))) 2))) b) (.f64 2 a))
	35.7b	(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 c (.f64 a -4) (.f64 b b)) 1/4) 2) b) (*.f64 2 a))
	45.7b	(/.f64 (.f64 (-.f64 (fma.f64 b b (.f64 a (.f64 c -4))) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	32.2b	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))) -1)
	45.9b	(neg.f64 (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))
	40.7b	(/.f64 (neg.f64 c) b)
	47.6b	(pow.f64 (.f64 2 (/.f64 a (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b))) -1)
	43.4b	(/.f64 (-.f64 (-.f64 (.f64 2 (.f64 (/.f64 c b) a)) b) b) (*.f64 2 a))
	45.4b	(pow.f64 (.f64 2 (fma.f64 1/2 (/.f64 a b) (.f64 (/.f64 2 (.f64 a (.f64 -4 c))) (*.f64 a b)))) -1)
	47.2b	(.f64 1/4 (/.f64 a (/.f64 (.f64 a b) (*.f64 -4 c))))
	43.3b	(/.f64 (neg.f64 b) a)
	52.5b	(-.f64 (.f64 -2 (.f64 (/.f64 (pow.f64 c 3) (pow.f64 b 5)) (.f64 a a))) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))

Compiler

Compiled 5300 to 3354 computations (36.7% saved)

regimes2.9s (36.9%)

Accuracy

Total 6.9b remaining (72.3%)

Threshold costs 0b (0%)

Counts

222 → 3

Compiler

Compiled 4226 to 2547 computations (39.7% saved)

bsearch71.0ms (0.9%)

Algorithm

2×	binary-search

Calls

2 calls:

39.0ms	b
30.0ms	b

Steps

Iters	Point		Range
3.1e-89	∈ [	8.7468426915874e-90	,	8.69570712673793e-87	]
-6.8e+148	∈ [	-7.658699911855324e+156	,	-5.891345877016106e+148	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-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	25	50
1	37	50
2	48	50
3	55	50
4	58	50

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 b -68000000000000005601788420534006932377548335890104754289792133620000380304007035858461519343183309932278721878853841197202513458050861837058584870912) (-.f64 (/.f64 c b) (/.f64 b a)) (if (<=.f64 b 8887307136961527/286687326998758938951352611912760867599570623646035140467198604923365359511060601008752319138765710819328) (/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))) b) (*.f64 2 a)) (/.f64 (neg.f64 c) b)))

Outputs

(if (<=.f64 b -68000000000000005601788420534006932377548335890104754289792133620000380304007035858461519343183309932278721878853841197202513458050861837058584870912) (-.f64 (/.f64 c b) (/.f64 b a)) (if (<=.f64 b 8887307136961527/286687326998758938951352611912760867599570623646035140467198604923365359511060601008752319138765710819328) (/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))) b) (*.f64 2 a)) (/.f64 (neg.f64 c) b)))

(if (<=.f64 b -68000000000000005601788420534006932377548335890104754289792133620000380304007035858461519343183309932278721878853841197202513458050861837058584870912) (-.f64 (/.f64 c b) (/.f64 b a)) (if (<=.f64 b 8887307136961527/286687326998758938951352611912760867599570623646035140467198604923365359511060601008752319138765710819328) (/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 c a) -4))) b) (*.f64 a 2)) (/.f64 (neg.f64 c) b)))

end177.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 327 to 220 computations (32.7% saved)

Details

analyze966.0ms (12.2%)

sample2.2s (27.8%)

preprocess50.0ms (0.6%)

simplify28.0ms (0.4%)

prune3.0ms (0%)

localize13.0ms (0.2%)

series35.0ms (0.4%)

rewrite77.0ms (1%)

simplify48.0ms (0.6%)

prune174.0ms (2.2%)

localize11.0ms (0.1%)

series15.0ms (0.2%)

rewrite81.0ms (1%)

simplify48.0ms (0.6%)

prune195.0ms (2.5%)

localize10.0ms (0.1%)

series199.0ms (2.5%)

rewrite74.0ms (0.9%)

simplify38.0ms (0.5%)

prune178.0ms (2.2%)

localize9.0ms (0.1%)

series26.0ms (0.3%)

rewrite58.0ms (0.7%)

simplify29.0ms (0.4%)

prune183.0ms (2.3%)

regimes2.9s (36.9%)

bsearch71.0ms (0.9%)

simplify3.0ms (0%)

end177.0ms (2.2%)

Profiling