Details

analyze617.0ms (9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.1s (31.2%)

Results

674.0ms	5345×	body	128	valid
596.0ms	1183×	body	2048	valid
312.0ms	760×	body	1024	valid
249.0ms	401×	body	4096	valid
136.0ms	1101×	body	128	invalid
122.0ms	387×	body	512	valid
40.0ms	180×	body	256	valid

Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess36.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

423×	`rules-4_binary64`
275×	`rules-13_binary64`
233×	`rules-15-rev_binary64`
207×	`rules-15_binary64`
182×	`rules-20_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	104
1	94	100
2	254	100
3	747	88
4	2965	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 (.f64 4 a) c)))) (.f64 2 a))
(/.f64 (+.f64 (neg.f64 a) (sqrt.f64 (-.f64 (.f64 a a) (.f64 (.f64 4 b) c)))) (.f64 2 b))
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 c) a)))) (.f64 2 c))
(/.f64 (+.f64 (neg.f64 c) (sqrt.f64 (-.f64 (.f64 c c) (.f64 (.f64 4 a) b)))) (.f64 2 a))

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

Compiler

Compiled 20 to 14 computations (30% saved)

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

353×	`rules-1_binary64`
331×	`rules-6-rev_binary64`
292×	`rules-5-rev_binary64`
266×	`rules-1-rev_binary64`
247×	`rules-20_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	32	25
2	77	25
3	223	22
4	905	22
5	4381	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 (.f64 4 a) c)))) (.f64 2 a))

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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

34.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.3b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b) (*.f64 a 2))

Compiler

Compiled 71 to 47 computations (33.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
✓	1.3b	(fma.f64 b b (.f64 a (.f64 c -4)))
✓	1.3b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)
✓	22.6b	(sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4))))

series112.0ms (1.6%)

Counts

4 → 96

Calls

36 calls:

Time	Variable		Point	Expression
9.0ms	a	@	inf	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
9.0ms	a	@	-inf	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
8.0ms	c	@	inf	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
7.0ms	c	@	-inf	(/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b) (*.f64 a 2))
5.0ms	c	@	-inf	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) b)

rewrite73.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

297×	`rules-34-rev_binary64`
151×	`rules-24_binary64`
138×	`add-sqr-sqrt_binary64`
131×	`pow1_binary64`
131×	`rules-40_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	311	59
2	4046	59

Stop Event

1×	node limit

Counts

4 → 178

Calls

Call 1

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

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

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

526×	`rules-20_binary64`
452×	`rules-13_binary64`
370×	`rules-15-rev_binary64`
353×	`rules-14-rev_binary64`
203×	`rules-21_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2301
1	454	2116
2	2123	2107

Stop Event

1×	node limit

Counts

274 → 252

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

prune200.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	242	10	252
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	243	10	253

Error

6.4b

Counts

253 → 10

Alt Table

Status	Error	Program
	40.6b	(/.f64 (neg.f64 c) b)
	37.8b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b) (*.f64 a 2))
	36.2b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b))) (*.f64 a 2))
	38.7b	(/.f64 (-.f64 (.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) b) (.f64 a 2))
	34.4b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)) (.f64 a 2)))
	43.6b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 3/2)) b) (*.f64 a 2))
▶	34.3b	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1 (.f64 a 2)))
	51.7b	(/.f64 (-.f64 (sqrt.f64 (pow.f64 b 2)) b) (*.f64 a 2))
	34.9b	(/.f64 (-.f64 (/.f64 1 (fabs.f64 (/.f64 1 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) b) (*.f64 a 2))
	46.0b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 6001 to 3937 computations (34.4% 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 (.f64 a 2)))
✓	0.5b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
✓	14.2b	(sqrt.f64 (.f64 a (.f64 c -4)))

series279.0ms (4.1%)

Counts

4 → 38

Calls

33 calls:

Time	Variable		Point	Expression
25.0ms	a	@	-inf	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1 (.f64 a 2)))
25.0ms	a	@	inf	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1 (.f64 a 2)))
24.0ms	c	@	inf	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1 (.f64 a 2)))
19.0ms	c	@	-inf	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1 (.f64 a 2)))
17.0ms	c	@	inf	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)

rewrite74.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

328×	`rules-34-rev_binary64`
154×	`add-sqr-sqrt_binary64`
146×	`pow1_binary64`
146×	`rules-40_binary64`
146×	`rules-41_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
1	356	57
2	4572	57

Stop Event

1×	node limit

Counts

4 → 158

Calls

Call 1

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

Outputs
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(hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 a) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a)) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))) 2) (cbrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))) (sqrt.f64 (.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))) 0)))) (#(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 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (#(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)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))) (#(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 /.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 3/2) (fma.f64 b b (.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 (pow.f64 (fma.f64 b b (.f64 a (.f64 c -4))) 3/2) 1/3)))) (#(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 neg.f64 (neg.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))) (#(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 fabs.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.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 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 fma.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) 1 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -4)))) (cbrt.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x fma.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))))) 0)))) (#(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))))))))))

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

549×	`rules-15-rev_binary64`
510×	`rules-20_binary64`
273×	`rules-14-rev_binary64`
265×	`rules-13_binary64`
177×	`rules-21_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	119	1408
1	427	1300
2	2097	1300

Stop Event

1×	node limit

Counts

196 → 227

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

prune164.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	222	5	227
Fresh	7	2	9
Picked	0	1	1
Done	0	0	0
Total	229	8	237

Error

0.2b

Counts

237 → 8

Alt Table

Status	Error	Program
	40.6b	(/.f64 (neg.f64 c) b)
▶	34.2b	(/.f64 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) a) 2)
✓	34.3b	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1 (.f64 a 2)))
	34.2b	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))
	45.5b	(.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (.f64 c -4)) (sqrt.f64 a))) b) (/.f64 1 (.f64 a 2)))
	47.2b	(.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4)))) b) (/.f64 1 (.f64 a 2)))
	34.4b	(.f64 (-.f64 (hypot.f64 b (.f64 (cbrt.f64 (.f64 a (.f64 c -4))) (cbrt.f64 (sqrt.f64 (.f64 a (.f64 c -4)))))) b) (/.f64 1 (*.f64 a 2)))
	46.0b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 5675 to 3966 computations (30.1% saved)

localize8.0ms (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))))
✓	0.1b	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) a)
	0.5b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
	14.2b	(sqrt.f64 (.f64 a (.f64 c -4)))

series113.0ms (1.6%)

Counts

1 → 12

Calls

9 calls:

Time	Variable		Point	Expression
27.0ms	a	@	-inf	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) a)
21.0ms	a	@	inf	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) a)
21.0ms	c	@	inf	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) a)
15.0ms	c	@	-inf	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) a)
10.0ms	c	@	0	(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) a)

rewrite47.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

254×	`rules-34-rev_binary64`
203×	`rules-21_binary64`
140×	`rules-22_binary64`
139×	`rules-24_binary64`
119×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	264	18
2	3516	18

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

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

Outputs

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

simplify23.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

327×	`rules-6_binary64`
282×	`rules-12-rev_binary64`
264×	`rules-15-rev_binary64`
257×	`rules-6-rev_binary64`
239×	`rules-20_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	67	539
1	235	500
2	1021	500

Stop Event

1×	node limit

Counts

46 → 58

Calls

Call 1

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

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

prune160.0ms (2.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	213	9	222

Error

0.2b

Counts

222 → 9

Alt Table

Status	Error	Program
	45.5b	(.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (.f64 c -4)) (sqrt.f64 a))) b) (/.f64 1 (.f64 a 2)))
	34.3b	(/.f64 (/.f64 (-.f64 (hypot.f64 b (.f64 (cbrt.f64 (sqrt.f64 (.f64 a (.f64 c -4)))) (cbrt.f64 (.f64 a (*.f64 c -4))))) b) a) 2)
	40.6b	(/.f64 (neg.f64 c) b)
✓	34.2b	(/.f64 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) a) 2)
✓	34.3b	(.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) (/.f64 1 (.f64 a 2)))
▶	34.2b	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))
	47.2b	(/.f64 (/.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4)))) b) a) 2)
	45.5b	(/.f64 (/.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (.f64 c -4)))) b) a) 2)
	46.0b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 5157 to 3533 computations (31.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))
✓	0.1b	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))
	0.5b	(-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b)
	14.2b	(sqrt.f64 (.f64 a (.f64 c -4)))

series325.0ms (4.7%)

Counts

2 → 24

Calls

18 calls:

Time	Variable		Point	Expression
48.0ms	c	@	inf	(/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))
42.0ms	a	@	-inf	(/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))
37.0ms	a	@	inf	(/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))
36.0ms	c	@	-inf	(/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b))
27.0ms	a	@	-inf	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))) b)))

rewrite60.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

328×	`rules-34-rev_binary64`
154×	`add-sqr-sqrt_binary64`
146×	`pow1_binary64`
146×	`rules-40_binary64`
146×	`rules-41_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	45
1	354	42
2	4501	42

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

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

Outputs

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

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

497×	`rules-20_binary64`
474×	`rules-12-rev_binary64`
471×	`rules-15-rev_binary64`
253×	`rules-14-rev_binary64`
245×	`rules-13_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	106	1078
1	400	969
2	1963	969

Stop Event

1×	node limit

Counts

96 → 120

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))))
(.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (*.f64 c a)))))
(+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (*.f64 c a))))))
(+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (+.f64 (.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))) (/.f64 (.f64 a (pow.f64 b 2)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3))))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (+.f64 (.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))) (/.f64 (.f64 a (pow.f64 b 2)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)))) (.f64 1/4 (/.f64 (.f64 a (pow.f64 b 4)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 5))))
(.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)))
(+.f64 (.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (/.f64 a b))
(-.f64 (+.f64 (.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (/.f64 a b)) (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (+.f64 (.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (/.f64 a b))) (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))))
(*.f64 -1 (/.f64 a b))
(-.f64 (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (/.f64 a b))
(-.f64 (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (+.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (/.f64 a b)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (.f64 5/64 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6)) (pow.f64 b 7)))) (+.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (/.f64 a b)))

Outputs
(.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) a))
(.f64 1/2 (/.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) a))
(/.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) (/.f64 a 1/2))
(-.f64 (.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a)) (.f64 1/2 (/.f64 b a)))
(fma.f64 1/2 (/.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) a) (neg.f64 (*.f64 1/2 (/.f64 b a))))
(.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) 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)))
(-.f64 (.f64 1/4 (/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 c (.f64 -4 a)))))) (.f64 1/2 (-.f64 (/.f64 b a) (/.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) a))))
(-.f64 (.f64 b (/.f64 b (.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) (/.f64 a 1/4)))) (.f64 1/2 (-.f64 (/.f64 b a) (/.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) 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 (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 c (.f64 -4 a))) a) (.f64 1/4 (/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 c (.f64 -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 -4 a))) 3))))))
(-.f64 (fma.f64 1/4 (/.f64 (/.f64 (.f64 b b) (sqrt.f64 (.f64 c (.f64 -4 a)))) a) (/.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) (/.f64 a 1/2))) (fma.f64 1/16 (/.f64 (/.f64 (pow.f64 b 4) a) (pow.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) 3)) (/.f64 b (/.f64 a 1/2))))
(.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)))
(.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (.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)))))
(fma.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)) (neg.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (/.f64 (.f64 a (pow.f64 b 3)) 1/16))))
(-.f64 (.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (.f64 a b))) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (*.f64 a (/.f64 (pow.f64 b 3) 1/16))))
(-.f64 (.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (.f64 a b))) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (*.f64 (pow.f64 b 3) (/.f64 a 1/16))))
(-.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 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (/.f64 (.f64 a (pow.f64 b 3)) 1/16)))
(-.f64 (fma.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (.f64 a b)) (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 6) (.f64 a (pow.f64 b 5))))) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (.f64 a (/.f64 (pow.f64 b 3) 1/16))))
(-.f64 (fma.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (.f64 a b)) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 6) (.f64 a (/.f64 (pow.f64 b 5) 1/32)))) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (*.f64 (pow.f64 b 3) (/.f64 a 1/16))))
(-.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 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (/.f64 (*.f64 a (pow.f64 b 3)) 1/16))))
(-.f64 (fma.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (.f64 a b)) (.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 6) (.f64 a (pow.f64 b 5))))) (fma.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 8) (.f64 a (pow.f64 b 7))) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (*.f64 a (/.f64 (pow.f64 b 3) 1/16)))))
(-.f64 (fma.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (.f64 a b)) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 6) (.f64 a (/.f64 (pow.f64 b 5) 1/32)))) (fma.f64 5/256 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 8) (.f64 a (pow.f64 b 7))) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (.f64 (pow.f64 b 3) (/.f64 a 1/16)))))
(*.f64 -1 (/.f64 b a))
(*.f64 (/.f64 b a) -1)
(/.f64 b (neg.f64 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)))
(neg.f64 (fma.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (*.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 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (/.f64 (.f64 a (pow.f64 b 3)) 1/16)) (fma.f64 1/4 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (.f64 a b)) (/.f64 b a)))
(-.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (.f64 a (/.f64 (pow.f64 b 3) 1/16))) (fma.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (.f64 a b)) (/.f64 b a)))
(-.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (.f64 (pow.f64 b 3) (/.f64 a 1/16))) (fma.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (.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 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (/.f64 (.f64 a (pow.f64 b 3)) 1/16)) (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 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (.f64 a (/.f64 (pow.f64 b 3) 1/16))) (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 6) (.f64 a (pow.f64 b 5))) (fma.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (*.f64 a b)) (/.f64 b a))))
(-.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (.f64 (pow.f64 b 3) (/.f64 a 1/16))) (fma.f64 1/32 (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 6) (.f64 a (pow.f64 b 5))) (fma.f64 1/4 (/.f64 (.f64 c (.f64 -4 a)) (*.f64 a b)) (/.f64 b a))))
(.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (*.f64 c a)))))
(.f64 2 (/.f64 a (sqrt.f64 (.f64 c (*.f64 -4 a)))))
(+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (*.f64 c a))))))
(.f64 2 (+.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 2 (fma.f64 a (/.f64 b (.f64 c (.f64 -4 a))) (/.f64 a (sqrt.f64 (.f64 c (*.f64 -4 a))))))
(+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (+.f64 (.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))) (/.f64 (.f64 a (pow.f64 b 2)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3))))
(fma.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (fma.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a)))) (/.f64 (.f64 a (.f64 b b)) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 3))))
(fma.f64 a (.f64 b (/.f64 b (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 3))) (.f64 2 (fma.f64 a (/.f64 b (.f64 c (.f64 -4 a))) (/.f64 a (sqrt.f64 (.f64 c (.f64 -4 a)))))))
(-.f64 (+.f64 (.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (+.f64 (.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a))))) (/.f64 (.f64 a (pow.f64 b 2)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)))) (.f64 1/4 (/.f64 (.f64 a (pow.f64 b 4)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 5))))
(-.f64 (fma.f64 2 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (fma.f64 2 (/.f64 a (sqrt.f64 (.f64 -4 (.f64 c a)))) (/.f64 (.f64 a (.f64 b b)) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 3)))) (.f64 1/4 (.f64 a (/.f64 (pow.f64 b 4) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 5)))))
(-.f64 (fma.f64 a (.f64 b (/.f64 b (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 3))) (.f64 2 (fma.f64 a (/.f64 b (.f64 c (.f64 -4 a))) (/.f64 a (sqrt.f64 (.f64 c (.f64 -4 a))))))) (.f64 a (/.f64 (pow.f64 b 4) (/.f64 (pow.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) 5) 1/4))))
(.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)))
(/.f64 (.f64 a b) (/.f64 (.f64 c (*.f64 -4 a)) 4))
(.f64 b (/.f64 a (/.f64 (.f64 c (*.f64 -4 a)) 4)))
(+.f64 (.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (/.f64 a b))
(fma.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2)) (/.f64 a b))
(fma.f64 4 (.f64 b (/.f64 a (.f64 c (*.f64 -4 a)))) (/.f64 a b))
(fma.f64 4 (.f64 a (/.f64 b (.f64 c (*.f64 -4 a)))) (/.f64 a b))
(-.f64 (+.f64 (.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (/.f64 a b)) (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))))
(-.f64 (fma.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (/.f64 a b)) (.f64 1/4 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2) (pow.f64 b 3)))))
(-.f64 (fma.f64 4 (.f64 b (/.f64 a (.f64 c (.f64 -4 a)))) (/.f64 a b)) (.f64 (/.f64 (.f64 c (.f64 -4 a)) (pow.f64 b 3)) (*.f64 1/4 a)))
(-.f64 (fma.f64 4 (.f64 a (/.f64 b (.f64 c (.f64 -4 a)))) (/.f64 a b)) (.f64 a (/.f64 (.f64 c (.f64 -4 a)) (/.f64 (pow.f64 b 3) 1/4))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (+.f64 (.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2))) (/.f64 a b))) (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))))
(-.f64 (fma.f64 1/8 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 5))) (fma.f64 4 (/.f64 (.f64 a b) (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (/.f64 a b))) (.f64 1/4 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (pow.f64 b 3)))))
(-.f64 (fma.f64 1/8 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (pow.f64 b 5))) (fma.f64 4 (.f64 b (/.f64 a (.f64 c (.f64 -4 a)))) (/.f64 a b))) (.f64 (/.f64 (.f64 c (.f64 -4 a)) (pow.f64 b 3)) (.f64 1/4 a)))
(-.f64 (fma.f64 4 (.f64 a (/.f64 b (.f64 c (.f64 -4 a)))) (fma.f64 1/8 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (pow.f64 b 5))) (/.f64 a b))) (.f64 a (/.f64 (.f64 c (*.f64 -4 a)) (/.f64 (pow.f64 b 3) 1/4))))
(*.f64 -1 (/.f64 a b))
(/.f64 a (neg.f64 b))
(-.f64 (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (/.f64 a b))
(fma.f64 1/4 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 2) (pow.f64 b 3))) (neg.f64 (/.f64 a b)))
(-.f64 (.f64 (/.f64 (.f64 c (.f64 -4 a)) (pow.f64 b 3)) (.f64 1/4 a)) (/.f64 a b))
(-.f64 (.f64 a (/.f64 (.f64 c (*.f64 -4 a)) (/.f64 (pow.f64 b 3) 1/4))) (/.f64 a b))
(-.f64 (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (+.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (/.f64 a b)))
(-.f64 (.f64 1/4 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (pow.f64 b 3)))) (fma.f64 1/8 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) 4) (pow.f64 b 5))) (/.f64 a b)))
(-.f64 (.f64 (/.f64 (.f64 c (.f64 -4 a)) (pow.f64 b 3)) (.f64 1/4 a)) (fma.f64 1/8 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) 4) (pow.f64 b 5))) (/.f64 a b)))
(-.f64 (.f64 a (/.f64 (.f64 c (.f64 -4 a)) (/.f64 (pow.f64 b 3) 1/4))) (fma.f64 1/8 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 4) (pow.f64 b 5))) (/.f64 a b)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2)) (pow.f64 b 3))) (.f64 5/64 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6)) (pow.f64 b 7)))) (+.f64 (.f64 1/8 (/.f64 (.f64 a (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4)) (pow.f64 b 5))) (/.f64 a b)))
(-.f64 (fma.f64 1/4 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 2) (pow.f64 b 3))) (.f64 5/64 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 6) (pow.f64 b 7))))) (fma.f64 1/8 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 5))) (/.f64 a b)))
(-.f64 (fma.f64 1/4 (.f64 a (/.f64 (.f64 c (.f64 -4 a)) (pow.f64 b 3))) (.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 6) (/.f64 a (/.f64 (pow.f64 b 7) 5/64)))) (fma.f64 1/8 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) 4) (pow.f64 b 5))) (/.f64 a b)))
(-.f64 (fma.f64 5/64 (.f64 (pow.f64 (sqrt.f64 (.f64 c (.f64 -4 a))) 6) (/.f64 a (pow.f64 b 7))) (.f64 a (/.f64 (.f64 c (.f64 -4 a)) (/.f64 (pow.f64 b 3) 1/4)))) (fma.f64 1/8 (.f64 a (/.f64 (pow.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) 4) (pow.f64 b 5))) (/.f64 a b)))

prune155.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	222	2	224
Fresh	1	5	6
Picked	1	0	1
Done	1	1	2
Total	225	8	233

Error

0.2b

Counts

233 → 8

Alt Table

Status	Error	Program
	45.5b	(.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 (.f64 c -4)) (sqrt.f64 a))) b) (/.f64 1 (.f64 a 2)))
	34.3b	(/.f64 (/.f64 (-.f64 (hypot.f64 b (.f64 (cbrt.f64 (sqrt.f64 (.f64 a (.f64 c -4)))) (cbrt.f64 (.f64 a (*.f64 c -4))))) b) a) 2)
	47.2b	(/.f64 (/.f64 (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4)))) b) a) 2)
	47.2b	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4)))) b)))
	40.6b	(/.f64 (neg.f64 c) b)
✓	34.2b	(/.f64 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) b) a) 2)
	45.5b	(/.f64 1 (/.f64 (.f64 a 2) (-.f64 (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4)))) b)))
	46.0b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 5518 to 3839 computations (30.4% saved)

regimes1.8s (26.6%)

Accuracy

Total 9.9b remaining (97.4%)

Threshold costs 0b (0%)

Counts

147 → 5

Compiler

Compiled 10780 to 7946 computations (26.3% saved)

bsearch150.0ms (2.2%)

Algorithm

4×	binary-search

Calls

4 calls:

52.0ms	b
43.0ms	b
32.0ms	b
22.0ms	b

Steps

Iters	Point		Range
6.6e-22	∈ [	6.599747056875067e-22	,	5.554315795988415e-13	]
1.7e-46	∈ [	2.1227376748448865e-47	,	1.940649758097077e-46	]
6.2e-55	∈ [	7.597203000434052e-58	,	3.556640626292547e-53	]
-2.15e+105	∈ [	-9.888637842155317e+105	,	-4.943632541545772e+104	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	89

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 b -2150000000000000083690419259895400527725463227111497240051511683964300337512812128222177233987927780884480) (-.f64 (/.f64 c b) (/.f64 b a)) (if (<=.f64 b 8558165470020299/13803492693581127574869511724554050904902217944340773110325048447598592) (/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2)) (if (<=.f64 b 8741742960768907/51422017416287688817342786954917203280710495801049370729644032) (/.f64 (neg.f64 c) b) (if (<=.f64 b 1754580954436089/2658455991569831745807614120560689152) (/.f64 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) a) 2) (/.f64 (neg.f64 c) b)))))

Outputs

(if (<=.f64 b -2150000000000000083690419259895400527725463227111497240051511683964300337512812128222177233987927780884480) (-.f64 (/.f64 c b) (/.f64 b a)) (if (<=.f64 b 8558165470020299/13803492693581127574869511724554050904902217944340773110325048447598592) (/.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2)) (if (<=.f64 b 8741742960768907/51422017416287688817342786954917203280710495801049370729644032) (/.f64 (neg.f64 c) b) (if (<=.f64 b 1754580954436089/2658455991569831745807614120560689152) (/.f64 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) a) 2) (/.f64 (neg.f64 c) b)))))

end114.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 263 to 175 computations (33.5% saved)

Details

analyze617.0ms (9%)

sample2.1s (31.2%)

preprocess36.0ms (0.5%)

simplify33.0ms (0.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series112.0ms (1.6%)

rewrite73.0ms (1.1%)

simplify51.0ms (0.7%)

prune200.0ms (2.9%)

localize9.0ms (0.1%)

series279.0ms (4.1%)

rewrite74.0ms (1.1%)

simplify43.0ms (0.6%)

prune164.0ms (2.4%)

localize8.0ms (0.1%)

series113.0ms (1.6%)

rewrite47.0ms (0.7%)

simplify23.0ms (0.3%)

prune160.0ms (2.3%)

localize9.0ms (0.1%)

series325.0ms (4.7%)

rewrite60.0ms (0.9%)

simplify33.0ms (0.5%)

prune155.0ms (2.2%)

regimes1.8s (26.6%)

bsearch150.0ms (2.2%)

simplify1.0ms (0%)

end114.0ms (1.7%)

Profiling