Details

analyze689.0ms (11.5%)

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)

sample2.2s (37.1%)

Results

746.0ms	5461×	body	128	valid
601.0ms	1136×	body	2048	valid
297.0ms	708×	body	1024	valid
232.0ms	377×	body	4096	valid
154.0ms	1093×	body	128	invalid
129.0ms	388×	body	512	valid
49.0ms	186×	body	256	valid

Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess40.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

531×	`associate-/l*_binary64`
461×	`fma-neg_binary64`
449×	`div-sub_binary64`
277×	`fma-def_binary64`
251×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	104
1	115	96
2	308	96
3	784	88
4	1482	88
5	2839	88
0	3	3

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

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

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

Compiler

Compiled 20 to 14 computations (30% saved)

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
544×	`div-sub_binary64`
489×	`fma-neg_binary64`
405×	`times-frac_binary64`
262×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	100	24
3	259	22
4	460	22
5	840	22
6	1790	22
7	2999	22
8	3682	22
9	4742	22

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

36.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	36.3b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
▶	36.2b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.9b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	24.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series40.0ms (0.7%)

Counts

4 → 96

Calls

36 calls:

Time	Variable		Point	Expression
4.0ms	b	@	0	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	c	@	inf	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.0ms	a	@	inf	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
3.0ms	c	@	-inf	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
2.0ms	c	@	inf	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite50.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

176×	`add-sqr-sqrt_binary64`
169×	`*-un-lft-identity_binary64`
169×	`pow1_binary64`
165×	`add-exp-log_binary64`
165×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	347	62

Stop Event

1×	node limit

Counts

4 → 160

Calls

Call 1

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

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

simplify46.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

743×	`times-frac_binary64`
469×	`associate-/l*_binary64`
434×	`fma-def_binary64`
425×	`associate-/r*_binary64`
158×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	2060
1	415	1984
2	1475	1904

Stop Event

1×	node limit

Counts

256 → 236

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

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

prune169.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	228	8	236
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	229	9	238

Error

5.1b

Counts

238 → 9

Alt Table

Status	Error	Program
	56.6b	(.f64 (/.f64 1 (sqrt.f64 (.f64 a 2))) (/.f64 (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (sqrt.f64 (*.f64 a 2))))
	39.2b	(/.f64 (neg.f64 c) b)
▶	36.3b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.2b	(neg.f64 (/.f64 b a))
	46.3b	(/.f64 (/.f64 (neg.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	36.9b	(/.f64 (-.f64 (neg.f64 b) (pow.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 1/4) 2)) (*.f64 2 a))
	46.2b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 c (.f64 a -4)))) (*.f64 2 a))
	51.6b	(-.f64 (.f64 -2 (.f64 (/.f64 (.f64 a a) (pow.f64 b 5)) (pow.f64 c 3))) (fma.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a (/.f64 c b)))

Compiler

Compiled 6285 to 3667 computations (41.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
✓	1.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	24.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series20.0ms (0.3%)

Counts

4 → 96

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	b	@	0	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	c	@	inf	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	a	@	inf	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	c	@	-inf	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	a	@	-inf	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))

rewrite70.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

954×	`prod-diff_binary64`
141×	`add-sqr-sqrt_binary64`
134×	`*-un-lft-identity_binary64`
134×	`pow1_binary64`
131×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	279	62
2	3630	62

Stop Event

1×	node limit

Counts

4 → 130

Calls

Call 1

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

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

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
465×	`associate-/l*_binary64`
423×	`associate-/r*_binary64`
372×	`fma-def_binary64`
147×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	2045
1	381	1971
2	1339	1891

Stop Event

1×	node limit

Counts

226 → 204

Calls

Call 1

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

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

prune141.0ms (2.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	198	6	204
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	201	12	213

Error

5.1b

Counts

213 → 12

Alt Table

Status	Error	Program
	39.2b	(/.f64 (neg.f64 c) b)
	43.2b	(*.f64 (+.f64 b b) (/.f64 -1/2 a))
	46.2b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (.f64 c (.f64 a -4)))) (*.f64 2 a))
	42.1b	(neg.f64 (fma.f64 (/.f64 c (/.f64 (pow.f64 b 3) c)) a (/.f64 c b)))
✓	36.3b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
	43.7b	(.f64 (/.f64 1 (/.f64 (fma.f64 b b (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (+.f64 (pow.f64 b 3) (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 3/2)))) (/.f64 -1/2 a))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.2b	(neg.f64 (/.f64 b a))
	46.3b	(/.f64 (/.f64 (neg.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
	46.3b	(/.f64 (.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 -1/2 a)) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
▶	36.2b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
	56.6b	(.f64 (+.f64 b (-.f64 (.f64 2 (*.f64 (/.f64 c b) a)) b)) (/.f64 -1/2 a))

Compiler

Compiled 5267 to 3088 computations (41.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
	1.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	24.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series4.0ms (0.1%)

Counts

1 → 20

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	a	@	inf	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
1.0ms	a	@	-inf	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
0.0ms	c	@	inf	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
0.0ms	c	@	-inf	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))
0.0ms	a	@	0	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) -1/2)))

rewrite57.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

972×	`prod-diff_binary64`
160×	`add-sqr-sqrt_binary64`
151×	`*-un-lft-identity_binary64`
151×	`pow1_binary64`
148×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	320	22
2	4222	22

Stop Event

1×	node limit

Counts

1 → 49

Calls

Call 1

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

Outputs

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

simplify35.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

351×	`unswap-sqr_binary64`
329×	`times-frac_binary64`
263×	`distribute-neg-frac_binary64`
222×	`associate-/l*_binary64`
216×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	531
1	217	529
2	739	507
3	3896	507

Stop Event

1×	node limit

Counts

69 → 72

Calls

Call 1

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

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

prune153.0ms (2.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	206	3	209
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	209	12	221

Error

5.1b

Counts

221 → 12

Alt Table

Status	Error	Program
✓	36.3b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
	43.5b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (fma.f64 (.f64 (/.f64 c b) a) -2 b)) -1/2)))
	39.2b	(/.f64 (neg.f64 c) b)
	43.2b	(*.f64 (+.f64 b b) (/.f64 -1/2 a))
	43.7b	(.f64 (/.f64 1 (/.f64 (fma.f64 b b (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (+.f64 (pow.f64 b 3) (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 3/2)))) (/.f64 -1/2 a))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.2b	(neg.f64 (/.f64 b a))
	46.3b	(/.f64 (/.f64 (neg.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
▶	36.2b	(pow.f64 (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a)) 1)
	37.3b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) 3))) -1/2)))
	42.1b	(neg.f64 (fma.f64 (/.f64 c (/.f64 (pow.f64 b 3) c)) a (/.f64 c b)))
	56.6b	(.f64 (+.f64 b (-.f64 (.f64 2 (*.f64 (/.f64 c b) a)) b)) (/.f64 -1/2 a))

Compiler

Compiled 5582 to 3441 computations (38.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
	1.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	24.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series6.0ms (0.1%)

Counts

1 → 20

Calls

9 calls:

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

rewrite46.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

963×	`prod-diff_binary64`
122×	`add-sqr-sqrt_binary64`
117×	`*-un-lft-identity_binary64`
117×	`pow1_binary64`
113×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	236	19
2	3192	19

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

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

Outputs

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

simplify35.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

751×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
351×	`unswap-sqr_binary64`
285×	`fma-neg_binary64`
234×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	567
1	198	555
2	663	529
3	3612	529

Stop Event

1×	node limit

Counts

53 → 57

Calls

Call 1

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

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

prune145.0ms (2.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	194	12	206

Error

5.1b

Counts

206 → 12

Alt Table

Status	Error	Program
✓	36.3b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 -1/2 a))
	56.6b	(pow.f64 (.f64 -1/2 (/.f64 (+.f64 b (-.f64 (.f64 2 (*.f64 (/.f64 c b) a)) b)) a)) 1)
	43.5b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (fma.f64 (.f64 (/.f64 c b) a) -2 b)) -1/2)))
	39.2b	(/.f64 (neg.f64 c) b)
	43.2b	(*.f64 (+.f64 b b) (/.f64 -1/2 a))
	43.7b	(.f64 (/.f64 1 (/.f64 (fma.f64 b b (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (+.f64 (pow.f64 b 3) (pow.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) 3/2)))) (/.f64 -1/2 a))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.2b	(neg.f64 (/.f64 b a))
	46.3b	(/.f64 (/.f64 (neg.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 (.f64 a c) -4)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 2 a))
✓	36.2b	(pow.f64 (.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a)) 1)
	37.3b	(/.f64 1 (/.f64 a (.f64 (+.f64 b (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) 3))) -1/2)))
	42.1b	(neg.f64 (fma.f64 (/.f64 c (/.f64 (pow.f64 b 3) c)) a (/.f64 c b)))

Compiler

Compiled 5184 to 3270 computations (36.9% saved)

regimes1.6s (27.4%)

Accuracy

Total 5.2b remaining (47.5%)

Threshold costs 0b (0%)

Counts

131 → 3

Compiler

Compiled 2549 to 1497 computations (41.3% saved)

bsearch76.0ms (1.3%)

Algorithm

2×	binary-search

Calls

2 calls:

45.0ms	b
30.0ms	b

Steps

Iters	Point		Range
2.35e+95	∈ [	1.4207986499139543e+94	,	2.937033851030537e+95	]
-1.22e-135	∈ [	-1.2284966536175126e-135	,	-1.437779468124281e-141	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	50
1	39	50
2	48	50
3	55	50
4	59	50
5	60	50

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 b -3993536541633293/3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376) (/.f64 (neg.f64 c) b) (if (<=.f64 b 234999999999999986224702316911056274544025034565308812644180014706390694861355171433193247080448) (pow.f64 (*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)) 1) (-.f64 (/.f64 c b) (/.f64 b a))))

Outputs

(if (<=.f64 b -3993536541633293/3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376) (/.f64 (neg.f64 c) b) (if (<=.f64 b 234999999999999986224702316911056274544025034565308812644180014706390694861355171433193247080448) (pow.f64 (*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)) 1) (-.f64 (/.f64 c b) (/.f64 b a))))

(if (<=.f64 b -3993536541633293/3273390607896141870013189696827599152216642046043064789483291368096133796404674554883270092325904157150886684127560071009217256545885393053328527589376) (/.f64 (neg.f64 c) b) (if (<=.f64 b 234999999999999986224702316911056274544025034565308812644180014706390694861355171433193247080448) (*.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) a)) (-.f64 (/.f64 c b) (/.f64 b a))))

end172.0ms (2.9%)

Stop Event

1×

fuel

Compiler

Compiled 303 to 196 computations (35.3% saved)

Details

analyze689.0ms (11.5%)

sample2.2s (37.1%)

preprocess40.0ms (0.7%)

simplify39.0ms (0.6%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series40.0ms (0.7%)

rewrite50.0ms (0.8%)

simplify46.0ms (0.8%)

prune169.0ms (2.8%)

localize10.0ms (0.2%)

series20.0ms (0.3%)

rewrite70.0ms (1.2%)

simplify44.0ms (0.7%)

prune141.0ms (2.3%)

localize15.0ms (0.2%)

series4.0ms (0.1%)

rewrite57.0ms (1%)

simplify35.0ms (0.6%)

prune153.0ms (2.6%)

localize13.0ms (0.2%)

series6.0ms (0.1%)

rewrite46.0ms (0.8%)

simplify35.0ms (0.6%)

prune145.0ms (2.4%)

regimes1.6s (27.4%)

bsearch76.0ms (1.3%)

simplify3.0ms (0.1%)

end172.0ms (2.9%)

Profiling