Details

analyze41.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
14%	42.1%	43.8%	3
21.1%	35.1%	43.8%	4
31.6%	24.6%	43.8%	5
36.9%	19.3%	43.8%	6
43%	13.2%	43.8%	7
46.1%	10.1%	43.8%	8
49.4%	6.8%	43.8%	9
51%	5.2%	43.8%	10
52.7%	3.5%	43.8%	11
53.6%	2.6%	43.8%	12

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.8s (32.8%)

Results

839.0ms	5999×	body	64	valid
550.0ms	1080×	body	1024	valid
227.0ms	604×	body	512	valid
87.0ms	307×	body	256	valid
58.0ms	93×	body	2048	valid
33.0ms	173×	body	128	valid

preprocess58.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

954×	`fma-neg_binary64`
549×	`div-sub_binary64`
451×	`sub-neg_binary64`
376×	`times-frac_binary64`
249×	`distribute-frac-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	39	38
2	64	38
3	109	38
4	201	38
5	404	34
6	859	34
7	2060	34
8	5476	34
9	7969	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
(/.f64 (+.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) 1) 2)

Outputs
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2))) 1) 2)
(-.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2))) 2) -1/2)
(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 2 (+.f64 beta alpha) 4)))
(+.f64 1/2 (/.f64 (-.f64 beta alpha) (fma.f64 2 (+.f64 beta alpha) 4)))
(/.f64 (+.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) 1) 2)
(/.f64 (+.f64 1 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 alpha 2)))) 2)
(-.f64 (/.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 alpha 2))) 2) -1/2)
(+.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 2 (+.f64 beta alpha) 4)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

511×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
401×	`associate-/l*_binary64`
372×	`div-sub_binary64`
347×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	40	19
3	67	19
4	118	19
5	238	17
6	445	17
7	753	17
8	1572	17
9	3643	17
10	7178	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)

Outputs
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 beta 2))) 1) 2)
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 2 alpha) beta)) 1) 2)
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2))) 1) 2)
(-.f64 (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2))) 2) -1/2)
(+.f64 1/2 (/.f64 (-.f64 beta alpha) (fma.f64 (+.f64 beta alpha) 2 4)))
(+.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) -2 -4)))
(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

16.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.4b	(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4))
✓	2.0b	(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))

series13.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	alpha	@	inf	(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))
1.0ms	alpha	@	0	(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))
1.0ms	alpha	@	-inf	(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))
1.0ms	beta	@	0	(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))
1.0ms	beta	@	-inf	(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))

rewrite72.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

594×	`log-prod_binary64`
385×	`fma-def_binary64`
347×	`pow2_binary64`
238×	`pow1/3_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	260	31
2	3738	31

Stop Event

1×	node limit

Counts

2 → 98

Calls

Call 1

Inputs
(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))
(/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (/.f64 (neg.f64 (-.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) 2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) 2 4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) 2 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1/2 (/.f64 alpha (fma.f64 (+.f64 alpha beta) 2 4))) (/.f64 beta (fma.f64 (+.f64 alpha beta) 2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 alpha beta) (neg.f64 (/.f64 1 (fma.f64 (+.f64 alpha beta) 2 4))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (neg.f64 (-.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) 2 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))) 2) (neg.f64 (cbrt.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))) (neg.f64 (sqrt.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (-.f64 alpha beta)) (/.f64 1 (fma.f64 (+.f64 alpha beta) 2 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) (fma.f64 (+.f64 alpha beta) 2 4))) 2) (cbrt.f64 (/.f64 (neg.f64 (-.f64 alpha beta)) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 alpha (fma.f64 (+.f64 alpha beta) 2 4)) (neg.f64 (/.f64 beta (fma.f64 (+.f64 alpha beta) 2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 alpha (fma.f64 (+.f64 alpha beta) 2 4)) (/.f64 beta (fma.f64 (+.f64 alpha beta) 2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha 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Outputs

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(neg.f64 (/.f64 beta (fma.f64 (+.f64 alpha beta) 2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 alpha) 2) (sqrt.f64 (fma.f64 (+.f64 alpha beta) 2 4))) (/.f64 (cbrt.f64 alpha) (sqrt.f64 (fma.f64 (+.f64 alpha beta) 2 4))) (neg.f64 (/.f64 beta (fma.f64 (+.f64 alpha beta) 2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 alpha) (sqrt.f64 (fma.f64 (+.f64 alpha beta) 2 4))) (/.f64 (sqrt.f64 alpha) (sqrt.f64 (fma.f64 (+.f64 alpha beta) 2 4))) (neg.f64 (/.f64 beta (fma.f64 (+.f64 alpha beta) 2 4))))))))

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

901×	`associate-/l*_binary64`
723×	`distribute-rgt-in_binary64`
701×	`distribute-lft-in_binary64`
311×	`associate-/r/_binary64`
246×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	2786
1	853	2310
2	3430	2133

Stop Event

1×	node limit

Counts

146 → 176

Calls

Call 1

Inputs
(+.f64 (/.f64 beta (+.f64 4 (*.f64 2 beta))) 1/2)
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha))))
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (+.f64 (.f64 (-.f64 (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 beta)) 2))) (.f64 -4 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 3)))) (pow.f64 alpha 2)) (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (*.f64 2 beta)) 2)))) alpha)))))
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (+.f64 (.f64 (-.f64 (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 beta)) 2))) (.f64 -4 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 3)))) (pow.f64 alpha 2)) (+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha)) (.f64 -1 (.f64 (+.f64 (.f64 8 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 4))) (.f64 4 (/.f64 1 (pow.f64 (+.f64 4 (*.f64 2 beta)) 3)))) (pow.f64 alpha 3)))))))
(/.f64 (+.f64 (.f64 1/2 beta) (.f64 1/4 (+.f64 4 (*.f64 2 beta)))) alpha)
(-.f64 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 2) (pow.f64 alpha 2))) (+.f64 (.f64 1/4 (/.f64 (+.f64 4 (.f64 2 beta)) alpha)) (.f64 1/2 (/.f64 beta alpha)))) (.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 3) (pow.f64 alpha 3))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 2) (pow.f64 alpha 2))) (+.f64 (.f64 1/4 (/.f64 (+.f64 4 (.f64 2 beta)) alpha)) (.f64 1/2 (/.f64 beta alpha))))) (+.f64 (.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (.f64 -1/8 (/.f64 (.f64 beta (pow.f64 (+.f64 4 (*.f64 2 beta)) 2)) (pow.f64 alpha 3)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 3) (pow.f64 alpha 3))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 2) (pow.f64 alpha 2))) (+.f64 (.f64 1/4 (/.f64 (+.f64 4 (.f64 2 beta)) alpha)) (+.f64 (.f64 1/2 (/.f64 beta alpha)) (.f64 -1/32 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 4) (pow.f64 alpha 4))))))) (+.f64 (.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (+.f64 (.f64 -1/8 (/.f64 (.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/16 (/.f64 (.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 3)) (pow.f64 alpha 4))))))
(.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (+.f64 (.f64 -1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2)))))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (+.f64 (.f64 1/8 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 3)) (pow.f64 alpha 4))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))))
(-.f64 1/2 (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
(-.f64 (+.f64 1/2 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
(-.f64 (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (.f64 -4 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))))) (+.f64 1/2 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))
(-.f64 (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (.f64 -4 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))))) (+.f64 1/2 (+.f64 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (.f64 (pow.f64 beta 3) (+.f64 (.f64 4 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 8 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 4)))))))) (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
1
(+.f64 1 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 1/2 alpha)) beta)))
(-.f64 (+.f64 1 (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 1/2 alpha)) beta)) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2))))) (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (*.f64 2 alpha)) 2) (pow.f64 beta 2))))
(-.f64 (+.f64 1 (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 1/2 alpha)) beta)) (+.f64 (.f64 -1/8 (/.f64 (.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (pow.f64 beta 3))) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2)))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3) (pow.f64 beta 3))) (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (pow.f64 beta 2)))))
1
(+.f64 1 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (pow.f64 beta 2))) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (*.f64 2 alpha))) (pow.f64 beta 2))))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3)) (.f64 1/8 (.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)))) (pow.f64 beta 3))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (pow.f64 beta 2))) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (*.f64 2 alpha))) (pow.f64 beta 2)))))))
(.f64 -1 (/.f64 beta (+.f64 4 (.f64 2 beta))))
(+.f64 (.f64 -1 (/.f64 beta (+.f64 4 (.f64 2 beta)))) (.f64 (-.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 -2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha))
(+.f64 (.f64 -2 (/.f64 (.f64 (-.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 -2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) (pow.f64 alpha 2)) (+.f64 4 (.f64 2 beta)))) (+.f64 (.f64 -1 (/.f64 beta (+.f64 4 (.f64 2 beta)))) (.f64 (-.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 -2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha)))
(+.f64 (.f64 4 (/.f64 (.f64 (-.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 -2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) (pow.f64 alpha 3)) (pow.f64 (+.f64 4 (.f64 2 beta)) 2))) (+.f64 (.f64 -2 (/.f64 (.f64 (-.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 -2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) (pow.f64 alpha 2)) (+.f64 4 (.f64 2 beta)))) (+.f64 (.f64 -1 (/.f64 beta (+.f64 4 (.f64 2 beta)))) (.f64 (-.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 -2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha))))
1/2
(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) 1/2) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) (+.f64 1/2 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) (+.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (.f64 1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3)))))) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
1/2
(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) 1/2) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) (+.f64 1/2 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) (+.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (.f64 1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3)))))) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
(/.f64 alpha (+.f64 4 (*.f64 2 alpha)))
(+.f64 (.f64 -1 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))
(+.f64 (.f64 -1 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 beta 2) (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (+.f64 4 (.f64 2 alpha)))) (/.f64 alpha (+.f64 4 (.f64 2 alpha)))))
(+.f64 (.f64 -4 (/.f64 (.f64 (pow.f64 beta 3) (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (+.f64 (.f64 -1 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 beta 2) (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (+.f64 4 (.f64 2 alpha)))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))))
-1/2
(-.f64 (.f64 1/2 (/.f64 alpha beta)) (+.f64 1/2 (.f64 -1/4 (/.f64 (+.f64 4 (*.f64 2 alpha)) beta))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 alpha beta)) (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 1/2 alpha) (.f64 -1/4 (+.f64 4 (.f64 2 alpha)))) (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2)))) (+.f64 1/2 (.f64 -1/4 (/.f64 (+.f64 4 (*.f64 2 alpha)) beta))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (-.f64 (.f64 1/2 alpha) (.f64 -1/4 (+.f64 4 (.f64 2 alpha)))) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (pow.f64 beta 3))) (+.f64 (.f64 1/2 (/.f64 alpha beta)) (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 1/2 alpha) (.f64 -1/4 (+.f64 4 (.f64 2 alpha)))) (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2))))) (+.f64 1/2 (.f64 -1/4 (/.f64 (+.f64 4 (*.f64 2 alpha)) beta))))
-1/2
(-.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) 1/2)
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2)))) 1/2)
(-.f64 (+.f64 (.f64 -1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (pow.f64 beta 3))) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2))))) 1/2)

Outputs
(+.f64 (/.f64 beta (+.f64 4 (*.f64 2 beta))) 1/2)
(+.f64 (/.f64 beta (+.f64 4 (*.f64 beta 2))) 1/2)
(+.f64 (/.f64 beta (fma.f64 beta 2 4)) 1/2)
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha))))
(+.f64 (+.f64 (/.f64 beta (+.f64 4 (.f64 beta 2))) 1/2) (neg.f64 (.f64 alpha (+.f64 (/.f64 1 (+.f64 4 (.f64 beta 2))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (*.f64 beta 2)) 2)))))))
(+.f64 (/.f64 beta (fma.f64 beta 2 4)) (-.f64 1/2 (*.f64 alpha (fma.f64 2 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 2)) (/.f64 1 (fma.f64 beta 2 4))))))
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (+.f64 (.f64 (-.f64 (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 beta)) 2))) (.f64 -4 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 3)))) (pow.f64 alpha 2)) (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (*.f64 2 beta)) 2)))) alpha)))))
(+.f64 (/.f64 beta (+.f64 4 (.f64 beta 2))) (+.f64 1/2 (fma.f64 (-.f64 (/.f64 2 (pow.f64 (+.f64 4 (.f64 beta 2)) 2)) (.f64 -4 (/.f64 beta (pow.f64 (+.f64 4 (.f64 beta 2)) 3)))) (.f64 alpha alpha) (neg.f64 (.f64 alpha (+.f64 (/.f64 1 (+.f64 4 (.f64 beta 2))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (*.f64 beta 2)) 2)))))))))
(+.f64 (/.f64 beta (fma.f64 beta 2 4)) (+.f64 1/2 (-.f64 (.f64 alpha (.f64 alpha (+.f64 (/.f64 2 (pow.f64 (fma.f64 beta 2 4) 2)) (.f64 4 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 3)))))) (.f64 alpha (fma.f64 2 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 2)) (/.f64 1 (fma.f64 beta 2 4)))))))
(+.f64 (+.f64 (/.f64 beta (fma.f64 beta 2 4)) 1/2) (.f64 alpha (-.f64 (.f64 (+.f64 (/.f64 2 (pow.f64 (fma.f64 beta 2 4) 2)) (/.f64 (*.f64 beta 4) (pow.f64 (fma.f64 beta 2 4) 3))) alpha) (fma.f64 2 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 2)) (/.f64 1 (fma.f64 beta 2 4))))))
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (+.f64 (.f64 (-.f64 (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 beta)) 2))) (.f64 -4 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 3)))) (pow.f64 alpha 2)) (+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha)) (.f64 -1 (.f64 (+.f64 (.f64 8 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 4))) (.f64 4 (/.f64 1 (pow.f64 (+.f64 4 (*.f64 2 beta)) 3)))) (pow.f64 alpha 3)))))))
(+.f64 (+.f64 (/.f64 beta (+.f64 4 (.f64 beta 2))) 1/2) (fma.f64 (-.f64 (/.f64 2 (pow.f64 (+.f64 4 (.f64 beta 2)) 2)) (.f64 -4 (/.f64 beta (pow.f64 (+.f64 4 (.f64 beta 2)) 3)))) (.f64 alpha alpha) (.f64 -1 (+.f64 (.f64 alpha (+.f64 (/.f64 1 (+.f64 4 (.f64 beta 2))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 beta 2)) 2))))) (.f64 (fma.f64 8 (/.f64 beta (pow.f64 (+.f64 4 (.f64 beta 2)) 4)) (/.f64 4 (pow.f64 (+.f64 4 (*.f64 beta 2)) 3))) (pow.f64 alpha 3))))))
(+.f64 (/.f64 beta (fma.f64 beta 2 4)) (+.f64 1/2 (fma.f64 (+.f64 (/.f64 2 (pow.f64 (fma.f64 beta 2 4) 2)) (.f64 4 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 3)))) (.f64 alpha alpha) (neg.f64 (fma.f64 alpha (fma.f64 2 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 2)) (/.f64 1 (fma.f64 beta 2 4))) (*.f64 (fma.f64 8 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 4)) (/.f64 4 (pow.f64 (fma.f64 beta 2 4) 3))) (pow.f64 alpha 3)))))))
(+.f64 (/.f64 beta (fma.f64 beta 2 4)) (+.f64 1/2 (-.f64 (.f64 alpha (-.f64 (.f64 (+.f64 (/.f64 2 (pow.f64 (fma.f64 beta 2 4) 2)) (/.f64 (.f64 beta 4) (pow.f64 (fma.f64 beta 2 4) 3))) alpha) (fma.f64 2 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 2)) (/.f64 1 (fma.f64 beta 2 4))))) (.f64 (fma.f64 8 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 4)) (/.f64 4 (pow.f64 (fma.f64 beta 2 4) 3))) (pow.f64 alpha 3)))))
(/.f64 (+.f64 (.f64 1/2 beta) (.f64 1/4 (+.f64 4 (*.f64 2 beta)))) alpha)
(/.f64 (fma.f64 1/2 beta (+.f64 1 (.f64 (.f64 beta 2) 1/4))) alpha)
(/.f64 (fma.f64 beta 1/2 (+.f64 1 (*.f64 beta 1/2))) alpha)
(/.f64 (+.f64 1 beta) alpha)
(-.f64 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 2) (pow.f64 alpha 2))) (+.f64 (.f64 1/4 (/.f64 (+.f64 4 (.f64 2 beta)) alpha)) (.f64 1/2 (/.f64 beta alpha)))) (.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))
(+.f64 (fma.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 beta 2)) 2) (.f64 alpha alpha)) (fma.f64 1/4 (/.f64 (+.f64 4 (.f64 beta 2)) alpha) (.f64 1/2 (/.f64 beta alpha)))) (.f64 -1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 beta 2))) (.f64 alpha alpha))))
(-.f64 (fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (+.f64 1 (.f64 beta 1/2)) alpha))) (/.f64 (.f64 (+.f64 1 (.f64 beta 1/2)) beta) (*.f64 alpha alpha)))
(fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (+.f64 (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (+.f64 1 (.f64 beta 1/2)) alpha)) (/.f64 (.f64 (fma.f64 beta -1/2 -1) beta) (.f64 alpha alpha))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 3) (pow.f64 alpha 3))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 2) (pow.f64 alpha 2))) (+.f64 (.f64 1/4 (/.f64 (+.f64 4 (.f64 2 beta)) alpha)) (.f64 1/2 (/.f64 beta alpha))))) (+.f64 (.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (.f64 -1/8 (/.f64 (.f64 beta (pow.f64 (+.f64 4 (*.f64 2 beta)) 2)) (pow.f64 alpha 3)))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 beta 2)) 3) (pow.f64 alpha 3)) (fma.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 beta 2)) 2) (.f64 alpha alpha)) (fma.f64 1/4 (/.f64 (+.f64 4 (.f64 beta 2)) alpha) (.f64 1/2 (/.f64 beta alpha))))) (fma.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 beta 2))) (.f64 alpha alpha)) (.f64 -1/8 (/.f64 beta (/.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 4 (.f64 beta 2)) 2))))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 (fma.f64 beta 2 4) 3) (pow.f64 alpha 3)) (fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (+.f64 1 (.f64 beta 1/2)) alpha)))) (fma.f64 -1/8 (.f64 (/.f64 beta (pow.f64 alpha 3)) (pow.f64 (fma.f64 beta 2 4) 2)) (/.f64 (.f64 (+.f64 1 (.f64 beta 1/2)) beta) (.f64 alpha alpha))))
(+.f64 (fma.f64 1/16 (pow.f64 (/.f64 (fma.f64 beta 2 4) alpha) 3) (fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (+.f64 1 (.f64 beta 1/2)) alpha)))) (-.f64 (/.f64 (.f64 (fma.f64 beta -1/2 -1) beta) (.f64 alpha alpha)) (.f64 (/.f64 -1/8 (pow.f64 alpha 3)) (.f64 beta (pow.f64 (fma.f64 beta 2 4) 2)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 3) (pow.f64 alpha 3))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 2) (pow.f64 alpha 2))) (+.f64 (.f64 1/4 (/.f64 (+.f64 4 (.f64 2 beta)) alpha)) (+.f64 (.f64 1/2 (/.f64 beta alpha)) (.f64 -1/32 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 4) (pow.f64 alpha 4))))))) (+.f64 (.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (+.f64 (.f64 -1/8 (/.f64 (.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/16 (/.f64 (.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 3)) (pow.f64 alpha 4))))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 beta 2)) 3) (pow.f64 alpha 3)) (fma.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 beta 2)) 2) (.f64 alpha alpha)) (fma.f64 1/4 (/.f64 (+.f64 4 (.f64 beta 2)) alpha) (fma.f64 1/2 (/.f64 beta alpha) (.f64 -1/32 (/.f64 (pow.f64 (+.f64 4 (.f64 beta 2)) 4) (pow.f64 alpha 4))))))) (fma.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 beta 2))) (.f64 alpha alpha)) (fma.f64 -1/8 (/.f64 beta (/.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 4 (.f64 beta 2)) 2))) (.f64 1/16 (/.f64 beta (/.f64 (pow.f64 alpha 4) (pow.f64 (+.f64 4 (.f64 beta 2)) 3)))))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 (fma.f64 beta 2 4) 3) (pow.f64 alpha 3)) (fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (fma.f64 1/4 (/.f64 (fma.f64 beta 2 4) alpha) (fma.f64 1/2 (/.f64 beta alpha) (.f64 -1/32 (/.f64 (pow.f64 (fma.f64 beta 2 4) 4) (pow.f64 alpha 4))))))) (fma.f64 1/4 (.f64 (/.f64 (fma.f64 beta 2 4) alpha) (/.f64 beta alpha)) (fma.f64 1/16 (.f64 (/.f64 beta (pow.f64 alpha 4)) (pow.f64 (fma.f64 beta 2 4) 3)) (/.f64 (.f64 (.f64 -1/8 beta) (pow.f64 (fma.f64 beta 2 4) 2)) (pow.f64 alpha 3)))))
(+.f64 (fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (fma.f64 1/4 (/.f64 (fma.f64 beta 2 4) alpha) (fma.f64 1/2 (/.f64 beta alpha) (.f64 (/.f64 -1/32 (pow.f64 alpha 4)) (pow.f64 (fma.f64 beta 2 4) 4))))) (fma.f64 1/16 (pow.f64 (/.f64 (fma.f64 beta 2 4) alpha) 3) (-.f64 (/.f64 (.f64 (fma.f64 beta -1/2 -1) beta) (.f64 alpha alpha)) (fma.f64 1/16 (.f64 (/.f64 beta (pow.f64 alpha 4)) (pow.f64 (fma.f64 beta 2 4) 3)) (.f64 (/.f64 -1/8 (pow.f64 alpha 3)) (*.f64 beta (pow.f64 (fma.f64 beta 2 4) 2)))))))
(.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha))
(neg.f64 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (*.f64 beta 2)))) alpha))
(neg.f64 (/.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(/.f64 (neg.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) alpha)
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))
(fma.f64 -1 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) alpha) (.f64 1/2 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) (/.f64 (.f64 alpha alpha) (+.f64 4 (*.f64 beta 2))))))
(-.f64 (.f64 1/2 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (/.f64 alpha (/.f64 (fma.f64 beta 2 4) alpha)))) (/.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(-.f64 (/.f64 (.f64 (+.f64 beta 2) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (.f64 alpha alpha)) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (+.f64 (.f64 -1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2)))))
(fma.f64 -1 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) alpha) (fma.f64 -1/4 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) (/.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 4 (.f64 beta 2)) 2))) (.f64 1/2 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) (/.f64 (.f64 alpha alpha) (+.f64 4 (*.f64 beta 2)))))))
(-.f64 (fma.f64 1/2 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (/.f64 alpha (/.f64 (fma.f64 beta 2 4) alpha))) (.f64 -1/4 (.f64 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (pow.f64 alpha 3)) (pow.f64 (fma.f64 beta 2 4) 2)))) (/.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(-.f64 (fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (pow.f64 alpha 3)) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (/.f64 (.f64 (+.f64 beta 2) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (*.f64 alpha alpha))) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))
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1
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1
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(.f64 -1 (/.f64 beta (+.f64 4 (.f64 2 beta))))
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(/.f64 (neg.f64 beta) (fma.f64 beta 2 4))
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1/2
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(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) (+.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (.f64 1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3)))))) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
(+.f64 (+.f64 (fma.f64 -1/2 (/.f64 beta alpha) 1/2) (fma.f64 -1/2 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) (/.f64 (.f64 alpha alpha) (+.f64 4 (.f64 beta 2)))) (.f64 1/4 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) (/.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 4 (.f64 beta 2)) 2)))))) (.f64 -1/4 (/.f64 (+.f64 4 (.f64 beta 2)) alpha)))
(+.f64 (+.f64 1/2 (fma.f64 -1/2 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (/.f64 alpha (/.f64 (fma.f64 beta 2 4) alpha))) (/.f64 (.f64 (.f64 1/4 (pow.f64 (fma.f64 beta 2 4) 2)) (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4))) (pow.f64 alpha 3)))) (/.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(+.f64 (+.f64 (fma.f64 -1/2 (.f64 (/.f64 (fma.f64 beta 2 4) (.f64 alpha alpha)) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) 1/2) (.f64 (/.f64 1/4 (pow.f64 alpha 3)) (.f64 (pow.f64 (fma.f64 beta 2 4) 2) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))))) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))
1/2
(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) 1/2) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
(-.f64 (fma.f64 -1/2 (/.f64 beta alpha) 1/2) (/.f64 (+.f64 1 (.f64 (.f64 beta 2) 1/4)) alpha))
(+.f64 1/2 (/.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(+.f64 1/2 (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) (+.f64 1/2 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
(+.f64 (+.f64 (fma.f64 -1/2 (/.f64 beta alpha) 1/2) (.f64 -1/2 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) (/.f64 (.f64 alpha alpha) (+.f64 4 (.f64 beta 2)))))) (.f64 -1/4 (/.f64 (+.f64 4 (.f64 beta 2)) alpha)))
(+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (/.f64 alpha (/.f64 (fma.f64 beta 2 4) alpha))) 1/2) (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(+.f64 (fma.f64 -1/2 (.f64 (/.f64 (fma.f64 beta 2 4) (.f64 alpha alpha)) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) 1/2) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))
(-.f64 (+.f64 (.f64 -1/2 (/.f64 beta alpha)) (+.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (.f64 1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3)))))) (.f64 1/4 (/.f64 (+.f64 4 (*.f64 2 beta)) alpha)))
(+.f64 (+.f64 (fma.f64 -1/2 (/.f64 beta alpha) 1/2) (fma.f64 -1/2 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) (/.f64 (.f64 alpha alpha) (+.f64 4 (.f64 beta 2)))) (.f64 1/4 (/.f64 (+.f64 (.f64 beta -1/2) (.f64 -1/4 (+.f64 4 (.f64 beta 2)))) (/.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 4 (.f64 beta 2)) 2)))))) (.f64 -1/4 (/.f64 (+.f64 4 (.f64 beta 2)) alpha)))
(+.f64 (+.f64 1/2 (fma.f64 -1/2 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (/.f64 alpha (/.f64 (fma.f64 beta 2 4) alpha))) (/.f64 (.f64 (.f64 1/4 (pow.f64 (fma.f64 beta 2 4) 2)) (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4))) (pow.f64 alpha 3)))) (/.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(+.f64 (+.f64 (fma.f64 -1/2 (.f64 (/.f64 (fma.f64 beta 2 4) (.f64 alpha alpha)) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) 1/2) (.f64 (/.f64 1/4 (pow.f64 alpha 3)) (.f64 (pow.f64 (fma.f64 beta 2 4) 2) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))))) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))
(/.f64 alpha (+.f64 4 (*.f64 2 alpha)))
(/.f64 alpha (fma.f64 2 alpha 4))
(+.f64 (.f64 -1 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))
(fma.f64 -1 (.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))
(fma.f64 (neg.f64 beta) (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4))) (/.f64 alpha (fma.f64 2 alpha 4)))
(-.f64 (/.f64 alpha (fma.f64 2 alpha 4)) (fma.f64 beta (/.f64 (*.f64 2 alpha) (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 beta (fma.f64 2 alpha 4))))
(+.f64 (.f64 -1 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 beta 2) (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (+.f64 4 (.f64 2 alpha)))) (/.f64 alpha (+.f64 4 (.f64 2 alpha)))))
(fma.f64 -1 (.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (fma.f64 2 (/.f64 (.f64 (fma.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (/.f64 1 (+.f64 4 (.f64 2 alpha)))) (.f64 beta beta)) (+.f64 4 (.f64 2 alpha))) (/.f64 alpha (+.f64 4 (*.f64 2 alpha)))))
(-.f64 (fma.f64 2 (.f64 (/.f64 (.f64 beta beta) (fma.f64 2 alpha 4)) (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4)))) (/.f64 alpha (fma.f64 2 alpha 4))) (*.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4)))))
(-.f64 (fma.f64 2 (.f64 (/.f64 (.f64 beta beta) (fma.f64 2 alpha 4)) (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4)))) (/.f64 alpha (fma.f64 2 alpha 4))) (fma.f64 beta (/.f64 (*.f64 2 alpha) (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 beta (fma.f64 2 alpha 4))))
(+.f64 (.f64 -4 (/.f64 (.f64 (pow.f64 beta 3) (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (+.f64 (.f64 -1 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 beta 2) (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (+.f64 4 (.f64 2 alpha)))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))))
(fma.f64 -4 (/.f64 (pow.f64 beta 3) (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (fma.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (fma.f64 -1 (.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (fma.f64 2 (/.f64 (.f64 (fma.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (/.f64 1 (+.f64 4 (.f64 2 alpha)))) (.f64 beta beta)) (+.f64 4 (.f64 2 alpha))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))))
(fma.f64 -4 (.f64 (/.f64 (pow.f64 beta 3) (pow.f64 (fma.f64 2 alpha 4) 2)) (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4)))) (-.f64 (fma.f64 2 (.f64 (/.f64 (.f64 beta beta) (fma.f64 2 alpha 4)) (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4)))) (/.f64 alpha (fma.f64 2 alpha 4))) (.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4))))))
(fma.f64 -4 (.f64 (/.f64 (pow.f64 beta 3) (pow.f64 (fma.f64 2 alpha 4) 2)) (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4)))) (-.f64 (fma.f64 2 (.f64 (/.f64 (.f64 beta beta) (fma.f64 2 alpha 4)) (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4)))) (/.f64 alpha (fma.f64 2 alpha 4))) (fma.f64 beta (/.f64 (.f64 2 alpha) (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 beta (fma.f64 2 alpha 4)))))
-1/2
(-.f64 (.f64 1/2 (/.f64 alpha beta)) (+.f64 1/2 (.f64 -1/4 (/.f64 (+.f64 4 (*.f64 2 alpha)) beta))))
(-.f64 (-.f64 (.f64 1/2 (/.f64 alpha beta)) 1/2) (.f64 -1/4 (/.f64 (+.f64 4 (*.f64 2 alpha)) beta)))
(+.f64 -1/2 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (*.f64 1/2 alpha))) beta))
(+.f64 -1/2 (/.f64 (+.f64 1 (*.f64 alpha 1)) beta))
(-.f64 (+.f64 (.f64 1/2 (/.f64 alpha beta)) (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 1/2 alpha) (.f64 -1/4 (+.f64 4 (.f64 2 alpha)))) (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2)))) (+.f64 1/2 (.f64 -1/4 (/.f64 (+.f64 4 (*.f64 2 alpha)) beta))))
(-.f64 (fma.f64 1/2 (/.f64 alpha beta) (.f64 -1/2 (/.f64 (fma.f64 1/4 (+.f64 4 (.f64 2 alpha)) (.f64 1/2 alpha)) (/.f64 (.f64 beta beta) (+.f64 4 (.f64 2 alpha)))))) (+.f64 1/2 (.f64 -1/4 (/.f64 (+.f64 4 (*.f64 2 alpha)) beta))))
(+.f64 (.f64 -1/2 (.f64 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) beta) (/.f64 (fma.f64 2 alpha 4) beta))) (+.f64 -1/2 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) beta)))
(+.f64 (/.f64 (.f64 (+.f64 -1/2 (.f64 -1/2 (.f64 alpha 1))) (fma.f64 2 alpha 4)) (.f64 beta beta)) (+.f64 -1/2 (/.f64 (+.f64 1 (*.f64 alpha 1)) beta)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (-.f64 (.f64 1/2 alpha) (.f64 -1/4 (+.f64 4 (.f64 2 alpha)))) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (pow.f64 beta 3))) (+.f64 (.f64 1/2 (/.f64 alpha beta)) (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 1/2 alpha) (.f64 -1/4 (+.f64 4 (.f64 2 alpha)))) (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2))))) (+.f64 1/2 (.f64 -1/4 (/.f64 (+.f64 4 (*.f64 2 alpha)) beta))))
(-.f64 (fma.f64 1/4 (/.f64 (fma.f64 1/4 (+.f64 4 (.f64 2 alpha)) (.f64 1/2 alpha)) (/.f64 (pow.f64 beta 3) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (fma.f64 1/2 (/.f64 alpha beta) (.f64 -1/2 (/.f64 (fma.f64 1/4 (+.f64 4 (.f64 2 alpha)) (.f64 1/2 alpha)) (/.f64 (.f64 beta beta) (+.f64 4 (.f64 2 alpha))))))) (+.f64 1/2 (.f64 -1/4 (/.f64 (+.f64 4 (.f64 2 alpha)) beta))))
(fma.f64 1/4 (.f64 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) (pow.f64 beta 3)) (pow.f64 (fma.f64 2 alpha 4) 2)) (+.f64 (.f64 -1/2 (.f64 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) beta) (/.f64 (fma.f64 2 alpha 4) beta))) (+.f64 -1/2 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) beta))))
(fma.f64 1/4 (.f64 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (pow.f64 beta 3)) (+.f64 1 (.f64 alpha 1))) (+.f64 (/.f64 (.f64 (+.f64 -1/2 (.f64 -1/2 (.f64 alpha 1))) (fma.f64 2 alpha 4)) (.f64 beta beta)) (+.f64 -1/2 (/.f64 (+.f64 1 (*.f64 alpha 1)) beta))))
-1/2
(-.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) 1/2)
(-.f64 (-.f64 (.f64 1/2 (/.f64 alpha beta)) 1/2) (.f64 -1/4 (/.f64 (+.f64 4 (*.f64 2 alpha)) beta)))
(+.f64 -1/2 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (*.f64 1/2 alpha))) beta))
(+.f64 -1/2 (/.f64 (+.f64 1 (*.f64 alpha 1)) beta))
(-.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2)))) 1/2)
(+.f64 (fma.f64 -1 (/.f64 (+.f64 (.f64 alpha -1/2) (+.f64 -1 (.f64 (.f64 2 alpha) -1/4))) beta) (.f64 1/2 (/.f64 (+.f64 (.f64 alpha -1/2) (+.f64 -1 (.f64 (.f64 2 alpha) -1/4))) (/.f64 (.f64 beta beta) (+.f64 4 (*.f64 2 alpha)))))) -1/2)
(+.f64 -1/2 (fma.f64 1/2 (.f64 (/.f64 (fma.f64 2 alpha 4) beta) (/.f64 (fma.f64 alpha -1/2 (+.f64 -1 (.f64 alpha -1/2))) beta)) (/.f64 (fma.f64 1/2 alpha (+.f64 1 (*.f64 1/2 alpha))) beta)))
(+.f64 -1/2 (fma.f64 1/2 (.f64 (/.f64 (+.f64 -1 (neg.f64 (.f64 alpha 1))) (.f64 beta beta)) (fma.f64 2 alpha 4)) (/.f64 (+.f64 1 (.f64 alpha 1)) beta)))
(-.f64 (+.f64 (.f64 -1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (pow.f64 beta 3))) (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2))))) 1/2)
(+.f64 (fma.f64 -1/4 (/.f64 (+.f64 (.f64 alpha -1/2) (+.f64 -1 (.f64 (.f64 2 alpha) -1/4))) (/.f64 (pow.f64 beta 3) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (fma.f64 -1 (/.f64 (+.f64 (.f64 alpha -1/2) (+.f64 -1 (.f64 (.f64 2 alpha) -1/4))) beta) (.f64 1/2 (/.f64 (+.f64 (.f64 alpha -1/2) (+.f64 -1 (.f64 (.f64 2 alpha) -1/4))) (/.f64 (.f64 beta beta) (+.f64 4 (*.f64 2 alpha))))))) -1/2)
(+.f64 (fma.f64 -1/4 (.f64 (/.f64 (fma.f64 alpha -1/2 (+.f64 -1 (.f64 alpha -1/2))) (pow.f64 beta 3)) (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) beta)) (fma.f64 1/2 (.f64 (/.f64 (fma.f64 2 alpha 4) beta) (/.f64 (fma.f64 alpha -1/2 (+.f64 -1 (*.f64 alpha -1/2))) beta)) -1/2))
(fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (pow.f64 beta 3)) (+.f64 -1 (neg.f64 (.f64 alpha 1)))) (+.f64 -1/2 (fma.f64 1/2 (.f64 (/.f64 (+.f64 -1 (neg.f64 (.f64 alpha 1))) (.f64 beta beta)) (fma.f64 2 alpha 4)) (/.f64 (+.f64 1 (.f64 alpha 1)) beta))))

prune555.0ms (10%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	172	4	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	4	177

Error

0.0b

Counts

177 → 4

Alt Table

Status	Error	Program
▶	16.4b	(expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))
	45.2b	(/.f64 (+.f64 1 beta) alpha)
	47.1b	(fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (+.f64 (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (+.f64 1 (.f64 beta 1/2)) alpha)) (/.f64 (.f64 (fma.f64 beta -1/2 -1) beta) (.f64 alpha alpha))))
	46.9b	(-.f64 (fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (pow.f64 alpha 3)) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (/.f64 (.f64 (+.f64 beta 2) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (*.f64 alpha alpha))) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))

Compiler

Compiled 5687 to 4015 computations (29.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))
✓	0.0b	(log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))
✓	0.0b	(/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))
✓	2.0b	(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))

series25.0ms (0.4%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
5.0ms	alpha	@	inf	(log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))
3.0ms	alpha	@	-inf	(log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))
3.0ms	beta	@	inf	(log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))
2.0ms	beta	@	0	(log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))
2.0ms	alpha	@	0	(log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))

rewrite158.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`prod-diff_binary64`
622×	`log-prod_binary64`
323×	`fma-def_binary64`
247×	`expm1-udef_binary64`
247×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	67
1	275	67
2	3803	67

Stop Event

1×	node limit

Counts

4 → 295

Calls

Call 1

Inputs
(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))
(/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))
(log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))
(expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))

Outputs
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simplify145.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-def_binary64`
395×	`cancel-sign-sub-inv_binary64`
286×	`*-commutative_binary64`
285×	`associate-r_binary64`
263×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	463	7413
1	1602	6198
2	6491	6011

Stop Event

1×	node limit

Counts

391 → 363

Calls

Call 1

Inputs
(+.f64 (/.f64 beta (+.f64 4 (*.f64 2 beta))) 1/2)
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha))))
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1
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1
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(.f64 -1 (/.f64 beta (+.f64 4 (.f64 2 beta))))
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1/2
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1/2
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(/.f64 alpha (+.f64 4 (*.f64 2 alpha)))
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-1/2
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-1/2
(-.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) 1/2)
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(log.f64 (+.f64 (/.f64 beta (+.f64 4 (*.f64 2 beta))) 3/2))
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(/.f64 (+.f64 (.f64 1/2 beta) (.f64 1/4 (+.f64 4 (*.f64 2 beta)))) alpha)
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(.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha))
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(log.f64 (-.f64 3/2 (/.f64 alpha (+.f64 4 (*.f64 2 alpha)))))
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(+.f64 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (-.f64 3/2 (/.f64 alpha (+.f64 4 (.f64 2 alpha))))))) (/.f64 1 (.f64 (+.f64 4 (.f64 2 alpha)) (-.f64 3/2 (/.f64 alpha (+.f64 4 (.f64 2 alpha)))))))) (+.f64 (.f64 1/2 (.f64 (pow.f64 beta 2) (+.f64 (.f64 -1 (/.f64 (pow.f64 (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))) 2) (pow.f64 (-.f64 3/2 (/.f64 alpha (+.f64 4 (.f64 2 alpha)))) 2))) (.f64 2 (/.f64 (-.f64 (.f64 -4 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)))) (-.f64 3/2 (/.f64 alpha (+.f64 4 (.f64 2 alpha))))))))) (log.f64 (-.f64 3/2 (/.f64 alpha (+.f64 4 (.f64 2 alpha)))))))
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(log.f64 2)
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) (log.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) (+.f64 (log.f64 2) (.f64 1/2 (/.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 (+.f64 (.f64 1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) 2)) (.f64 1/4 (.f64 alpha (+.f64 4 (.f64 2 alpha))))) (.f64 -1/8 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (pow.f64 beta 2)))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) beta)) (+.f64 (.f64 1/6 (/.f64 (+.f64 (.f64 3/2 (.f64 (+.f64 (.f64 1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) (-.f64 (.f64 1/4 (.f64 alpha (+.f64 4 (.f64 2 alpha)))) (.f64 -1/8 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))))) (+.f64 (.f64 -1/4 (pow.f64 (+.f64 (.f64 1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) 3)) (.f64 3 (-.f64 (.f64 -1/8 (.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (.f64 1/16 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3)))))) (pow.f64 beta 3))) (+.f64 (log.f64 2) (.f64 1/2 (/.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 (+.f64 (.f64 1/2 alpha) (.f64 1/4 (+.f64 4 (.f64 2 alpha)))) 2)) (.f64 1/4 (.f64 alpha (+.f64 4 (.f64 2 alpha))))) (.f64 -1/8 (pow.f64 (+.f64 4 (*.f64 2 alpha)) 2))) (pow.f64 beta 2))))))
(log.f64 2)
(+.f64 (log.f64 2) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/8 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (+.f64 (.f64 -1/4 (pow.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) 2)) (.f64 1/4 (.f64 alpha (+.f64 4 (.f64 2 alpha)))))) (pow.f64 beta 2))) (+.f64 (log.f64 2) (.f64 -1/2 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta))))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 1/8 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (+.f64 (.f64 -1/4 (pow.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) 2)) (.f64 1/4 (.f64 alpha (+.f64 4 (.f64 2 alpha)))))) (pow.f64 beta 2))) (+.f64 (log.f64 2) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)) (.f64 -1/6 (/.f64 (+.f64 (.f64 -3/2 (.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) (+.f64 (.f64 1/8 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (.f64 1/4 (.f64 alpha (+.f64 4 (.f64 2 alpha))))))) (+.f64 (.f64 3 (+.f64 (.f64 1/8 (.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (.f64 1/16 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3)))) (.f64 1/4 (pow.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (*.f64 -1/2 alpha)) 3)))) (pow.f64 beta 3))))))
(+.f64 (/.f64 beta (+.f64 4 (*.f64 2 beta))) 1/2)
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha))))
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (+.f64 (.f64 (-.f64 (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 beta)) 2))) (.f64 -4 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 3)))) (pow.f64 alpha 2)) (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (*.f64 2 beta)) 2)))) alpha)))))
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (+.f64 (.f64 (-.f64 (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 beta)) 2))) (.f64 -4 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 3)))) (pow.f64 alpha 2)) (+.f64 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha)) (.f64 -1 (.f64 (+.f64 (.f64 8 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 4))) (.f64 4 (/.f64 1 (pow.f64 (+.f64 4 (*.f64 2 beta)) 3)))) (pow.f64 alpha 3)))))))
(/.f64 (+.f64 (.f64 1/2 beta) (.f64 1/4 (+.f64 4 (*.f64 2 beta)))) alpha)
(-.f64 (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 2) (pow.f64 alpha 2))) (+.f64 (.f64 1/4 (/.f64 (+.f64 4 (.f64 2 beta)) alpha)) (.f64 1/2 (/.f64 beta alpha)))) (.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 3) (pow.f64 alpha 3))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 2) (pow.f64 alpha 2))) (+.f64 (.f64 1/4 (/.f64 (+.f64 4 (.f64 2 beta)) alpha)) (.f64 1/2 (/.f64 beta alpha))))) (+.f64 (.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (.f64 -1/8 (/.f64 (.f64 beta (pow.f64 (+.f64 4 (*.f64 2 beta)) 2)) (pow.f64 alpha 3)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 3) (pow.f64 alpha 3))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 2) (pow.f64 alpha 2))) (+.f64 (.f64 1/4 (/.f64 (+.f64 4 (.f64 2 beta)) alpha)) (+.f64 (.f64 1/2 (/.f64 beta alpha)) (.f64 -1/32 (/.f64 (pow.f64 (+.f64 4 (.f64 2 beta)) 4) (pow.f64 alpha 4))))))) (+.f64 (.f64 1/4 (/.f64 (.f64 beta (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))) (+.f64 (.f64 -1/8 (/.f64 (.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/16 (/.f64 (.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 3)) (pow.f64 alpha 4))))))
(.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (+.f64 (.f64 -1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2)))))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (+.f64 (.f64 1/8 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 3)) (pow.f64 alpha 4))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))))
(-.f64 1/2 (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
(-.f64 (+.f64 1/2 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
(-.f64 (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (.f64 -4 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))))) (+.f64 1/2 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))
(-.f64 (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (.f64 -4 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))))) (+.f64 1/2 (+.f64 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (.f64 (pow.f64 beta 3) (+.f64 (.f64 4 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 8 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 4)))))))) (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
1
(+.f64 1 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 1/2 alpha)) beta)))
(-.f64 (+.f64 1 (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 1/2 alpha)) beta)) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2))))) (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (*.f64 2 alpha)) 2) (pow.f64 beta 2))))
(-.f64 (+.f64 1 (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 1/2 alpha)) beta)) (+.f64 (.f64 -1/8 (/.f64 (.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (pow.f64 beta 3))) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2)))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3) (pow.f64 beta 3))) (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (pow.f64 beta 2)))))
1
(+.f64 1 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (pow.f64 beta 2))) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (*.f64 2 alpha))) (pow.f64 beta 2))))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3)) (.f64 1/8 (.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)))) (pow.f64 beta 3))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (pow.f64 beta 2))) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (*.f64 2 alpha))) (pow.f64 beta 2)))))))

Outputs
(+.f64 (/.f64 beta (+.f64 4 (*.f64 2 beta))) 1/2)
(+.f64 (/.f64 beta (+.f64 4 (*.f64 beta 2))) 1/2)
(+.f64 (/.f64 beta (fma.f64 beta 2 4)) 1/2)
(+.f64 (/.f64 beta (+.f64 4 (.f64 2 beta))) (+.f64 1/2 (.f64 -1 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 2 beta))) (.f64 2 (/.f64 beta (pow.f64 (+.f64 4 (.f64 2 beta)) 2)))) alpha))))
(+.f64 (/.f64 beta (+.f64 4 (.f64 beta 2))) (+.f64 1/2 (neg.f64 (.f64 (+.f64 (/.f64 1 (+.f64 4 (.f64 beta 2))) (/.f64 (.f64 beta 2) (pow.f64 (+.f64 4 (*.f64 beta 2)) 2))) alpha))))
(+.f64 (/.f64 beta (fma.f64 beta 2 4)) (-.f64 1/2 (*.f64 (fma.f64 2 (/.f64 beta (pow.f64 (fma.f64 beta 2 4) 2)) (/.f64 1 (fma.f64 beta 2 4))) alpha)))
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1
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1/2
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1/2
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(-.f64 (fma.f64 1/16 (pow.f64 (/.f64 (fma.f64 beta 2 4) alpha) 3) (fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (fma.f64 1/4 (/.f64 (fma.f64 beta 2 4) alpha) (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (pow.f64 (fma.f64 beta 2 4) 4) (/.f64 (pow.f64 alpha 4) -1/32)))))) (fma.f64 1/4 (.f64 (/.f64 beta (.f64 alpha alpha)) (fma.f64 beta 2 4)) (fma.f64 -1/8 (.f64 (/.f64 beta (pow.f64 alpha 3)) (pow.f64 (fma.f64 beta 2 4) 2)) (*.f64 1/16 (/.f64 (pow.f64 (fma.f64 beta 2 4) 3) (/.f64 (pow.f64 alpha 4) beta))))))
(.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha))
(neg.f64 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (*.f64 beta 2) 1/4))) alpha))
(/.f64 (neg.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4))) alpha)
(/.f64 (neg.f64 (fma.f64 beta -1/2 (-.f64 -1 (*.f64 beta 1/2)))) alpha)
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))
(fma.f64 -1 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (.f64 beta 2) 1/4))) alpha) (.f64 1/2 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (.f64 beta 2) 1/4))) (/.f64 (.f64 alpha alpha) (+.f64 4 (*.f64 beta 2))))))
(-.f64 (.f64 1/2 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (/.f64 alpha (/.f64 (fma.f64 beta 2 4) alpha)))) (/.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(-.f64 (/.f64 (.f64 (.f64 1/2 (fma.f64 beta 2 4)) (fma.f64 beta -1/2 (-.f64 -1 (.f64 beta 1/2)))) (.f64 alpha alpha)) (/.f64 (fma.f64 beta -1/2 (-.f64 -1 (*.f64 beta 1/2))) alpha))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (+.f64 (.f64 -1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2)))))
(fma.f64 -1 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (.f64 beta 2) 1/4))) alpha) (fma.f64 -1/4 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (.f64 beta 2) 1/4))) (/.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 4 (.f64 beta 2)) 2))) (.f64 1/2 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (.f64 beta 2) 1/4))) (/.f64 (.f64 alpha alpha) (+.f64 4 (*.f64 beta 2)))))))
(-.f64 (fma.f64 1/2 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (/.f64 alpha (/.f64 (fma.f64 beta 2 4) alpha))) (.f64 -1/4 (.f64 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (pow.f64 alpha 3)) (pow.f64 (fma.f64 beta 2 4) 2)))) (/.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 (fma.f64 beta 2 4) alpha) (/.f64 (fma.f64 beta -1/2 (-.f64 -1 (.f64 beta 1/2))) alpha)) (.f64 -1/4 (.f64 (/.f64 (fma.f64 beta -1/2 (-.f64 -1 (.f64 beta 1/2))) (pow.f64 alpha 3)) (pow.f64 (fma.f64 beta 2 4) 2)))) (/.f64 (fma.f64 beta -1/2 (-.f64 -1 (.f64 beta 1/2))) alpha))
(+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) alpha)) (+.f64 (.f64 1/8 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 3)) (pow.f64 alpha 4))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (pow.f64 (+.f64 4 (.f64 2 beta)) 2)) (pow.f64 alpha 3))) (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 beta) (.f64 1/4 (+.f64 4 (.f64 2 beta)))) (+.f64 4 (.f64 2 beta))) (pow.f64 alpha 2))))))
(fma.f64 -1 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (.f64 beta 2) 1/4))) alpha) (fma.f64 1/8 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (.f64 beta 2) 1/4))) (/.f64 (pow.f64 alpha 4) (pow.f64 (+.f64 4 (.f64 beta 2)) 3))) (fma.f64 -1/4 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (.f64 beta 2) 1/4))) (/.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 4 (.f64 beta 2)) 2))) (.f64 1/2 (/.f64 (-.f64 (.f64 beta -1/2) (+.f64 1 (.f64 (.f64 beta 2) 1/4))) (/.f64 (.f64 alpha alpha) (+.f64 4 (*.f64 beta 2))))))))
(-.f64 (fma.f64 1/8 (.f64 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (pow.f64 alpha 4)) (pow.f64 (fma.f64 beta 2 4) 3)) (fma.f64 1/2 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (/.f64 alpha (/.f64 (fma.f64 beta 2 4) alpha))) (.f64 -1/4 (.f64 (/.f64 (fma.f64 beta -1/2 (.f64 (fma.f64 beta 2 4) -1/4)) (pow.f64 alpha 3)) (pow.f64 (fma.f64 beta 2 4) 2))))) (/.f64 (fma.f64 beta -1/2 (*.f64 (fma.f64 beta 2 4) -1/4)) alpha))
(-.f64 (fma.f64 1/8 (.f64 (/.f64 (fma.f64 beta -1/2 (-.f64 -1 (.f64 beta 1/2))) (pow.f64 alpha 4)) (pow.f64 (fma.f64 beta 2 4) 3)) (fma.f64 1/2 (.f64 (/.f64 (fma.f64 beta 2 4) alpha) (/.f64 (fma.f64 beta -1/2 (-.f64 -1 (.f64 beta 1/2))) alpha)) (.f64 -1/4 (.f64 (/.f64 (fma.f64 beta -1/2 (-.f64 -1 (.f64 beta 1/2))) (pow.f64 alpha 3)) (pow.f64 (fma.f64 beta 2 4) 2))))) (/.f64 (fma.f64 beta -1/2 (-.f64 -1 (.f64 beta 1/2))) alpha))
(-.f64 1/2 (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
(-.f64 1/2 (/.f64 alpha (fma.f64 2 alpha 4)))
(-.f64 (+.f64 1/2 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha)))))) (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
(+.f64 1/2 (-.f64 (.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (/.f64 alpha (+.f64 4 (.f64 2 alpha)))))
(-.f64 (fma.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4))) 1/2) (/.f64 alpha (fma.f64 2 alpha 4)))
(-.f64 (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (.f64 -4 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))))) (+.f64 1/2 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))
(-.f64 (fma.f64 (.f64 beta beta) (-.f64 (/.f64 (.f64 -4 alpha) (pow.f64 (+.f64 4 (.f64 2 alpha)) 3)) (/.f64 2 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (+.f64 1/2 (.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (/.f64 1 (+.f64 4 (.f64 2 alpha))))))) (/.f64 alpha (+.f64 4 (.f64 2 alpha))))
(-.f64 (fma.f64 (*.f64 beta beta) (fma.f64 -4 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 3)) (/.f64 -2 (pow.f64 (fma.f64 2 alpha 4) 2))) (fma.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4))) 1/2)) (/.f64 alpha (fma.f64 2 alpha 4)))
(-.f64 (+.f64 (.f64 (pow.f64 beta 2) (-.f64 (.f64 -4 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 2 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))))) (+.f64 1/2 (+.f64 (.f64 beta (+.f64 (.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (/.f64 1 (+.f64 4 (.f64 2 alpha))))) (.f64 (pow.f64 beta 3) (+.f64 (.f64 4 (/.f64 1 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3))) (.f64 8 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 4)))))))) (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
(-.f64 (fma.f64 (.f64 beta beta) (-.f64 (/.f64 (.f64 -4 alpha) (pow.f64 (+.f64 4 (.f64 2 alpha)) 3)) (/.f64 2 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (+.f64 1/2 (fma.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (/.f64 1 (+.f64 4 (.f64 2 alpha)))) (.f64 (pow.f64 beta 3) (+.f64 (/.f64 4 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3)) (/.f64 (.f64 8 alpha) (pow.f64 (+.f64 4 (.f64 2 alpha)) 4))))))) (/.f64 alpha (+.f64 4 (*.f64 2 alpha))))
(+.f64 (fma.f64 (.f64 beta beta) (fma.f64 -4 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 3)) (/.f64 -2 (pow.f64 (fma.f64 2 alpha 4) 2))) 1/2) (-.f64 (fma.f64 beta (fma.f64 2 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 1 (fma.f64 2 alpha 4))) (.f64 (pow.f64 beta 3) (fma.f64 8 (/.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 4)) (/.f64 4 (pow.f64 (fma.f64 2 alpha 4) 3))))) (/.f64 alpha (fma.f64 2 alpha 4))))
1
(+.f64 1 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 1/2 alpha)) beta)))
(+.f64 1 (neg.f64 (/.f64 (fma.f64 1/4 (+.f64 4 (.f64 2 alpha)) (.f64 1/2 alpha)) beta)))
(-.f64 1 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (*.f64 1/2 alpha))) beta))
(+.f64 1 (/.f64 (fma.f64 alpha -1/2 (fma.f64 alpha -1/2 -1)) beta))
(-.f64 (+.f64 1 (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 1/2 alpha)) beta)) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2))))) (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (*.f64 2 alpha)) 2) (pow.f64 beta 2))))
(fma.f64 1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (.f64 beta beta)) (+.f64 1 (fma.f64 -1 (/.f64 (fma.f64 1/4 (+.f64 4 (.f64 2 alpha)) (.f64 1/2 alpha)) beta) (.f64 1/4 (/.f64 alpha (/.f64 (.f64 beta beta) (+.f64 4 (*.f64 2 alpha))))))))
(+.f64 (-.f64 (/.f64 (.f64 alpha (+.f64 1 (.f64 1/2 alpha))) (.f64 beta beta)) (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) beta)) (fma.f64 1/8 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (*.f64 beta beta)) 1))
(+.f64 (+.f64 (/.f64 (fma.f64 alpha -1/2 (fma.f64 alpha -1/2 -1)) beta) (/.f64 (.f64 alpha (fma.f64 1/2 alpha 1)) (.f64 beta beta))) (fma.f64 1/8 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (*.f64 beta beta)) 1))
(-.f64 (+.f64 1 (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 1/2 alpha)) beta)) (+.f64 (.f64 -1/8 (/.f64 (.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)) (pow.f64 beta 3))) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (.f64 2 alpha))) (pow.f64 beta 2)))))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3) (pow.f64 beta 3))) (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (pow.f64 beta 2)))))
(+.f64 1 (-.f64 (fma.f64 -1 (/.f64 (fma.f64 1/4 (+.f64 4 (.f64 2 alpha)) (.f64 1/2 alpha)) beta) (fma.f64 -1/8 (/.f64 alpha (/.f64 (pow.f64 beta 3) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (.f64 1/4 (/.f64 alpha (/.f64 (.f64 beta beta) (+.f64 4 (.f64 2 alpha))))))) (fma.f64 1/16 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3) (pow.f64 beta 3)) (.f64 -1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (.f64 beta beta))))))
(+.f64 (-.f64 1 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) beta)) (-.f64 (fma.f64 -1/8 (.f64 (/.f64 alpha (pow.f64 beta 3)) (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 (.f64 alpha (+.f64 1 (.f64 1/2 alpha))) (.f64 beta beta))) (fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (.f64 beta beta)) (*.f64 1/16 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 3) (pow.f64 beta 3))))))
(+.f64 (+.f64 1 (/.f64 (fma.f64 alpha -1/2 (fma.f64 alpha -1/2 -1)) beta)) (-.f64 (fma.f64 -1/8 (.f64 (/.f64 alpha (pow.f64 beta 3)) (pow.f64 (fma.f64 2 alpha 4) 2)) (/.f64 (.f64 alpha (fma.f64 1/2 alpha 1)) (.f64 beta beta))) (fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (.f64 beta beta)) (*.f64 1/16 (pow.f64 (/.f64 (fma.f64 2 alpha 4) beta) 3)))))
1
(+.f64 1 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)))
(+.f64 1 (neg.f64 (/.f64 (fma.f64 1/4 (+.f64 4 (.f64 2 alpha)) (.f64 1/2 alpha)) beta)))
(-.f64 1 (/.f64 (fma.f64 1/2 alpha (+.f64 1 (*.f64 1/2 alpha))) beta))
(+.f64 1 (/.f64 (fma.f64 alpha -1/2 (fma.f64 alpha -1/2 -1)) beta))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (pow.f64 beta 2))) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (*.f64 2 alpha))) (pow.f64 beta 2))))))
(fma.f64 1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (.f64 beta beta)) (+.f64 1 (fma.f64 -1 (/.f64 (fma.f64 1/4 (+.f64 4 (.f64 2 alpha)) (.f64 1/2 alpha)) beta) (.f64 1/4 (/.f64 alpha (/.f64 (.f64 beta beta) (+.f64 4 (*.f64 2 alpha))))))))
(+.f64 (-.f64 (/.f64 (.f64 alpha (+.f64 1 (.f64 1/2 alpha))) (.f64 beta beta)) (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) beta)) (fma.f64 1/8 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (*.f64 beta beta)) 1))
(+.f64 (+.f64 (/.f64 (fma.f64 alpha -1/2 (fma.f64 alpha -1/2 -1)) beta) (/.f64 (.f64 alpha (fma.f64 1/2 alpha 1)) (.f64 beta beta))) (fma.f64 1/8 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (*.f64 beta beta)) 1))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/16 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3)) (.f64 1/8 (.f64 alpha (pow.f64 (+.f64 4 (.f64 2 alpha)) 2)))) (pow.f64 beta 3))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (pow.f64 beta 2))) (+.f64 1 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 1/4 (+.f64 4 (.f64 2 alpha))) (.f64 -1/2 alpha)) beta)) (.f64 1/4 (/.f64 (.f64 alpha (+.f64 4 (*.f64 2 alpha))) (pow.f64 beta 2)))))))
(fma.f64 -1 (/.f64 (fma.f64 1/16 (pow.f64 (+.f64 4 (.f64 2 alpha)) 3) (.f64 (.f64 1/8 alpha) (pow.f64 (+.f64 4 (.f64 2 alpha)) 2))) (pow.f64 beta 3)) (fma.f64 1/8 (/.f64 (pow.f64 (+.f64 4 (.f64 2 alpha)) 2) (.f64 beta beta)) (+.f64 1 (fma.f64 -1 (/.f64 (fma.f64 1/4 (+.f64 4 (.f64 2 alpha)) (.f64 1/2 alpha)) beta) (.f64 1/4 (/.f64 alpha (/.f64 (.f64 beta beta) (+.f64 4 (*.f64 2 alpha)))))))))
(-.f64 (+.f64 (-.f64 (/.f64 (.f64 alpha (+.f64 1 (.f64 1/2 alpha))) (.f64 beta beta)) (/.f64 (fma.f64 1/2 alpha (+.f64 1 (.f64 1/2 alpha))) beta)) (fma.f64 1/8 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (.f64 beta beta)) 1)) (/.f64 (fma.f64 1/16 (pow.f64 (fma.f64 2 alpha 4) 3) (.f64 1/8 (*.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)))) (pow.f64 beta 3)))
(+.f64 (fma.f64 1/8 (/.f64 (pow.f64 (fma.f64 2 alpha 4) 2) (.f64 beta beta)) 1) (-.f64 (+.f64 (/.f64 (fma.f64 alpha -1/2 (fma.f64 alpha -1/2 -1)) beta) (/.f64 (.f64 alpha (fma.f64 1/2 alpha 1)) (.f64 beta beta))) (/.f64 (fma.f64 1/16 (pow.f64 (fma.f64 2 alpha 4) 3) (.f64 1/8 (*.f64 alpha (pow.f64 (fma.f64 2 alpha 4) 2)))) (pow.f64 beta 3))))

prune2.1s (38%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	363	0	363
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	363	4	367

Error

0.0b

Counts

367 → 4

Alt Table

Status	Error	Program
✓	16.4b	(expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))
▶	45.2b	(/.f64 (+.f64 1 beta) alpha)
	47.1b	(fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (+.f64 (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (+.f64 1 (.f64 beta 1/2)) alpha)) (/.f64 (.f64 (fma.f64 beta -1/2 -1) beta) (.f64 alpha alpha))))
	46.9b	(-.f64 (fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (pow.f64 alpha 3)) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (/.f64 (.f64 (+.f64 beta 2) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (*.f64 alpha alpha))) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))

Compiler

Compiled 20868 to 14378 computations (31.1% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 beta) alpha)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	beta	@	-inf	(/.f64 (+.f64 1 beta) alpha)
1.0ms	alpha	@	inf	(/.f64 (+.f64 1 beta) alpha)
1.0ms	beta	@	0	(/.f64 (+.f64 1 beta) alpha)
1.0ms	alpha	@	0	(/.f64 (+.f64 1 beta) alpha)
1.0ms	alpha	@	-inf	(/.f64 (+.f64 1 beta) alpha)

rewrite43.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

701×	`pow1_binary64`
653×	`add-log-exp_binary64`
653×	`log1p-expm1-u_binary64`
653×	`expm1-log1p-u_binary64`
640×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	127	7
2	1723	7

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

Inputs
(/.f64 (+.f64 1 beta) alpha)

Outputs

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	186
1	13	186

Stop Event

1×

saturated

Counts

55 → 37

Calls

Call 1

Inputs
(/.f64 1 alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)

Outputs
(/.f64 1 alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 1 beta) alpha)

prune27.0ms (0.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	36	5	41

Error

0.0b

Counts

41 → 5

Alt Table

Status	Error	Program
✓	16.4b	(expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))
✓	45.2b	(/.f64 (+.f64 1 beta) alpha)
	47.1b	(fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (+.f64 (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (+.f64 1 (.f64 beta 1/2)) alpha)) (/.f64 (.f64 (fma.f64 beta -1/2 -1) beta) (.f64 alpha alpha))))
	46.9b	(-.f64 (fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (pow.f64 alpha 3)) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (/.f64 (.f64 (+.f64 beta 2) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (*.f64 alpha alpha))) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))
▶	45.5b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 alpha) 2)) (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))

Compiler

Compiled 573 to 408 computations (28.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (pow.f64 (cbrt.f64 alpha) 2))
✓	0.3b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 alpha) 2)) (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))
✓	0.5b	(pow.f64 (cbrt.f64 alpha) 2)
✓	0.6b	(cbrt.f64 alpha)

series12.0ms (0.2%)

Counts

4 → 24

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	alpha	@	-inf	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 alpha) 2)) (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))
2.0ms	beta	@	-inf	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 alpha) 2)) (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))
1.0ms	alpha	@	-inf	(pow.f64 (cbrt.f64 alpha) 2)
1.0ms	alpha	@	-inf	(cbrt.f64 alpha)
1.0ms	alpha	@	-inf	(/.f64 1 (pow.f64 (cbrt.f64 alpha) 2))

rewrite67.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

528×	`log-prod_binary64`
368×	`pow-prod-down_binary64`
274×	`pow2_binary64`
195×	`pow1/3_binary64`
192×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	243	22
2	3205	22

Stop Event

1×	node limit

Counts

4 → 167

Calls

Call 1

Inputs
(cbrt.f64 alpha)
(pow.f64 (cbrt.f64 alpha) 2)
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 alpha) 2)) (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))
(/.f64 1 (pow.f64 (cbrt.f64 alpha) 2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cbrt.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (cbrt.f64 alpha))) 2)) (log.f64 (cbrt.f64 (exp.f64 (cbrt.f64 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 alpha)))) (log.f64 (sqrt.f64 (exp.f64 (cbrt.f64 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 alpha))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 alpha) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (cbrt.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 2) (cbrt.f64 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (cbrt.f64 alpha)) (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 alpha 1/6) (pow.f64 alpha 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (.f64 alpha (cbrt.f64 alpha)))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 alpha 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 alpha) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 alpha) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 alpha alpha) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 alpha 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 2) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 alpha) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 alpha 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 alpha) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 alpha) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 alpha)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2/3 (log.f64 alpha)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (cbrt.f64 alpha))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 1/6 (log.f64 alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 alpha)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (cbrt.f64 alpha) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (cbrt.f64 alpha) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 alpha) (cbrt.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 alpha) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (cbrt.f64 alpha) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 2) (cbrt.f64 (.f64 alpha (cbrt.f64 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 alpha (cbrt.f64 alpha))) (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 alpha) (pow.f64 alpha 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 alpha 1/6) (sqrt.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 5) (cbrt.f64 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 alpha) (/.f64 1 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 alpha) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (cbrt.f64 alpha) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (.f64 alpha (cbrt.f64 alpha))) (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (cbrt.f64 alpha) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 alpha (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cbrt.f64 alpha) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 alpha alpha))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2/3 (log.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2/3 (log.f64 alpha)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 alpha) 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 alpha)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/3 (.f64 2/3 (log.f64 alpha))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 alpha) 2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 1 beta) alpha))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 beta) alpha))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 beta) alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1 beta) alpha)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1 beta) alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1 beta) alpha))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (.f64 (pow.f64 (cbrt.f64 alpha) 2) (/.f64 (cbrt.f64 alpha) (+.f64 1 beta))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (.f64 (/.f64 (cbrt.f64 alpha) (+.f64 1 beta)) (pow.f64 (cbrt.f64 alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 alpha (+.f64 1 beta)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 (cbrt.f64 alpha) 2) (/.f64 (+.f64 1 beta) (cbrt.f64 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (cbrt.f64 alpha) (.f64 (pow.f64 (cbrt.f64 alpha) -2) (+.f64 1 beta))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 alpha) -2) (/.f64 (cbrt.f64 alpha) (+.f64 1 beta)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 beta) alpha)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)) (pow.f64 (cbrt.f64 alpha) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (+.f64 1 beta) 2)) (/.f64 alpha (cbrt.f64 (+.f64 1 beta))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha))) 2) (/.f64 (pow.f64 (cbrt.f64 alpha) 2) (cbrt.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 beta)) (/.f64 alpha (sqrt.f64 (+.f64 1 beta))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha))) (/.f64 (pow.f64 (cbrt.f64 alpha) 2) (sqrt.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (.f64 (neg.f64 (pow.f64 (cbrt.f64 alpha) 2)) (/.f64 (cbrt.f64 alpha) (+.f64 1 beta))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (.f64 (/.f64 (cbrt.f64 alpha) (+.f64 1 beta)) (neg.f64 (pow.f64 (cbrt.f64 alpha) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (neg.f64 beta)) (neg.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (neg.f64 beta)) (.f64 (neg.f64 (pow.f64 (cbrt.f64 alpha) 2)) (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (neg.f64 beta)) (.f64 (pow.f64 (cbrt.f64 alpha) 2) (neg.f64 (cbrt.f64 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 beta 3)) (.f64 alpha (fma.f64 beta (-.f64 beta 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (.f64 beta beta)) (.f64 alpha (-.f64 1 beta)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (cbrt.f64 alpha) -2) (+.f64 1 beta)) (cbrt.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha))) (neg.f64 (pow.f64 (cbrt.f64 alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (pow.f64 (cbrt.f64 alpha) -2) (+.f64 1 beta))) (neg.f64 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 -1 (neg.f64 beta)) 1) (.f64 (neg.f64 (cbrt.f64 alpha)) (pow.f64 (cbrt.f64 alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (+.f64 -1 (neg.f64 beta))) (.f64 (neg.f64 (pow.f64 (cbrt.f64 alpha) 2)) (neg.f64 (cbrt.f64 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 beta) -1) (.f64 (cbrt.f64 alpha) (neg.f64 (pow.f64 (cbrt.f64 alpha) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 -1 (neg.f64 beta)) -1) (.f64 (neg.f64 (cbrt.f64 alpha)) (neg.f64 (pow.f64 (cbrt.f64 alpha) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1 beta) (sqrt.f64 alpha)) (sqrt.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)) (cbrt.f64 alpha)) (cbrt.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1 beta) 1) alpha)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)) 1) (pow.f64 (cbrt.f64 alpha) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)) (cbrt.f64 (.f64 alpha (cbrt.f64 alpha)))) (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 alpha) -2) (+.f64 1 beta)) 1) (cbrt.f64 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 alpha) -2) (+.f64 1 beta)) (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 2)) (cbrt.f64 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (cbrt.f64 alpha) -2) (+.f64 1 beta)) (pow.f64 alpha 1/6)) (pow.f64 alpha 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha))) (neg.f64 (pow.f64 (cbrt.f64 alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 -1 (neg.f64 beta)) (pow.f64 (cbrt.f64 alpha) -2)) (neg.f64 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (cbrt.f64 alpha) -2) (+.f64 -1 (neg.f64 beta))) (neg.f64 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)) -1) (neg.f64 (pow.f64 (cbrt.f64 alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 beta) alpha) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1 beta) alpha) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1 beta) alpha) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 1 beta) alpha)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) alpha)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 1 beta) 3) (pow.f64 alpha 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)) 3) (.f64 alpha alpha)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (cbrt.f64 alpha) 2) (/.f64 (cbrt.f64 alpha) (+.f64 1 beta))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (cbrt.f64 alpha) (+.f64 1 beta)) (pow.f64 (cbrt.f64 alpha) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 alpha (+.f64 1 beta)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (cbrt.f64 alpha) 2) (/.f64 (+.f64 1 beta) (cbrt.f64 alpha))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 alpha) (.f64 (pow.f64 (cbrt.f64 alpha) -2) (+.f64 1 beta))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) alpha) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 1 beta) alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 1 beta) alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) alpha) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1 beta) 3) (pow.f64 alpha 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)) 3) (.f64 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log1p.f64 beta) (log.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (-.f64 (log1p.f64 beta) (log.f64 alpha)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (-.f64 (log1p.f64 beta) (log.f64 alpha))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/3 (-.f64 (log1p.f64 beta) (log.f64 alpha))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/2 (-.f64 (log1p.f64 beta) (log.f64 alpha))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 1 beta) alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 1 beta) alpha)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (cbrt.f64 alpha) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) -2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (cbrt.f64 alpha) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (cbrt.f64 alpha) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 alpha) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) -2) (cbrt.f64 (pow.f64 (cbrt.f64 alpha) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (cbrt.f64 alpha) -4)) (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (pow.f64 (cbrt.f64 alpha) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 alpha)) (/.f64 1 (cbrt.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) -4) (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 alpha -2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 alpha) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 alpha) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 alpha) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 alpha (cbrt.f64 alpha)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 alpha alpha) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 alpha 3) -2/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 alpha) -4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 alpha -2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) 2) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 alpha)) -6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 alpha)) -2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 alpha) -4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 alpha 1/6) -4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 alpha)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (pow.f64 (cbrt.f64 alpha) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 alpha) -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 alpha) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cbrt.f64 alpha) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 alpha -2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -2/3 (log.f64 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 alpha)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2/3 (log.f64 alpha)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -2/3 (log.f64 alpha)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 alpha) -2/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 alpha -2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 1/3 (.f64 -2/3 (log.f64 alpha))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -1/3 (log.f64 alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 alpha) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 alpha) -2)))))))

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	186
1	13	186

Stop Event

1×

saturated

Counts

191 → 172

Calls

Call 1

Inputs
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 1 alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))

Outputs
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 (+.f64 beta 1) alpha)
(/.f64 1 alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(/.f64 beta alpha)
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))
(+.f64 (/.f64 beta alpha) (/.f64 1 alpha))
(+.f64 (/.f64 1 alpha) (/.f64 beta alpha))

prune136.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	203	5	208

Error

0.0b

Counts

208 → 5

Alt Table

Status	Error	Program
✓	45.2b	(/.f64 (+.f64 1 beta) alpha)
	45.7b	(/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha))) (/.f64 (pow.f64 (cbrt.f64 alpha) 2) (sqrt.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))))
✓	16.4b	(expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))
	47.1b	(fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (+.f64 (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (+.f64 1 (.f64 beta 1/2)) alpha)) (/.f64 (.f64 (fma.f64 beta -1/2 -1) beta) (.f64 alpha alpha))))
	46.9b	(-.f64 (fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (pow.f64 alpha 3)) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (/.f64 (.f64 (+.f64 beta 2) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (*.f64 alpha alpha))) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))

Compiler

Compiled 3031 to 1908 computations (37.1% saved)

regimes49.0ms (0.9%)

Accuracy

Total -62.6b remaining (-39480.4%)

Threshold costs -62.6b (-39480.4%)

Counts

8 → 2

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha))) (/.f64 (pow.f64 (cbrt.f64 alpha) 2) (sqrt.f64 (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 alpha) 2)) (/.f64 (+.f64 1 beta) (cbrt.f64 alpha)))
(expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))
(/.f64 (+.f64 1 beta) alpha)
(fma.f64 -1/8 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (.f64 alpha alpha)) (+.f64 (fma.f64 1/2 (/.f64 beta alpha) (/.f64 (+.f64 1 (.f64 beta 1/2)) alpha)) (/.f64 (.f64 (fma.f64 beta -1/2 -1) beta) (.f64 alpha alpha))))
(-.f64 (fma.f64 -1/4 (.f64 (/.f64 (pow.f64 (fma.f64 beta 2 4) 2) (pow.f64 alpha 3)) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (/.f64 (.f64 (+.f64 beta 2) (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1))) (*.f64 alpha alpha))) (/.f64 (fma.f64 beta -1/2 (fma.f64 beta -1/2 -1)) alpha))
(-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4)))
(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)

Outputs
(/.f64 (+.f64 1 beta) alpha)
(expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4)))))

Results

10.0ms	3.4b	`alpha`
16.0ms	14.8b	`beta`
4.0ms	0.2b	`(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)`
4.0ms	0.2b	`(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)`
7.0ms	0.2b	`(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))`

Compiler

Compiled 204 to 137 computations (32.8% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

Steps

Iters	Point		Range
-0.99998	∈ [	-0.9999999999884134	,	-0.9999797521275441	]

Compiler

Compiled 20 to 15 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	46
1	34	46
2	46	46
3	57	46
4	73	46
5	88	46
6	90	46
7	92	46
8	93	46

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) -18446375138828077056/18446744073709551616) (/.f64 (+.f64 1 beta) alpha) (expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))))

Outputs

(if (<=.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) -18446375138828077056/18446744073709551616) (/.f64 (+.f64 1 beta) alpha) (expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 alpha beta) 2 4))))))

(if (<=.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) -9007019110755897/9007199254740992) (/.f64 (+.f64 beta 1) alpha) (expm1.f64 (log1p.f64 (-.f64 1/2 (/.f64 (-.f64 alpha beta) (fma.f64 (+.f64 beta alpha) 2 4))))))

end25.0ms (0.4%)

Stop Event

1×

fuel

Compiler

Compiled 66 to 44 computations (33.3% saved)

Details

analyze41.0ms (0.7%)

sample1.8s (32.8%)

preprocess58.0ms (1.1%)

simplify64.0ms (1.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series13.0ms (0.2%)

rewrite72.0ms (1.3%)

simplify65.0ms (1.2%)

prune555.0ms (10%)

localize13.0ms (0.2%)

series25.0ms (0.4%)

rewrite158.0ms (2.9%)

simplify145.0ms (2.6%)

prune2.1s (38%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite43.0ms (0.8%)

simplify10.0ms (0.2%)

prune27.0ms (0.5%)

localize9.0ms (0.2%)

series12.0ms (0.2%)

rewrite67.0ms (1.2%)

simplify12.0ms (0.2%)

prune136.0ms (2.5%)

regimes49.0ms (0.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end25.0ms (0.4%)

Profiling