Details

analyze134.0ms (4.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
0%	50%	50%	5
6.2%	31.2%	62.5%	6
9.4%	28.1%	62.5%	7
14%	17.2%	68.8%	8
14.8%	16.4%	68.8%	9
17.6%	10.1%	72.3%	10
18.1%	9.2%	72.7%	11
19.6%	5.5%	74.9%	12
20%	4.8%	75.2%	13
20.7%	2.8%	76.5%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.2s (42.3%)

Results

1.1s	8256×	body	128	valid
85.0ms	591×	body	128	invalid

preprocess49.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

692×	`fma-def_binary64`
438×	`fma-neg_binary64`
227×	`sub-neg_binary64`
210×	`distribute-rgt-neg-in_binary64`
204×	`unsub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	52	42
2	141	38
3	395	38
4	1005	38
5	1898	38
6	2873	38
7	4197	38
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs

(*.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

(*.f64 (-.f64 rand (/.f64 1 3)) (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 rand (/.f64 1 3))))) a)))

Outputs
(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
(.f64 (+.f64 a -1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 (+.f64 a -1/3) 9))) rand)))
(.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 (.f64 a 9) -3)))))
(*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
(.f64 (-.f64 rand (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 rand (/.f64 1 3))))) a)))
(.f64 (+.f64 rand -1/3) (+.f64 1 (.f64 a (/.f64 1 (sqrt.f64 (*.f64 9 (+.f64 rand -1/3)))))))
(.f64 (+.f64 rand -1/3) (+.f64 1 (/.f64 a (sqrt.f64 (+.f64 (.f64 rand 9) -3)))))
(*.f64 (+.f64 rand -1/3) (+.f64 1 (/.f64 a (sqrt.f64 (fma.f64 9 rand -3)))))
(*.f64 (-.f64 rand 1/3) (+.f64 1 (/.f64 a (sqrt.f64 (fma.f64 9 rand -3)))))
(*.f64 (-.f64 1/3 rand) (-.f64 -1 (/.f64 a (sqrt.f64 (fma.f64 9 rand -3)))))

Compiler

Compiled 22 to 19 computations (13.6% saved)

simplify69.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1035×	`fma-def_binary64`
742×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
177×	`cancel-sign-sub-inv_binary64`
156×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	32	21
2	82	19
3	199	19
4	510	19
5	969	19
6	1470	19
7	2421	19
8	3626	19
9	4073	19
10	4231	19
11	4272	19
12	4275	19
13	4828	19
14	4828	19

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

Outputs
(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
(.f64 (+.f64 a -1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 (+.f64 a -1/3) 9))) rand)))
(.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (+.f64 (.f64 a 9) -3)))))
(*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 109 to 91 computations (16.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
✓	0.3b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
✓	0.4b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

series20.0ms (0.7%)

Counts

4 → 41

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	a	@	-inf	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
2.0ms	a	@	0	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
1.0ms	rand	@	0	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
1.0ms	a	@	0	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
1.0ms	a	@	inf	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)

rewrite68.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`prod-diff_binary64`
147×	`add-sqr-sqrt_binary64`
139×	`*-un-lft-identity_binary64`
139×	`pow1_binary64`
138×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	307	49
2	3916	49

Stop Event

1×	node limit

Counts

4 → 126

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 3 (sqrt.f64 (-.f64 a 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (.f64 9 a) -3)) (cbrt.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3)))) (cbrt.f64 (+.f64 (.f64 9 a) -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 a 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (-.f64 a 1/3)) (pow.f64 9 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 (.f64 9 a) -3) 1/4) (pow.f64 (+.f64 (.f64 9 a) -3) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (-.f64 a 1/3) 2) 81))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 9 a) -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 9 1/2) (sqrt.f64 (-.f64 a 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (.f64 3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (-.f64 a 1/3) 2) 81)) 1/2) (pow.f64 (cbrt.f64 (+.f64 (.f64 9 a) -3)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 3 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 (.f64 9 a) -3)) (cbrt.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (+.f64 (.f64 9 a) -3) 1/4) (sqrt.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -3 (sqrt.f64 (-.f64 a 1/3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (.f64 9 a) -3) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (.f64 9 a) -3) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (.f64 9 a) -3) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 3) (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (.f64 9 a) -3) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 (.f64 9 a) -3)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 3 (sqrt.f64 (-.f64 a 1/3)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/3 (pow.f64 (sqrt.f64 (-.f64 a 1/3)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))) (cbrt.f64 (/.f64 1 (+.f64 (.f64 9 a) -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1 (+.f64 (.f64 9 a) -3))) (cbrt.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (.f64 -3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (.f64 9 a) -3)) -1) (pow.f64 (cbrt.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (+.f64 (.f64 9 a) -3) 1/4) -1) (pow.f64 (pow.f64 (+.f64 (.f64 9 a) -3) 1/4) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (.f64 9 a) -3) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (+.f64 (.f64 9 a) -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))) rand))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 rand (.f64 3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (.f64 rand rand)) (/.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))) (cbrt.f64 rand)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 rand) (/.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 rand)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 rand) (.f64 -3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 rand (pow.f64 (+.f64 (.f64 9 a) -3) 1/4)) (pow.f64 (+.f64 (.f64 9 a) -3) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 rand 1) (.f64 3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 rand 3) (sqrt.f64 (-.f64 a 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 rand (cbrt.f64 (+.f64 (.f64 9 a) -3))) (cbrt.f64 (.f64 3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 rand) (.f64 -3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 rand -1) (.f64 -3 (sqrt.f64 (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 rand) (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 a (+.f64 -1/3 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 a 1/3) (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 a 1/3) (.f64 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))) (-.f64 a 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)) (.f64 -1/3 (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1) a) (.f64 (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 a (-.f64 1/3 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 a 3) -1/27) (+.f64 1 (pow.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))) 3))) (.f64 (fma.f64 a a (+.f64 1/9 (.f64 a 1/3))) (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)) (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 a a -1/9) (+.f64 1 (pow.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))) 3))) (.f64 (+.f64 a 1/3) (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)) (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 a 3) -1/27) (-.f64 1 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)))) (.f64 (fma.f64 a a (+.f64 1/9 (.f64 a 1/3))) (-.f64 1 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 a a -1/9) (-.f64 1 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)))) (.f64 (+.f64 a 1/3) (-.f64 1 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))) 3)) (+.f64 (pow.f64 a 3) -1/27)) (.f64 (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)) (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))) (fma.f64 a a (+.f64 1/9 (.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3))) (+.f64 (pow.f64 a 3) -1/27)) (.f64 (-.f64 1 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))) (fma.f64 a a (+.f64 1/9 (.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))) 3)) (fma.f64 a a -1/9)) (.f64 (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)) (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))) (+.f64 a 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3))) (fma.f64 a a -1/9)) (.f64 (-.f64 1 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))) (+.f64 a 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 a 1/3) 3) (pow.f64 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))) 3)) (+.f64 (pow.f64 (-.f64 a 1/3) 2) (-.f64 (.f64 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))) (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3)))) (.f64 (-.f64 a 1/3) (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 a 1/3) 2) (.f64 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))) (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))))) (-.f64 (-.f64 a 1/3) (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 a 3) -1/27) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)) (fma.f64 a a (+.f64 1/9 (.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 a a -1/9) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)) (+.f64 a 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))) 3)) (-.f64 a 1/3)) (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)) (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3))) (-.f64 a 1/3)) (-.f64 1 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (pow.f64 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))) 3))) (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)) (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 a 1/3) (-.f64 1 (/.f64 (.f64 rand rand) (+.f64 (.f64 9 a) -3)))) (-.f64 1 (.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1) (+.f64 (pow.f64 a 3) -1/27)) (fma.f64 a a (+.f64 1/9 (.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1) (fma.f64 a a -1/9)) (+.f64 a 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (-.f64 a 1/3)) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (-.f64 a 1/3) 3) (pow.f64 (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1) 3) (pow.f64 (-.f64 a 1/3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 a 1/3) (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 a 1/3) 1 (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (-.f64 a 1/3) 2)) (cbrt.f64 (-.f64 a 1/3)) (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 a 1/3)) (sqrt.f64 (-.f64 a 1/3)) (.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand (-.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (-.f64 a 1/3) (fma.f64 (/.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand 1))))))))

simplify60.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

460×	`fma-def_binary64`
313×	`associate-r_binary64`
276×	`associate-l_binary64`
210×	`distribute-rgt-out_binary64`
206×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1031
1	314	998
2	989	982
3	4346	946

Stop Event

1×	node limit

Counts

167 → 166

Calls

Call 1

Inputs
(*.f64 3 (sqrt.f64 -1/3))
(+.f64 (.f64 3/2 (/.f64 a (sqrt.f64 -1/3))) (.f64 3 (sqrt.f64 -1/3)))
(+.f64 (.f64 -3/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 3/2 (/.f64 a (sqrt.f64 -1/3))) (*.f64 3 (sqrt.f64 -1/3))))
(+.f64 (.f64 -3/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 3/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5))) (+.f64 (.f64 3/2 (/.f64 a (sqrt.f64 -1/3))) (.f64 3 (sqrt.f64 -1/3)))))
(*.f64 1/3 (sqrt.f64 -3))
(+.f64 (.f64 -3/2 (/.f64 a (sqrt.f64 -3))) (.f64 1/3 (sqrt.f64 -3)))
(+.f64 (.f64 -3/2 (/.f64 a (sqrt.f64 -3))) (+.f64 (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 a 2)) (sqrt.f64 -3))) (.f64 1/3 (sqrt.f64 -3))))
(+.f64 (.f64 -1/6 (/.f64 (.f64 (+.f64 81 (.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 (sqrt.f64 -3) 2)))) (pow.f64 a 3)) (sqrt.f64 -3))) (+.f64 (.f64 -3/2 (/.f64 a (sqrt.f64 -3))) (+.f64 (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 a 2)) (sqrt.f64 -3))) (*.f64 1/3 (sqrt.f64 -3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 -3)))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (.f64 -3/2 (/.f64 (.f64 a rand) (sqrt.f64 -3))))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 (.f64 -3/2 (/.f64 (.f64 a rand) (sqrt.f64 -3))) (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (*.f64 (pow.f64 a 2) rand)) (sqrt.f64 -3)))))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 (.f64 -1/6 (/.f64 (.f64 (+.f64 81 (.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 (sqrt.f64 -3) 2)))) (.f64 (pow.f64 a 3) rand)) (sqrt.f64 -3))) (+.f64 (.f64 -3/2 (/.f64 (.f64 a rand) (sqrt.f64 -3))) (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (*.f64 (pow.f64 a 2) rand)) (sqrt.f64 -3))))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 -1/3 (+.f64 (.f64 1/3 (*.f64 rand (sqrt.f64 -3))) 1))
(+.f64 (.f64 a (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 1 (.f64 1/2 (/.f64 rand (sqrt.f64 -3)))))) (.f64 -1/3 (+.f64 (.f64 1/3 (*.f64 rand (sqrt.f64 -3))) 1)))
(+.f64 (.f64 a (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 1 (.f64 1/2 (/.f64 rand (sqrt.f64 -3)))))) (+.f64 (.f64 -1/3 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) 1)) (.f64 (+.f64 (.f64 -3/2 (/.f64 rand (sqrt.f64 -3))) (.f64 1/18 (/.f64 (*.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) rand) (sqrt.f64 -3)))) (pow.f64 a 2))))
(+.f64 (.f64 (pow.f64 a 3) (+.f64 (.f64 1/18 (/.f64 (.f64 (+.f64 81 (.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 (sqrt.f64 -3) 2)))) rand) (sqrt.f64 -3))) (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) rand) (sqrt.f64 -3))))) (+.f64 (.f64 a (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 1 (.f64 1/2 (/.f64 rand (sqrt.f64 -3)))))) (+.f64 (.f64 -1/3 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) 1)) (.f64 (+.f64 (.f64 -3/2 (/.f64 rand (sqrt.f64 -3))) (.f64 1/18 (/.f64 (*.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) rand) (sqrt.f64 -3)))) (pow.f64 a 2)))))
a
(-.f64 a 1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)

Outputs
(*.f64 3 (sqrt.f64 -1/3))
(+.f64 (.f64 3/2 (/.f64 a (sqrt.f64 -1/3))) (.f64 3 (sqrt.f64 -1/3)))
(fma.f64 3/2 (/.f64 a (sqrt.f64 -1/3)) (*.f64 3 (sqrt.f64 -1/3)))
(fma.f64 3 (sqrt.f64 -1/3) (*.f64 3/2 (/.f64 a (sqrt.f64 -1/3))))
(+.f64 (.f64 -3/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 3/2 (/.f64 a (sqrt.f64 -1/3))) (*.f64 3 (sqrt.f64 -1/3))))
(fma.f64 -3/8 (/.f64 (.f64 a a) (pow.f64 (sqrt.f64 -1/3) 3)) (fma.f64 3/2 (/.f64 a (sqrt.f64 -1/3)) (.f64 3 (sqrt.f64 -1/3))))
(+.f64 (fma.f64 3 (sqrt.f64 -1/3) (.f64 3/2 (/.f64 a (sqrt.f64 -1/3)))) (.f64 9/8 (/.f64 (*.f64 a a) (sqrt.f64 -1/3))))
(fma.f64 3 (sqrt.f64 -1/3) (fma.f64 3/2 (/.f64 a (sqrt.f64 -1/3)) (*.f64 9/8 (/.f64 a (/.f64 (sqrt.f64 -1/3) a)))))
(fma.f64 3 (sqrt.f64 -1/3) (.f64 (/.f64 a (sqrt.f64 -1/3)) (+.f64 3/2 (/.f64 (.f64 a -3/8) -1/3))))
(+.f64 (.f64 -3/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 3/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5))) (+.f64 (.f64 3/2 (/.f64 a (sqrt.f64 -1/3))) (.f64 3 (sqrt.f64 -1/3)))))
(fma.f64 -3/8 (/.f64 (.f64 a a) (pow.f64 (sqrt.f64 -1/3) 3)) (fma.f64 3/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (fma.f64 3/2 (/.f64 a (sqrt.f64 -1/3)) (.f64 3 (sqrt.f64 -1/3)))))
(+.f64 (.f64 9/8 (/.f64 (.f64 a a) (sqrt.f64 -1/3))) (fma.f64 3/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (fma.f64 3 (sqrt.f64 -1/3) (*.f64 3/2 (/.f64 a (sqrt.f64 -1/3))))))
(fma.f64 9/8 (/.f64 a (/.f64 (sqrt.f64 -1/3) a)) (fma.f64 3/2 (/.f64 a (sqrt.f64 -1/3)) (fma.f64 3 (sqrt.f64 -1/3) (/.f64 (*.f64 3/16 (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5)))))
(fma.f64 3/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (fma.f64 3 (sqrt.f64 -1/3) (.f64 (/.f64 a (sqrt.f64 -1/3)) (+.f64 3/2 (/.f64 (.f64 a -3/8) -1/3)))))
(*.f64 1/3 (sqrt.f64 -3))
(+.f64 (.f64 -3/2 (/.f64 a (sqrt.f64 -3))) (.f64 1/3 (sqrt.f64 -3)))
(fma.f64 -3/2 (/.f64 a (sqrt.f64 -3)) (*.f64 1/3 (sqrt.f64 -3)))
(fma.f64 1/3 (sqrt.f64 -3) (/.f64 -3/2 (/.f64 (sqrt.f64 -3) a)))
(+.f64 (.f64 -3/2 (/.f64 a (sqrt.f64 -3))) (+.f64 (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 a 2)) (sqrt.f64 -3))) (.f64 1/3 (sqrt.f64 -3))))
(fma.f64 -3/2 (/.f64 a (sqrt.f64 -3)) (fma.f64 -1/6 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) (.f64 a a))) (.f64 1/3 (sqrt.f64 -3))))
(fma.f64 -3/2 (/.f64 a (sqrt.f64 -3)) (fma.f64 1/3 (sqrt.f64 -3) (.f64 -1/6 (.f64 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (sqrt.f64 -3)) (*.f64 a a)))))
(fma.f64 1/3 (sqrt.f64 -3) (fma.f64 -3/2 (/.f64 a (sqrt.f64 -3)) (.f64 -1/6 (.f64 (*.f64 a a) (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (sqrt.f64 -3))))))
(fma.f64 1/3 (sqrt.f64 -3) (.f64 a (+.f64 (/.f64 (+.f64 -9/2 (.f64 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2) -1/6)) (/.f64 (sqrt.f64 -3) a)) (/.f64 -3/2 (sqrt.f64 -3)))))
(+.f64 (.f64 -1/6 (/.f64 (.f64 (+.f64 81 (.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 (sqrt.f64 -3) 2)))) (pow.f64 a 3)) (sqrt.f64 -3))) (+.f64 (.f64 -3/2 (/.f64 a (sqrt.f64 -3))) (+.f64 (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 a 2)) (sqrt.f64 -3))) (*.f64 1/3 (sqrt.f64 -3)))))
(fma.f64 -1/6 (/.f64 (+.f64 81 (.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 (sqrt.f64 -3) 2)))) (/.f64 (sqrt.f64 -3) (pow.f64 a 3))) (fma.f64 -3/2 (/.f64 a (sqrt.f64 -3)) (fma.f64 -1/6 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) (.f64 a a))) (*.f64 1/3 (sqrt.f64 -3)))))
(fma.f64 -1/6 (.f64 (/.f64 (fma.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) -3) 81) (sqrt.f64 -3)) (pow.f64 a 3)) (fma.f64 -3/2 (/.f64 a (sqrt.f64 -3)) (fma.f64 1/3 (sqrt.f64 -3) (.f64 -1/6 (.f64 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (sqrt.f64 -3)) (.f64 a a))))))
(fma.f64 -3/2 (/.f64 a (sqrt.f64 -3)) (fma.f64 -1/6 (.f64 (pow.f64 a 3) (/.f64 (+.f64 81 (.f64 -3/2 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)))) (sqrt.f64 -3))) (fma.f64 1/3 (sqrt.f64 -3) (.f64 -1/6 (.f64 (*.f64 a a) (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (sqrt.f64 -3)))))))
(+.f64 (fma.f64 1/3 (sqrt.f64 -3) (/.f64 -3/2 (/.f64 (sqrt.f64 -3) a))) (.f64 (/.f64 -1/6 (sqrt.f64 -3)) (+.f64 (.f64 a (.f64 a (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)))) (.f64 (pow.f64 a 3) (+.f64 81 (*.f64 -3/2 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2))))))))
(.f64 1/3 (.f64 rand (sqrt.f64 -3)))
(.f64 1/3 (.f64 (sqrt.f64 -3) rand))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (.f64 -3/2 (/.f64 (.f64 a rand) (sqrt.f64 -3))))
(fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (/.f64 (.f64 -3/2 (*.f64 a rand)) (sqrt.f64 -3)))
(fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (.f64 -3/2 (*.f64 (/.f64 a (sqrt.f64 -3)) rand)))
(fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (.f64 -3/2 (/.f64 (*.f64 a rand) (sqrt.f64 -3))))
(*.f64 rand (fma.f64 1/3 (sqrt.f64 -3) (/.f64 -3/2 (/.f64 (sqrt.f64 -3) a))))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 (.f64 -3/2 (/.f64 (.f64 a rand) (sqrt.f64 -3))) (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (*.f64 (pow.f64 a 2) rand)) (sqrt.f64 -3)))))
(fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 -3/2 (/.f64 a (/.f64 (sqrt.f64 -3) rand)) (.f64 -1/6 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) (.f64 (.f64 a a) rand))))))
(fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 -3/2 (.f64 (/.f64 a (sqrt.f64 -3)) rand) (.f64 -1/6 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (/.f64 (sqrt.f64 -3) rand) (.f64 a a))))))
(fma.f64 -1/6 (.f64 (/.f64 (.f64 a (.f64 a rand)) (sqrt.f64 -3)) (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2))) (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (.f64 -3/2 (/.f64 (.f64 a rand) (sqrt.f64 -3)))))
(fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (.f64 rand (.f64 a (+.f64 (/.f64 (+.f64 -9/2 (.f64 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2) -1/6)) (/.f64 (sqrt.f64 -3) a)) (/.f64 -3/2 (sqrt.f64 -3))))))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 (.f64 -1/6 (/.f64 (.f64 (+.f64 81 (.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 (sqrt.f64 -3) 2)))) (.f64 (pow.f64 a 3) rand)) (sqrt.f64 -3))) (+.f64 (.f64 -3/2 (/.f64 (.f64 a rand) (sqrt.f64 -3))) (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (*.f64 (pow.f64 a 2) rand)) (sqrt.f64 -3))))))
(fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 -1/6 (/.f64 (+.f64 81 (.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 (sqrt.f64 -3) 2)))) (/.f64 (sqrt.f64 -3) (.f64 (pow.f64 a 3) rand))) (fma.f64 -3/2 (/.f64 a (/.f64 (sqrt.f64 -3) rand)) (.f64 -1/6 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) (.f64 (.f64 a a) rand)))))))
(fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 -1/6 (.f64 (/.f64 (fma.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) -3) 81) (sqrt.f64 -3)) (.f64 (pow.f64 a 3) rand)) (fma.f64 -3/2 (.f64 (/.f64 a (sqrt.f64 -3)) rand) (.f64 -1/6 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (/.f64 (sqrt.f64 -3) rand) (.f64 a a)))))))
(fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 -3/2 (/.f64 (.f64 a rand) (sqrt.f64 -3)) (.f64 -1/6 (+.f64 (.f64 (/.f64 (.f64 a (.f64 a rand)) (sqrt.f64 -3)) (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2))) (.f64 (/.f64 (.f64 (pow.f64 a 3) rand) (sqrt.f64 -3)) (+.f64 81 (*.f64 -3/2 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)))))))))
(+.f64 (.f64 rand (fma.f64 1/3 (sqrt.f64 -3) (/.f64 -3/2 (/.f64 (sqrt.f64 -3) a)))) (.f64 rand (.f64 (/.f64 -1/6 (sqrt.f64 -3)) (+.f64 (.f64 a (.f64 a (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)))) (.f64 (pow.f64 a 3) (+.f64 81 (*.f64 -3/2 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)))))))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (-.f64 a 1/3))) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 a -1/3)))))
(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (+.f64 -1/3 a)))))
(.f64 -1/3 (+.f64 (.f64 1/3 (*.f64 rand (sqrt.f64 -3))) 1))
(.f64 -1/3 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1))
(+.f64 -1/3 (.f64 (.f64 (sqrt.f64 -3) rand) -1/9))
(fma.f64 (*.f64 (sqrt.f64 -3) rand) -1/9 -1/3)
(+.f64 (.f64 a (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 1 (.f64 1/2 (/.f64 rand (sqrt.f64 -3)))))) (.f64 -1/3 (+.f64 (.f64 1/3 (*.f64 rand (sqrt.f64 -3))) 1)))
(fma.f64 a (+.f64 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1) (.f64 1/2 (/.f64 rand (sqrt.f64 -3)))) (.f64 -1/3 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1)))
(fma.f64 a (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 1/2 (/.f64 rand (sqrt.f64 -3)) 1)) (+.f64 -1/3 (.f64 (*.f64 (sqrt.f64 -3) rand) -1/9)))
(fma.f64 a (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 1/2 (/.f64 rand (sqrt.f64 -3)) 1)) (fma.f64 (.f64 (sqrt.f64 -3) rand) -1/9 -1/3))
(+.f64 (.f64 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1) (+.f64 -1/3 a)) (*.f64 a (/.f64 rand (/.f64 (sqrt.f64 -3) 1/2))))
(+.f64 (.f64 a (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 1 (.f64 1/2 (/.f64 rand (sqrt.f64 -3)))))) (+.f64 (.f64 -1/3 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) 1)) (.f64 (+.f64 (.f64 -3/2 (/.f64 rand (sqrt.f64 -3))) (.f64 1/18 (/.f64 (*.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) rand) (sqrt.f64 -3)))) (pow.f64 a 2))))
(fma.f64 a (+.f64 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1) (.f64 1/2 (/.f64 rand (sqrt.f64 -3)))) (fma.f64 -1/3 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1) (.f64 (.f64 a a) (fma.f64 -3/2 (/.f64 rand (sqrt.f64 -3)) (.f64 1/18 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) rand)))))))
(fma.f64 a (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 1/2 (/.f64 rand (sqrt.f64 -3)) 1)) (fma.f64 (.f64 a a) (fma.f64 -3/2 (/.f64 rand (sqrt.f64 -3)) (.f64 1/18 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) rand)))) (+.f64 -1/3 (.f64 (*.f64 (sqrt.f64 -3) rand) -1/9))))
(fma.f64 a (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 1/2 (/.f64 rand (sqrt.f64 -3)) 1)) (fma.f64 a (.f64 a (fma.f64 -3/2 (/.f64 rand (sqrt.f64 -3)) (.f64 1/18 (.f64 (/.f64 rand (sqrt.f64 -3)) (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)))))) (fma.f64 (*.f64 (sqrt.f64 -3) rand) -1/9 -1/3)))
(fma.f64 a (.f64 a (.f64 rand (+.f64 (/.f64 -3/2 (sqrt.f64 -3)) (/.f64 (+.f64 3/2 (.f64 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2) 1/18)) (sqrt.f64 -3))))) (+.f64 (.f64 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1) (+.f64 -1/3 a)) (.f64 a (/.f64 rand (/.f64 (sqrt.f64 -3) 1/2)))))
(+.f64 (.f64 (pow.f64 a 3) (+.f64 (.f64 1/18 (/.f64 (.f64 (+.f64 81 (.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 (sqrt.f64 -3) 2)))) rand) (sqrt.f64 -3))) (.f64 -1/6 (/.f64 (.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) rand) (sqrt.f64 -3))))) (+.f64 (.f64 a (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) (+.f64 1 (.f64 1/2 (/.f64 rand (sqrt.f64 -3)))))) (+.f64 (.f64 -1/3 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -3))) 1)) (.f64 (+.f64 (.f64 -3/2 (/.f64 rand (sqrt.f64 -3))) (.f64 1/18 (/.f64 (*.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) rand) (sqrt.f64 -3)))) (pow.f64 a 2)))))
(fma.f64 (pow.f64 a 3) (fma.f64 1/18 (/.f64 (+.f64 81 (.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (pow.f64 (sqrt.f64 -3) 2)))) (/.f64 (sqrt.f64 -3) rand)) (.f64 -1/6 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) rand)))) (fma.f64 a (+.f64 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1) (.f64 1/2 (/.f64 rand (sqrt.f64 -3)))) (fma.f64 -1/3 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1) (.f64 (.f64 a a) (fma.f64 -3/2 (/.f64 rand (sqrt.f64 -3)) (.f64 1/18 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) rand))))))))
(fma.f64 (pow.f64 a 3) (fma.f64 -1/6 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) rand)) (.f64 1/18 (/.f64 (fma.f64 9/2 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) -3) 81) (/.f64 (sqrt.f64 -3) rand)))) (fma.f64 a (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 1/2 (/.f64 rand (sqrt.f64 -3)) 1)) (fma.f64 (.f64 a a) (fma.f64 -3/2 (/.f64 rand (sqrt.f64 -3)) (.f64 1/18 (/.f64 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)) (/.f64 (sqrt.f64 -3) rand)))) (+.f64 -1/3 (.f64 (.f64 (sqrt.f64 -3) rand) -1/9)))))
(fma.f64 a (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) (fma.f64 1/2 (/.f64 rand (sqrt.f64 -3)) 1)) (fma.f64 (pow.f64 a 3) (fma.f64 -1/6 (.f64 (/.f64 rand (sqrt.f64 -3)) (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2))) (/.f64 (+.f64 81 (.f64 -3/2 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)))) (/.f64 (/.f64 (sqrt.f64 -3) rand) 1/18))) (fma.f64 a (.f64 a (fma.f64 -3/2 (/.f64 rand (sqrt.f64 -3)) (.f64 1/18 (.f64 (/.f64 rand (sqrt.f64 -3)) (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2)))))) (fma.f64 (*.f64 (sqrt.f64 -3) rand) -1/9 -1/3))))
(fma.f64 (pow.f64 a 3) (.f64 rand (+.f64 (/.f64 (+.f64 9/2 (.f64 (.f64 -3/2 (+.f64 27 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2))) 1/18)) (sqrt.f64 -3)) (/.f64 (+.f64 -9/2 (.f64 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2) -1/6)) (sqrt.f64 -3)))) (fma.f64 a (.f64 a (.f64 rand (+.f64 (/.f64 -3/2 (sqrt.f64 -3)) (/.f64 (+.f64 3/2 (.f64 (pow.f64 (/.f64 -9/2 (sqrt.f64 -3)) 2) 1/18)) (sqrt.f64 -3))))) (+.f64 (.f64 (fma.f64 1/3 (.f64 (sqrt.f64 -3) rand) 1) (+.f64 -1/3 a)) (.f64 a (/.f64 rand (/.f64 (sqrt.f64 -3) 1/2))))))
a
(-.f64 a 1/3)
(+.f64 a -1/3)
(+.f64 -1/3 a)
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 a -1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 a -1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 a -1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3))))
(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 a -1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 a -1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 a -1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3))))
(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 a -1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 a -1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 a -1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a))
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))

prune277.0ms (9.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	164	4	168

Error

Counts

168 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
▶	0.1b	(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
	0.1b	(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)

Compiler

Compiled 4059 to 3358 computations (17.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 -1/3 a))
✓	0.1b	(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
✓	0.3b	(*.f64 1/3 rand)

series6.0ms (0.2%)

Counts

3 → 22

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	a	@	0	(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
1.0ms	a	@	inf	(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
1.0ms	a	@	-inf	(sqrt.f64 (+.f64 -1/3 a))
1.0ms	rand	@	0	(*.f64 1/3 rand)
1.0ms	rand	@	0	(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))

rewrite47.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

860×	`log1p-expm1-u_binary64`
860×	`expm1-log1p-u_binary64`
96×	`add-sqr-sqrt_binary64`
90×	`*-un-lft-identity_binary64`
90×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	191	26
2	2288	26

Stop Event

1×	node limit

Counts

3 → 64

Calls

Call 1

Inputs
(*.f64 1/3 rand)
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
(sqrt.f64 (+.f64 -1/3 a))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/3 rand))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/3 rand) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 1/3 rand) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/3 rand)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/3 rand)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 1/3 rand) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) rand))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/3 rand))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 1/3 rand) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/3 rand)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/3 rand)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/3 rand)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/3 rand)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 -1/3 a) (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))) 1) (+.f64 -1/3 a))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))) -1/3) a)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))) a) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 -1/3 a)) (+.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))) (pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))) 2) (cbrt.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))) (sqrt.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))) 3) (pow.f64 (+.f64 -1/3 a) 3)) (+.f64 (.f64 (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))) (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))) (-.f64 (pow.f64 (+.f64 -1/3 a) 2) (.f64 (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))) (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))) (pow.f64 (+.f64 -1/3 a) 2)) (-.f64 (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand) (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 -1/3 a)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 -1/3 a)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (+.f64 -1/3 a))) (cbrt.f64 (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 -1/3 a)) (cbrt.f64 (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 -1/3 a) 1/4) (pow.f64 (+.f64 -1/3 a) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 -1/3 a) 2))) (sqrt.f64 (cbrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 -1/3 a) 2)) 1/2) (pow.f64 (cbrt.f64 (+.f64 -1/3 a)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1/9 (.f64 a a))) (sqrt.f64 (-.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 -1/27 (pow.f64 a 3))) (sqrt.f64 (+.f64 1/9 (.f64 a (-.f64 a -1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 -1/3 a) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 -1/3 a)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 -1/3 a) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 -1/3 a))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 -1/3 a) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 -1/3 a)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 -1/3 a) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 -1/3 a)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 -1/3 a))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 -1/3 a))))))))

Outputs

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

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 -1/3 a)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 -1/3 a)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 -1/3 a))) (cbrt.f64 (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 -1/3 a)) (cbrt.f64 (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 -1/3 a) 1/4) (pow.f64 (+.f64 -1/3 a) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 -1/3 a) 2))) (sqrt.f64 (cbrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 -1/3 a) 2)) 1/2) (pow.f64 (cbrt.f64 (+.f64 -1/3 a)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1/9 (*.f64 a a))) (sqrt.f64 (-.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 -1/27 (pow.f64 a 3))) (sqrt.f64 (+.f64 1/9 (*.f64 a (-.f64 a -1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 -1/3 a) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 -1/3 a)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 -1/3 a) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 -1/3 a))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 -1/3 a) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 -1/3 a)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 -1/3 a)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 -1/3 a) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 -1/3 a)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 -1/3 a))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 -1/3 a))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 -1/3 a))))))))

simplify29.0ms (1%)

Algorithm

1×	egg-herbie

Rules

516×	`associate-r_binary64`
490×	`associate-/r*_binary64`
447×	`associate-l_binary64`
417×	`associate-*l/_binary64`
288×	`associate-*r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	403
1	160	389
2	476	381
3	1783	378

Stop Event

1×	node limit

Counts

86 → 87

Calls

Call 1

Inputs
(-.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) 1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a)) 1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a))) 1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a) (.f64 1/48 (/.f64 (.f64 (pow.f64 a 3) rand) (pow.f64 (sqrt.f64 -1/3) 5)))))) 1/3)
a
a
(-.f64 a 1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(sqrt.f64 -1/3)
(+.f64 (*.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3)))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (*.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3))))

Outputs
(-.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) 1/3)
(fma.f64 1/3 (*.f64 rand (sqrt.f64 -1/3)) -1/3)
(fma.f64 (*.f64 1/3 rand) (sqrt.f64 -1/3) -1/3)
(fma.f64 rand (*.f64 1/3 (sqrt.f64 -1/3)) -1/3)
(-.f64 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a)) 1/3)
(+.f64 (fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (.f64 (+.f64 1 (*.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a)) -1/3)
(fma.f64 1/3 (*.f64 rand (sqrt.f64 -1/3)) (fma.f64 (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1) a -1/3))
(-.f64 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a))) 1/3)
(+.f64 (fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 -1/24 (/.f64 (.f64 rand (.f64 a a)) (pow.f64 (sqrt.f64 -1/3) 3)) (.f64 (+.f64 1 (*.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a))) -1/3)
(+.f64 (fma.f64 (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1) a (.f64 1/8 (/.f64 (.f64 rand (.f64 a a)) (sqrt.f64 -1/3)))) (fma.f64 (.f64 1/3 rand) (sqrt.f64 -1/3) -1/3))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1) a (fma.f64 1/8 (/.f64 (.f64 rand a) (/.f64 (sqrt.f64 -1/3) a)) -1/3)))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1) a (fma.f64 1/8 (.f64 rand (*.f64 a (/.f64 a (sqrt.f64 -1/3)))) -1/3)))
(-.f64 (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a) (.f64 1/48 (/.f64 (.f64 (pow.f64 a 3) rand) (pow.f64 (sqrt.f64 -1/3) 5)))))) 1/3)
(+.f64 (fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 -1/24 (/.f64 (.f64 rand (.f64 a a)) (pow.f64 (sqrt.f64 -1/3) 3)) (fma.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a (.f64 1/48 (/.f64 (.f64 rand (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5)))))) -1/3)
(+.f64 -1/3 (+.f64 (fma.f64 (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1) a (/.f64 (.f64 (.f64 1/48 rand) (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5))) (fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/8 (/.f64 (.f64 rand (.f64 a a)) (sqrt.f64 -1/3))))))
(+.f64 (fma.f64 (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1) a (fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/8 (/.f64 (.f64 rand a) (/.f64 (sqrt.f64 -1/3) a))))) (fma.f64 1/48 (.f64 rand (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5))) -1/3))
(+.f64 -1/3 (fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/48 (.f64 (/.f64 rand (pow.f64 (sqrt.f64 -1/3) 5)) (pow.f64 a 3)) (+.f64 a (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 (.f64 a 1/6) (.f64 -1/24 (/.f64 (.f64 a a) -1/3))))))))
a
a
(-.f64 a 1/3)
(+.f64 -1/3 a)
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
(+.f64 a (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) -1/3))
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
(+.f64 a (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) -1/3))
(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
(+.f64 a (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) -1/3))
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 1/3 rand))
(.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
(+.f64 a (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) -1/3))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
(+.f64 a (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) -1/3))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
(+.f64 a (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) -1/3))
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 1/3 rand))
(.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
(+.f64 a (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) -1/3))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
(+.f64 a (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) -1/3))
(-.f64 (+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))) 1/3)
(+.f64 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a) -1/3)
(+.f64 -1/3 (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) a))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) (+.f64 -1/3 a))
(+.f64 a (fma.f64 1/3 (*.f64 rand (sqrt.f64 (-.f64 a 1/3))) -1/3))
(sqrt.f64 -1/3)
(+.f64 (*.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3))
(fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3)))
(fma.f64 -1/8 (/.f64 (*.f64 a a) (pow.f64 (sqrt.f64 -1/3) 3)) (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3)))
(+.f64 (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3)) (.f64 3/8 (/.f64 (.f64 a a) (sqrt.f64 -1/3))))
(fma.f64 3/8 (/.f64 a (/.f64 (sqrt.f64 -1/3) a)) (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3)))
(+.f64 (sqrt.f64 -1/3) (.f64 (/.f64 a (sqrt.f64 -1/3)) (+.f64 1/2 (/.f64 (.f64 a -1/8) -1/3))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (*.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3))))
(fma.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (fma.f64 -1/8 (/.f64 (*.f64 a a) (pow.f64 (sqrt.f64 -1/3) 3)) (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3))))
(+.f64 (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3)) (fma.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (.f64 3/8 (/.f64 (.f64 a a) (sqrt.f64 -1/3)))))
(fma.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (fma.f64 3/8 (/.f64 a (/.f64 (sqrt.f64 -1/3) a)) (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3))))
(+.f64 (sqrt.f64 -1/3) (fma.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (.f64 (/.f64 a (sqrt.f64 -1/3)) (+.f64 1/2 (/.f64 (.f64 a -1/8) -1/3)))))

prune82.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	87	4	91

Error

Counts

91 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
▶	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
	0.1b	(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)

Compiler

Compiled 1512 to 1194 computations (21% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a 9 -3)
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
✓	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series19.0ms (0.6%)

Counts

4 → 50

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	a	@	-inf	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
3.0ms	a	@	0	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	a	@	0	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
1.0ms	rand	@	0	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
1.0ms	a	@	-inf	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))

rewrite69.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`prod-diff_binary64`
237×	`log1p-udef_binary64`
140×	`add-sqr-sqrt_binary64`
132×	`*-un-lft-identity_binary64`
132×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	287	40
2	3734	40

Stop Event

1×	node limit

Counts

4 → 127

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 a 9 -3))
(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
(fma.f64 a 9 -3)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 a 9 -3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 a 9 -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 a 9 -3) 1/4) (pow.f64 (fma.f64 a 9 -3) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 a 9 -3) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 a 9 -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 a 9 -3) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 a 9 -3) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 a 9 -3)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 a 9 -3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 a 9 -3))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (cbrt.f64 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 rand rand)) (.f64 (cbrt.f64 rand) (pow.f64 (fma.f64 a 9 -3) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 rand) (.f64 (sqrt.f64 rand) (pow.f64 (fma.f64 a 9 -3) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 rand) (/.f64 1 (neg.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 a 9 -3) -1/2) rand)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 rand rand)) 1) (/.f64 (cbrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 rand) 1) (/.f64 (sqrt.f64 rand) (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 rand rand)) (cbrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 rand) (cbrt.f64 (fma.f64 a 9 -3))) (/.f64 (sqrt.f64 rand) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 (fma.f64 a 9 -3) 1/4)) (/.f64 rand (pow.f64 (fma.f64 a 9 -3) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 rand rand)) (pow.f64 (fma.f64 a 9 -3) 1/4)) (/.f64 (cbrt.f64 rand) (pow.f64 (fma.f64 a 9 -3) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 rand (neg.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 a (+.f64 -1/3 (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 a -1/3) (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 a -1/3) (.f64 (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))) (+.f64 a -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (.f64 -1/3 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1) a) (.f64 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 a (-.f64 1/3 (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 a 3) -1/27) (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3))) (.f64 (fma.f64 a a (+.f64 1/9 (.f64 a 1/3))) (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 a a -1/9) (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3))) (.f64 (+.f64 a 1/3) (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 a 3) -1/27) (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)))) (.f64 (fma.f64 a a (+.f64 1/9 (.f64 a 1/3))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 a a -1/9) (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)))) (.f64 (+.f64 a 1/3) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3)) (+.f64 (pow.f64 a 3) -1/27)) (.f64 (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (fma.f64 a a (+.f64 1/9 (.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (+.f64 (pow.f64 a 3) -1/27)) (.f64 (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (fma.f64 a a (+.f64 1/9 (.f64 a 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3)) (fma.f64 a a -1/9)) (.f64 (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (+.f64 a 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (fma.f64 a a -1/9)) (.f64 (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (+.f64 a 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 a -1/3) 3) (pow.f64 (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))) 3)) (+.f64 (pow.f64 (+.f64 a -1/3) 2) (-.f64 (.f64 (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3)))) (.f64 (+.f64 a -1/3) (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 a -1/3) 2) (.f64 (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))))) (-.f64 (+.f64 a -1/3) (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (pow.f64 a 3) -1/27) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (fma.f64 a a (+.f64 1/9 (.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 a a -1/9) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) (+.f64 a 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3)) (+.f64 a -1/3)) (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3))) (+.f64 a -1/3)) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 a -1/3) (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3))) (+.f64 1 (-.f64 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 a -1/3) (-.f64 1 (/.f64 (.f64 rand rand) (fma.f64 a 9 -3)))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1) (+.f64 (pow.f64 a 3) -1/27)) (fma.f64 a a (+.f64 1/9 (.f64 a 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1) (fma.f64 a a -1/9)) (+.f64 a 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 a -1/3)) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (+.f64 a -1/3) 3) (pow.f64 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1) 3) (pow.f64 (+.f64 a -1/3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log1p.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (log.f64 (+.f64 a -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (+.f64 (log1p.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (log.f64 (+.f64 a -1/3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 a -1/3) 1 (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 a -1/3) (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 a -1/3) 2)) (cbrt.f64 (+.f64 a -1/3)) (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 a -1/3)) (sqrt.f64 (+.f64 a -1/3)) (/.f64 (.f64 rand (+.f64 a -1/3)) (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 a -1/3) (fma.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2) 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 -3 (.f64 a 9))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a 9) -3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 a 9) 1) -3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 a 9 -3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 a 9 -3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 a 9 -3)) (sqrt.f64 (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 a 9 -3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 a 9 -3)) (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 a 9 -3)) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 2) (cbrt.f64 (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 a 9 -3) 1/4) (.f64 (pow.f64 (fma.f64 a 9 -3) 1/4) (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (fma.f64 a 9 -3)) (pow.f64 (fma.f64 a 9 -3) 1/4)) (pow.f64 (fma.f64 a 9 -3) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (fma.f64 a 9 -3)) (cbrt.f64 (fma.f64 a 9 -3))) (cbrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 a 9) 3) -27) (+.f64 (.f64 (.f64 a 9) (.f64 a 9)) (-.f64 9 (.f64 (.f64 a 9) -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 a 9) (.f64 a 9)) 9) (-.f64 (.f64 a 9) -3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 a 9 -3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 a 9 -3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 a 9 -3) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 a 9 -3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 a 9 -3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 a 9 -3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 a 9 -3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 a 9 -3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 a 9 -3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 a 9 -3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 a 9 -3)))))))

simplify47.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

408×	`fma-def_binary64`
351×	`associate-r_binary64`
312×	`associate-l_binary64`
289×	`distribute-rgt-out_binary64`
197×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	969
1	277	935
2	932	906
3	4276	888

Stop Event

1×	node limit

Counts

177 → 163

Calls

Call 1

Inputs
(sqrt.f64 -3)
(+.f64 (*.f64 9/2 (/.f64 a (sqrt.f64 -3))) (sqrt.f64 -3))
(+.f64 (.f64 -81/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -3) 3))) (+.f64 (.f64 9/2 (/.f64 a (sqrt.f64 -3))) (sqrt.f64 -3)))
(+.f64 (.f64 -81/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -3) 3))) (+.f64 (.f64 729/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -3) 5))) (+.f64 (*.f64 9/2 (/.f64 a (sqrt.f64 -3))) (sqrt.f64 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 -1/3))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (*.f64 rand (sqrt.f64 -1/3)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (.f64 (pow.f64 a 2) rand)) (sqrt.f64 -1/3))) (.f64 rand (sqrt.f64 -1/3))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (.f64 (pow.f64 a 2) rand)) (sqrt.f64 -1/3))) (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a 3) (.f64 rand (+.f64 9 (.f64 1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (pow.f64 (sqrt.f64 -1/3) 2)))))) (sqrt.f64 -1/3))))))
(.f64 -1/3 (+.f64 (.f64 rand (sqrt.f64 -1/3)) 1))
(+.f64 (.f64 a (+.f64 1 (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))))) (.f64 -1/3 (+.f64 (*.f64 rand (sqrt.f64 -1/3)) 1)))
(+.f64 (.f64 a (+.f64 1 (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))))) (+.f64 (.f64 (pow.f64 a 2) (+.f64 (.f64 1/6 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) rand) (sqrt.f64 -1/3))) (.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3))))) (.f64 -1/3 (+.f64 (*.f64 rand (sqrt.f64 -1/3)) 1))))
(+.f64 (.f64 (pow.f64 a 3) (+.f64 (.f64 1/6 (/.f64 (.f64 rand (+.f64 9 (.f64 1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (pow.f64 (sqrt.f64 -1/3) 2))))) (sqrt.f64 -1/3))) (.f64 -1/2 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) rand) (sqrt.f64 -1/3))))) (+.f64 (.f64 a (+.f64 1 (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))))) (+.f64 (.f64 (pow.f64 a 2) (+.f64 (.f64 1/6 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) rand) (sqrt.f64 -1/3))) (.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3))))) (.f64 -1/3 (+.f64 (*.f64 rand (sqrt.f64 -1/3)) 1)))))
a
a
(-.f64 a 1/3)
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
-3
(-.f64 (*.f64 9 a) 3)
(-.f64 (*.f64 9 a) 3)
(-.f64 (*.f64 9 a) 3)
(*.f64 9 a)
(-.f64 (*.f64 9 a) 3)
(-.f64 (*.f64 9 a) 3)
(-.f64 (*.f64 9 a) 3)
(*.f64 9 a)
(-.f64 (*.f64 9 a) 3)
(-.f64 (*.f64 9 a) 3)
(-.f64 (*.f64 9 a) 3)

Outputs
(sqrt.f64 -3)
(+.f64 (*.f64 9/2 (/.f64 a (sqrt.f64 -3))) (sqrt.f64 -3))
(fma.f64 9/2 (/.f64 a (sqrt.f64 -3)) (sqrt.f64 -3))
(+.f64 (.f64 -81/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -3) 3))) (+.f64 (.f64 9/2 (/.f64 a (sqrt.f64 -3))) (sqrt.f64 -3)))
(fma.f64 -81/8 (/.f64 (*.f64 a a) (pow.f64 (sqrt.f64 -3) 3)) (fma.f64 9/2 (/.f64 a (sqrt.f64 -3)) (sqrt.f64 -3)))
(+.f64 (fma.f64 9/2 (/.f64 a (sqrt.f64 -3)) (sqrt.f64 -3)) (.f64 27/8 (/.f64 (.f64 a a) (sqrt.f64 -3))))
(fma.f64 9/2 (/.f64 a (sqrt.f64 -3)) (fma.f64 27/8 (/.f64 a (/.f64 (sqrt.f64 -3) a)) (sqrt.f64 -3)))
(+.f64 (sqrt.f64 -3) (.f64 (/.f64 a (sqrt.f64 -3)) (+.f64 9/2 (/.f64 (.f64 a -81/8) -3))))
(+.f64 (.f64 -81/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -3) 3))) (+.f64 (.f64 729/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -3) 5))) (+.f64 (*.f64 9/2 (/.f64 a (sqrt.f64 -3))) (sqrt.f64 -3))))
(fma.f64 -81/8 (/.f64 (*.f64 a a) (pow.f64 (sqrt.f64 -3) 3)) (fma.f64 729/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -3) 5)) (fma.f64 9/2 (/.f64 a (sqrt.f64 -3)) (sqrt.f64 -3))))
(+.f64 (.f64 27/8 (/.f64 (.f64 a a) (sqrt.f64 -3))) (fma.f64 729/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -3) 5)) (fma.f64 9/2 (/.f64 a (sqrt.f64 -3)) (sqrt.f64 -3))))
(fma.f64 729/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -3) 5)) (fma.f64 9/2 (/.f64 a (sqrt.f64 -3)) (fma.f64 27/8 (/.f64 a (/.f64 (sqrt.f64 -3) a)) (sqrt.f64 -3))))
(+.f64 (fma.f64 729/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -3) 5)) (sqrt.f64 -3)) (.f64 (/.f64 a (sqrt.f64 -3)) (+.f64 9/2 (/.f64 (.f64 a -81/8) -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))))
(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
(*.f64 rand (sqrt.f64 -1/3))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (*.f64 rand (sqrt.f64 -1/3)))
(fma.f64 -1/2 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand)) (*.f64 rand (sqrt.f64 -1/3)))
(fma.f64 -1/2 (.f64 (/.f64 a (sqrt.f64 -1/3)) rand) (.f64 rand (sqrt.f64 -1/3)))
(fma.f64 rand (sqrt.f64 -1/3) (*.f64 -1/2 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand))))
(.f64 rand (+.f64 (sqrt.f64 -1/3) (/.f64 (.f64 a -1/2) (sqrt.f64 -1/3))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (.f64 (pow.f64 a 2) rand)) (sqrt.f64 -1/3))) (.f64 rand (sqrt.f64 -1/3))))
(fma.f64 -1/2 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand)) (fma.f64 -1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) (.f64 (.f64 a a) rand))) (*.f64 rand (sqrt.f64 -1/3))))
(fma.f64 -1/2 (.f64 (/.f64 a (sqrt.f64 -1/3)) rand) (fma.f64 rand (sqrt.f64 -1/3) (.f64 -1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) (.f64 a (.f64 a rand)))))))
(fma.f64 rand (sqrt.f64 -1/3) (.f64 -1/2 (fma.f64 (/.f64 a (sqrt.f64 -1/3)) rand (.f64 a (.f64 a (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2))))))))
(fma.f64 rand (sqrt.f64 -1/3) (.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) (+.f64 (.f64 a rand) (.f64 a (.f64 a (*.f64 rand (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2))))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (.f64 (pow.f64 a 2) rand)) (sqrt.f64 -1/3))) (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a 3) (.f64 rand (+.f64 9 (.f64 1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (pow.f64 (sqrt.f64 -1/3) 2)))))) (sqrt.f64 -1/3))))))
(fma.f64 -1/2 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand)) (fma.f64 -1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) (.f64 (.f64 a a) rand))) (fma.f64 rand (sqrt.f64 -1/3) (.f64 -1/2 (/.f64 (.f64 (.f64 (pow.f64 a 3) rand) (+.f64 9 (.f64 1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (pow.f64 (sqrt.f64 -1/3) 2))))) (sqrt.f64 -1/3))))))
(fma.f64 -1/2 (.f64 (/.f64 a (sqrt.f64 -1/3)) rand) (fma.f64 -1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) (.f64 a (.f64 a rand)))) (fma.f64 rand (sqrt.f64 -1/3) (/.f64 (.f64 (pow.f64 a 3) -1/2) (/.f64 (/.f64 (sqrt.f64 -1/3) rand) (fma.f64 1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) -1/3) 9))))))
(fma.f64 -1/2 (fma.f64 (/.f64 a (sqrt.f64 -1/3)) rand (.f64 a (.f64 a (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)))))) (fma.f64 rand (sqrt.f64 -1/3) (.f64 (/.f64 (pow.f64 a 3) (sqrt.f64 -1/3)) (.f64 (.f64 rand -1/2) (+.f64 9 (*.f64 -3/2 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2))))))))
(+.f64 (.f64 rand (+.f64 (sqrt.f64 -1/3) (/.f64 (.f64 -1/2 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2))) (/.f64 (sqrt.f64 -1/3) (.f64 a a))))) (.f64 -1/2 (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 (.f64 (pow.f64 a 3) (+.f64 9 (*.f64 -3/2 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2))))) a))))
(.f64 -1/3 (+.f64 (.f64 rand (sqrt.f64 -1/3)) 1))
(*.f64 -1/3 (fma.f64 rand (sqrt.f64 -1/3) 1))
(fma.f64 rand (*.f64 -1/3 (sqrt.f64 -1/3)) -1/3)
(+.f64 (.f64 a (+.f64 1 (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))))) (.f64 -1/3 (+.f64 (*.f64 rand (sqrt.f64 -1/3)) 1)))
(fma.f64 a (+.f64 (fma.f64 rand (sqrt.f64 -1/3) 1) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) (.f64 -1/3 (fma.f64 rand (sqrt.f64 -1/3) 1)))
(fma.f64 a (+.f64 1 (fma.f64 rand (sqrt.f64 -1/3) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3))))) (.f64 -1/3 (fma.f64 rand (sqrt.f64 -1/3) 1)))
(fma.f64 a (fma.f64 rand (sqrt.f64 -1/3) (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1)) (fma.f64 rand (*.f64 -1/3 (sqrt.f64 -1/3)) -1/3))
(+.f64 (.f64 (fma.f64 rand (sqrt.f64 -1/3) 1) (+.f64 a -1/3)) (.f64 a (/.f64 1/6 (/.f64 (sqrt.f64 -1/3) rand))))
(+.f64 (.f64 a (+.f64 1 (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))))) (+.f64 (.f64 (pow.f64 a 2) (+.f64 (.f64 1/6 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) rand) (sqrt.f64 -1/3))) (.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3))))) (.f64 -1/3 (+.f64 (*.f64 rand (sqrt.f64 -1/3)) 1))))
(fma.f64 a (+.f64 (fma.f64 rand (sqrt.f64 -1/3) 1) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) (fma.f64 (.f64 a a) (fma.f64 1/6 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) rand)) (.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3)))) (.f64 -1/3 (fma.f64 rand (sqrt.f64 -1/3) 1))))
(fma.f64 a (+.f64 1 (fma.f64 rand (sqrt.f64 -1/3) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3))))) (fma.f64 (.f64 a a) (fma.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) rand)))) (.f64 -1/3 (fma.f64 rand (sqrt.f64 -1/3) 1))))
(fma.f64 -1/3 (fma.f64 rand (sqrt.f64 -1/3) 1) (.f64 a (+.f64 (fma.f64 rand (sqrt.f64 -1/3) (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1)) (.f64 a (fma.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)))))))))
(fma.f64 a (.f64 a (.f64 rand (+.f64 (/.f64 (+.f64 1/2 (.f64 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2) 1/6)) (sqrt.f64 -1/3)) (/.f64 -1/2 (sqrt.f64 -1/3))))) (+.f64 (.f64 (fma.f64 rand (sqrt.f64 -1/3) 1) (+.f64 a -1/3)) (*.f64 a (/.f64 1/6 (/.f64 (sqrt.f64 -1/3) rand)))))
(+.f64 (.f64 (pow.f64 a 3) (+.f64 (.f64 1/6 (/.f64 (.f64 rand (+.f64 9 (.f64 1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (pow.f64 (sqrt.f64 -1/3) 2))))) (sqrt.f64 -1/3))) (.f64 -1/2 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) rand) (sqrt.f64 -1/3))))) (+.f64 (.f64 a (+.f64 1 (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))))) (+.f64 (.f64 (pow.f64 a 2) (+.f64 (.f64 1/6 (/.f64 (.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) rand) (sqrt.f64 -1/3))) (.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3))))) (.f64 -1/3 (+.f64 (*.f64 rand (sqrt.f64 -1/3)) 1)))))
(fma.f64 (pow.f64 a 3) (fma.f64 1/6 (/.f64 rand (/.f64 (sqrt.f64 -1/3) (+.f64 9 (.f64 1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (pow.f64 (sqrt.f64 -1/3) 2)))))) (.f64 -1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) rand)))) (fma.f64 a (+.f64 (fma.f64 rand (sqrt.f64 -1/3) 1) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) (fma.f64 (.f64 a a) (fma.f64 1/6 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) rand)) (.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3)))) (.f64 -1/3 (fma.f64 rand (sqrt.f64 -1/3) 1)))))
(fma.f64 (pow.f64 a 3) (fma.f64 -1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) rand)) (.f64 1/6 (.f64 (/.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) -1/3) 9)))) (fma.f64 a (+.f64 1 (fma.f64 rand (sqrt.f64 -1/3) (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3))))) (fma.f64 (.f64 a a) (fma.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (/.f64 (sqrt.f64 -1/3) rand)))) (.f64 -1/3 (fma.f64 rand (sqrt.f64 -1/3) 1)))))
(fma.f64 (pow.f64 a 3) (fma.f64 -1/2 (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2))) (.f64 1/6 (.f64 (+.f64 9 (.f64 -3/2 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)))) (/.f64 rand (sqrt.f64 -1/3))))) (fma.f64 -1/3 (fma.f64 rand (sqrt.f64 -1/3) 1) (.f64 a (+.f64 (fma.f64 rand (sqrt.f64 -1/3) (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1)) (.f64 a (fma.f64 -1/2 (/.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2))))))))))
(fma.f64 (pow.f64 a 3) (.f64 rand (+.f64 (.f64 -1/2 (/.f64 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)) (sqrt.f64 -1/3))) (/.f64 1/6 (/.f64 (sqrt.f64 -1/3) (+.f64 9 (.f64 -3/2 (+.f64 3 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2)))))))) (fma.f64 a (.f64 a (.f64 rand (+.f64 (/.f64 (+.f64 1/2 (.f64 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1/3)) 2) 1/6)) (sqrt.f64 -1/3)) (/.f64 -1/2 (sqrt.f64 -1/3))))) (+.f64 (.f64 (fma.f64 rand (sqrt.f64 -1/3) 1) (+.f64 a -1/3)) (.f64 a (/.f64 1/6 (/.f64 (sqrt.f64 -1/3) rand))))))
a
a
(-.f64 a 1/3)
(+.f64 a -1/3)
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(+.f64 a (-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3))) 1/3))
(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
(.f64 (+.f64 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) 1) (+.f64 a -1/3))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(+.f64 a (-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3))) 1/3))
(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
(.f64 (+.f64 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) 1) (+.f64 a -1/3))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(+.f64 a (-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3))) 1/3))
(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
(.f64 (+.f64 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) 1) (+.f64 a -1/3))
(.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))
(.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3)))
(.f64 rand (.f64 (+.f64 a -1/3) (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))))
(.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (.f64 rand (+.f64 a -1/3)))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(+.f64 a (-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3))) 1/3))
(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
(.f64 (+.f64 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) 1) (+.f64 a -1/3))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(+.f64 a (-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3))) 1/3))
(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
(.f64 (+.f64 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) 1) (+.f64 a -1/3))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(+.f64 a (-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3))) 1/3))
(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
(.f64 (+.f64 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) 1) (+.f64 a -1/3))
(.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))
(.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3)))
(.f64 rand (.f64 (+.f64 a -1/3) (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))))
(.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (.f64 rand (+.f64 a -1/3)))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(+.f64 a (-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3))) 1/3))
(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
(.f64 (+.f64 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) 1) (+.f64 a -1/3))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(+.f64 a (-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3))) 1/3))
(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
(.f64 (+.f64 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) 1) (+.f64 a -1/3))
(-.f64 (+.f64 a (.f64 (.f64 (-.f64 a 1/3) rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))) 1/3)
(+.f64 a (-.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 9 a -3))) (.f64 rand (+.f64 a -1/3))) 1/3))
(+.f64 a (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (*.f64 rand (+.f64 a -1/3)) -1/3))
(.f64 (+.f64 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) 1) (+.f64 a -1/3))
-3
(-.f64 (*.f64 9 a) 3)
(fma.f64 9 a -3)
(fma.f64 a 9 -3)
(-.f64 (*.f64 9 a) 3)
(fma.f64 9 a -3)
(fma.f64 a 9 -3)
(-.f64 (*.f64 9 a) 3)
(fma.f64 9 a -3)
(fma.f64 a 9 -3)
(*.f64 9 a)
(*.f64 a 9)
(-.f64 (*.f64 9 a) 3)
(fma.f64 9 a -3)
(fma.f64 a 9 -3)
(-.f64 (*.f64 9 a) 3)
(fma.f64 9 a -3)
(fma.f64 a 9 -3)
(-.f64 (*.f64 9 a) 3)
(fma.f64 9 a -3)
(fma.f64 a 9 -3)
(*.f64 9 a)
(*.f64 a 9)
(-.f64 (*.f64 9 a) 3)
(fma.f64 9 a -3)
(fma.f64 a 9 -3)
(-.f64 (*.f64 9 a) 3)
(fma.f64 9 a -3)
(fma.f64 a 9 -3)
(-.f64 (*.f64 9 a) 3)
(fma.f64 9 a -3)
(fma.f64 a 9 -3)

prune214.0ms (7.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	163	4	167

Error

Counts

167 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
▶	0.1b	(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)

Compiler

Compiled 3512 to 2784 computations (20.7% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a)
✓	0.0b	(sqrt.f64 (-.f64 a 1/3))
✓	0.3b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
✓	0.4b	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))

series11.0ms (0.4%)

Counts

4 → 27

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	a	@	0	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
1.0ms	rand	@	0	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
1.0ms	a	@	inf	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
1.0ms	rand	@	inf	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
1.0ms	a	@	-inf	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))

rewrite57.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

490×	`log-prod_binary64`
338×	`fma-def_binary64`
183×	`fma-neg_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	40
1	204	40
2	2749	40

Stop Event

1×	node limit

Counts

4 → 120

Calls

Call 1

Inputs
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
(sqrt.f64 (-.f64 a 1/3))
(+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 1/3) (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) (cbrt.f64 (pow.f64 (exp.f64 1/3) (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/3) (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/3) (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/3) (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/27 (pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 1/27 (pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/3 (*.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))) rand)) (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))) rand)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))) rand))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))) rand))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))) rand))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (+.f64 a -1/3) (.f64 rand rand)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))) rand))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (+.f64 a -1/3) 3/2) (pow.f64 rand 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 rand 3) (pow.f64 (+.f64 a -1/3) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 a -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3)))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 a -1/3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 a -1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (+.f64 a -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (+.f64 a -1/3))) (cbrt.f64 (+.f64 a -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 a -1/3)) (cbrt.f64 (sqrt.f64 (+.f64 a -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 a -1/3) 1/4) (pow.f64 (+.f64 a -1/3) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 a -1/3)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 a -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 a -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 a -1/3)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 a -1/3)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 a 3) -1/27)) (hypot.f64 a (sqrt.f64 (fma.f64 1/3 a 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 a a -1/9)) (sqrt.f64 (-.f64 a -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 a -1/3) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 a -1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 a -1/3) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 a -1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 a -1/3) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 a -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 a -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 a -1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 a -1/3) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (+.f64 a -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 a -1/3)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 a -1/3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 a -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 a -1/3))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand))) (-.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) a)) (/.f64 (.f64 a a) (-.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) a)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)) (pow.f64 (cbrt.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)) 2) (cbrt.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)) (sqrt.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/27 (pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 3) (pow.f64 a 3)) (/.f64 1 (fma.f64 a (-.f64 a (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand)) (neg.f64 (.f64 a a))) (/.f64 1 (-.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) a)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 a (-.f64 a (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand)))) (fma.f64 1/27 (pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 3) (pow.f64 a 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) a) (fma.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand)) (neg.f64 (.f64 a a)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/27 (pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 3) (pow.f64 a 3)) (fma.f64 a (-.f64 a (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/27 (pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 3) (pow.f64 a 3)) (fma.f64 a a (-.f64 (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand))) (.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) (.f64 1/3 a)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand)) (neg.f64 (.f64 a a))) (-.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) a))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 1/27 (pow.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 3) (pow.f64 a 3))) (neg.f64 (fma.f64 a (-.f64 a (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand)) (neg.f64 (.f64 a a)))) (neg.f64 (-.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) a)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 a a) (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand)))) (-.f64 a (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 a)) (pow.f64 (exp.f64 1/3) (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 a) (+.f64 1 (expm1.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 a)) (+.f64 1 (expm1.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))) (exp.f64 a)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 1/3) (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) (+.f64 1 (expm1.f64 a))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))) (+.f64 1 (expm1.f64 a))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a 1 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 a -1/3)) (.f64 rand 1/3) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 rand (.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) 1/3 a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) 1 a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 a (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) (cbrt.f64 (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand)))) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 1/9 (.f64 (+.f64 a -1/3) (.f64 rand rand)))) (cbrt.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 a) (cbrt.f64 (.f64 a a)) (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 a a)) (cbrt.f64 a) (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (+.f64 a -1/3) (.f64 rand rand))) (.f64 (cbrt.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) 1/3) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) (sqrt.f64 (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 a) (sqrt.f64 a) (.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) (.f64 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) 1/3) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) rand a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 a -1/3)) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/3 (cbrt.f64 (.f64 (+.f64 a -1/3) (.f64 rand rand)))) (cbrt.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 1/3 (sqrt.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand))) (sqrt.f64 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand)) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) 1) rand a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) (cbrt.f64 (.f64 rand rand))) (cbrt.f64 rand) a)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 1/3 (sqrt.f64 (+.f64 a -1/3))) (sqrt.f64 rand)) (sqrt.f64 rand) a)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/3 (.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/3 (*.f64 (sqrt.f64 (+.f64 a -1/3)) rand) a)))))))

simplify32.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

661×	`associate-l_binary64`
590×	`associate-*l/_binary64`
545×	`associate-/r*_binary64`
387×	`associate-*r/_binary64`
310×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	576
1	201	540
2	584	534
3	1961	509

Stop Event

1×	node limit

Counts

147 → 153

Calls

Call 1

Inputs
(.f64 1/3 (.f64 rand (sqrt.f64 -1/3)))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (.f64 1/6 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 1/6 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3)))))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 1/6 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (.f64 1/48 (/.f64 (.f64 (pow.f64 a 3) rand) (pow.f64 (sqrt.f64 -1/3) 5))))))
(*.f64 rand (sqrt.f64 -1/3))
(+.f64 (.f64 1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (*.f64 rand (sqrt.f64 -1/3)))
(+.f64 (.f64 1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 rand (sqrt.f64 -1/3)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 a 3) rand) (pow.f64 (sqrt.f64 -1/3) 5))) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))))))
(sqrt.f64 -1/3)
(+.f64 (*.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3)))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (*.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3))))
(.f64 1/3 (.f64 rand (sqrt.f64 -1/3)))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a)))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a) (.f64 1/48 (/.f64 (.f64 (pow.f64 a 3) rand) (pow.f64 (sqrt.f64 -1/3) 5))))))
a
a
a
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))

Outputs
(.f64 1/3 (.f64 rand (sqrt.f64 -1/3)))
(.f64 (sqrt.f64 -1/3) (.f64 1/3 rand))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (.f64 1/6 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/6 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand))))
(fma.f64 (.f64 1/3 rand) (sqrt.f64 -1/3) (/.f64 (.f64 a 1/6) (/.f64 (sqrt.f64 -1/3) rand)))
(fma.f64 (sqrt.f64 -1/3) (.f64 1/3 rand) (.f64 (/.f64 a (sqrt.f64 -1/3)) (*.f64 rand 1/6)))
(.f64 rand (+.f64 (.f64 1/3 (sqrt.f64 -1/3)) (*.f64 1/6 (/.f64 a (sqrt.f64 -1/3)))))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 1/6 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3)))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/6 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand)) (.f64 -1/24 (/.f64 (.f64 rand (.f64 a a)) (pow.f64 (sqrt.f64 -1/3) 3)))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/6 (/.f64 rand (/.f64 (sqrt.f64 -1/3) a)) (.f64 1/8 (/.f64 (.f64 rand (.f64 a a)) (sqrt.f64 -1/3)))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/6 (.f64 rand (/.f64 a (sqrt.f64 -1/3))) (/.f64 (/.f64 (.f64 rand (.f64 a a)) 8) (sqrt.f64 -1/3))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 (.f64 1/6 a) (.f64 -1/24 (*.f64 a (/.f64 a -1/3))))))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 1/6 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (.f64 1/48 (/.f64 (.f64 (pow.f64 a 3) rand) (pow.f64 (sqrt.f64 -1/3) 5))))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/6 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand)) (fma.f64 -1/24 (/.f64 (.f64 rand (.f64 a a)) (pow.f64 (sqrt.f64 -1/3) 3)) (.f64 1/48 (/.f64 (*.f64 rand (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5))))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/6 (/.f64 rand (/.f64 (sqrt.f64 -1/3) a)) (fma.f64 1/48 (/.f64 (.f64 rand (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5)) (.f64 1/8 (/.f64 (.f64 rand (*.f64 a a)) (sqrt.f64 -1/3))))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/8 (/.f64 rand (/.f64 (sqrt.f64 -1/3) (.f64 a a))) (fma.f64 1/6 (.f64 rand (/.f64 a (sqrt.f64 -1/3))) (/.f64 (.f64 rand (pow.f64 a 3)) (/.f64 (pow.f64 (sqrt.f64 -1/3) 5) 1/48)))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/48 (/.f64 (.f64 rand (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5)) (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 (.f64 1/6 a) (.f64 -1/24 (.f64 a (/.f64 a -1/3)))))))
(*.f64 rand (sqrt.f64 -1/3))
(+.f64 (.f64 1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (*.f64 rand (sqrt.f64 -1/3)))
(fma.f64 1/2 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand)) (*.f64 rand (sqrt.f64 -1/3)))
(fma.f64 rand (sqrt.f64 -1/3) (/.f64 (*.f64 a 1/2) (/.f64 (sqrt.f64 -1/3) rand)))
(fma.f64 rand (sqrt.f64 -1/3) (*.f64 (/.f64 1/2 (/.f64 (sqrt.f64 -1/3) a)) rand))
(*.f64 rand (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3)))
(+.f64 (.f64 1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 rand (sqrt.f64 -1/3)) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3)))))
(fma.f64 1/2 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand)) (fma.f64 rand (sqrt.f64 -1/3) (.f64 (/.f64 (.f64 rand (*.f64 a a)) (pow.f64 (sqrt.f64 -1/3) 3)) -1/8)))
(fma.f64 (/.f64 rand (/.f64 (sqrt.f64 -1/3) a)) 1/2 (fma.f64 rand (sqrt.f64 -1/3) (.f64 3/8 (/.f64 (.f64 rand (*.f64 a a)) (sqrt.f64 -1/3)))))
(fma.f64 3/8 (/.f64 rand (/.f64 (sqrt.f64 -1/3) (.f64 a a))) (fma.f64 rand (sqrt.f64 -1/3) (.f64 (/.f64 1/2 (/.f64 (sqrt.f64 -1/3) a)) rand)))
(fma.f64 rand (sqrt.f64 -1/3) (.f64 rand (.f64 (/.f64 a (sqrt.f64 -1/3)) (+.f64 1/2 (*.f64 -1/8 (/.f64 a -1/3))))))
(+.f64 (.f64 1/2 (/.f64 (.f64 a rand) (sqrt.f64 -1/3))) (+.f64 (.f64 rand (sqrt.f64 -1/3)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 a 3) rand) (pow.f64 (sqrt.f64 -1/3) 5))) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))))))
(fma.f64 1/2 (/.f64 a (/.f64 (sqrt.f64 -1/3) rand)) (fma.f64 rand (sqrt.f64 -1/3) (fma.f64 1/16 (/.f64 (.f64 rand (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5)) (.f64 (/.f64 (.f64 rand (.f64 a a)) (pow.f64 (sqrt.f64 -1/3) 3)) -1/8))))
(fma.f64 (/.f64 rand (/.f64 (sqrt.f64 -1/3) a)) 1/2 (fma.f64 rand (sqrt.f64 -1/3) (fma.f64 (/.f64 (.f64 rand (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5)) 1/16 (.f64 3/8 (/.f64 (.f64 rand (.f64 a a)) (sqrt.f64 -1/3))))))
(fma.f64 (.f64 rand (/.f64 a (sqrt.f64 -1/3))) 1/2 (fma.f64 3/8 (/.f64 rand (/.f64 (sqrt.f64 -1/3) (.f64 a a))) (fma.f64 rand (sqrt.f64 -1/3) (/.f64 (.f64 (pow.f64 a 3) (.f64 rand 1/16)) (pow.f64 (sqrt.f64 -1/3) 5)))))
(+.f64 (.f64 rand (+.f64 (sqrt.f64 -1/3) (/.f64 (pow.f64 a 3) (/.f64 (pow.f64 (sqrt.f64 -1/3) 5) 1/16)))) (.f64 rand (.f64 (/.f64 a (sqrt.f64 -1/3)) (+.f64 1/2 (.f64 -1/8 (/.f64 a -1/3))))))
(sqrt.f64 -1/3)
(+.f64 (*.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3))
(fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3)))
(fma.f64 -1/8 (/.f64 (*.f64 a a) (pow.f64 (sqrt.f64 -1/3) 3)) (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3)))
(+.f64 (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3)) (.f64 3/8 (/.f64 (.f64 a a) (sqrt.f64 -1/3))))
(fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (fma.f64 3/8 (/.f64 a (/.f64 (sqrt.f64 -1/3) a)) (sqrt.f64 -1/3)))
(+.f64 (sqrt.f64 -1/3) (.f64 (/.f64 a (sqrt.f64 -1/3)) (+.f64 1/2 (.f64 -1/8 (/.f64 a -1/3)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a 2) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (*.f64 1/2 (/.f64 a (sqrt.f64 -1/3))) (sqrt.f64 -1/3))))
(fma.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (fma.f64 -1/8 (/.f64 (*.f64 a a) (pow.f64 (sqrt.f64 -1/3) 3)) (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3))))
(+.f64 (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (sqrt.f64 -1/3)) (fma.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (.f64 3/8 (/.f64 (.f64 a a) (sqrt.f64 -1/3)))))
(fma.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (fma.f64 1/2 (/.f64 a (sqrt.f64 -1/3)) (fma.f64 3/8 (/.f64 a (/.f64 (sqrt.f64 -1/3) a)) (sqrt.f64 -1/3))))
(fma.f64 1/16 (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5)) (+.f64 (sqrt.f64 -1/3) (.f64 (/.f64 a (sqrt.f64 -1/3)) (+.f64 1/2 (.f64 -1/8 (/.f64 a -1/3))))))
(.f64 1/3 (.f64 rand (sqrt.f64 -1/3)))
(.f64 (sqrt.f64 -1/3) (.f64 1/3 rand))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (.f64 a (+.f64 1 (*.f64 1/6 (/.f64 rand (sqrt.f64 -1/3))))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (.f64 a (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1)))
(fma.f64 1/3 (*.f64 rand (sqrt.f64 -1/3)) (fma.f64 a (/.f64 rand (/.f64 (sqrt.f64 -1/3) 1/6)) a))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 a (/.f64 (.f64 rand 1/6) (sqrt.f64 -1/3)) a))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a)))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 -1/24 (/.f64 (.f64 rand (.f64 a a)) (pow.f64 (sqrt.f64 -1/3) 3)) (.f64 a (+.f64 1 (*.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 a (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1) (.f64 1/8 (/.f64 (.f64 rand (.f64 a a)) (sqrt.f64 -1/3)))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 1/8 (/.f64 rand (/.f64 (sqrt.f64 -1/3) (.f64 a a))) (fma.f64 a (/.f64 rand (/.f64 (sqrt.f64 -1/3) 1/6)) a)))
(+.f64 a (fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 (.f64 1/6 a) (.f64 -1/24 (*.f64 a (/.f64 a -1/3)))))))
(+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 -1/3))) (+.f64 (.f64 -1/24 (/.f64 (.f64 (pow.f64 a 2) rand) (pow.f64 (sqrt.f64 -1/3) 3))) (+.f64 (.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a) (.f64 1/48 (/.f64 (.f64 (pow.f64 a 3) rand) (pow.f64 (sqrt.f64 -1/3) 5))))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 -1/24 (/.f64 (.f64 rand (.f64 a a)) (pow.f64 (sqrt.f64 -1/3) 3)) (fma.f64 (+.f64 1 (.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)))) a (.f64 1/48 (/.f64 (.f64 rand (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5))))))
(+.f64 (fma.f64 a (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1) (/.f64 (.f64 1/48 (.f64 rand (pow.f64 a 3))) (pow.f64 (sqrt.f64 -1/3) 5))) (fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (.f64 1/8 (/.f64 (.f64 rand (.f64 a a)) (sqrt.f64 -1/3)))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (fma.f64 a (fma.f64 1/6 (/.f64 rand (sqrt.f64 -1/3)) 1) (fma.f64 1/48 (.f64 rand (/.f64 (pow.f64 a 3) (pow.f64 (sqrt.f64 -1/3) 5))) (/.f64 (/.f64 (.f64 rand (.f64 a a)) 8) (sqrt.f64 -1/3)))))
(fma.f64 1/3 (.f64 rand (sqrt.f64 -1/3)) (+.f64 a (fma.f64 1/48 (/.f64 (.f64 rand (pow.f64 a 3)) (pow.f64 (sqrt.f64 -1/3) 5)) (.f64 (/.f64 rand (sqrt.f64 -1/3)) (+.f64 (.f64 1/6 a) (.f64 -1/24 (.f64 a (/.f64 a -1/3))))))))
a
a
a
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3))))
(.f64 rand (.f64 1/3 (sqrt.f64 (+.f64 -1/3 a))))
(.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand))
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3)))))
(fma.f64 (*.f64 1/3 (sqrt.f64 (+.f64 -1/3 a))) rand a)
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) a)
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3)))))
(fma.f64 (*.f64 1/3 (sqrt.f64 (+.f64 -1/3 a))) rand a)
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) a)
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3)))))
(fma.f64 (*.f64 1/3 (sqrt.f64 (+.f64 -1/3 a))) rand a)
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) a)
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)
(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3))))
(.f64 rand (.f64 1/3 (sqrt.f64 (+.f64 -1/3 a))))
(.f64 (sqrt.f64 (+.f64 -1/3 a)) (.f64 1/3 rand))
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3)))))
(fma.f64 (*.f64 1/3 (sqrt.f64 (+.f64 -1/3 a))) rand a)
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) a)
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3)))))
(fma.f64 (*.f64 1/3 (sqrt.f64 (+.f64 -1/3 a))) rand a)
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) a)
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)
(+.f64 a (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 a -1/3)))))
(fma.f64 (*.f64 1/3 (sqrt.f64 (+.f64 -1/3 a))) rand a)
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) a)
(fma.f64 1/3 (*.f64 rand (sqrt.f64 (+.f64 -1/3 a))) a)

prune141.0ms (4.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	153	4	157

Error

Counts

157 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.1b	(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))
✓	0.1b	(-.f64 (+.f64 (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)) a) 1/3)

Compiler

Compiled 2986 to 2301 computations (22.9% saved)

regimes104.0ms (3.6%)

Accuracy

Total -0.1b remaining (-119.2%)

Threshold costs -0.1b (-119.2%)

Counts

39 → 1

Compiler

Compiled 548 to 434 computations (20.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	11	16

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))

Outputs
(fma.f64 (sqrt.f64 (+.f64 -1/3 a)) (*.f64 1/3 rand) (+.f64 -1/3 a))

end106.0ms (3.6%)

Stop Event

1×

done

Compiler

Compiled 82 to 64 computations (22% saved)

Details

analyze134.0ms (4.6%)

sample1.2s (42.3%)

preprocess49.0ms (1.7%)

simplify69.0ms (2.4%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series20.0ms (0.7%)

rewrite68.0ms (2.3%)

simplify60.0ms (2.1%)

prune277.0ms (9.5%)

localize6.0ms (0.2%)

series6.0ms (0.2%)

rewrite47.0ms (1.6%)

simplify29.0ms (1%)

prune82.0ms (2.8%)

localize8.0ms (0.3%)

series19.0ms (0.6%)

rewrite69.0ms (2.4%)

simplify47.0ms (1.6%)

prune214.0ms (7.4%)

localize7.0ms (0.3%)

series11.0ms (0.4%)

rewrite57.0ms (1.9%)

simplify32.0ms (1.1%)

prune141.0ms (4.8%)

regimes104.0ms (3.6%)

simplify2.0ms (0.1%)

end106.0ms (3.6%)

Profiling