Details

analyze5.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample974.0ms (44.9%)

Results

962.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

preprocess32.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

1332×	`fma-def_binary64`
553×	`distribute-rgt-in_binary64`
496×	`unsub-neg_binary64`
223×	`distribute-rgt-neg-out_binary64`
221×	`distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	42	28
2	109	26
3	321	26
4	968	26
5	1747	24
6	3706	24
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Outputs
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (+.f64 2 (.f64 -6 (.f64 v v))))))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))

Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify23.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1332×	`fma-def_binary64`
553×	`distribute-rgt-in_binary64`
496×	`unsub-neg_binary64`
223×	`distribute-rgt-neg-out_binary64`
221×	`distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	42	28
2	109	26
3	321	26
4	968	26
5	1747	24
6	3706	24

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Outputs
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (+.f64 2 (.f64 -6 (.f64 v v))))))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))

prune5.0ms (0.2%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
▶	0.0b	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))

Status

Error

Program

1.0b

(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))

▶

0.0b

(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))

Compiler

Compiled 113 to 85 computations (24.8% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
✓	0.0b	(/.f64 -4/3 (fma.f64 v v -1))
✓	0.0b	(.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
✓	0.0b	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))

series11.0ms (0.5%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	v	@	0	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
2.0ms	v	@	inf	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
1.0ms	v	@	-inf	(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
1.0ms	v	@	0	(.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
1.0ms	v	@	inf	(.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

rewrite60.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`
205×	`log-pow_binary64`
143×	`add-sqr-sqrt_binary64`
134×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	294	56
2	3679	56

Stop Event

1×	node limit

Counts

4 → 107

Calls

Call 1

Inputs
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))
(.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
(/.f64 -4/3 (fma.f64 v v -1))
(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -4/3 (/.f64 (/.f64 1 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -4/3 (/.f64 1 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (.f64 (PI.f64) (fma.f64 v v -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -4/3 (.f64 (/.f64 1 (fma.f64 v v -1)) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -4/3 (fma.f64 v v -1)) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (pow.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 2) (cbrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2) (.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (sqrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 4/3 (fma.f64 v v -1)) (/.f64 1 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (neg.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (/.f64 -4/3 (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (/.f64 1 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -4/3 (PI.f64)) (/.f64 (/.f64 1 (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (PI.f64)) (/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2) (PI.f64)) (/.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (PI.f64)) (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (/.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2) 1) (/.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 1) (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -4/3 (cbrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2)))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (cbrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2)))) (/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (cbrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2) (cbrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2)))) (cbrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (cbrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2)))) (/.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (cbrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -4/3 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))) (/.f64 (/.f64 1 (fma.f64 v v -1)) (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))) (/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2) (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))) (/.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (neg.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 -4/3 (fma.f64 v v -1)) 3) (pow.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (fma.f64 v (.f64 v -6) 2) (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (PI.f64) 3) (pow.f64 (fma.f64 v (.f64 v -6) 2) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 v (.f64 v -6) 2) 3/2) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 -4/3 (fma.f64 v v -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -4/3 (/.f64 1 (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -4/3 (fma.f64 v v -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 -4/3 (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2) (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4/3 (/.f64 1 (neg.f64 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (fma.f64 v v -1)) -4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 -4/3 (fma.f64 v v -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 -4/3 (fma.f64 v v -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 -4/3 (fma.f64 v v -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (fma.f64 v v -1) -3/4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 16/9 (pow.f64 (fma.f64 v v -1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 -4/3 (fma.f64 v v -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 -4/3 (fma.f64 v v -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 -4/3 (fma.f64 v v -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 -4/3 (fma.f64 v v -1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 v (.f64 v -6) 2)) (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (cbrt.f64 (fma.f64 v (.f64 v -6) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 v (.f64 v -6) 2) 1/4) (pow.f64 (fma.f64 v (.f64 v -6) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 v (.f64 v -6) 2)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 v (.f64 v -6) 2)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 v (.f64 v -6) 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 v (.f64 v -6) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 v (.f64 v -6) 2) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 v (.f64 v -6) 2) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 v (.f64 v -6) 2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 v (.f64 v -6) 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))))))

simplify49.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

459×	`times-frac_binary64`
388×	`associate-/l*_binary64`
224×	`fma-def_binary64`
182×	`distribute-rgt-in_binary64`
165×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	1977
1	717	1881
2	2406	1830

Stop Event

1×	node limit

Counts

155 → 192

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 6) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 27/2 (.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (.f64 -4/3 (/.f64 (-.f64 (+.f64 (.f64 -1/2 (/.f64 (+.f64 1/162 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64)))))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (.f64 -1/2 (/.f64 (+.f64 1/162 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64)))))))
(*.f64 (sqrt.f64 2) (PI.f64))
(+.f64 (.f64 -3 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (PI.f64)))
(+.f64 (.f64 -9/2 (/.f64 (.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (.f64 -3 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (PI.f64))))
(+.f64 (.f64 -9/2 (/.f64 (.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (.f64 -3 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (+.f64 (.f64 -27/2 (/.f64 (.f64 (pow.f64 v 6) (PI.f64)) (pow.f64 (sqrt.f64 2) 5))) (*.f64 (sqrt.f64 2) (PI.f64)))))
(.f64 (sqrt.f64 -6) (.f64 v (PI.f64)))
(+.f64 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) v)) (.f64 (sqrt.f64 -6) (*.f64 v (PI.f64))))
(+.f64 (.f64 (sqrt.f64 -6) (.f64 v (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (/.f64 (PI.f64) (*.f64 v (sqrt.f64 -6)))))
(+.f64 (.f64 (sqrt.f64 -6) (.f64 v (PI.f64))) (+.f64 (.f64 1/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))) (+.f64 (.f64 -1/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (/.f64 (PI.f64) (*.f64 v (sqrt.f64 -6))))))
(.f64 -1 (.f64 v (*.f64 (sqrt.f64 -6) (PI.f64))))
(+.f64 (.f64 -1 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 -1 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))))
(+.f64 (.f64 -1 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 -1 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) v))) (.f64 1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))))
(+.f64 (.f64 -1 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 -1 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) v))) (+.f64 (.f64 -1/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))) (.f64 1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))))))
4/3
(+.f64 4/3 (*.f64 4/3 (pow.f64 v 2)))
(+.f64 4/3 (+.f64 (.f64 4/3 (pow.f64 v 4)) (.f64 4/3 (pow.f64 v 2))))
(+.f64 4/3 (+.f64 (.f64 4/3 (pow.f64 v 4)) (+.f64 (.f64 4/3 (pow.f64 v 6)) (*.f64 4/3 (pow.f64 v 2)))))
(/.f64 -4/3 (pow.f64 v 2))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 4))) (.f64 4/3 (/.f64 1 (pow.f64 v 2)))))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 2))) (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 4))) (*.f64 4/3 (/.f64 1 (pow.f64 v 6))))))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 8))) (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 2))) (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 6))) (.f64 4/3 (/.f64 1 (pow.f64 v 4)))))))
(/.f64 -4/3 (pow.f64 v 2))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 4))) (.f64 4/3 (/.f64 1 (pow.f64 v 2)))))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 2))) (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 4))) (*.f64 4/3 (/.f64 1 (pow.f64 v 6))))))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 8))) (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 2))) (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 6))) (.f64 4/3 (/.f64 1 (pow.f64 v 4)))))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 -3 (/.f64 (pow.f64 v 2) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (/.f64 (pow.f64 v 2) (sqrt.f64 2)))))
(+.f64 (.f64 -27/2 (/.f64 (pow.f64 v 6) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (+.f64 (.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3))) (*.f64 -3 (/.f64 (pow.f64 v 2) (sqrt.f64 2))))))
(*.f64 (sqrt.f64 -6) v)
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -6) v)) (.f64 (sqrt.f64 -6) v))
(-.f64 (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (.f64 (sqrt.f64 -6) v)) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))))
(-.f64 (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))) (.f64 (sqrt.f64 -6) v))) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))))
(.f64 -1 (.f64 v (sqrt.f64 -6)))
(-.f64 (.f64 -1 (.f64 v (sqrt.f64 -6))) (/.f64 1 (*.f64 (sqrt.f64 -6) v)))
(-.f64 (+.f64 (.f64 -1 (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))) (/.f64 1 (*.f64 v (sqrt.f64 -6))))
(-.f64 (+.f64 (.f64 -1 (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))) (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5))))))

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 -4/3 (.f64 (.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 (.f64 -4/3 (.f64 v v)) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) -1 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -4/3 (.f64 v (*.f64 v (-.f64 (/.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (PI.f64)) (/.f64 (sqrt.f64 1/2) (PI.f64)))))))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(fma.f64 -4/3 (.f64 (.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 -4/3 (.f64 (pow.f64 v 4) (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(fma.f64 -4/3 (.f64 v (.f64 v (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) -1 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -4/3 (.f64 (pow.f64 v 4) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) -1 (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))))))))
(fma.f64 -4/3 (.f64 v (.f64 v (-.f64 (/.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (PI.f64)) (/.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -4/3 (.f64 (pow.f64 v 4) (-.f64 (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 6) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 27/2 (.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(fma.f64 -4/3 (.f64 (pow.f64 v 6) (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -1/2 (+.f64 (/.f64 (+.f64 27/2 (.f64 -3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 -4/3 (.f64 (.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 -4/3 (.f64 (pow.f64 v 4) (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(fma.f64 -4/3 (.f64 (pow.f64 v 6) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) -1 (fma.f64 -1/2 (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (+.f64 27/2 (.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) 1/2) -3/4)) (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (fma.f64 -4/3 (.f64 v (.f64 v (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) -1 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -4/3 (.f64 (pow.f64 v 4) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) -1 (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))))))))
(+.f64 (.f64 -4/3 (+.f64 (.f64 (pow.f64 v 6) (+.f64 (.f64 (/.f64 -1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (PI.f64)) (/.f64 135/16 (PI.f64)))) (-.f64 (/.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (PI.f64)) (/.f64 (sqrt.f64 1/2) (PI.f64))))) (+.f64 (.f64 v (.f64 v (-.f64 (/.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (PI.f64)) (/.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 (pow.f64 v 4) (-.f64 (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))) (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))
(.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))))
(+.f64 (.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(.f64 -4/3 (+.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5))))
(+.f64 (.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))))
(fma.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (.f64 -4/3 (+.f64 (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (-.f64 (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6)))) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))))) (pow.f64 v 7)) (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))))))
(.f64 -4/3 (+.f64 (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 -1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6))))) (pow.f64 v 7)))))
(.f64 -4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 -1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6))))) (pow.f64 v 7))))
(+.f64 (.f64 -4/3 (/.f64 (-.f64 (+.f64 (.f64 -1/2 (/.f64 (+.f64 1/162 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64)))))))
(fma.f64 -4/3 (/.f64 (-.f64 (fma.f64 -1/2 (/.f64 (+.f64 1/162 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (.f64 (PI.f64) (sqrt.f64 -1/6))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6)))))) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 9)) (fma.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (.f64 -4/3 (+.f64 (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (-.f64 (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6)))) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))))) (pow.f64 v 7)) (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))))))
(fma.f64 -4/3 (/.f64 (+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) -1/6) 1/162) (.f64 (PI.f64) (sqrt.f64 -1/6))) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 9)) (.f64 -4/3 (+.f64 (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))))) (pow.f64 v 7))))))
(.f64 -4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))))) (pow.f64 v 7))) (+.f64 (/.f64 (+.f64 (+.f64 (.f64 (/.f64 -1/2 (sqrt.f64 -1/6)) (+.f64 (/.f64 (+.f64 1/162 (.f64 -1/6 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)))) (PI.f64)) (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (PI.f64)))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 9)) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))))
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(.f64 4/3 (+.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))))
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4/3
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(-.f64 (/.f64 -4/3 (*.f64 v v)) (+.f64 (/.f64 4/3 (pow.f64 v 4)) (/.f64 4/3 (pow.f64 v 6))))
(+.f64 (/.f64 -4/3 (*.f64 v v)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 6))))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 8))) (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 2))) (+.f64 (.f64 4/3 (/.f64 1 (pow.f64 v 6))) (.f64 4/3 (/.f64 1 (pow.f64 v 4)))))))
(neg.f64 (+.f64 (/.f64 4/3 (pow.f64 v 8)) (+.f64 (/.f64 4/3 (*.f64 v v)) (+.f64 (/.f64 4/3 (pow.f64 v 4)) (/.f64 4/3 (pow.f64 v 6))))))
(+.f64 (/.f64 -4/3 (pow.f64 v 8)) (-.f64 (/.f64 -4/3 (*.f64 v v)) (+.f64 (/.f64 4/3 (pow.f64 v 4)) (/.f64 4/3 (pow.f64 v 6)))))
(+.f64 (/.f64 -4/3 (pow.f64 v 8)) (+.f64 (/.f64 -4/3 (*.f64 v v)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 6)))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 -3 (/.f64 (pow.f64 v 2) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (.f64 -3 (/.f64 (.f64 v v) (sqrt.f64 2))))
(fma.f64 -3 (/.f64 v (/.f64 (sqrt.f64 2) v)) (sqrt.f64 2))
(fma.f64 -3 (*.f64 (/.f64 v (sqrt.f64 2)) v) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (/.f64 (pow.f64 v 2) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (/.f64 (.f64 v v) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -3 (/.f64 v (/.f64 (sqrt.f64 2) v)) (*.f64 -9/4 (/.f64 (pow.f64 v 4) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -3 (.f64 (/.f64 v (sqrt.f64 2)) v) (.f64 (/.f64 (pow.f64 v 4) (sqrt.f64 2)) -9/4)))
(+.f64 (.f64 -27/2 (/.f64 (pow.f64 v 6) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (+.f64 (.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3))) (*.f64 -3 (/.f64 (pow.f64 v 2) (sqrt.f64 2))))))
(fma.f64 -27/2 (/.f64 (pow.f64 v 6) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) (fma.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (/.f64 (.f64 v v) (sqrt.f64 2))))))
(fma.f64 -27/2 (/.f64 (pow.f64 v 6) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) (fma.f64 -3 (/.f64 v (/.f64 (sqrt.f64 2) v)) (*.f64 -9/4 (/.f64 (pow.f64 v 4) (sqrt.f64 2))))))
(fma.f64 -27/2 (/.f64 (pow.f64 v 6) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) (fma.f64 -3 (.f64 (/.f64 v (sqrt.f64 2)) v) (.f64 (/.f64 (pow.f64 v 4) (sqrt.f64 2)) -9/4))))
(*.f64 (sqrt.f64 -6) v)
(*.f64 v (sqrt.f64 -6))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -6) v)) (.f64 (sqrt.f64 -6) v))
(+.f64 (*.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 1 v) (sqrt.f64 -6)))
(fma.f64 v (sqrt.f64 -6) (/.f64 (/.f64 1 (sqrt.f64 -6)) v))
(-.f64 (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (.f64 (sqrt.f64 -6) v)) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))))
(+.f64 (/.f64 (/.f64 1 v) (sqrt.f64 -6)) (-.f64 (.f64 v (sqrt.f64 -6)) (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))))
(+.f64 (/.f64 (/.f64 1 (sqrt.f64 -6)) v) (fma.f64 v (sqrt.f64 -6) (/.f64 -1/2 (.f64 (sqrt.f64 -6) (.f64 -6 (pow.f64 v 3))))))
(+.f64 (/.f64 (/.f64 1 (sqrt.f64 -6)) v) (fma.f64 v (sqrt.f64 -6) (.f64 -1/2 (/.f64 -1/6 (.f64 (pow.f64 v 3) (sqrt.f64 -6))))))
(-.f64 (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))) (.f64 (sqrt.f64 -6) v))) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))))
(+.f64 (/.f64 (/.f64 1 v) (sqrt.f64 -6)) (-.f64 (+.f64 (.f64 v (sqrt.f64 -6)) (/.f64 1/2 (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5)))) (/.f64 1/2 (*.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))))
(+.f64 (fma.f64 v (sqrt.f64 -6) (/.f64 1/2 (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5)))) (-.f64 (/.f64 (/.f64 1 (sqrt.f64 -6)) v) (/.f64 1/2 (.f64 (sqrt.f64 -6) (*.f64 -6 (pow.f64 v 3))))))
(+.f64 (fma.f64 v (sqrt.f64 -6) (/.f64 1/2 (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5)))) (+.f64 (/.f64 (/.f64 1 (sqrt.f64 -6)) v) (.f64 -1/2 (/.f64 -1/6 (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))))
(.f64 -1 (.f64 v (sqrt.f64 -6)))
(neg.f64 (*.f64 v (sqrt.f64 -6)))
(*.f64 v (neg.f64 (sqrt.f64 -6)))
(-.f64 (.f64 -1 (.f64 v (sqrt.f64 -6))) (/.f64 1 (*.f64 (sqrt.f64 -6) v)))
(-.f64 (neg.f64 (*.f64 v (sqrt.f64 -6))) (/.f64 (/.f64 1 v) (sqrt.f64 -6)))
(neg.f64 (fma.f64 v (sqrt.f64 -6) (/.f64 (/.f64 1 (sqrt.f64 -6)) v)))
(-.f64 (/.f64 (/.f64 -1 v) (sqrt.f64 -6)) (*.f64 v (sqrt.f64 -6)))
(-.f64 (+.f64 (.f64 -1 (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))) (/.f64 1 (*.f64 v (sqrt.f64 -6))))
(-.f64 (fma.f64 -1 (.f64 v (sqrt.f64 -6)) (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))) (/.f64 (/.f64 1 v) (sqrt.f64 -6)))
(fma.f64 (neg.f64 v) (sqrt.f64 -6) (fma.f64 1/2 (/.f64 (/.f64 -1/6 (sqrt.f64 -6)) (pow.f64 v 3)) (/.f64 -1 (*.f64 v (sqrt.f64 -6)))))
(-.f64 (.f64 1/2 (/.f64 -1/6 (.f64 (pow.f64 v 3) (sqrt.f64 -6)))) (fma.f64 v (sqrt.f64 -6) (/.f64 (/.f64 1 (sqrt.f64 -6)) v)))
(-.f64 (+.f64 (.f64 -1 (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))) (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5))))))
(-.f64 (fma.f64 -1 (.f64 v (sqrt.f64 -6)) (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))) (+.f64 (/.f64 (/.f64 1 v) (sqrt.f64 -6)) (/.f64 1/2 (*.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5)))))
(-.f64 (fma.f64 (neg.f64 v) (sqrt.f64 -6) (fma.f64 1/2 (/.f64 (/.f64 -1/6 (sqrt.f64 -6)) (pow.f64 v 3)) (/.f64 -1 (.f64 v (sqrt.f64 -6))))) (/.f64 1/2 (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))))
(+.f64 (-.f64 (.f64 1/2 (/.f64 -1/6 (.f64 (pow.f64 v 3) (sqrt.f64 -6)))) (fma.f64 v (sqrt.f64 -6) (/.f64 (/.f64 1 (sqrt.f64 -6)) v))) (/.f64 -1/2 (*.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))))

prune207.0ms (9.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	192	2	194

Error

Counts

194 → 2

Alt Table

Status	Error	Program
	1.0b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 2)
▶	0.0b	(.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 1)

Status

Error

Program

1.0b

(pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 2)

▶

0.0b

(*.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 1)

Compiler

Compiled 5282 to 4087 computations (22.6% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
✓	0.0b	(*.f64 (PI.f64) (fma.f64 v v -1))
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
✓	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series8.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	v	@	inf	(*.f64 (PI.f64) (fma.f64 v v -1))
1.0ms	v	@	inf	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
1.0ms	v	@	0	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
1.0ms	v	@	-inf	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
1.0ms	v	@	-inf	(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite59.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`
206×	`log-pow_binary64`
153×	`log-div_binary64`
143×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	45
1	294	45
2	3604	45

Stop Event

1×	node limit

Counts

3 → 80

Calls

Call 1

Inputs
(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
(*.f64 (PI.f64) (fma.f64 v v -1))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -4/3 (/.f64 (/.f64 1 (PI.f64)) (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) (pow.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) 2) (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) (sqrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4/3 (/.f64 1 (.f64 (PI.f64) (neg.f64 (fma.f64 v v -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 1 (PI.f64)) (fma.f64 v v -1)) -4/3)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -4/3 (PI.f64)) (/.f64 1 (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (PI.f64) (/.f64 -4/3 (fma.f64 v v -1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 16/9 (pow.f64 (.f64 (PI.f64) (fma.f64 v v -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -4/3 (/.f64 (/.f64 (/.f64 1 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -4/3 (/.f64 1 (.f64 (.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -4/3 (.f64 (/.f64 (/.f64 1 (PI.f64)) (fma.f64 v v -1)) (pow.f64 (fma.f64 (.f64 v v) -6 2) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (pow.f64 (fma.f64 (.f64 v v) -6 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) (cbrt.f64 (/.f64 (/.f64 16/9 (pow.f64 (.f64 (PI.f64) (fma.f64 v v -1)) 2)) (fma.f64 (.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (/.f64 16/9 (pow.f64 (.f64 (PI.f64) (fma.f64 v v -1)) 2)) (fma.f64 (.f64 v v) -6 2))) (cbrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) 2) (.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) (pow.f64 (fma.f64 (.f64 v v) -6 2) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))) (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (.f64 v v) 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Outputs

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(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)) (/.f64 (PI.f64) (/.f64 -4/3 (fma.f64 v v -1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (/.f64 16/9 (pow.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) 2)) (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) 3) (pow.f64 (fma.f64 (*.f64 v v) -6 2) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))))

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

simplify43.0ms (2%)

Algorithm

1×	egg-herbie

Rules

530×	`fma-def_binary64`
329×	`associate-/r*_binary64`
324×	`associate-l_binary64`
201×	`associate-/l*_binary64`
184×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	1483
1	460	1427
2	1546	1354

Stop Event

1×	node limit

Counts

116 → 124

Calls

Call 1

Inputs
(/.f64 4/3 (PI.f64))
(+.f64 (.f64 4/3 (/.f64 (pow.f64 v 2) (PI.f64))) (.f64 4/3 (/.f64 1 (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (pow.f64 v 4) (PI.f64))) (*.f64 4/3 (/.f64 1 (PI.f64)))))
(+.f64 (.f64 4/3 (/.f64 (pow.f64 v 6) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (pow.f64 v 4) (PI.f64))) (.f64 4/3 (/.f64 1 (PI.f64))))))
(/.f64 -4/3 (*.f64 (pow.f64 v 2) (PI.f64)))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 2) (PI.f64))))))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 2) (PI.f64)))) (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 6) (PI.f64)))))))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 2) (PI.f64)))) (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 6) (PI.f64))))))))
(/.f64 -4/3 (*.f64 (pow.f64 v 2) (PI.f64)))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 2) (PI.f64))))))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 2) (PI.f64)))) (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 6) (PI.f64)))))))
(neg.f64 (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 2) (PI.f64)))) (+.f64 (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 4/3 (/.f64 1 (.f64 (pow.f64 v 6) (PI.f64))))))))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 6) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 27/2 (.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (.f64 -4/3 (/.f64 (-.f64 (+.f64 (.f64 -1/2 (/.f64 (+.f64 1/162 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (+.f64 (.f64 -4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64)))))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (.f64 -1/2 (/.f64 (+.f64 1/162 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64)))))))
(*.f64 -1 (PI.f64))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (pow.f64 v 2) (PI.f64))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(*.f64 (pow.f64 v 2) (PI.f64))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))

Outputs
(/.f64 4/3 (PI.f64))
(+.f64 (.f64 4/3 (/.f64 (pow.f64 v 2) (PI.f64))) (.f64 4/3 (/.f64 1 (PI.f64))))
(fma.f64 4/3 (/.f64 (*.f64 v v) (PI.f64)) (/.f64 4/3 (PI.f64)))
(fma.f64 4/3 (/.f64 v (/.f64 (PI.f64) v)) (/.f64 4/3 (PI.f64)))
(fma.f64 4/3 (*.f64 (/.f64 v (PI.f64)) v) (/.f64 4/3 (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (pow.f64 v 4) (PI.f64))) (*.f64 4/3 (/.f64 1 (PI.f64)))))
(fma.f64 4/3 (/.f64 (*.f64 v v) (PI.f64)) (fma.f64 4/3 (/.f64 (pow.f64 v 4) (PI.f64)) (/.f64 4/3 (PI.f64))))
(fma.f64 4/3 (/.f64 v (/.f64 (PI.f64) v)) (fma.f64 4/3 (/.f64 (pow.f64 v 4) (PI.f64)) (/.f64 4/3 (PI.f64))))
(fma.f64 4/3 (+.f64 (*.f64 (/.f64 v (PI.f64)) v) (/.f64 (pow.f64 v 4) (PI.f64))) (/.f64 4/3 (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (pow.f64 v 6) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (pow.f64 v 2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (pow.f64 v 4) (PI.f64))) (.f64 4/3 (/.f64 1 (PI.f64))))))
(fma.f64 4/3 (/.f64 (pow.f64 v 6) (PI.f64)) (fma.f64 4/3 (/.f64 (*.f64 v v) (PI.f64)) (fma.f64 4/3 (/.f64 (pow.f64 v 4) (PI.f64)) (/.f64 4/3 (PI.f64)))))
(fma.f64 4/3 (/.f64 (pow.f64 v 6) (PI.f64)) (fma.f64 4/3 (/.f64 v (/.f64 (PI.f64) v)) (fma.f64 4/3 (/.f64 (pow.f64 v 4) (PI.f64)) (/.f64 4/3 (PI.f64)))))
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(fma.f64 -4/3 (/.f64 (-.f64 (fma.f64 -1/2 (/.f64 (+.f64 1/162 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (.f64 (PI.f64) (sqrt.f64 -1/6))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6)))))) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 9)) (fma.f64 -4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (.f64 -4/3 (+.f64 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))))) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7)) (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))))))
(fma.f64 -4/3 (/.f64 (+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) -1/6) 1/162) (.f64 (PI.f64) (sqrt.f64 -1/6))) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 9)) (.f64 -4/3 (+.f64 (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7))))))
(fma.f64 -4/3 (+.f64 (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (fma.f64 -1/2 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) -1/108) (.f64 (PI.f64) (sqrt.f64 -1/6))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))))) (pow.f64 v 7)))) (/.f64 (fma.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 (/.f64 -1/2 (sqrt.f64 -1/6)) (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (PI.f64)) (/.f64 (+.f64 1/162 (.f64 -1/6 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)))) (PI.f64))))) (/.f64 1/27 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 9)))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))))
(/.f64 (/.f64 (*.f64 4/3 (sqrt.f64 -1/6)) (PI.f64)) (pow.f64 v 3))
(/.f64 (/.f64 (sqrt.f64 -1/6) (/.f64 (PI.f64) 4/3)) (pow.f64 v 3))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(.f64 4/3 (+.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/27 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))))
(fma.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))))) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7)) (.f64 4/3 (+.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))))))
(.f64 4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5))) (/.f64 (+.f64 (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 -1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7))))
(fma.f64 4/3 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5))) (/.f64 (fma.f64 4/3 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 (fma.f64 -1/2 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) -1/108) (.f64 (PI.f64) (sqrt.f64 -1/6)))) (/.f64 -1/27 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7)))
(+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (.f64 -1/2 (/.f64 (+.f64 1/162 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 9))) (+.f64 (.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 7))) (+.f64 (.f64 4/3 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64))))) (pow.f64 v 5))) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64)))))))
(fma.f64 4/3 (/.f64 (-.f64 (fma.f64 -1/2 (/.f64 (+.f64 1/162 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)))) (.f64 (PI.f64) (sqrt.f64 -1/6))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6)))))) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 9)) (fma.f64 4/3 (/.f64 (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))))) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7)) (.f64 4/3 (+.f64 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))))))
(fma.f64 4/3 (/.f64 (+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) -1/6) 1/162) (.f64 (PI.f64) (sqrt.f64 -1/6))) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 9)) (.f64 4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5))) (/.f64 (+.f64 (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7)))))
(fma.f64 4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5))) (/.f64 (+.f64 (/.f64 (fma.f64 -1/2 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) -1/108) (.f64 (PI.f64) (sqrt.f64 -1/6))) (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))))) (pow.f64 v 7))) (/.f64 (fma.f64 4/3 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (.f64 (/.f64 -1/2 (sqrt.f64 -1/6)) (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (PI.f64)) (/.f64 (+.f64 1/162 (.f64 -1/6 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)))) (PI.f64))))) (/.f64 -1/27 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 9)))
(*.f64 -1 (PI.f64))
(neg.f64 (PI.f64))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(.f64 (PI.f64) (+.f64 (.f64 v v) -1))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(.f64 (PI.f64) (+.f64 (.f64 v v) -1))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(.f64 (PI.f64) (+.f64 (.f64 v v) -1))
(*.f64 (PI.f64) (fma.f64 v v -1))
(*.f64 (pow.f64 v 2) (PI.f64))
(.f64 (PI.f64) (.f64 v v))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(.f64 (PI.f64) (+.f64 (.f64 v v) -1))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(.f64 (PI.f64) (+.f64 (.f64 v v) -1))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(.f64 (PI.f64) (+.f64 (.f64 v v) -1))
(*.f64 (PI.f64) (fma.f64 v v -1))
(*.f64 (pow.f64 v 2) (PI.f64))
(.f64 (PI.f64) (.f64 v v))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(.f64 (PI.f64) (+.f64 (.f64 v v) -1))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(.f64 (PI.f64) (+.f64 (.f64 v v) -1))
(*.f64 (PI.f64) (fma.f64 v v -1))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(.f64 (PI.f64) (+.f64 (.f64 v v) -1))
(*.f64 (PI.f64) (fma.f64 v v -1))

prune165.0ms (7.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	170	2	172

Error

Counts

172 → 2

Alt Table

Status

Error

Program

▶

1.0b

(pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 2)

✓

0.0b

(*.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 1)

Compiler

Compiled 4962 to 3872 computations (22% saved)

localize15.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (PI.f64) (fma.f64 v v -1))
	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
✓	1.0b	(pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 2)
	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series7.0ms (0.3%)

Counts

1 → 4

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

(pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 2)

3.0ms

inf

(pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 2)

1.0ms

-inf

(pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 2)

rewrite61.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

263×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`
152×	`add-sqr-sqrt_binary64`
144×	`pow1_binary64`
143×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	338	24
2	3864	24

Stop Event

1×	node limit

Counts

1 → 64

Calls

Call 1

Inputs
(pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4/3 (/.f64 (/.f64 (/.f64 1 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4/3 (/.f64 1 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4/3 (*.f64 (/.f64 (/.f64 1 (PI.f64)) (fma.f64 v v -1)) (pow.f64 (fma.f64 (*.f64 v v) -6 2) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (pow.f64 (fma.f64 (*.f64 v v) -6 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) 2) (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))) (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) 2) (fma.f64 (*.f64 v v) -6 2))) (cbrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) 2) (*.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) (pow.f64 (fma.f64 (*.f64 v v) -6 2) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))) 1/4) (*.f64 (pow.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))) 1/4) (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) (*.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) (pow.f64 (fma.f64 (*.f64 v v) -6 2) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (/.f64 1 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 (*.f64 v v) -6 2) -1/2) (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) (pow.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))) 1/4)) (pow.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) 2) 1) (/.f64 (cbrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (/.f64 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(*.f64 v v) -6 2))))) (cbrt.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -4/3 (*.f64 (*.f64 (PI.f64) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -4/3 (/.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)) (/.f64 (/.f64 1 (PI.f64)) (fma.f64 v v -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (*.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)) (/.f64 (fma.f64 v v -1) (/.f64 -4/3 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)) (/.f64 (fma.f64 v v -1) (/.f64 -4/3 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (/.f64 (fma.f64 v v -1) (/.f64 -4/3 (PI.f64))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 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(fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4/3 (*.f64 (*.f64 (fma.f64 v v -1) (neg.f64 (PI.f64))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4/3 (*.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)) (*.f64 (fma.f64 v v -1) (neg.f64 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (fma.f64 (*.f64 v v) -6 2) -1/2) (/.f64 (fma.f64 v v -1) (/.f64 -4/3 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 -4/3 (PI.f64)) (*.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)) (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 -4/3 (PI.f64)) 1) (*.f64 (fma.f64 v v -1) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (pow.f64 (fma.f64 (*.f64 v v) -6 2) 1/4)) (pow.f64 (fma.f64 (*.f64 v v) -6 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 -4/3 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))) (*.f64 (PI.f64) (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) 1) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (cbrt.f64 (fma.f64 (*.f64 v v) -6 2))) (cbrt.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -4/3 (pow.f64 (fma.f64 (*.f64 v v) -6 2) -1/2)) (*.f64 (PI.f64) (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4/3 (pow.f64 (fma.f64 (*.f64 v v) -6 2) -1/2)) (*.f64 (fma.f64 v v -1) (neg.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 -4/3 (PI.f64)) (pow.f64 (fma.f64 (*.f64 v v) -6 2) -1/2)) (fma.f64 v v -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))) (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))) (pow.f64 (fma.f64 (*.f64 v v) -6 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))) (sqrt.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)))) (pow.f64 (fma.f64 (*.f64 v v) -6 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (neg.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) 2) (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change 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(log1p.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))))))

simplify38.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

269×	`fma-neg_binary64`
239×	`associate-r_binary64`
231×	`associate-l_binary64`
206×	`unsub-neg_binary64`
199×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	530
1	208	476
2	723	440
3	3957	438

Stop Event

1×	node limit

Counts

68 → 72

Calls

Call 1

Inputs
(/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2)) (PI.f64))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2)) (PI.f64)))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -4/3 (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 4/9 (/.f64 (.f64 (pow.f64 (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))) 2) (PI.f64)) (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2))))) (pow.f64 (.f64 -2/3 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))) (sqrt.f64 4/3)))) 2))) (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2)) (PI.f64))))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 6) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 27/2 (.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -4/3 (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 4/9 (/.f64 (.f64 (pow.f64 (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))) 2) (PI.f64)) (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2))))) (pow.f64 (.f64 -2/3 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))) (sqrt.f64 4/3)))) 2))) (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2)) (PI.f64)))))

Outputs
(/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2)) (PI.f64))
(/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 4/3) 2)))
(/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) 4/3))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2)) (PI.f64)))
(fma.f64 -4/3 (.f64 (.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))) (/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 4/3) 2))))
(fma.f64 -4/3 (.f64 v (.f64 v (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))))) (/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) 4/3)))
(fma.f64 -4/3 (.f64 (.f64 v v) (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -4/3 (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 4/9 (/.f64 (.f64 (pow.f64 (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))) 2) (PI.f64)) (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2))))) (pow.f64 (.f64 -2/3 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))) (sqrt.f64 4/3)))) 2))) (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2)) (PI.f64))))
(fma.f64 -4/3 (.f64 (.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 (pow.f64 v 4) (-.f64 (fma.f64 -4/3 (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 -1/2 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2))) (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 4/9 (/.f64 (pow.f64 (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) 2) (/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 4/3) 2)))))) (pow.f64 (.f64 (.f64 -2/3 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2)))) (/.f64 (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (sqrt.f64 4/3))) 2)) (/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 4/3) 2)))))
(fma.f64 -4/3 (.f64 v (.f64 v (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (fma.f64 (pow.f64 v 4) (-.f64 (fma.f64 -4/3 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 1/3 (/.f64 (PI.f64) (/.f64 (sqrt.f64 1/2) (pow.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) 2))))) (pow.f64 (.f64 -2/3 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (sqrt.f64 4/3)))) 2)) (/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) 4/3))))
(fma.f64 -4/3 (.f64 (.f64 v v) (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) 4/3 (.f64 (pow.f64 v 4) (-.f64 (fma.f64 -4/3 (-.f64 (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (PI.f64)) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 1/2)) (pow.f64 (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))) 2)) 1/3)) (pow.f64 (.f64 -2/3 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (-.f64 (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (sqrt.f64 4/3)))) 2)))))
(+.f64 (.f64 -4/3 (.f64 (pow.f64 v 6) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 27/2 (.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 -4/3 (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (+.f64 (.f64 (pow.f64 v 4) (-.f64 (+.f64 (.f64 -4/3 (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 4/9 (/.f64 (.f64 (pow.f64 (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))) 2) (PI.f64)) (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2))))) (pow.f64 (.f64 -2/3 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (-.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64))))) (sqrt.f64 4/3)))) 2))) (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (sqrt.f64 4/3) 2)) (PI.f64)))))
(fma.f64 -4/3 (.f64 (pow.f64 v 6) (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -1/2 (+.f64 (/.f64 (+.f64 27/2 (.f64 -3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 -4/3 (.f64 (.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 (pow.f64 v 4) (-.f64 (fma.f64 -4/3 (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 -1/2 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2))) (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 4/9 (/.f64 (pow.f64 (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) 2) (/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 4/3) 2)))))) (pow.f64 (.f64 (.f64 -2/3 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2)))) (/.f64 (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (sqrt.f64 4/3))) 2)) (/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 4/3) 2))))))
(fma.f64 -4/3 (.f64 (pow.f64 v 6) (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 -1/2 (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (+.f64 27/2 (.f64 (-.f64 9 (/.f64 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2) 1/2)) -3/4)) (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (fma.f64 -4/3 (.f64 v (.f64 v (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (fma.f64 (pow.f64 v 4) (-.f64 (fma.f64 -4/3 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (.f64 1/3 (/.f64 (PI.f64) (/.f64 (sqrt.f64 1/2) (pow.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) 2))))) (pow.f64 (.f64 -2/3 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (sqrt.f64 4/3)))) 2)) (/.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) 4/3)))))
(fma.f64 -4/3 (fma.f64 (pow.f64 v 6) (+.f64 (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 (/.f64 -1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (PI.f64)) (/.f64 135/16 (PI.f64))))) (.f64 (.f64 v v) (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) 4/3 (.f64 (pow.f64 v 4) (-.f64 (fma.f64 -4/3 (-.f64 (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (PI.f64)) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 1/2)) (pow.f64 (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))) 2)) 1/3)) (pow.f64 (.f64 -2/3 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (-.f64 (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (sqrt.f64 4/3)))) 2)))))
(fma.f64 -4/3 (fma.f64 (pow.f64 v 6) (-.f64 (fma.f64 (/.f64 -1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (PI.f64)) (/.f64 135/16 (PI.f64))) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 (.f64 v v) (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) 4/3 (.f64 (pow.f64 v 4) (-.f64 (fma.f64 -4/3 (-.f64 (fma.f64 -1/2 (/.f64 (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (PI.f64)) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 1/2)) (pow.f64 (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))) 2)) 1/3)) (pow.f64 (.f64 -2/3 (.f64 (sqrt.f64 (/.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (sqrt.f64 4/3)))) 2)))))

prune190.0ms (8.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	196	2	198

Error

Counts

198 → 2

Alt Table

Status

Error

Program

✓

1.0b

(pow.f64 (sqrt.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 2)

✓

0.0b

(*.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) 1)

Compiler

Compiled 6061 to 4623 computations (23.7% saved)

regimes130.0ms (6%)

Accuracy

Total 0.0b remaining (44.9%)

Threshold costs 0.0b (44.9%)

Counts

81 → 1

Compiler

Compiled 1460 to 1034 computations (29.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log1p.f64 (expm1.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))

Outputs
(log1p.f64 (expm1.f64 (/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))

end64.0ms (2.9%)

Stop Event

1×

done

Compiler

Compiled 77 to 61 computations (20.8% saved)

Details

analyze5.0ms (0.3%)

sample974.0ms (44.9%)

preprocess32.0ms (1.5%)

simplify23.0ms (1.1%)

prune5.0ms (0.2%)

localize11.0ms (0.5%)

series11.0ms (0.5%)

rewrite60.0ms (2.8%)

simplify49.0ms (2.3%)

prune207.0ms (9.5%)

localize10.0ms (0.5%)

series8.0ms (0.4%)

rewrite59.0ms (2.7%)

simplify43.0ms (2%)

prune165.0ms (7.6%)

localize15.0ms (0.7%)

series7.0ms (0.3%)

rewrite61.0ms (2.8%)

simplify38.0ms (1.8%)

prune190.0ms (8.8%)

regimes130.0ms (6%)

simplify2.0ms (0.1%)

end64.0ms (2.9%)

Profiling