Details

analyze5.0ms (0.1%)

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

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.4s (26.8%)

Results

1.4s	8256×	body	256	valid
1.0ms	14×	body	256	invalid

preprocess58.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

1332×	`fma-def_binary64`
576×	`fma-neg_binary64`
553×	`distribute-rgt-in_binary64`
496×	`unsub-neg_binary64`
440×	`distribute-lft-in_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
7	6366	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 22 to 17 computations (22.7% saved)

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1332×	`fma-def_binary64`
576×	`fma-neg_binary64`
553×	`distribute-rgt-in_binary64`
496×	`unsub-neg_binary64`
440×	`distribute-lft-in_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
7	6366	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))))

eval1.0ms (0%)

Compiler: Compiled 37 to 27 computations (27% saved)

prune2.0ms (0%)

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

Click to see full 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 38 to 29 computations (23.7% saved)

localize9.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series10.0ms (0.2%)

Counts

3 → 36

Calls

9 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)))

rewrite134.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`log-prod_binary64`
362×	`pow2_binary64`
255×	`pow1/3_binary64`
251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	294	46
2	3679	46

Stop Event

1×	node limit

Counts

3 → 103

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))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.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 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))) 2)) (log.f64 (cbrt.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 +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))))) (log.f64 (sqrt.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 -.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 (pow.f64 (fma.f64 v (.f64 v -6) 2) -1/2) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -4/3 (fma.f64 v v -1)) (/.f64 (pow.f64 (fma.f64 v (.f64 v -6) 2) -1/2) (PI.f64)))))) (#(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)))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) 2) (fma.f64 v (.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) 2) (fma.f64 v (.f64 v -6) 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 (pow.f64 (fma.f64 v (.f64 v -6) 2) -1/2) (PI.f64))))))) (#(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 (pow.f64 (fma.f64 v (.f64 v -6) 2) -1/2) (PI.f64))))))) (#(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 (pow.f64 (fma.f64 v (.f64 v -6) 2) -1/2) (PI.f64)) (/.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))) (pow.f64 (fma.f64 v (.f64 v -6) 2) -1/2))))) (#(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 (pow.f64 (fma.f64 v (.f64 v -6) 2) -1/2) (/.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 (pow.f64 (cbrt.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) -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 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pow.f64 (.f64 (.f64 (fma.f64 v v -1) -3/4) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (.f64 (PI.f64) (fma.f64 v v -1))) -4/3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1)))) 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 (/.f64 (pow.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) 2) (fma.f64 v (.f64 v -6) 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 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Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.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 (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 (*.f64 (fma.f64 v (*.f64 v -6) 2) (pow.f64 (PI.f64) 2)) 1/2)))) (#(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 pow.f64 (*.f64 (pow.f64 (PI.f64) 3) (pow.f64 (fma.f64 v (*.f64 v -6) 2) 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (fma.f64 v (*.f64 v -6) 2) 3/2) (pow.f64 (PI.f64) 3)) 1/3)))) (#(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 expm1.f64 (log1p.f64 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(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 +.f64 0 (/.f64 -4/3 (fma.f64 v v -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 -4/3 (fma.f64 v v -1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 -4/3 (fma.f64 v v -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 -4/3 (fma.f64 v v -1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 -4/3 (fma.f64 v v -1))))))))) (#(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 (/.f64 16/9 (pow.f64 (fma.f64 v v -1) 2)) 1/2)))) (#(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 pow.f64 (/.f64 (*.f64 (fma.f64 v v -1) -3/4) 1) -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 expm1.f64 (log1p.f64 (/.f64 -4/3 (fma.f64 v v -1))))))) (#(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))))))

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
483×	`associate-/r*_binary64`
425×	`associate-l_binary64`
420×	`times-frac_binary64`
414×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	1656
1	616	1582
2	2109	1505

Stop Event

1×	node limit

Counts

139 → 165

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)))))))

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 (-.f64 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -4/3 (.f64 v v)) (.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)))))
(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 (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 -4/3 (pow.f64 v 4)))))
(fma.f64 -4/3 (fma.f64 v (.f64 v (-.f64 (/.f64 -3/4 (.f64 (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 (/.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 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))))))
(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 (.f64 -4/3 (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 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 (/.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 (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 -4/3 (pow.f64 v 4))))))
(fma.f64 (pow.f64 v 6) (.f64 (+.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 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64)))) -4/3) (fma.f64 -4/3 (fma.f64 v (.f64 v (-.f64 (/.f64 -3/4 (.f64 (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 (/.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 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 -4/3 (/.f64 (/.f64 (sqrt.f64 -1/6) (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 -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) (pow.f64 v 3)) (PI.f64)) (/.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 (/.f64 (sqrt.f64 -1/6) (pow.f64 v 3)) (PI.f64)) (/.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 (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))))))
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(fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (fma.f64 1/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))) (fma.f64 -1/2 (/.f64 (/.f64 (/.f64 (PI.f64) -6) (sqrt.f64 -6)) (pow.f64 v 3)) (/.f64 (PI.f64) (*.f64 v (sqrt.f64 -6))))))
(fma.f64 1/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))) (fma.f64 (PI.f64) (.f64 v (sqrt.f64 -6)) (fma.f64 (/.f64 1/12 (sqrt.f64 -6)) (/.f64 (PI.f64) (pow.f64 v 3)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6)))))
(.f64 -1 (.f64 v (*.f64 (sqrt.f64 -6) (PI.f64))))
(neg.f64 (.f64 (sqrt.f64 -6) (.f64 (PI.f64) v)))
(.f64 (sqrt.f64 -6) (neg.f64 (.f64 (PI.f64) v)))
(.f64 (PI.f64) (.f64 (sqrt.f64 -6) (neg.f64 v)))
(+.f64 (.f64 -1 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 -1 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))))
(.f64 -1 (+.f64 (.f64 (sqrt.f64 -6) (*.f64 (PI.f64) v)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6))))
(neg.f64 (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (.f64 v (sqrt.f64 -6)))))
(neg.f64 (fma.f64 (PI.f64) (*.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6))))
(+.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))))))
(fma.f64 -1 (.f64 (sqrt.f64 -6) (.f64 (PI.f64) v)) (fma.f64 -1 (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6)) (/.f64 (.f64 1/2 (PI.f64)) (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))))
(fma.f64 -1 (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (.f64 v (sqrt.f64 -6)))) (/.f64 (/.f64 (.f64 1/2 (PI.f64)) (pow.f64 v 3)) (.f64 (sqrt.f64 -6) -6)))
(-.f64 (.f64 (/.f64 -1/12 (sqrt.f64 -6)) (/.f64 (PI.f64) (pow.f64 v 3))) (fma.f64 (PI.f64) (.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6))))
(+.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)))))))
(fma.f64 -1 (.f64 (sqrt.f64 -6) (.f64 (PI.f64) v)) (fma.f64 -1 (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6)) (fma.f64 -1/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))) (/.f64 (.f64 1/2 (PI.f64)) (*.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3))))))
(fma.f64 -1 (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (.f64 v (sqrt.f64 -6)))) (fma.f64 1/2 (/.f64 (/.f64 (/.f64 (PI.f64) -6) (sqrt.f64 -6)) (pow.f64 v 3)) (*.f64 (/.f64 -1/2 (pow.f64 v 5)) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)))))
(-.f64 (fma.f64 (/.f64 -1/12 (sqrt.f64 -6)) (/.f64 (PI.f64) (pow.f64 v 3)) (/.f64 (/.f64 (.f64 (PI.f64) -1/2) (pow.f64 v 5)) (pow.f64 (sqrt.f64 -6) 5))) (fma.f64 (PI.f64) (.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6))))
4/3
(+.f64 4/3 (*.f64 4/3 (pow.f64 v 2)))
(+.f64 4/3 (.f64 4/3 (.f64 v v)))
(fma.f64 4/3 (*.f64 v v) 4/3)
(*.f64 (fma.f64 v v 1) 4/3)
(+.f64 4/3 (+.f64 (.f64 4/3 (pow.f64 v 4)) (.f64 4/3 (pow.f64 v 2))))
(+.f64 4/3 (.f64 4/3 (+.f64 (pow.f64 v 4) (.f64 v v))))
(fma.f64 4/3 (+.f64 (*.f64 v v) (pow.f64 v 4)) 4/3)
(fma.f64 4/3 (fma.f64 v v (pow.f64 v 4)) 4/3)
(+.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 (fma.f64 4/3 (pow.f64 v 4) (.f64 4/3 (+.f64 (pow.f64 v 6) (.f64 v v)))))
(+.f64 4/3 (.f64 4/3 (+.f64 (+.f64 (.f64 v v) (pow.f64 v 6)) (pow.f64 v 4))))
(fma.f64 4/3 (+.f64 (fma.f64 v v (pow.f64 v 6)) (pow.f64 v 4)) 4/3)
(/.f64 -4/3 (pow.f64 v 2))
(/.f64 -4/3 (*.f64 v v))
(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 (pow.f64 v 4)) (/.f64 4/3 (*.f64 v v))))
(+.f64 (/.f64 -4/3 (*.f64 v v)) (/.f64 -4/3 (pow.f64 v 4)))
(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 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))))
(+.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 (/.f64 -4/3 (*.f64 v v)) (/.f64 -4/3 (pow.f64 v 4))) (-.f64 (/.f64 -4/3 (pow.f64 v 6)) (/.f64 4/3 (pow.f64 v 8))))
(/.f64 -4/3 (pow.f64 v 2))
(/.f64 -4/3 (*.f64 v v))
(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 (pow.f64 v 4)) (/.f64 4/3 (*.f64 v v))))
(+.f64 (/.f64 -4/3 (*.f64 v v)) (/.f64 -4/3 (pow.f64 v 4)))
(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 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))))
(+.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 (/.f64 -4/3 (*.f64 v v)) (/.f64 -4/3 (pow.f64 v 4))) (-.f64 (/.f64 -4/3 (pow.f64 v 6)) (/.f64 4/3 (pow.f64 v 8))))

localize11.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	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))))))
	0.2b	(.f64 6 (.f64 v v))
	0.0b	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
✓	0.0b	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
✓	0.2b	(.f64 6 (.f64 v v))
✓	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

series9.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

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

rewrite73.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`log-prod_binary64`
329×	`prod-diff_binary64`
303×	`expm1-udef_binary64`
302×	`log1p-udef_binary64`
251×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	66
1	375	63
2	4676	59

Stop Event

1×	node limit

Counts

3 → 60

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))))))

(*.f64 6 (*.f64 v v))

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

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 v (.f64 v 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 6) (.f64 v v))) (cbrt.f64 (pow.f64 (exp.f64 6) (.f64 v v))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 6) (.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 6) (.f64 v v)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 6) (.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 v (.f64 v 6)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 v (.f64 v 6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 v (.f64 v 6))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 v (sqrt.f64 6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 216 (pow.f64 v 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 36 (pow.f64 v 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 6) (.f64 v v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 v (.f64 v 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 216 (pow.f64 v 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 v (.f64 v 6))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 v (.f64 v 6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 2 (log.f64 v) (log.f64 6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 2 (log.f64 v) (log.f64 6)) 1))))))
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Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 v (*.f64 v 6)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 6) (*.f64 v v))) (cbrt.f64 (pow.f64 (exp.f64 6) (*.f64 v v))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 6) (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 6) (*.f64 v v)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 6) (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 v (*.f64 v 6)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 v (*.f64 v 6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 v (*.f64 v 6))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 v (sqrt.f64 6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 216 (pow.f64 v 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 36 (pow.f64 v 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 6) (*.f64 v v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 v (*.f64 v 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 216 (pow.f64 v 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 v (*.f64 v 6))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 v (*.f64 v 6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 2 (log.f64 v) (log.f64 6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 2 (log.f64 v) (log.f64 6)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))) (*.f64 (PI.f64) (*.f64 3 (-.f64 1 (*.f64 v v)))))) (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))) (*.f64 (PI.f64) (*.f64 3 (-.f64 1 (*.f64 v v)))))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))) (*.f64 (PI.f64) (*.f64 3 (-.f64 1 (*.f64 v v))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))) (*.f64 (PI.f64) (*.f64 3 (-.f64 1 (*.f64 v v))))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))) (*.f64 (PI.f64) (*.f64 3 (-.f64 1 (*.f64 v v))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2)))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2)))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (fma.f64 (*.f64 -6 v) v 2) (pow.f64 (*.f64 (PI.f64) (*.f64 3 (-.f64 1 (*.f64 v v)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))) (*.f64 (PI.f64) (*.f64 3 (-.f64 1 (*.f64 v v))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 3 (-.f64 1 (*.f64 v v)))) 3) (pow.f64 (fma.f64 (*.f64 -6 v) v 2) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 (*.f64 -6 v) v 2) 3/2) (pow.f64 (*.f64 (PI.f64) (*.f64 3 (-.f64 1 (*.f64 v v)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 3 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2)))))) 1))))))

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

878×	`associate-l_binary64`
775×	`associate-r_binary64`
407×	`associate-+l+_binary64`
365×	`associate-*l/_binary64`
341×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	1767
1	569	1699
2	2200	1603

Stop Event

1×	node limit

Counts

96 → 109

Calls

Call 1

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

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v (*.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64)))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (*.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))))))
(+.f64 (.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.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 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))))
(fma.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.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 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))))))
(.f64 4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64)))))) (.f64 (pow.f64 v 4) (+.f64 (/.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 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64)))))))
(.f64 4/3 (+.f64 (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.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 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))))) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2)))))))
(+.f64 (.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.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 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (.f64 (pow.f64 v 6) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.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 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.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 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))))
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(fma.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.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 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64))))) (.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 (pow.f64 v 6) (+.f64 (/.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))) (fma.f64 1/2 (/.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 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64))))) (.f64 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64)))))))))
(.f64 4/3 (+.f64 (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.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 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))))) (+.f64 (fma.f64 (pow.f64 v 6) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2)) (.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 135/16 (PI.f64)) (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (PI.f64)))))) (.f64 (*.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))))) (/.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 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -4/3 (pow.f64 v 3)))
(+.f64 (.f64 4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.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 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (neg.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5)) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (.f64 4/3 (-.f64 (/.f64 1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5)))
(fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (.f64 (/.f64 4/3 (pow.f64 v 5)) (-.f64 (/.f64 1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64)))))
(+.f64 (.f64 4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.f64 -1 (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5))) (+.f64 (.f64 4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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)))))) (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 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (neg.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5)) (fma.f64 4/3 (/.f64 (+.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (fma.f64 -1 (/.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)))))) (pow.f64 v 7)) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))))))
(fma.f64 4/3 (/.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (pow.f64 v 5)) (fma.f64 4/3 (/.f64 (+.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (-.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 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 7)) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))))))
(fma.f64 4/3 (/.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (pow.f64 v 5)) (fma.f64 4/3 (/.f64 (+.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (.f64 (/.f64 1/2 (.f64 (PI.f64) (sqrt.f64 -1/6))) (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)))) (pow.f64 v 7)) (*.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -4/3 (pow.f64 v 3)))))
(+.f64 (.f64 4/3 (/.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 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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))))))) (pow.f64 v 9))) (+.f64 (.f64 4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.f64 -1 (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5))) (+.f64 (.f64 4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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)))))) (pow.f64 v 7))) (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))))
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(fma.f64 3 (/.f64 (+.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (.f64 -1/12 (/.f64 (PI.f64) (sqrt.f64 -6)))) v) (fma.f64 3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (.f64 (pow.f64 v 3) (.f64 (.f64 (PI.f64) (sqrt.f64 -6)) -3))))
(fma.f64 3 (/.f64 (.f64 11/12 (/.f64 (PI.f64) (sqrt.f64 -6))) v) (fma.f64 3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (.f64 (PI.f64) (.f64 (sqrt.f64 -6) (.f64 (pow.f64 v 3) -3)))))
(+.f64 (.f64 3 (/.f64 (+.f64 (.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3))) (/.f64 (PI.f64) (sqrt.f64 -6))) v)) (+.f64 (.f64 3 (/.f64 (+.f64 (.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5))) (.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)))) (pow.f64 v 3))) (+.f64 (.f64 -3 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 3 (.f64 v (+.f64 (.f64 (sqrt.f64 -6) (PI.f64)) (.f64 -1 (/.f64 (PI.f64) (sqrt.f64 -6)))))))))
(fma.f64 3 (/.f64 (fma.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)) (/.f64 (PI.f64) (sqrt.f64 -6))) v) (fma.f64 3 (/.f64 (.f64 -1/2 (+.f64 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)))) (pow.f64 v 3)) (fma.f64 -3 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -6))) (.f64 3 (*.f64 v (fma.f64 (sqrt.f64 -6) (PI.f64) (neg.f64 (/.f64 (PI.f64) (sqrt.f64 -6)))))))))
(fma.f64 3 (/.f64 (+.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (.f64 -1/12 (/.f64 (PI.f64) (sqrt.f64 -6)))) v) (fma.f64 3 (/.f64 (fma.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (.f64 1/12 (/.f64 (PI.f64) (sqrt.f64 -6)))) (pow.f64 v 3)) (fma.f64 3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (.f64 (pow.f64 v 3) (.f64 (*.f64 (PI.f64) (sqrt.f64 -6)) -3)))))
(fma.f64 3 (/.f64 (.f64 11/12 (/.f64 (PI.f64) (sqrt.f64 -6))) v) (fma.f64 3 (/.f64 (fma.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) 1/12)) (pow.f64 v 3)) (fma.f64 3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (.f64 (PI.f64) (.f64 (sqrt.f64 -6) (*.f64 (pow.f64 v 3) -3))))))
(.f64 3 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -6) (PI.f64))))
(.f64 3 (.f64 (pow.f64 v 3) (*.f64 (PI.f64) (sqrt.f64 -6))))
(.f64 3 (.f64 (PI.f64) (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))
(+.f64 (.f64 -3 (.f64 v (+.f64 (.f64 (sqrt.f64 -6) (PI.f64)) (.f64 -1 (/.f64 (PI.f64) (sqrt.f64 -6)))))) (.f64 3 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -6) (PI.f64)))))
(fma.f64 -3 (.f64 v (fma.f64 (sqrt.f64 -6) (PI.f64) (neg.f64 (/.f64 (PI.f64) (sqrt.f64 -6))))) (.f64 3 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -6)))))
(fma.f64 3 (.f64 (PI.f64) (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (.f64 (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6))) (*.f64 v -3)))
(fma.f64 (.f64 v -3) (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6))) (.f64 3 (.f64 (PI.f64) (*.f64 (pow.f64 v 3) (sqrt.f64 -6)))))
(+.f64 (.f64 -3 (.f64 v (+.f64 (.f64 (sqrt.f64 -6) (PI.f64)) (.f64 -1 (/.f64 (PI.f64) (sqrt.f64 -6)))))) (+.f64 (.f64 3 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 -3 (/.f64 (+.f64 (*.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3))) (/.f64 (PI.f64) (sqrt.f64 -6))) v))))
(fma.f64 -3 (.f64 v (fma.f64 (sqrt.f64 -6) (PI.f64) (neg.f64 (/.f64 (PI.f64) (sqrt.f64 -6))))) (fma.f64 3 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -6))) (.f64 -3 (/.f64 (fma.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)) (/.f64 (PI.f64) (sqrt.f64 -6))) v))))
(fma.f64 -3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (fma.f64 3 (.f64 (PI.f64) (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (.f64 -3 (/.f64 (+.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (.f64 -1/12 (/.f64 (PI.f64) (sqrt.f64 -6)))) v))))
(fma.f64 -3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (fma.f64 3 (.f64 (PI.f64) (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (.f64 (/.f64 -3 v) (.f64 11/12 (/.f64 (PI.f64) (sqrt.f64 -6))))))
(+.f64 (.f64 -3 (.f64 v (+.f64 (.f64 (sqrt.f64 -6) (PI.f64)) (.f64 -1 (/.f64 (PI.f64) (sqrt.f64 -6)))))) (+.f64 (.f64 -3 (/.f64 (+.f64 (.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5))) (.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)))) (pow.f64 v 3))) (+.f64 (.f64 3 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 -3 (/.f64 (+.f64 (.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3))) (/.f64 (PI.f64) (sqrt.f64 -6))) v)))))
(fma.f64 -3 (.f64 v (fma.f64 (sqrt.f64 -6) (PI.f64) (neg.f64 (/.f64 (PI.f64) (sqrt.f64 -6))))) (fma.f64 -3 (/.f64 (.f64 -1/2 (+.f64 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)))) (pow.f64 v 3)) (fma.f64 3 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -6))) (*.f64 -3 (/.f64 (fma.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)) (/.f64 (PI.f64) (sqrt.f64 -6))) v)))))
(fma.f64 -3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (fma.f64 -3 (/.f64 (fma.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (.f64 1/12 (/.f64 (PI.f64) (sqrt.f64 -6)))) (pow.f64 v 3)) (fma.f64 3 (.f64 (PI.f64) (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (.f64 -3 (/.f64 (+.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (*.f64 -1/12 (/.f64 (PI.f64) (sqrt.f64 -6)))) v)))))
(fma.f64 -3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (fma.f64 -3 (/.f64 (fma.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) 1/12)) (pow.f64 v 3)) (fma.f64 3 (.f64 (PI.f64) (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (.f64 (/.f64 -3 v) (*.f64 11/12 (/.f64 (PI.f64) (sqrt.f64 -6)))))))

eval226.0ms (4.4%)

Compiler: Compiled 8183 to 6392 computations (21.9% saved)

prune39.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	270	4	274
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	271	5	276

Error

Counts

276 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(.f64 4 (/.f64 (/.f64 1 (.f64 3 (PI.f64))) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2)))))
✓	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
▶	1.9b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
▶	0.0b	(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (/.f64 1 (sqrt.f64 (fma.f64 (.f64 -6 v) v 2))))
▶	0.9b	(/.f64 4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 2))))

Compiler

Compiled 79 to 66 computations (16.5% saved)

localize5.0ms (0.1%)

Local error

Found 6 expressions with local error:

New	Error	Program
	1.0b	(/.f64 4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 2))))
	1.0b	(.f64 (PI.f64) (.f64 3 (sqrt.f64 2)))
	1.0b	(*.f64 3 (sqrt.f64 2))
✓	1.0b	(*.f64 3 (sqrt.f64 2))
✓	1.0b	(.f64 (PI.f64) (.f64 3 (sqrt.f64 2)))
✓	1.0b	(/.f64 4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 2))))

series0.0ms (0%)

Counts: 3 → 0

rewrite53.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

825×	`pow1_binary64`
773×	`add-log-exp_binary64`
773×	`log1p-expm1-u_binary64`
773×	`expm1-log1p-u_binary64`
760×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	191	20
2	2178	20

Stop Event

1×	node limit

Counts

3 → 45

Calls

Call 1

Inputs
(/.f64 4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 2))))
(.f64 (PI.f64) (.f64 3 (sqrt.f64 2)))
(*.f64 3 (sqrt.f64 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (/.f64 1 (*.f64 (PI.f64) (sqrt.f64 18))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))) (cbrt.f64 (/.f64 16 (*.f64 (pow.f64 (PI.f64) 2) 18))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 16 (*.f64 (pow.f64 (PI.f64) 2) 18))) (cbrt.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))) (sqrt.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -4 (/.f64 1 (*.f64 (PI.f64) (neg.f64 (sqrt.f64 18)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (PI.f64) (sqrt.f64 18))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4 (PI.f64)) (/.f64 1 (sqrt.f64 18)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 18)) 1/4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 16 (*.f64 (pow.f64 (PI.f64) 2) 18)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 4 (*.f64 (PI.f64) (sqrt.f64 18)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (PI.f64) (sqrt.f64 18))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (sqrt.f64 18)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 18)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (PI.f64) (sqrt.f64 18))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (sqrt.f64 18))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (PI.f64) 2) 18))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (PI.f64)) (sqrt.f64 18)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (PI.f64) (sqrt.f64 18)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (sqrt.f64 18) 18)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (sqrt.f64 18) 18) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (PI.f64) (sqrt.f64 18))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (PI.f64) (sqrt.f64 18))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (PI.f64) (sqrt.f64 18))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 18)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 18) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 18) 18) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 18)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 18)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 18)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 18)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (sqrt.f64 18) 18))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 18)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 18)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 18)))))))

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

45 → 45

Calls

Call 1

Inputs

Outputs

localize11.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

series9.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

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

rewrite88.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

774×	`log-prod_binary64`
286×	`expm1-udef_binary64`
285×	`log1p-udef_binary64`
264×	`pow3_binary64`
238×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	64
1	351	62
2	4457	62

Stop Event

1×	node limit

Counts

4 → 159

Calls

Call 1

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

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

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-def_binary64`
518×	`associate-l_binary64`
483×	`associate-r_binary64`
441×	`associate-/r*_binary64`
344×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	1984
1	573	1884
2	2011	1755

Stop Event

1×	node limit

Counts

207 → 225

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 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (.f64 (pow.f64 v 4) (+.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 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (.f64 (pow.f64 v 6) (+.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 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.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 (.f64 4/3 (.f64 (pow.f64 v 4) (+.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 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.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 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.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 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.f64 -1 (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5))) (+.f64 (.f64 4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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)))))) (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 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 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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))))))) (pow.f64 v 9))) (+.f64 (.f64 4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.f64 -1 (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5))) (+.f64 (.f64 4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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)))))) (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 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.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 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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)))))) (pow.f64 v 7))) (+.f64 (.f64 -4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.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 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 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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))))))) (pow.f64 v 9))) (+.f64 (.f64 -4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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)))))) (pow.f64 v 7))) (+.f64 (.f64 -4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.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)))))))
(sqrt.f64 1/2)
(+.f64 (*.f64 3/4 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (sqrt.f64 1/2))
(+.f64 (.f64 3/4 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (.f64 1/2 (/.f64 (*.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (sqrt.f64 1/2)))))
(+.f64 (.f64 3/4 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (sqrt.f64 1/2))) (.f64 1/2 (/.f64 (.f64 (pow.f64 v 6) (-.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))))) (sqrt.f64 1/2))))))
(/.f64 (sqrt.f64 -1/6) v)
(-.f64 (/.f64 (sqrt.f64 -1/6) v) (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) v) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (sqrt.f64 -1/6))))) (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(-.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 (pow.f64 v 7) (sqrt.f64 -1/6)))) (+.f64 (/.f64 (sqrt.f64 -1/6) v) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))))) (.f64 1/36 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(*.f64 -1 (/.f64 (sqrt.f64 -1/6) v))
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 -1/6) v)) (.f64 1/36 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 -1/6) v)) (+.f64 (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))) (.f64 1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6))))))
(+.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 (pow.f64 v 7) (sqrt.f64 -1/6)))) (+.f64 (.f64 -1 (/.f64 (sqrt.f64 -1/6) v)) (+.f64 (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))) (.f64 1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))))))
(PI.f64)
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(.f64 -1 (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(.f64 -1 (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (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)))))
(fma.f64 4/3 (+.f64 (/.f64 (pow.f64 v 6) (PI.f64)) (*.f64 (/.f64 v (PI.f64)) v)) (fma.f64 4/3 (/.f64 (pow.f64 v 4) (PI.f64)) (/.f64 4/3 (PI.f64))))
(/.f64 -4/3 (*.f64 (pow.f64 v 2) (PI.f64)))
(/.f64 -4/3 (.f64 (PI.f64) (.f64 v v)))
(/.f64 (/.f64 -4/3 (PI.f64)) (*.f64 v v))
(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 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (*.f64 v v)))))
(+.f64 (/.f64 -4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 -4/3 (.f64 (PI.f64) (*.f64 v v))))
(+.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (pow.f64 v 4)) (/.f64 (/.f64 -4/3 (PI.f64)) (*.f64 v v)))
(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 (PI.f64) (.f64 v v))) (+.f64 (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 6))))))
(-.f64 (/.f64 -4/3 (.f64 (PI.f64) (.f64 v v))) (+.f64 (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 6)))))
(+.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (pow.f64 v 4)) (-.f64 (/.f64 -4/3 (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (/.f64 4/3 (PI.f64)) (.f64 v v))))
(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))))))))
(neg.f64 (+.f64 (+.f64 (/.f64 4/3 (.f64 (PI.f64) (.f64 v v))) (+.f64 (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 6))))) (/.f64 4/3 (*.f64 (PI.f64) (pow.f64 v 8)))))
(+.f64 (-.f64 (/.f64 -4/3 (.f64 (PI.f64) (.f64 v v))) (+.f64 (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 6))))) (/.f64 -4/3 (*.f64 (PI.f64) (pow.f64 v 8))))
(+.f64 (+.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (pow.f64 v 4)) (-.f64 (/.f64 -4/3 (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (/.f64 4/3 (PI.f64)) (.f64 v v)))) (/.f64 (/.f64 -4/3 (PI.f64)) (pow.f64 v 8)))
(/.f64 -4/3 (*.f64 (pow.f64 v 2) (PI.f64)))
(/.f64 -4/3 (.f64 (PI.f64) (.f64 v v)))
(/.f64 (/.f64 -4/3 (PI.f64)) (*.f64 v v))
(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 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (*.f64 v v)))))
(+.f64 (/.f64 -4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 -4/3 (.f64 (PI.f64) (*.f64 v v))))
(+.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (pow.f64 v 4)) (/.f64 (/.f64 -4/3 (PI.f64)) (*.f64 v v)))
(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 (PI.f64) (.f64 v v))) (+.f64 (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 6))))))
(-.f64 (/.f64 -4/3 (.f64 (PI.f64) (.f64 v v))) (+.f64 (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 6)))))
(+.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (pow.f64 v 4)) (-.f64 (/.f64 -4/3 (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (/.f64 4/3 (PI.f64)) (.f64 v v))))
(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))))))))
(neg.f64 (+.f64 (+.f64 (/.f64 4/3 (.f64 (PI.f64) (.f64 v v))) (+.f64 (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 6))))) (/.f64 4/3 (*.f64 (PI.f64) (pow.f64 v 8)))))
(+.f64 (-.f64 (/.f64 -4/3 (.f64 (PI.f64) (.f64 v v))) (+.f64 (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 4/3 (.f64 (PI.f64) (pow.f64 v 6))))) (/.f64 -4/3 (*.f64 (PI.f64) (pow.f64 v 8))))
(+.f64 (+.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (pow.f64 v 4)) (-.f64 (/.f64 -4/3 (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (/.f64 4/3 (PI.f64)) (.f64 v v)))) (/.f64 (/.f64 -4/3 (PI.f64)) (pow.f64 v 8)))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 (*.f64 4/3 (sqrt.f64 1/2)) (PI.f64))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (PI.f64) (sqrt.f64 1/2)))))))
(.f64 4/3 (fma.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (*.f64 (PI.f64) (sqrt.f64 1/2)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (.f64 (pow.f64 v 4) (+.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 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (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 (.f64 (pow.f64 v 4) (fma.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (PI.f64) (sqrt.f64 1/2))) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (PI.f64) (sqrt.f64 1/2)))))) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (*.f64 (PI.f64) (sqrt.f64 1/2))))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 (pow.f64 v 4) (+.f64 (/.f64 3/4 (.f64 (PI.f64) (sqrt.f64 1/2))) (fma.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (PI.f64) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (PI.f64) (sqrt.f64 1/2))))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 1/2 (.f64 (pow.f64 v 4) (/.f64 (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (PI.f64))) (.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (PI.f64) (sqrt.f64 1/2)))) (+.f64 (pow.f64 v 4) (*.f64 v v))))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (.f64 (pow.f64 v 6) (+.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 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.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 (.f64 4/3 (.f64 (pow.f64 v 4) (+.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 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))))
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(sqrt.f64 1/2)
(+.f64 (*.f64 3/4 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (sqrt.f64 1/2))
(fma.f64 3/4 (/.f64 (*.f64 v v) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(fma.f64 3/4 (/.f64 v (/.f64 (sqrt.f64 1/2) v)) (sqrt.f64 1/2))
(fma.f64 3/4 (*.f64 (/.f64 v (sqrt.f64 1/2)) v) (sqrt.f64 1/2))
(+.f64 (.f64 3/4 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (.f64 1/2 (/.f64 (*.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (sqrt.f64 1/2)))))
(+.f64 (fma.f64 3/4 (/.f64 (.f64 v v) (sqrt.f64 1/2)) (sqrt.f64 1/2)) (.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 v 4)))))
(fma.f64 3/4 (/.f64 v (/.f64 (sqrt.f64 1/2) v)) (fma.f64 1/2 (*.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (pow.f64 v 4)) (sqrt.f64 1/2)))
(fma.f64 1/2 (.f64 (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (pow.f64 v 4)) (fma.f64 3/4 (.f64 (/.f64 v (sqrt.f64 1/2)) v) (sqrt.f64 1/2)))
(+.f64 (.f64 3/4 (/.f64 (pow.f64 v 2) (sqrt.f64 1/2))) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (sqrt.f64 1/2))) (.f64 1/2 (/.f64 (.f64 (pow.f64 v 6) (-.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))))) (sqrt.f64 1/2))))))
(+.f64 (fma.f64 3/4 (/.f64 (.f64 v v) (sqrt.f64 1/2)) (sqrt.f64 1/2)) (.f64 1/2 (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (sqrt.f64 1/2) (pow.f64 v 4))) (/.f64 (pow.f64 v 6) (/.f64 (sqrt.f64 1/2) (+.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)))))))))
(fma.f64 3/4 (/.f64 v (/.f64 (sqrt.f64 1/2) v)) (fma.f64 1/2 (+.f64 (.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (pow.f64 v 4)) (.f64 (/.f64 (pow.f64 v 6) (sqrt.f64 1/2)) (+.f64 27/2 (*.f64 (-.f64 9 (/.f64 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2) 1/2)) -3/4)))) (sqrt.f64 1/2)))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (pow.f64 v 4) (/.f64 (pow.f64 v 6) (/.f64 (sqrt.f64 1/2) 135/16))) (fma.f64 3/4 (*.f64 (/.f64 v (sqrt.f64 1/2)) v) (sqrt.f64 1/2)))
(/.f64 (sqrt.f64 -1/6) v)
(-.f64 (/.f64 (sqrt.f64 -1/6) v) (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(-.f64 (/.f64 (sqrt.f64 -1/6) v) (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) v) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (sqrt.f64 -1/6))))) (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(+.f64 (/.f64 (sqrt.f64 -1/6) v) (-.f64 (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))) (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
(+.f64 (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (/.f64 (sqrt.f64 -1/6) v)) (/.f64 -1/36 (.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(+.f64 (/.f64 (fma.f64 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) -1/2 -1/108) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (-.f64 (/.f64 (sqrt.f64 -1/6) v) (/.f64 1/36 (.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
(-.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 (pow.f64 v 7) (sqrt.f64 -1/6)))) (+.f64 (/.f64 (sqrt.f64 -1/6) v) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))))) (.f64 1/36 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(-.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 (sqrt.f64 -1/6) (pow.f64 v 7))) (+.f64 (/.f64 (sqrt.f64 -1/6) v) (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))))) (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(+.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 (sqrt.f64 -1/6) (pow.f64 v 7))) (fma.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (/.f64 (sqrt.f64 -1/6) v))) (/.f64 -1/36 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(+.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)))) (pow.f64 v 7)) (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 v 5)))) (-.f64 (/.f64 (sqrt.f64 -1/6) v) (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
(*.f64 -1 (/.f64 (sqrt.f64 -1/6) v))
(neg.f64 (/.f64 (sqrt.f64 -1/6) v))
(/.f64 (neg.f64 (sqrt.f64 -1/6)) v)
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 -1/6) v)) (.f64 1/36 (/.f64 1 (*.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))))
(fma.f64 -1 (/.f64 (sqrt.f64 -1/6) v) (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(-.f64 (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))) (/.f64 (sqrt.f64 -1/6) v))
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 -1/6) v)) (+.f64 (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))) (.f64 1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (pow.f64 v 5) (sqrt.f64 -1/6))))))
(+.f64 (fma.f64 -1 (/.f64 (sqrt.f64 -1/6) v) (/.f64 1/36 (.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))) (.f64 1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))))
(-.f64 (fma.f64 1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (/.f64 1/36 (.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))) (/.f64 (sqrt.f64 -1/6) v))
(+.f64 (/.f64 1/36 (.f64 (sqrt.f64 -1/6) (pow.f64 v 3))) (-.f64 (/.f64 (fma.f64 1/2 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) 1/108) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (/.f64 (sqrt.f64 -1/6) v)))
(+.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 (pow.f64 v 7) (sqrt.f64 -1/6)))) (+.f64 (.f64 -1 (/.f64 (sqrt.f64 -1/6) v)) (+.f64 (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 3) (sqrt.f64 -1/6)))) (.f64 1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (sqrt.f64 -1/6)))))))
(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 (sqrt.f64 -1/6) (pow.f64 v 7))) (+.f64 (fma.f64 -1 (/.f64 (sqrt.f64 -1/6) v) (/.f64 1/36 (.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))) (.f64 1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5))))))
(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 (sqrt.f64 -1/6) (pow.f64 v 7))) (-.f64 (fma.f64 1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5))) (/.f64 1/36 (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))) (/.f64 (sqrt.f64 -1/6) v)))
(+.f64 (-.f64 (/.f64 1/36 (.f64 (sqrt.f64 -1/6) (pow.f64 v 3))) (/.f64 (sqrt.f64 -1/6) v)) (.f64 (/.f64 1/2 (sqrt.f64 -1/6)) (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 v 5)) (/.f64 (+.f64 1/162 (*.f64 -1/6 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)))) (pow.f64 v 7)))))
(PI.f64)
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(*.f64 (fma.f64 (neg.f64 v) v 1) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(*.f64 (fma.f64 (neg.f64 v) v 1) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(*.f64 (fma.f64 (neg.f64 v) v 1) (PI.f64))
(.f64 -1 (.f64 (pow.f64 v 2) (PI.f64)))
(neg.f64 (.f64 (PI.f64) (.f64 v v)))
(.f64 v (neg.f64 (.f64 v (PI.f64))))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(*.f64 (fma.f64 (neg.f64 v) v 1) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(*.f64 (fma.f64 (neg.f64 v) v 1) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(*.f64 (fma.f64 (neg.f64 v) v 1) (PI.f64))
(.f64 -1 (.f64 (pow.f64 v 2) (PI.f64)))
(neg.f64 (.f64 (PI.f64) (.f64 v v)))
(.f64 v (neg.f64 (.f64 v (PI.f64))))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(*.f64 (fma.f64 (neg.f64 v) v 1) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(*.f64 (fma.f64 (neg.f64 v) v 1) (PI.f64))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(*.f64 (fma.f64 (neg.f64 v) v 1) (PI.f64))

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	1.0b	(/.f64 (sqrt.f64 1/2) (PI.f64))
✓	1.0b	(/.f64 (sqrt.f64 1/2) (PI.f64))

series0.0ms (0%)

Counts: 1 → 0

rewrite43.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`pow1_binary64`
486×	`add-sqr-sqrt_binary64`
469×	`add-log-exp_binary64`
469×	`log1p-expm1-u_binary64`
469×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	105	7
2	1261	7

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 1/2) (PI.f64))

Outputs

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

30 → 30

Calls

Call 1

Inputs

Outputs

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series6.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite93.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

789×	`log-prod_binary64`
281×	`expm1-udef_binary64`
280×	`log1p-udef_binary64`
260×	`pow3_binary64`
235×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	45
1	346	45
2	4405	45

Stop Event

1×	node limit

Counts

2 → 84

Calls

Call 1

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

Outputs

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

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-def_binary64`
563×	`associate-l_binary64`
541×	`associate-r_binary64`
425×	`associate-+l+_binary64`
367×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	1504
1	569	1420
2	1966	1351

Stop Event

1×	node limit

Counts

108 → 130

Calls

Call 1

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

Outputs
(*.f64 1/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 1/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 1/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(.f64 1/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))))
(.f64 1/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (*.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))))))
(.f64 1/3 (fma.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (.f64 1/3 (.f64 (pow.f64 v 4) (+.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 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))))) (+.f64 (.f64 1/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 1/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))))
(fma.f64 1/3 (.f64 (pow.f64 v 4) (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 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 1/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))))))
(.f64 1/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))))) (.f64 (pow.f64 v 4) (+.f64 (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2)) (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 (sqrt.f64 1/2) (PI.f64)))))))
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(fma.f64 -1/3 (/.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))) (+.f64 (/.f64 1/36 (.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 (neg.f64 (sqrt.f64 -1/6)) (PI.f64))))) (pow.f64 v 9)) (fma.f64 -1/3 (+.f64 (/.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (pow.f64 v 5)) (/.f64 (+.f64 (/.f64 1/36 (.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 (neg.f64 (sqrt.f64 -1/6)) (PI.f64)))) (pow.f64 v 7))) (*.f64 1/3 (/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 3)))))
(fma.f64 -1/3 (/.f64 (+.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.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))))) (pow.f64 v 9)) (fma.f64 -1/3 (/.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (pow.f64 v 5)) (fma.f64 1/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (fma.f64 -1/3 (-.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 (sqrt.f64 -1/6) (PI.f64))) (/.f64 -1/108 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7)))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (sqrt.f64 2)) (*.f64 3 (/.f64 1 (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (.f64 (.f64 v v) (-.f64 (neg.f64 (sqrt.f64 2)) (/.f64 3 (sqrt.f64 2)))))
(fma.f64 (*.f64 v v) (fma.f64 -1 (sqrt.f64 2) (/.f64 -3 (sqrt.f64 2))) (sqrt.f64 2))
(fma.f64 (*.f64 v v) (-.f64 (/.f64 -3 (sqrt.f64 2)) (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 v 4) (-.f64 (.f64 3 (/.f64 1 (sqrt.f64 2))) (.f64 9/2 (/.f64 1 (pow.f64 (sqrt.f64 2) 3))))) (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (sqrt.f64 2)) (.f64 3 (/.f64 1 (sqrt.f64 2)))))))
(+.f64 (sqrt.f64 2) (fma.f64 (pow.f64 v 4) (-.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 9/2 (pow.f64 (sqrt.f64 2) 3))) (.f64 (.f64 v v) (-.f64 (neg.f64 (sqrt.f64 2)) (/.f64 3 (sqrt.f64 2))))))
(+.f64 (.f64 (pow.f64 v 4) (-.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 9/4 (sqrt.f64 2)))) (fma.f64 (.f64 v v) (fma.f64 -1 (sqrt.f64 2) (/.f64 -3 (sqrt.f64 2))) (sqrt.f64 2)))
(fma.f64 (pow.f64 v 4) (+.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 -9/4 (sqrt.f64 2))) (fma.f64 (*.f64 v v) (-.f64 (/.f64 -3 (sqrt.f64 2)) (sqrt.f64 2)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 v 4) (-.f64 (.f64 3 (/.f64 1 (sqrt.f64 2))) (.f64 9/2 (/.f64 1 (pow.f64 (sqrt.f64 2) 3))))) (+.f64 (.f64 (-.f64 (.f64 9/2 (/.f64 1 (pow.f64 (sqrt.f64 2) 3))) (.f64 27/2 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)))) (pow.f64 v 6)) (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (sqrt.f64 2)) (*.f64 3 (/.f64 1 (sqrt.f64 2))))))))
(+.f64 (sqrt.f64 2) (fma.f64 (pow.f64 v 4) (-.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 9/2 (pow.f64 (sqrt.f64 2) 3))) (fma.f64 (-.f64 (/.f64 9/2 (pow.f64 (sqrt.f64 2) 3)) (/.f64 27/2 (pow.f64 (sqrt.f64 2) 5))) (pow.f64 v 6) (.f64 (.f64 v v) (-.f64 (neg.f64 (sqrt.f64 2)) (/.f64 3 (sqrt.f64 2)))))))
(+.f64 (sqrt.f64 2) (fma.f64 (pow.f64 v 4) (-.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 9/4 (sqrt.f64 2))) (fma.f64 (pow.f64 v 6) (+.f64 (/.f64 9/4 (sqrt.f64 2)) (/.f64 -27/2 (pow.f64 (sqrt.f64 2) 5))) (.f64 v (.f64 v (fma.f64 -1 (sqrt.f64 2) (/.f64 -3 (sqrt.f64 2))))))))
(+.f64 (sqrt.f64 2) (fma.f64 v (.f64 v (-.f64 (/.f64 -3 (sqrt.f64 2)) (sqrt.f64 2))) (fma.f64 (pow.f64 v 4) (+.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 -9/4 (sqrt.f64 2))) (.f64 (pow.f64 v 6) (+.f64 (/.f64 9/4 (sqrt.f64 2)) (/.f64 -27/2 (pow.f64 (sqrt.f64 2) 5)))))))
(.f64 -1 (.f64 (pow.f64 v 3) (sqrt.f64 -6)))
(neg.f64 (*.f64 (pow.f64 v 3) (sqrt.f64 -6)))
(*.f64 (pow.f64 v 3) (neg.f64 (sqrt.f64 -6)))
(*.f64 (sqrt.f64 -6) (neg.f64 (pow.f64 v 3)))
(+.f64 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))) (.f64 -1 (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))
(fma.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))) (neg.f64 (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))
(-.f64 (.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6)))) (.f64 (pow.f64 v 3) (sqrt.f64 -6)))
(.f64 v (-.f64 (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (.f64 (*.f64 v v) (sqrt.f64 -6))))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -6) v)) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) v))) (+.f64 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))) (.f64 -1 (.f64 (pow.f64 v 3) (sqrt.f64 -6))))))
(+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (+.f64 (fma.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))) (neg.f64 (.f64 (pow.f64 v 3) (sqrt.f64 -6)))) (/.f64 1/2 (*.f64 v (pow.f64 (sqrt.f64 -6) 3)))))
(+.f64 (/.f64 (/.f64 1 v) (sqrt.f64 -6)) (-.f64 (fma.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) v)) (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))
(+.f64 (fma.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (/.f64 (/.f64 1 v) (sqrt.f64 -6))) (-.f64 (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) v) (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))
(+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (+.f64 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) v))) (+.f64 (.f64 -1 (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 (sqrt.f64 -6) 5))) (*.f64 1/2 (/.f64 1 (pow.f64 (sqrt.f64 -6) 3)))) (pow.f64 v 3)))))))
(+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (fma.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))) (+.f64 (/.f64 1/2 (.f64 v (pow.f64 (sqrt.f64 -6) 3))) (.f64 -1 (+.f64 (.f64 (pow.f64 v 3) (sqrt.f64 -6)) (/.f64 (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 5)) (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 3))) (pow.f64 v 3)))))))
(+.f64 (/.f64 (/.f64 1 v) (sqrt.f64 -6)) (fma.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (fma.f64 -1 (fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (/.f64 (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 5)) (/.f64 -1/12 (sqrt.f64 -6))) (pow.f64 v 3))) (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) v))))
(+.f64 (-.f64 (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) v) (fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (/.f64 (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 5)) (/.f64 -1/12 (sqrt.f64 -6))) (pow.f64 v 3)))) (fma.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (/.f64 (/.f64 1 v) (sqrt.f64 -6))))
(*.f64 (sqrt.f64 -6) (pow.f64 v 3))
(*.f64 (pow.f64 v 3) (sqrt.f64 -6))
(+.f64 (.f64 (sqrt.f64 -6) (pow.f64 v 3)) (.f64 -1 (*.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))))))
(fma.f64 (sqrt.f64 -6) (pow.f64 v 3) (neg.f64 (*.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))))))
(fma.f64 (neg.f64 v) (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (*.f64 (pow.f64 v 3) (sqrt.f64 -6)))
(-.f64 (.f64 (pow.f64 v 3) (sqrt.f64 -6)) (.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6)))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (.f64 1/2 (/.f64 1 (pow.f64 (sqrt.f64 -6) 3)))) v)) (+.f64 (.f64 (sqrt.f64 -6) (pow.f64 v 3)) (.f64 -1 (*.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))))))
(fma.f64 -1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 3))) v) (fma.f64 (sqrt.f64 -6) (pow.f64 v 3) (neg.f64 (*.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))))))
(-.f64 (fma.f64 (neg.f64 v) (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (*.f64 (pow.f64 v 3) (sqrt.f64 -6))) (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (/.f64 -1/12 (sqrt.f64 -6))) v))
(fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (fma.f64 v (neg.f64 (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6)))) (/.f64 (+.f64 (/.f64 -1 (sqrt.f64 -6)) (/.f64 1/12 (sqrt.f64 -6))) v)))
(+.f64 (.f64 -1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (.f64 1/2 (/.f64 1 (pow.f64 (sqrt.f64 -6) 3)))) v)) (+.f64 (.f64 (sqrt.f64 -6) (pow.f64 v 3)) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 3)))) (+.f64 (.f64 -1 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))))) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))))))
(fma.f64 -1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 3))) v) (fma.f64 (sqrt.f64 -6) (pow.f64 v 3) (+.f64 (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 5))) (fma.f64 -1 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))) (/.f64 1/2 (*.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))))))
(-.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) (pow.f64 v 3)) (.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))))) (fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 5))))) (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (/.f64 -1/12 (sqrt.f64 -6))) v))
(+.f64 (+.f64 (/.f64 (+.f64 (/.f64 -1 (sqrt.f64 -6)) (/.f64 1/12 (sqrt.f64 -6))) v) (fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 5))))) (-.f64 (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) (pow.f64 v 3)) (.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))))))

eval276.0ms (5.4%)

Compiler: Compiled 11477 to 8884 computations (22.6% saved)

prune83.0ms (1.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	428	2	430
Fresh	0	0	0
Picked	0	1	1
Done	1	3	4
Total	429	6	435

Error

Counts

435 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.9b	(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 1/2))
✓	0.9b	(/.f64 4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 2))))
✓	0.0b	(.f64 4 (/.f64 (/.f64 1 (.f64 3 (PI.f64))) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2)))))
✓	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 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v))))
✓	1.9b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Compiler

Compiled 90 to 75 computations (16.7% saved)

localize10.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series5.0ms (0.1%)

Counts

3 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	v	@	0	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v)))
1.0ms	v	@	0	(/.f64 (/.f64 4/3 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v))))
1.0ms	v	@	inf	(/.f64 (/.f64 4/3 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v))))
1.0ms	v	@	-inf	(/.f64 (/.f64 4/3 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v))))
0.0ms	v	@	inf	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v)))

rewrite181.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

754×	`log-prod_binary64`
276×	`pow1/3_binary64`
271×	`expm1-udef_binary64`
270×	`log1p-udef_binary64`
251×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	325	50
2	4194	50

Stop Event

1×	node limit

Counts

3 → 124

Calls

Call 1

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

Outputs

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

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-def_binary64`
514×	`associate-l_binary64`
490×	`associate-r_binary64`
417×	`associate-+l+_binary64`
366×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	1506
1	558	1422
2	1944	1350

Stop Event

1×	node limit

Counts

148 → 170

Calls

Call 1

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

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (*.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))))))
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(+.f64 (.f64 -4/3 (/.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 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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))))))) (pow.f64 v 9))) (+.f64 (.f64 -4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (+.f64 (.f64 -1 (/.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)))))) (pow.f64 v 7))) (+.f64 (.f64 -4/3 (/.f64 (+.f64 (.f64 1/36 (/.f64 1 (.f64 (sqrt.f64 -1/6) (PI.f64)))) (.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 (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 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (fma.f64 -1 (/.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))))))) (pow.f64 v 9)) (fma.f64 -4/3 (/.f64 (+.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (fma.f64 -1 (/.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)))))) (pow.f64 v 7)) (fma.f64 -4/3 (/.f64 (+.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (neg.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5)) (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))))))
(fma.f64 -4/3 (/.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))) (+.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 (+.f64 1/108 (.f64 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) 1/2)) (.f64 (PI.f64) (sqrt.f64 -1/6))))) (pow.f64 v 9)) (fma.f64 -4/3 (/.f64 (+.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 (+.f64 1/108 (.f64 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) 1/2)) (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7)) (fma.f64 4/3 (/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 3)) (/.f64 (.f64 -4/3 (-.f64 (/.f64 1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (pow.f64 v 5)))))
(fma.f64 -4/3 (/.f64 (+.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.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))))) (pow.f64 v 9)) (fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (fma.f64 -4/3 (/.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (pow.f64 v 5)) (/.f64 (fma.f64 -4/3 (-.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 (sqrt.f64 -1/6) (PI.f64))) (/.f64 -1/27 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7)))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (sqrt.f64 2)) (*.f64 3 (/.f64 1 (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (.f64 (.f64 v v) (-.f64 (neg.f64 (sqrt.f64 2)) (/.f64 3 (sqrt.f64 2)))))
(fma.f64 (*.f64 v v) (fma.f64 -1 (sqrt.f64 2) (/.f64 -3 (sqrt.f64 2))) (sqrt.f64 2))
(fma.f64 v (*.f64 v (-.f64 (/.f64 -3 (sqrt.f64 2)) (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 v 4) (-.f64 (.f64 3 (/.f64 1 (sqrt.f64 2))) (.f64 9/2 (/.f64 1 (pow.f64 (sqrt.f64 2) 3))))) (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (sqrt.f64 2)) (.f64 3 (/.f64 1 (sqrt.f64 2)))))))
(+.f64 (sqrt.f64 2) (fma.f64 (pow.f64 v 4) (-.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 9/2 (pow.f64 (sqrt.f64 2) 3))) (.f64 (.f64 v v) (-.f64 (neg.f64 (sqrt.f64 2)) (/.f64 3 (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 (pow.f64 v 4) (-.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 9/4 (sqrt.f64 2))) (.f64 v (.f64 v (fma.f64 -1 (sqrt.f64 2) (/.f64 -3 (sqrt.f64 2)))))))
(fma.f64 v (*.f64 v (-.f64 (/.f64 -3 (sqrt.f64 2)) (sqrt.f64 2))) (fma.f64 (pow.f64 v 4) (+.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 -9/4 (sqrt.f64 2))) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 v 4) (-.f64 (.f64 3 (/.f64 1 (sqrt.f64 2))) (.f64 9/2 (/.f64 1 (pow.f64 (sqrt.f64 2) 3))))) (+.f64 (.f64 (-.f64 (.f64 9/2 (/.f64 1 (pow.f64 (sqrt.f64 2) 3))) (.f64 27/2 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)))) (pow.f64 v 6)) (.f64 (pow.f64 v 2) (-.f64 (.f64 -1 (sqrt.f64 2)) (*.f64 3 (/.f64 1 (sqrt.f64 2))))))))
(+.f64 (sqrt.f64 2) (fma.f64 (pow.f64 v 4) (-.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 9/2 (pow.f64 (sqrt.f64 2) 3))) (fma.f64 (-.f64 (/.f64 9/2 (pow.f64 (sqrt.f64 2) 3)) (/.f64 27/2 (pow.f64 (sqrt.f64 2) 5))) (pow.f64 v 6) (.f64 (.f64 v v) (-.f64 (neg.f64 (sqrt.f64 2)) (/.f64 3 (sqrt.f64 2)))))))
(+.f64 (fma.f64 (pow.f64 v 4) (-.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 9/4 (sqrt.f64 2))) (.f64 (pow.f64 v 6) (+.f64 (/.f64 9/4 (sqrt.f64 2)) (/.f64 -27/2 (pow.f64 (sqrt.f64 2) 5))))) (fma.f64 (.f64 v v) (fma.f64 -1 (sqrt.f64 2) (/.f64 -3 (sqrt.f64 2))) (sqrt.f64 2)))
(+.f64 (fma.f64 (pow.f64 v 6) (+.f64 (/.f64 9/4 (sqrt.f64 2)) (/.f64 -27/2 (pow.f64 (sqrt.f64 2) 5))) (.f64 v (.f64 v (-.f64 (/.f64 -3 (sqrt.f64 2)) (sqrt.f64 2))))) (fma.f64 (pow.f64 v 4) (+.f64 (/.f64 3 (sqrt.f64 2)) (/.f64 -9/4 (sqrt.f64 2))) (sqrt.f64 2)))
(.f64 -1 (.f64 (pow.f64 v 3) (sqrt.f64 -6)))
(neg.f64 (*.f64 (pow.f64 v 3) (sqrt.f64 -6)))
(*.f64 (pow.f64 v 3) (neg.f64 (sqrt.f64 -6)))
(*.f64 (sqrt.f64 -6) (neg.f64 (pow.f64 v 3)))
(+.f64 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))) (.f64 -1 (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))
(fma.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))) (neg.f64 (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))
(-.f64 (.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6)))) (.f64 (pow.f64 v 3) (sqrt.f64 -6)))
(-.f64 (fma.f64 v (sqrt.f64 -6) (/.f64 (neg.f64 v) (sqrt.f64 -6))) (*.f64 (pow.f64 v 3) (sqrt.f64 -6)))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -6) v)) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) v))) (+.f64 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))) (.f64 -1 (.f64 (pow.f64 v 3) (sqrt.f64 -6))))))
(+.f64 (+.f64 (fma.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))) (neg.f64 (.f64 (pow.f64 v 3) (sqrt.f64 -6)))) (/.f64 1/2 (.f64 v (pow.f64 (sqrt.f64 -6) 3)))) (/.f64 1 (*.f64 v (sqrt.f64 -6))))
(+.f64 (-.f64 (fma.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) v)) (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (/.f64 1 (.f64 v (sqrt.f64 -6))))
(+.f64 (fma.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (/.f64 (/.f64 1 v) (sqrt.f64 -6))) (-.f64 (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) v) (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))
(+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (+.f64 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) v))) (+.f64 (.f64 -1 (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 (sqrt.f64 -6) 5))) (*.f64 1/2 (/.f64 1 (pow.f64 (sqrt.f64 -6) 3)))) (pow.f64 v 3)))))))
(+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (fma.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))) (+.f64 (/.f64 1/2 (.f64 v (pow.f64 (sqrt.f64 -6) 3))) (.f64 -1 (+.f64 (.f64 (pow.f64 v 3) (sqrt.f64 -6)) (/.f64 (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 5)) (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 3))) (pow.f64 v 3)))))))
(+.f64 (/.f64 1 (*.f64 v (sqrt.f64 -6))) (fma.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (fma.f64 -1 (fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (/.f64 (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 5)) (/.f64 -1/12 (sqrt.f64 -6))) (pow.f64 v 3))) (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) v))))
(+.f64 (/.f64 (/.f64 1 v) (sqrt.f64 -6)) (-.f64 (fma.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) v)) (fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (/.f64 (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 5)) (/.f64 -1/12 (sqrt.f64 -6))) (pow.f64 v 3)))))
(*.f64 (sqrt.f64 -6) (pow.f64 v 3))
(*.f64 (pow.f64 v 3) (sqrt.f64 -6))
(+.f64 (.f64 (sqrt.f64 -6) (pow.f64 v 3)) (.f64 -1 (*.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))))))
(fma.f64 (sqrt.f64 -6) (pow.f64 v 3) (neg.f64 (*.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))))))
(fma.f64 (neg.f64 v) (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (*.f64 (pow.f64 v 3) (sqrt.f64 -6)))
(-.f64 (*.f64 (pow.f64 v 3) (sqrt.f64 -6)) (fma.f64 v (sqrt.f64 -6) (/.f64 (neg.f64 v) (sqrt.f64 -6))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (.f64 1/2 (/.f64 1 (pow.f64 (sqrt.f64 -6) 3)))) v)) (+.f64 (.f64 (sqrt.f64 -6) (pow.f64 v 3)) (.f64 -1 (*.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))))))
(fma.f64 -1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 3))) v) (fma.f64 (sqrt.f64 -6) (pow.f64 v 3) (neg.f64 (*.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))))))
(-.f64 (fma.f64 (neg.f64 v) (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))) (*.f64 (pow.f64 v 3) (sqrt.f64 -6))) (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (/.f64 -1/12 (sqrt.f64 -6))) v))
(-.f64 (fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (/.f64 (+.f64 (/.f64 -1 (sqrt.f64 -6)) (/.f64 1/12 (sqrt.f64 -6))) v)) (fma.f64 v (sqrt.f64 -6) (/.f64 (neg.f64 v) (sqrt.f64 -6))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (.f64 1/2 (/.f64 1 (pow.f64 (sqrt.f64 -6) 3)))) v)) (+.f64 (.f64 (sqrt.f64 -6) (pow.f64 v 3)) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 3)))) (+.f64 (.f64 -1 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6))))) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))))))
(fma.f64 -1 (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 3))) v) (fma.f64 (sqrt.f64 -6) (pow.f64 v 3) (+.f64 (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 5))) (fma.f64 -1 (.f64 v (-.f64 (sqrt.f64 -6) (/.f64 1 (sqrt.f64 -6)))) (/.f64 1/2 (*.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))))))
(-.f64 (+.f64 (-.f64 (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) (pow.f64 v 3)) (.f64 v (+.f64 (sqrt.f64 -6) (/.f64 -1 (sqrt.f64 -6))))) (fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 5))))) (/.f64 (+.f64 (/.f64 1 (sqrt.f64 -6)) (/.f64 -1/12 (sqrt.f64 -6))) v))
(+.f64 (/.f64 (+.f64 (/.f64 -1 (sqrt.f64 -6)) (/.f64 1/12 (sqrt.f64 -6))) v) (+.f64 (-.f64 (/.f64 (/.f64 -1/12 (sqrt.f64 -6)) (pow.f64 v 3)) (fma.f64 v (sqrt.f64 -6) (/.f64 (neg.f64 v) (sqrt.f64 -6)))) (fma.f64 (pow.f64 v 3) (sqrt.f64 -6) (/.f64 1/2 (*.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 5))))))

localize8.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

0.0ms

-inf

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

rewrite51.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`log-prod_binary64`
332×	`pow-prod-down_binary64`
308×	`pow2_binary64`
215×	`pow1/3_binary64`
212×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	257	19
2	3145	19

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 4/3 (/.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))) (*.f64 4/3 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 1/2) (/.f64 (-.f64 1 (*.f64 v v)) (/.f64 4/3 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 4/3 (sqrt.f64 1/2)) (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 4/3 (sqrt.f64 1/2))) (*.f64 (PI.f64) (neg.f64 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 4/3 (sqrt.f64 1/2)) (PI.f64)) (-.f64 1 (*.f64 v v)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 4/3 (sqrt.f64 1/2)) 1) (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 4/3 (sqrt.f64 1/2)) (-.f64 1 (*.f64 v v))) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 4/3 (sqrt.f64 1/2)) (pow.f64 (cbrt.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) 2)) (cbrt.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 4/3 (sqrt.f64 1/2)) (sqrt.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))))) (sqrt.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -4/3 (sqrt.f64 1/2)) (*.f64 (PI.f64) (neg.f64 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2)) (-.f64 1 (*.f64 v v)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) -4/3) (*.f64 (PI.f64) (neg.f64 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (/.f64 4/3 (PI.f64))) (-.f64 1 (*.f64 v v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (pow.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v))) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))) (*.f64 4/3 (sqrt.f64 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v)))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (/.f64 4/3 (PI.f64)) (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v)))))) 2))))))

simplify49.0ms (1%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
731×	`times-frac_binary64`
665×	`associate-/r*_binary64`
511×	`associate-l_binary64`
481×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	447
1	146	440
2	421	376
3	1335	327
4	7234	327

Stop Event

1×	node limit

Counts

47 → 50

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64)))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 6)) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64))))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))))

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 v v)) (PI.f64))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 v v))))
(.f64 4/3 (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 4/3 (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 v v)) (PI.f64)) (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64)))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v v)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 4)))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (*.f64 v v) (pow.f64 v 4)))))
(*.f64 4/3 (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 v v (pow.f64 v 4)) (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 6)) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64))))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 v v)) (PI.f64)) (.f64 4/3 (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 6)) (PI.f64)) (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64))))))
(.f64 4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v v))) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 4)) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6)))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v v) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (pow.f64 v 4) (pow.f64 v 6))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (*.f64 v v))))
(.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -4/3 (PI.f64)) (.f64 v v)))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v)))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 4))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (*.f64 v v))))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6)))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 6)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (+.f64 (/.f64 -4/3 (pow.f64 v 6)) (/.f64 -4/3 (pow.f64 v 4)))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 8))) (.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v)))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (.f64 -4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 8)))))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 6)))) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 8)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (+.f64 (/.f64 -4/3 (pow.f64 v 8)) (/.f64 -4/3 (pow.f64 v 4))) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 6)))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (*.f64 v v))))
(.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -4/3 (PI.f64)) (.f64 v v)))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v)))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 4))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (*.f64 v v))))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6)))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 6)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (+.f64 (/.f64 -4/3 (pow.f64 v 6)) (/.f64 -4/3 (pow.f64 v 4)))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 8))) (.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v)))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (.f64 -4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 8)))))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 6)))) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 8)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (+.f64 (/.f64 -4/3 (pow.f64 v 8)) (/.f64 -4/3 (pow.f64 v 4))) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 6)))))

eval304.0ms (5.9%)

Compiler: Compiled 7432 to 5551 computations (25.3% saved)

prune42.0ms (0.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	302	4	306
Fresh	0	0	0
Picked	1	0	1
Done	2	3	5
Total	305	7	312

Error

Counts

312 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(/.f64 (/.f64 4/3 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v))))
▶	1.8b	(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
▶	0.0b	(/.f64 (.f64 4/3 (/.f64 1 (PI.f64))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (.f64 v v))))
▶	1.8b	(/.f64 (/.f64 (.f64 4/3 (sqrt.f64 1/2)) (PI.f64)) (-.f64 1 (.f64 v v)))
✓	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
✓	1.9b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
▶	0.9b	(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))

Compiler

Compiled 99 to 82 computations (17.2% saved)

localize3.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))
	1.0b	(/.f64 4/3 (PI.f64))
	1.0b	(/.f64 4/3 (PI.f64))
✓	1.0b	(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))

series0.0ms (0%)

Counts: 1 → 0

rewrite62.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

660×	`pow1_binary64`
618×	`add-log-exp_binary64`
618×	`log1p-expm1-u_binary64`
618×	`expm1-log1p-u_binary64`
607×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	149	10
2	1696	10

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))

Outputs

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

23 → 23

Calls

Call 1

Inputs

Outputs

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series1.0ms (0%)

Counts

2 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

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

0.0ms

inf

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

0.0ms

-inf

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

rewrite178.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`log-prod_binary64`
325×	`pow2_binary64`
224×	`pow1/3_binary64`
220×	`expm1-udef_binary64`
219×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	262	23
2	3523	23

Stop Event

1×	node limit

Counts

2 → 101

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 8/9) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4/3 (/.f64 1 (/.f64 (PI.f64) (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4/3 (*.f64 (sqrt.f64 1/2) (pow.f64 (PI.f64) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 1/2) (*.f64 4/3 (pow.f64 (PI.f64) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 8/9) (pow.f64 (PI.f64) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 8/9) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 8/9) (*.f64 (cbrt.f64 (sqrt.f64 8/9)) (pow.f64 (PI.f64) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) (cbrt.f64 (/.f64 8/9 (pow.f64 (PI.f64) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 8/9 (pow.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 8/9)) (*.f64 (sqrt.f64 (sqrt.f64 8/9)) (pow.f64 (PI.f64) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) (sqrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 8/9)) (/.f64 1 (neg.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) -1) (sqrt.f64 8/9))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 1/2) 1) (/.f64 4/3 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 8/9) 1) (/.f64 (cbrt.f64 (sqrt.f64 8/9)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sqrt.f64 8/9)) 1) (/.f64 (sqrt.f64 (sqrt.f64 8/9)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4/3 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (/.f64 (sqrt.f64 1/2) (cbrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (/.f64 4/3 (cbrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (PI.f64)) -2) (/.f64 (sqrt.f64 8/9) (cbrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 8/9) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sqrt.f64 8/9)) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (/.f64 (sqrt.f64 (sqrt.f64 8/9)) (cbrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4/3 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (PI.f64))) (/.f64 4/3 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) -1/2) (/.f64 (sqrt.f64 8/9) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 8/9) (sqrt.f64 (PI.f64))) (/.f64 (cbrt.f64 (sqrt.f64 8/9)) (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 8/9 (pow.f64 (PI.f64) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (PI.f64) (sqrt.f64 8/9)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (PI.f64) (sqrt.f64 8/9)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (sqrt.f64 8/9) 8/9) (pow.f64 (PI.f64) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (PI.f64) (sqrt.f64 8/9)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 8/9) (neg.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 8/9 (pow.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (PI.f64) (sqrt.f64 8/9)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (*.f64 (sqrt.f64 8/9) 8/9) (pow.f64 (PI.f64) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 8/9) (/.f64 1 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 8/9) (*.f64 (pow.f64 (PI.f64) -1) (/.f64 1 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (/.f64 1 (-.f64 1 (*.f64 v v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))) (cbrt.f64 (/.f64 8/9 (pow.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 8/9 (pow.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))) 2))) (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 8/9 (pow.f64 (PI.f64) 2))) (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) (/.f64 1 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) (*.f64 (sqrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) (/.f64 1 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) (/.f64 1 (neg.f64 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1 (*.f64 v v))) (/.f64 (sqrt.f64 8/9) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 4/3 (-.f64 1 (*.f64 v v))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 1/2) (-.f64 1 (*.f64 v v))) (/.f64 4/3 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 8/9) (-.f64 1 (*.f64 v v))) (/.f64 (cbrt.f64 (sqrt.f64 8/9)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sqrt.f64 8/9)) (-.f64 1 (*.f64 v v))) (/.f64 (sqrt.f64 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2)) (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 v v))) 2)) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) (cbrt.f64 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 8/9) (sqrt.f64 (-.f64 1 (*.f64 v v)))) (/.f64 (pow.f64 (PI.f64) -1) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 v v)) -1/2) (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 8/9 (pow.f64 (PI.f64) 2))) (sqrt.f64 (-.f64 1 (*.f64 v v)))) (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 8/9) (PI.f64))) (sqrt.f64 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (pow.f64 v 6))) (+.f64 1 (fma.f64 v v (pow.f64 v 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (pow.f64 v 4))) (fma.f64 v v 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 8/9 (pow.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (-.f64 1 (*.f64 v v)) (/.f64 (PI.f64) (sqrt.f64 8/9))) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (-.f64 1 (*.f64 v v)) (/.f64 (PI.f64) (sqrt.f64 8/9))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) (sqrt.f64 8/9)) -3) (pow.f64 (-.f64 1 (*.f64 v v)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (PI.f64) (sqrt.f64 8/9)) (-.f64 1 (*.f64 v v))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))) (sqrt.f64 8/9)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (-.f64 1 (*.f64 v v)) (/.f64 (PI.f64) (sqrt.f64 8/9))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (neg.f64 (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 8/9 (pow.f64 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (-.f64 1 (*.f64 v v)) (/.f64 (PI.f64) (sqrt.f64 8/9))) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) (sqrt.f64 8/9)) -3) (pow.f64 (-.f64 1 (*.f64 v v)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (-.f64 1 (*.f64 v v)))) 1))))))

simplify51.0ms (1%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
731×	`times-frac_binary64`
665×	`associate-/r*_binary64`
511×	`associate-l_binary64`
481×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	447
1	146	440
2	421	376
3	1335	327
4	7234	327

Stop Event

1×	node limit

Counts

113 → 115

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64)))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 6)) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64))))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))))

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 (sqrt.f64 1/2) (*.f64 v v)) (PI.f64))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 v v))))
(.f64 4/3 (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 4/3 (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 v v)) (PI.f64)) (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64)))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v v)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 4)))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (*.f64 v v) (pow.f64 v 4)))))
(*.f64 4/3 (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 v v (pow.f64 v 4)) (/.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 2)) (PI.f64))) (+.f64 (.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 6)) (PI.f64))) (.f64 4/3 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64))))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 4/3 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 v v)) (PI.f64)) (.f64 4/3 (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 v 6)) (PI.f64)) (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 v 4)) (PI.f64))))))
(.f64 4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v v))) (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 4)) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6)))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v v) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (pow.f64 v 4) (pow.f64 v 6))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (*.f64 v v))))
(.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -4/3 (PI.f64)) (.f64 v v)))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v)))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 4))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (*.f64 v v))))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6)))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 6)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (+.f64 (/.f64 -4/3 (pow.f64 v 6)) (/.f64 -4/3 (pow.f64 v 4)))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 8))) (.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v)))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (.f64 -4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 8)))))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 6)))) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 8)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (+.f64 (/.f64 -4/3 (pow.f64 v 8)) (/.f64 -4/3 (pow.f64 v 4))) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 6)))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))
(.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (*.f64 v v))))
(.f64 (sqrt.f64 1/2) (/.f64 (/.f64 -4/3 (PI.f64)) (.f64 v v)))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v)))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 4))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (*.f64 v v))))))
(.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6)))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 6)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (+.f64 (/.f64 -4/3 (pow.f64 v 6)) (/.f64 -4/3 (pow.f64 v 4)))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 4) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 8) (PI.f64)))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 6) (PI.f64)))) (.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 v 2) (PI.f64)))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 8))) (.f64 -4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 6))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v)))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (pow.f64 v 4))) (.f64 -4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) (.f64 v v))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 6))) (/.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 8)))))
(+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 6)))) (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 -4/3 (pow.f64 v 4)) (/.f64 -4/3 (pow.f64 v 8)))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (+.f64 (/.f64 -4/3 (pow.f64 v 8)) (/.f64 -4/3 (pow.f64 v 4))) (+.f64 (/.f64 -4/3 (.f64 v v)) (/.f64 -4/3 (pow.f64 v 6)))))

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

-inf

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

1.0ms

inf

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

rewrite70.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

853×	`log-prod_binary64`
289×	`expm1-udef_binary64`
288×	`log1p-udef_binary64`
239×	`log-pow_binary64`
219×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	349	26
2	4561	26

Stop Event

1×	node limit

Counts

1 → 59

Calls

Call 1

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

Outputs

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

simplify53.0ms (1%)

Algorithm

1×	egg-herbie

Rules

484×	`fma-def_binary64`
483×	`distribute-rgt-out_binary64`
367×	`associate-/l/_binary64`
340×	`distribute-lft-out_binary64`
329×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1031
1	332	988
2	1209	924
3	5435	763

Stop Event

1×	node limit

Counts

71 → 82

Calls

Call 1

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

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 v v))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))))))
(.f64 4/3 (fma.f64 v (.f64 v (+.f64 (/.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 (.f64 v v) (.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (.f64 (+.f64 (*.f64 v v) 1) (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(+.f64 (.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.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 (sqrt.f64 1/2) (PI.f64))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (*.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))))
(fma.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.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 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 v v)))))
(.f64 4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))))) (.f64 (pow.f64 v 4) (+.f64 (/.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 4/3 (fma.f64 (pow.f64 v 4) (fma.f64 (/.f64 1/2 (PI.f64)) (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64)))) (fma.f64 v (.f64 v (+.f64 (/.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 (fma.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2)) (/.f64 (/.f64 27/16 (PI.f64)) (sqrt.f64 1/2)))) (fma.f64 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2)))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(+.f64 (.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.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 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (.f64 (pow.f64 v 6) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.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 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.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 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))))
(fma.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.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)))))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 4/3 (+.f64 (.f64 (pow.f64 v 6) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.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 1/2 (/.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 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 v v))))))
(fma.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.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 4/3 (+.f64 (fma.f64 (pow.f64 v 6) (+.f64 (/.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))) (fma.f64 1/2 (/.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)))))) (.f64 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(.f64 4/3 (+.f64 (fma.f64 (pow.f64 v 4) (fma.f64 (/.f64 1/2 (PI.f64)) (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64)))) (fma.f64 v (.f64 v (+.f64 (/.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 (pow.f64 v 6) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64)) (.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 135/16 (PI.f64)) (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (PI.f64)))))))))
(.f64 4/3 (+.f64 (fma.f64 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2)))) (.f64 (pow.f64 v 6) (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))) (.f64 (/.f64 1/2 (*.f64 (sqrt.f64 1/2) (PI.f64))) 189/16)))) (fma.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2)) (/.f64 (/.f64 27/16 (PI.f64)) (sqrt.f64 1/2)))) (/.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 (/.f64 (sqrt.f64 -1/6) (pow.f64 v 3)) (PI.f64)))
(*.f64 -4/3 (/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 3)))
(.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))))
(.f64 (/.f64 -4/3 (.f64 (PI.f64) (pow.f64 v 3))) (sqrt.f64 -1/6))
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(fma.f64 -4/3 (/.f64 (+.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (.f64 (/.f64 1/2 (.f64 (PI.f64) (sqrt.f64 -1/6))) 23/1296)) (pow.f64 v 9)) (fma.f64 -4/3 (/.f64 (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (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 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))) (/.f64 -1/108 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 7)))))

localize31.0ms (0.6%)

Local error

Found 8 expressions with local error:

New	Error	Program
	1.0b	(/.f64 (sqrt.f64 1/2) (PI.f64))
	0.2b	(.f64 4/3 (.f64 v v))
	0.0b	(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
	0.0b	(+.f64 (.f64 4/3 (.f64 v v)) 4/3)
✓	0.0b	(+.f64 (.f64 4/3 (.f64 v v)) 4/3)
✓	0.0b	(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
✓	0.2b	(.f64 4/3 (.f64 v v))
	1.0b	(/.f64 (sqrt.f64 1/2) (PI.f64))

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	v	@	0	(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
1.0ms	v	@	inf	(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
1.0ms	v	@	0	(.f64 4/3 (.f64 v v))
1.0ms	v	@	inf	(.f64 4/3 (.f64 v v))
0.0ms	v	@	-inf	(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))

rewrite208.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

596×	`log-prod_binary64`
461×	`prod-diff_binary64`
308×	`pow2_binary64`
215×	`pow1/3_binary64`
211×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	247	32
2	3313	32

Stop Event

1×	node limit

Counts

3 → 153

Calls

Call 1

Inputs
(.f64 4/3 (.f64 v v))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
(+.f64 (.f64 4/3 (.f64 v v)) 4/3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 4/3 (*.f64 v v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 4/3) (*.f64 v v))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 4/3) (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4/3) (*.f64 v v)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4/3) (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 4/3 (*.f64 v v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4/3 (*.f64 v v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 16/9 (pow.f64 v 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 4/3 (*.f64 v v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 v (sqrt.f64 4/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 64/27 (pow.f64 v 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 16/9 (pow.f64 v 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 4/3) (*.f64 v v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 4/3 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 64/27 (pow.f64 v 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 4/3 (*.f64 v v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 4/3 (*.f64 v v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 4/3 (*.f64 v v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 4/3 (*.f64 v v))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 4/3 (*.f64 (*.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 4/3 (*.f64 (*.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 v v 1) 4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 4/3 (*.f64 (*.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64)))) 1) (*.f64 (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 (fma.f64 v v 1) 4/3))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 (fma.f64 v v 1) 4/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 (fma.f64 v v 1) 4/3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 (fma.f64 v v 1) 4/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 v v 1) 4/3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 1/2) (/.f64 (PI.f64) (*.f64 (fma.f64 v v 1) 4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 v v 1) 4/3) (/.f64 (PI.f64) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (PI.f64) (*.f64 (sqrt.f64 1/2) (*.f64 (fma.f64 v v 1) 4/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 64/27 (pow.f64 v 6) 64/27) (*.f64 (/.f64 (PI.f64) (sqrt.f64 1/2)) (-.f64 (fma.f64 16/9 (pow.f64 v 4) 16/9) (*.f64 (*.f64 v v) 16/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 16/9 (pow.f64 v 4) -16/9) (*.f64 (/.f64 (PI.f64) (sqrt.f64 1/2)) (fma.f64 4/3 (*.f64 v v) -4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (fma.f64 v v 1) 4/3)) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (fma.f64 v v 1) 4/3))) (neg.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (fma.f64 64/27 (pow.f64 v 6) 64/27)) (*.f64 (PI.f64) (-.f64 (fma.f64 16/9 (pow.f64 v 4) 16/9) (*.f64 (*.f64 v v) 16/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 1/2)) (fma.f64 64/27 (pow.f64 v 6) 64/27)) (*.f64 (neg.f64 (PI.f64)) (-.f64 (fma.f64 16/9 (pow.f64 v 4) 16/9) (*.f64 (*.f64 v v) 16/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (fma.f64 16/9 (pow.f64 v 4) -16/9)) (*.f64 (PI.f64) (fma.f64 4/3 (*.f64 v v) -4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 1/2)) (fma.f64 16/9 (pow.f64 v 4) -16/9)) (*.f64 (neg.f64 (PI.f64)) (fma.f64 4/3 (*.f64 v v) -4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 64/27 (pow.f64 v 6) 64/27) (sqrt.f64 1/2)) (*.f64 (-.f64 (fma.f64 16/9 (pow.f64 v 4) 16/9) (*.f64 (*.f64 v v) 16/9)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 16/9 (pow.f64 v 4) -16/9) (sqrt.f64 1/2)) (*.f64 (fma.f64 4/3 (*.f64 v v) -4/3) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 64/27 (pow.f64 v 6) 64/27) 1) (*.f64 (-.f64 (fma.f64 16/9 (pow.f64 v 4) 16/9) (*.f64 (*.f64 v v) 16/9)) (/.f64 (PI.f64) (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 16/9 (pow.f64 v 4) -16/9) 1) (*.f64 (fma.f64 4/3 (*.f64 v v) -4/3) (/.f64 (PI.f64) (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 64/27 (pow.f64 v 6) 64/27) (neg.f64 (sqrt.f64 1/2))) (*.f64 (-.f64 (fma.f64 16/9 (pow.f64 v 4) 16/9) (*.f64 (*.f64 v v) 16/9)) (neg.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 16/9 (pow.f64 v 4) -16/9) (neg.f64 (sqrt.f64 1/2))) (*.f64 (fma.f64 4/3 (*.f64 v v) -4/3) (neg.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 4/3 (*.f64 (*.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64)))) 3) (pow.f64 (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) 3)) (+.f64 (pow.f64 (*.f64 4/3 (*.f64 (*.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64)))) 2) (-.f64 (pow.f64 (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) 2) (*.f64 (*.f64 4/3 (*.f64 (*.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 4/3 (*.f64 (*.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64)))) 2) (pow.f64 (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) 2)) (-.f64 (*.f64 4/3 (*.f64 (*.f64 v v) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (fma.f64 v v 1) 4/3)) 1) (PI.f64))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (fma.f64 v v 1) 4/3)) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (fma.f64 v v 1) 4/3)) (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 1/2)) (*.f64 (fma.f64 v v 1) 4/3)) (neg.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 64/27 (pow.f64 v 6) 64/27) (/.f64 (sqrt.f64 1/2) (PI.f64))) (-.f64 (fma.f64 16/9 (pow.f64 v 4) 16/9) (*.f64 (*.f64 v v) 16/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 16/9 (pow.f64 v 4) -16/9) (/.f64 (sqrt.f64 1/2) (PI.f64))) (fma.f64 4/3 (*.f64 v v) -4/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 64/27 (pow.f64 v 6) 64/27)) (-.f64 (fma.f64 16/9 (pow.f64 v 4) 16/9) (*.f64 (*.f64 v v) 16/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 16/9 (pow.f64 v 4) -16/9)) (fma.f64 4/3 (*.f64 v v) -4/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (fma.f64 v v 1) 4/3) (neg.f64 (sqrt.f64 1/2))) (neg.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 v v 1) 4/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 v v 1) 4/3)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 v v 1) 4/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 v v 1) 4/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (fma.f64 v v 1) 4/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) 3) (pow.f64 (*.f64 (fma.f64 v v 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(fma.f64 v v 1) 4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (fma.f64 v v 1) 4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 v v 1) 4/3)) 1))))))

simplify116.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1123×	`fma-def_binary64`
736×	`*-commutative_binary64`
684×	`associate-*l/_binary64`
474×	`associate-/r/_binary64`
362×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	456
1	36	438
2	76	420
3	168	366
4	511	366
5	1940	366
6	3376	366
7	4418	366
8	4810	366
9	5035	366
10	5253	366
11	5516	366
12	6392	366
13	7274	366
14	7838	366

Stop Event

1×	node limit

Counts

189 → 163

Calls

Call 1

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

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

eval355.0ms (7%)

Compiler: Compiled 10322 to 7785 computations (24.6% saved)

prune87.0ms (1.7%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	503	1	504
Fresh	0	0	0
Picked	1	0	1
Done	0	6	6
Total	504	7	511

Error

Counts

511 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(/.f64 (.f64 4/3 (/.f64 1 (PI.f64))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (.f64 v v))))
✓	1.8b	(/.f64 (/.f64 (.f64 4/3 (sqrt.f64 1/2)) (PI.f64)) (-.f64 1 (.f64 v v)))
✓	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 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v))))
✓	1.9b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
	1.8b	(.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (/.f64 1 (-.f64 1 (.f64 v v))))
✓	0.9b	(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))

Compiler

Compiled 99 to 82 computations (17.2% saved)

regimes54.0ms (1.1%)

Counts

13 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 2))))
(.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (/.f64 1 (-.f64 1 (.f64 v v))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
(/.f64 (/.f64 (.f64 4/3 (sqrt.f64 1/2)) (PI.f64)) (-.f64 1 (.f64 v v)))
(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 1/2))
(/.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 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v))))
(/.f64 (.f64 4/3 (/.f64 1 (PI.f64))) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (.f64 v v))))
(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (/.f64 1 (sqrt.f64 (fma.f64 (.f64 -6 v) v 2))))
(.f64 4 (/.f64 (/.f64 1 (.f64 3 (PI.f64))) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (fma.f64 (*.f64 -6 v) v 2)))))
(/.f64 (/.f64 -4/3 (fma.f64 v v -1)) (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))))

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

Calls

7 calls:

25.0ms	(*.f64 v v)
9.0ms	v
3.0ms	(*.f64 v v)
3.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
3.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))

Results

Error	Segments	Branch
0.0b	1	`v`
0.0b	1	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
0.0b	1	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
0.0b	1	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
0.0b	1	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
0.0b	1	`(*.f64 v v)`
0.0b	1	`(*.f64 v v)`

Compiler

Compiled 271 to 193 computations (28.8% saved)

regimes47.0ms (0.9%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 2))))
(.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (/.f64 1 (-.f64 1 (.f64 v v))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
(/.f64 (/.f64 (.f64 4/3 (sqrt.f64 1/2)) (PI.f64)) (-.f64 1 (.f64 v v)))
(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 1/2))
(/.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 (PI.f64)) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (-.f64 1 (*.f64 v v))))

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

Calls

7 calls:

22.0ms	v
8.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
3.0ms	(*.f64 v v)
3.0ms	(*.f64 v v)
3.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))

Results

Error	Segments	Branch
0.0b	1	`v`
0.0b	1	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
0.0b	1	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
0.0b	1	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
0.0b	1	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
0.0b	1	`(*.f64 v v)`
0.0b	1	`(*.f64 v v)`

Compiler

Compiled 196 to 141 computations (28.1% saved)

regimes23.0ms (0.5%)

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 2))))
(.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (/.f64 1 (-.f64 1 (.f64 v v))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
(/.f64 (/.f64 (.f64 4/3 (sqrt.f64 1/2)) (PI.f64)) (-.f64 1 (.f64 v v)))
(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 1/2))
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

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

Calls

6 calls:

5.0ms	v
4.0ms	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
3.0ms	(*.f64 v v)
3.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
3.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))

Results

Error	Segments	Branch
0.9b	1	`v`
0.9b	1	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
0.9b	1	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
0.9b	1	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
0.9b	1	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
0.9b	1	`(*.f64 v v)`

Compiler

Compiled 175 to 128 computations (26.9% saved)

regimes12.0ms (0.2%)

Accuracy

Total -1.0b remaining (-108.4%)

Threshold costs -1.0b (-108.4%)

Counts

6 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 2))))
(.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (/.f64 1 (-.f64 1 (.f64 v v))))
(.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 4/3 (*.f64 v v)) 4/3))
(/.f64 (/.f64 (.f64 4/3 (sqrt.f64 1/2)) (PI.f64)) (-.f64 1 (.f64 v v)))

Outputs
(*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 1/2))

Calls

2 calls:

7.0ms	v
3.0ms	(*.f64 v v)

Results

Error	Segments	Branch
0.9b	1	`v`
0.9b	1	`(*.f64 v v)`

Compiler

Compiled 63 to 47 computations (25.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	84
1	37	84
2	44	84
3	48	84
4	50	84

Stop Event

1×

saturated

Calls

Call 1

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

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

end51.0ms (1%)

Stop Event

1×

fuel

Compiler

Compiled 113 to 88 computations (22.1% saved)

Details

analyze5.0ms (0.1%)

sample1.4s (26.8%)

preprocess58.0ms (1.1%)

simplify39.0ms (0.8%)

eval1.0ms (0%)

prune2.0ms (0%)

localize9.0ms (0.2%)

series10.0ms (0.2%)

rewrite134.0ms (2.6%)

simplify82.0ms (1.6%)

localize11.0ms (0.2%)

series9.0ms (0.2%)

rewrite73.0ms (1.4%)

simplify65.0ms (1.3%)

eval226.0ms (4.4%)

prune39.0ms (0.8%)

localize5.0ms (0.1%)

series0.0ms (0%)

rewrite53.0ms (1%)

simplify8.0ms (0.2%)

localize11.0ms (0.2%)

series9.0ms (0.2%)

rewrite88.0ms (1.7%)

simplify62.0ms (1.2%)

localize3.0ms (0.1%)

series0.0ms (0%)

rewrite43.0ms (0.8%)

simplify6.0ms (0.1%)

localize13.0ms (0.3%)

series6.0ms (0.1%)

rewrite93.0ms (1.8%)

simplify58.0ms (1.1%)

eval276.0ms (5.4%)

prune83.0ms (1.6%)

localize10.0ms (0.2%)

series5.0ms (0.1%)

rewrite181.0ms (3.5%)

simplify63.0ms (1.2%)

localize8.0ms (0.2%)

series2.0ms (0%)

rewrite51.0ms (1%)

simplify49.0ms (1%)

eval304.0ms (5.9%)

prune42.0ms (0.8%)

localize3.0ms (0.1%)

series0.0ms (0%)

rewrite62.0ms (1.2%)

simplify6.0ms (0.1%)

localize8.0ms (0.2%)

series1.0ms (0%)

rewrite178.0ms (3.5%)

simplify51.0ms (1%)

localize13.0ms (0.2%)

series2.0ms (0%)

rewrite70.0ms (1.4%)

simplify53.0ms (1%)

localize31.0ms (0.6%)

series6.0ms (0.1%)

rewrite208.0ms (4.1%)

simplify116.0ms (2.3%)

eval355.0ms (7%)

prune87.0ms (1.7%)

regimes54.0ms (1.1%)

regimes47.0ms (0.9%)

regimes23.0ms (0.5%)

regimes12.0ms (0.2%)

simplify4.0ms (0.1%)

end51.0ms (1%)

Profiling