Details

analyze4.0ms (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)

sample1.1s (27%)

Results

1.1s	8256×	body	256	valid
2.0ms	17×	body	256	invalid

preprocess68.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

1332×	`fma-def_binary64`
576×	`fma-neg_binary64`
530×	`distribute-rgt-in_binary64`
496×	`unsub-neg_binary64`
430×	`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	967	26
5	1747	24
6	3707	24
7	6458	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 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (neg.f64 (fma.f64 v v -1))) (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 (/.f64 -4/3 (fma.f64 v v -1)) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 -4/3 (.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (fma.f64 v v -1)))

Compiler

Compiled 22 to 17 computations (22.7% saved)

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1332×	`fma-def_binary64`
576×	`fma-neg_binary64`
530×	`distribute-rgt-in_binary64`
496×	`unsub-neg_binary64`
430×	`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	967	26
5	1747	24
6	3707	24
7	6458	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 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (neg.f64 (fma.f64 v v -1))) (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 (/.f64 -4/3 (fma.f64 v v -1)) (PI.f64)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 -4/3 (.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (fma.f64 v v -1)))

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

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

Compiler

Compiled 38 to 29 computations (23.7% saved)

localize62.0ms (1.4%)

Local error

Found 3 expressions with local error:

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

New

Error

Program

✓

0.0b

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

✓

0.0b

(*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

✓

0.0b

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

Compiler

Compiled 66 to 45 computations (31.8% saved)

series11.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

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

rewrite127.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

631×	`log-prod_binary64`
405×	`pow-prod-down_binary64`
348×	`pow2_binary64`
246×	`pow1/3_binary64`
243×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
1	288	59
2	3355	59

Stop Event

1×	node limit

Counts

3 → 66

Calls

Call 1

Inputs

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

(*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

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

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

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

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

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

594×	`associate-l_binary64`
565×	`times-frac_binary64`
553×	`associate-/r*_binary64`
458×	`associate-/l*_binary64`
315×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2055
1	733	1945
2	2661	1820

Stop Event

1×	node limit

Counts

102 → 137

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

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 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -4/3 (.f64 (.f64 v 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 (-.f64 (/.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (PI.f64)) (/.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 -4/3 (*.f64 v v))))
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(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 (.f64 v v) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) -1 (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -4/3 (.f64 (pow.f64 v 4) (fma.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) -1 (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))))))))
(fma.f64 -4/3 (.f64 v (.f64 v (-.f64 (/.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (PI.f64)) (/.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (-.f64 (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (/.f64 -3/4 (sqrt.f64 1/2)) (PI.f64))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (*.f64 -4/3 (pow.f64 v 4)))))
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(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3))) (.f64 -1 (/.f64 (PI.f64) (sqrt.f64 -6)))) v)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3))) (.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)))) (pow.f64 v 3))) (+.f64 (.f64 -1 (.f64 v (+.f64 (.f64 -1 (.f64 (sqrt.f64 -6) (PI.f64))) (/.f64 (PI.f64) (sqrt.f64 -6))))) (.f64 -1 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -6) (PI.f64)))))))
(fma.f64 -1 (/.f64 (fma.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)) (neg.f64 (/.f64 (PI.f64) (sqrt.f64 -6)))) v) (fma.f64 -1 (/.f64 (.f64 1/2 (+.f64 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)))) (pow.f64 v 3)) (.f64 -1 (+.f64 (.f64 v (fma.f64 -1 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -6)))))))
(-.f64 (-.f64 (neg.f64 (fma.f64 v (fma.f64 (neg.f64 (sqrt.f64 -6)) (PI.f64) (/.f64 (PI.f64) (sqrt.f64 -6))) (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -6))))) (/.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))) (/.f64 (-.f64 (.f64 1/12 (/.f64 (PI.f64) (sqrt.f64 -6))) (/.f64 (PI.f64) (sqrt.f64 -6))) v))
(-.f64 (neg.f64 (+.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (+.f64 (pow.f64 v 3) (neg.f64 v))) (.f64 v (/.f64 (PI.f64) (sqrt.f64 -6))))) (+.f64 (/.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) -11/12) v) (*.f64 (/.f64 (PI.f64) (pow.f64 v 3)) (+.f64 (/.f64 -1/12 (sqrt.f64 -6)) (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 5))))))

localize29.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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 3 (PI.f64)) (-.f64 1 (*.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))))))

Compiler

Compiled 86 to 52 computations (39.5% saved)

series10.0ms (0.2%)

Counts

4 → 48

Calls

12 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 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.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	@	-inf	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

rewrite133.0ms (3.1%)

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	80
1	375	77
2	4681	73

Stop Event

1×	node limit

Counts

4 → 106

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 3 (PI.f64)) (-.f64 1 (*.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))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 3 (PI.f64)) (.f64 (.f64 v (neg.f64 v)) (.f64 3 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 3 (PI.f64)) (.f64 (.f64 3 (PI.f64)) (.f64 v (neg.f64 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 3 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 v (neg.f64 v) 1)) (.f64 3 (PI.f64)))) (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 v (neg.f64 v) 1)) (.f64 3 (PI.f64)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 v (neg.f64 v) 1)) (.f64 3 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 v (neg.f64 v) 1)) (.f64 3 (PI.f64))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (fma.f64 v (neg.f64 v) 1)) (.f64 3 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 3 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1))))) 1)))) (#(struct:change 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simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

869×	`associate-r_binary64`
406×	`associate-+l+_binary64`
366×	`associate-*l/_binary64`
351×	`associate-+r+_binary64`
338×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	1938
1	579	1852
2	2227	1756

Stop Event

1×	node limit

Counts

154 → 161

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 (PI.f64))
(+.f64 (.f64 -3 (.f64 (pow.f64 v 2) (PI.f64))) (*.f64 3 (PI.f64)))
(+.f64 (.f64 -3 (.f64 (pow.f64 v 2) (PI.f64))) (*.f64 3 (PI.f64)))
(+.f64 (.f64 -3 (.f64 (pow.f64 v 2) (PI.f64))) (*.f64 3 (PI.f64)))
(.f64 -3 (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -3 (.f64 (pow.f64 v 2) (PI.f64))) (*.f64 3 (PI.f64)))
(+.f64 (.f64 -3 (.f64 (pow.f64 v 2) (PI.f64))) (*.f64 3 (PI.f64)))
(+.f64 (.f64 -3 (.f64 (pow.f64 v 2) (PI.f64))) (*.f64 3 (PI.f64)))
(.f64 -3 (.f64 (pow.f64 v 2) (PI.f64)))
(+.f64 (.f64 -3 (.f64 (pow.f64 v 2) (PI.f64))) (*.f64 3 (PI.f64)))
(+.f64 (.f64 -3 (.f64 (pow.f64 v 2) (PI.f64))) (*.f64 3 (PI.f64)))
(+.f64 (.f64 -3 (.f64 (pow.f64 v 2) (PI.f64))) (*.f64 3 (PI.f64)))
(.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 (*.f64 v 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 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.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 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))))))
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(.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)))
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(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 4/3 (/.f64 (pow.f64 v 5) (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))))))
(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 (/.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 (.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 (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 (.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))))
(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)))))
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(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 -3 (.f64 (PI.f64) (*.f64 (pow.f64 v 3) (sqrt.f64 -6)))))))
(+.f64 (.f64 (PI.f64) (.f64 (.f64 -3 (sqrt.f64 -6)) (pow.f64 v 3))) (.f64 3 (+.f64 (+.f64 (/.f64 (.f64 11/12 (/.f64 (PI.f64) (sqrt.f64 -6))) v) (/.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))) (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))))))
(.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 (PI.f64) (.f64 (*.f64 3 (sqrt.f64 -6)) (pow.f64 v 3)))
(+.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 (PI.f64) (.f64 (*.f64 3 (sqrt.f64 -6)) (pow.f64 v 3))))
(+.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)))))))

eval278.0ms (6.5%)

Compiler: Compiled 9067 to 6934 computations (23.5% saved)

prune35.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	294	4	298
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	294	6	300

Error

Counts

300 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.0b	(/.f64 4 (+.f64 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))
✓	0.0b	(/.f64 -4/3 (.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (fma.f64 v v -1)))
▶	1.6b	(/.f64 4 (.f64 (.f64 (PI.f64) 3) (sqrt.f64 (-.f64 2 (.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))))))
▶	0.7b	(/.f64 -4/3 (*.f64 (PI.f64) (neg.f64 (sqrt.f64 2))))
▶	1.6b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Compiler

Compiled 90 to 75 computations (16.7% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 14 computations (12.5% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite75.0ms (1.8%)

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 1/2) (*.f64 (cbrt.f64 (sqrt.f64 1/2)) (/.f64 1 (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 (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))))))))

simplify14.0ms (0.3%)

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

localize11.0ms (0.3%)

Compiler: Compiled 21 to 19 computations (9.5% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 59 to 38 computations (35.6% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite77.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

667×	`log-prod_binary64`
357×	`pow2_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
246×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	51
1	307	48
2	3705	42

Stop Event

1×	node limit

Counts

3 → 105

Calls

Call 1

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

Outputs

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

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 2 (*.f64 (*.f64 v v) -6))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 2 (*.f64 (*.f64 (*.f64 v v) -6) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 v v) -6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 (*.f64 v v) -6 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 (*.f64 v v) -6 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (*.f64 v v) -6 2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (*.f64 v v) -6 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (*.f64 v v) -6 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (*.f64 v v) -6 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (*.f64 v v) -6 2)) (pow.f64 (cbrt.f64 (fma.f64 (*.f64 v v) -6 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (*.f64 v v) -6 2)) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (*.f64 v v) -6 2)) 2) (cbrt.f64 (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 (*.f64 v v) -6 2) 1/4) (*.f64 (pow.f64 (fma.f64 (*.f64 v v) -6 2) 1/4) (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 8 (*.f64 (pow.f64 (*.f64 v v) 3) 216)) (/.f64 1 (+.f64 4 (fma.f64 (pow.f64 v 4) 36 (*.f64 12 (*.f64 v v))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 4 (*.f64 (pow.f64 v 4) 36)) (/.f64 1 (fma.f64 6 (*.f64 v v) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (fma.f64 (*.f64 v v) -6 2) 1/4) 3) (pow.f64 (fma.f64 (*.f64 v v) -6 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)) (cbrt.f64 (fma.f64 (*.f64 v v) -6 2))) (cbrt.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 4 (fma.f64 (pow.f64 v 4) 36 (*.f64 12 (*.f64 v v)))) (-.f64 8 (*.f64 (pow.f64 (*.f64 v v) 3) 216))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 6 (*.f64 v v) 2) (-.f64 4 (*.f64 (pow.f64 v 4) 36))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 8 (*.f64 (pow.f64 (*.f64 v v) 3) 216)) (+.f64 4 (fma.f64 (pow.f64 v 4) 36 (*.f64 12 (*.f64 v v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 4 (*.f64 (pow.f64 v 4) 36)) (fma.f64 6 (*.f64 v v) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 8 (*.f64 (pow.f64 (*.f64 v v) 3) 216))) (neg.f64 (+.f64 4 (fma.f64 (pow.f64 v 4) 36 (*.f64 12 (*.f64 v v))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 4 (*.f64 (pow.f64 v 4) 36))) (neg.f64 (fma.f64 6 (*.f64 v v) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 8 (pow.f64 (*.f64 (*.f64 v v) -6) 3)) (+.f64 4 (-.f64 (pow.f64 (*.f64 (*.f64 v v) -6) 2) (*.f64 2 (*.f64 (*.f64 v v) -6)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 4 (pow.f64 (*.f64 (*.f64 v v) -6) 2)) (-.f64 2 (*.f64 (*.f64 v v) -6)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (*.f64 v v) -6 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (*.f64 v v) -6 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (*.f64 v v) -6 2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (*.f64 v v) -6 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (*.f64 v v) -6 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 4 (fma.f64 (pow.f64 v 4) 36 (*.f64 12 (*.f64 v v)))) (-.f64 8 (*.f64 (pow.f64 (*.f64 v v) 3) 216))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 6 (*.f64 v v) 2) (-.f64 4 (*.f64 (pow.f64 v 4) 36))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (*.f64 v v) -6 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (*.f64 v v) -6 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (*.f64 v v) -6 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (*.f64 v v) -6 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 (*.f64 v v) -6 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 6 (neg.f64 (*.f64 v v)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 v v) -6 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (*.f64 v v) -6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 v 4) 36)) (neg.f64 (cbrt.f64 (*.f64 6 (*.f64 v v)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 v (sqrt.f64 6)) (neg.f64 (*.f64 v (sqrt.f64 6))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -6 (*.f64 v v) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 6 v) (neg.f64 v) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 v v) -6)) 2) (cbrt.f64 (*.f64 (*.f64 v v) -6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (*.f64 v v) -6)) (sqrt.f64 (*.f64 (*.f64 v v) -6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 6 (*.f64 v v)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (*.f64 v v)) 6 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (*.f64 (pow.f64 v 4) 36))) (cbrt.f64 (*.f64 6 (*.f64 v v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (*.f64 v (sqrt.f64 6))) (*.f64 v (sqrt.f64 6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (*.f64 6 v)) v 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -6 v) v 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -6 (cbrt.f64 (pow.f64 v 4))) (pow.f64 (cbrt.f64 v) 2) 2)))))

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-def_binary64`
578×	`associate-/r*_binary64`
569×	`times-frac_binary64`
426×	`associate-/l*_binary64`
338×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	1127
1	452	1082
2	1543	1022
3	6708	1008

Stop Event

1×	node limit

Counts

141 → 157

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 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 2/3 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (*.f64 (sqrt.f64 1/2) (PI.f64))))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 2/3 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 2/3 (/.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))))) (*.f64 (sqrt.f64 1/2) (PI.f64)))))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64))))
(-.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -1/6) (PI.f64))))))
(-.f64 (+.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))))
(-.f64 (+.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (+.f64 (.f64 -2/3 (/.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) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64))))))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))))
(.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -1/6) (PI.f64))))))
(+.f64 (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64)))))))
(+.f64 (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (+.f64 (.f64 2/3 (/.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) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64))))))))
(.f64 3 (.f64 (sqrt.f64 2) (PI.f64)))
(+.f64 (.f64 -9 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (.f64 3 (.f64 (sqrt.f64 2) (PI.f64))))
(+.f64 (.f64 -9 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (+.f64 (.f64 -27/2 (/.f64 (.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (.f64 3 (.f64 (sqrt.f64 2) (PI.f64)))))
(+.f64 (.f64 -9 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (+.f64 (.f64 -27/2 (/.f64 (.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (.f64 3 (.f64 (sqrt.f64 2) (PI.f64))) (.f64 -81/2 (/.f64 (.f64 (pow.f64 v 6) (PI.f64)) (pow.f64 (sqrt.f64 2) 5))))))
(.f64 3 (.f64 v (*.f64 (sqrt.f64 -6) (PI.f64))))
(+.f64 (.f64 3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))))
(+.f64 (.f64 -3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (+.f64 (.f64 3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v)))))
(+.f64 (.f64 -3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (+.f64 (.f64 3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 3 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) v))) (.f64 3/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))))))
(.f64 -3 (.f64 v (*.f64 (sqrt.f64 -6) (PI.f64))))
(+.f64 (.f64 -3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 -3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))))
(+.f64 (.f64 -3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (.f64 -3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v)))))
(+.f64 (.f64 -3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (+.f64 (.f64 -3 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) v))) (.f64 -3/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))))))
2
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(*.f64 -6 (pow.f64 v 2))
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(*.f64 -6 (pow.f64 v 2))
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 v v) (.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (*.f64 (/.f64 v (sqrt.f64 1/2)) (/.f64 v (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 2/3 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (*.f64 (sqrt.f64 1/2) (PI.f64))))))
(+.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 v v) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 2/3 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 4)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 2/3 (.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (/.f64 (pow.f64 v 4) (PI.f64))) (.f64 (/.f64 v (sqrt.f64 1/2)) (/.f64 v (PI.f64)))))
(fma.f64 (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (.f64 2/3 (/.f64 (pow.f64 v 4) (PI.f64))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 v (sqrt.f64 1/2)) (/.f64 v (PI.f64)))))
(fma.f64 (+.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 -9/16 (sqrt.f64 1/2)) 1/2)) (.f64 2/3 (/.f64 (pow.f64 v 4) (PI.f64))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (/.f64 v (sqrt.f64 1/2)) (/.f64 v (PI.f64)))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 2/3 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 2/3 (/.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))))) (*.f64 (sqrt.f64 1/2) (PI.f64)))))))
(+.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 v v) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 2/3 (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 4))) (.f64 (/.f64 (pow.f64 v 6) (sqrt.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)))) (PI.f64))))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 2/3 (fma.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (/.f64 (pow.f64 v 4) (PI.f64)) (.f64 (/.f64 (pow.f64 v 6) (sqrt.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)) (PI.f64)))) (*.f64 (/.f64 v (sqrt.f64 1/2)) (/.f64 v (PI.f64)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 (/.f64 v (sqrt.f64 1/2)) (/.f64 v (PI.f64)) (.f64 (/.f64 2/3 (sqrt.f64 1/2)) (+.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (pow.f64 v 4) (PI.f64))) (/.f64 (pow.f64 v 6) (/.f64 (PI.f64) 135/16))))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)))
(-.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -1/6) (PI.f64))))))
(-.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v))) (/.f64 1/27 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -1/6)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (/.f64 -1/27 (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (/.f64 (/.f64 -1/27 (PI.f64)) (.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))
(-.f64 (+.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))))
(-.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 5))))) (/.f64 1/27 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -1/6)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (fma.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5)))) (/.f64 -1/27 (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))))
(+.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (/.f64 (/.f64 -1/27 (PI.f64)) (.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))) (/.f64 (fma.f64 -2/3 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) -1/81) (.f64 (PI.f64) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))))
(+.f64 (/.f64 (fma.f64 -2/3 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2) -1/81) (.f64 (PI.f64) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))) (fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (/.f64 (/.f64 -1/27 (PI.f64)) (.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
(-.f64 (+.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (+.f64 (.f64 -2/3 (/.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) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64))))))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))))
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(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (fma.f64 -2/3 (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5)))) (/.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) (.f64 (sqrt.f64 -1/6) (pow.f64 v 7))))) (/.f64 -1/27 (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))))
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(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (fma.f64 (/.f64 (/.f64 -2/3 (PI.f64)) (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))) (/.f64 (/.f64 -1/27 (PI.f64)) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
(.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64))))
(.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) -4/3)
(/.f64 (sqrt.f64 -1/6) (/.f64 (*.f64 (PI.f64) v) -4/3))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -1/6) (PI.f64))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (/.f64 1/27 (.f64 (pow.f64 v 3) (*.f64 (PI.f64) (sqrt.f64 -1/6)))))
(fma.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) -4/3 (/.f64 1/27 (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
(fma.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) -4/3 (/.f64 (/.f64 1/27 (sqrt.f64 -1/6)) (.f64 (PI.f64) (pow.f64 v 3))))
(+.f64 (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64)))))))
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(+.f64 (/.f64 1/27 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -1/6)))) (fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (.f64 2/3 (+.f64 (/.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 (.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 7))) (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (*.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 5)))))))
(+.f64 (/.f64 1/27 (.f64 (PI.f64) (.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))) (fma.f64 2/3 (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5)))) (/.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) (.f64 (sqrt.f64 -1/6) (pow.f64 v 7))))) (.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) -4/3)))
(+.f64 (.f64 (/.f64 (/.f64 2/3 (PI.f64)) (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)))) (fma.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) -4/3 (/.f64 (/.f64 1/27 (sqrt.f64 -1/6)) (.f64 (PI.f64) (pow.f64 v 3)))))
(.f64 3 (.f64 (sqrt.f64 2) (PI.f64)))
(.f64 3 (.f64 (PI.f64) (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (PI.f64) 3))
(.f64 (PI.f64) (.f64 3 (sqrt.f64 2)))
(+.f64 (.f64 -9 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (.f64 3 (.f64 (sqrt.f64 2) (PI.f64))))
(fma.f64 -9 (/.f64 (.f64 v v) (/.f64 (sqrt.f64 2) (PI.f64))) (.f64 3 (*.f64 (PI.f64) (sqrt.f64 2))))
(fma.f64 -9 (/.f64 (PI.f64) (/.f64 (sqrt.f64 2) (.f64 v v))) (.f64 (sqrt.f64 2) (*.f64 (PI.f64) 3)))
(fma.f64 (PI.f64) (.f64 3 (sqrt.f64 2)) (.f64 (/.f64 (.f64 v v) (sqrt.f64 2)) (.f64 (PI.f64) -9)))
(.f64 (PI.f64) (+.f64 (.f64 3 (sqrt.f64 2)) (/.f64 (.f64 (.f64 -9 v) v) (sqrt.f64 2))))
(+.f64 (.f64 -9 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (+.f64 (.f64 -27/2 (/.f64 (.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (.f64 3 (.f64 (sqrt.f64 2) (PI.f64)))))
(fma.f64 -9 (/.f64 (.f64 v v) (/.f64 (sqrt.f64 2) (PI.f64))) (fma.f64 -27/2 (/.f64 (.f64 (PI.f64) (pow.f64 v 4)) (pow.f64 (sqrt.f64 2) 3)) (.f64 3 (.f64 (PI.f64) (sqrt.f64 2)))))
(fma.f64 -9 (/.f64 (PI.f64) (/.f64 (sqrt.f64 2) (.f64 v v))) (fma.f64 3 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 -27/4 (/.f64 (.f64 (PI.f64) (pow.f64 v 4)) (sqrt.f64 2)))))
(fma.f64 (PI.f64) (.f64 3 (sqrt.f64 2)) (fma.f64 -27/4 (/.f64 (pow.f64 v 4) (/.f64 (sqrt.f64 2) (PI.f64))) (.f64 (/.f64 (.f64 v v) (sqrt.f64 2)) (.f64 (PI.f64) -9))))
(fma.f64 -27/4 (/.f64 (pow.f64 v 4) (/.f64 (sqrt.f64 2) (PI.f64))) (.f64 (PI.f64) (+.f64 (.f64 3 (sqrt.f64 2)) (/.f64 (.f64 (.f64 -9 v) v) (sqrt.f64 2)))))
(+.f64 (.f64 -9 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (+.f64 (.f64 -27/2 (/.f64 (.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (.f64 3 (.f64 (sqrt.f64 2) (PI.f64))) (.f64 -81/2 (/.f64 (.f64 (pow.f64 v 6) (PI.f64)) (pow.f64 (sqrt.f64 2) 5))))))
(fma.f64 -9 (/.f64 (.f64 v v) (/.f64 (sqrt.f64 2) (PI.f64))) (fma.f64 -27/2 (/.f64 (.f64 (PI.f64) (pow.f64 v 4)) (pow.f64 (sqrt.f64 2) 3)) (fma.f64 3 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 -81/2 (/.f64 (*.f64 (PI.f64) (pow.f64 v 6)) (pow.f64 (sqrt.f64 2) 5))))))
(+.f64 (fma.f64 -81/2 (/.f64 (pow.f64 v 6) (/.f64 (pow.f64 (sqrt.f64 2) 5) (PI.f64))) (.f64 (sqrt.f64 2) (.f64 (PI.f64) 3))) (fma.f64 -9 (/.f64 (PI.f64) (/.f64 (sqrt.f64 2) (.f64 v v))) (.f64 -27/4 (/.f64 (*.f64 (PI.f64) (pow.f64 v 4)) (sqrt.f64 2)))))
(fma.f64 -9 (.f64 (PI.f64) (/.f64 (.f64 v v) (sqrt.f64 2))) (fma.f64 (PI.f64) (.f64 3 (sqrt.f64 2)) (fma.f64 -81/2 (.f64 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 2) 5)) (pow.f64 v 6)) (*.f64 -27/4 (/.f64 (pow.f64 v 4) (/.f64 (sqrt.f64 2) (PI.f64)))))))
(fma.f64 -9 (.f64 (PI.f64) (/.f64 (.f64 v v) (sqrt.f64 2))) (fma.f64 -27/4 (/.f64 (pow.f64 v 4) (/.f64 (sqrt.f64 2) (PI.f64))) (.f64 (PI.f64) (+.f64 (.f64 3 (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 v 6) -81/2) (pow.f64 (sqrt.f64 2) 5))))))
(.f64 3 (.f64 v (*.f64 (sqrt.f64 -6) (PI.f64))))
(.f64 3 (.f64 v (*.f64 (PI.f64) (sqrt.f64 -6))))
(.f64 3 (.f64 (*.f64 (PI.f64) v) (sqrt.f64 -6)))
(.f64 (PI.f64) (.f64 (sqrt.f64 -6) (*.f64 v 3)))
(+.f64 (.f64 3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))))
(.f64 3 (+.f64 (.f64 v (.f64 (PI.f64) (sqrt.f64 -6))) (/.f64 (PI.f64) (.f64 v (sqrt.f64 -6)))))
(.f64 3 (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6))))
(.f64 3 (fma.f64 (PI.f64) (.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v)))
(+.f64 (.f64 -3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (+.f64 (.f64 3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v)))))
(fma.f64 -3/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3))) (.f64 3 (+.f64 (.f64 v (.f64 (PI.f64) (sqrt.f64 -6))) (/.f64 (PI.f64) (*.f64 v (sqrt.f64 -6))))))
(fma.f64 3 (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6))) (.f64 (/.f64 -3/2 (pow.f64 v 3)) (/.f64 (/.f64 (PI.f64) -6) (sqrt.f64 -6))))
(fma.f64 3 (fma.f64 (PI.f64) (.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v)) (/.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) 1/4) (pow.f64 v 3)))
(fma.f64 v (.f64 (sqrt.f64 -6) (.f64 (PI.f64) 3)) (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (+.f64 (/.f64 3 v) (/.f64 -3/2 (.f64 (pow.f64 v 3) -6)))))
(+.f64 (.f64 -3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (+.f64 (.f64 3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 3 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) v))) (.f64 3/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))))))
(fma.f64 -3/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3))) (fma.f64 3 (.f64 v (.f64 (PI.f64) (sqrt.f64 -6))) (fma.f64 3 (/.f64 (PI.f64) (.f64 v (sqrt.f64 -6))) (.f64 3/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5)))))))
(fma.f64 -3/2 (/.f64 (PI.f64) (.f64 (.f64 (pow.f64 v 3) -6) (sqrt.f64 -6))) (fma.f64 3 (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6))) (.f64 3/2 (/.f64 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (pow.f64 v 5)))))
(fma.f64 3 (fma.f64 (PI.f64) (.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v)) (fma.f64 3/2 (/.f64 (/.f64 (PI.f64) (pow.f64 v 5)) (pow.f64 (sqrt.f64 -6) 5)) (/.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) 1/4) (pow.f64 v 3))))
(+.f64 (.f64 (PI.f64) (+.f64 (.f64 (sqrt.f64 -6) (.f64 v 3)) (/.f64 3/2 (.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5))))) (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (+.f64 (/.f64 3 v) (/.f64 -3/2 (.f64 (pow.f64 v 3) -6)))))
(.f64 -3 (.f64 v (*.f64 (sqrt.f64 -6) (PI.f64))))
(.f64 (.f64 v (*.f64 (PI.f64) (sqrt.f64 -6))) -3)
(.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (*.f64 v -3))
(.f64 (sqrt.f64 -6) (.f64 v (*.f64 (PI.f64) -3)))
(+.f64 (.f64 -3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 -3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))))
(.f64 -3 (+.f64 (.f64 v (.f64 (PI.f64) (sqrt.f64 -6))) (/.f64 (PI.f64) (.f64 v (sqrt.f64 -6)))))
(.f64 -3 (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6))))
(.f64 -3 (fma.f64 (PI.f64) (.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v)))
(+.f64 (.f64 -3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (.f64 -3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v)))))
(fma.f64 -3 (.f64 v (.f64 (PI.f64) (sqrt.f64 -6))) (fma.f64 3/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3))) (.f64 (/.f64 (PI.f64) (*.f64 v (sqrt.f64 -6))) -3)))
(+.f64 (.f64 -3 (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6)))) (*.f64 (/.f64 3/2 (pow.f64 v 3)) (/.f64 (/.f64 (PI.f64) -6) (sqrt.f64 -6))))
(fma.f64 -3 (fma.f64 (PI.f64) (.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v)) (.f64 (/.f64 (PI.f64) (pow.f64 v 3)) (/.f64 -1/4 (sqrt.f64 -6))))
(fma.f64 v (.f64 (sqrt.f64 -6) (.f64 (PI.f64) -3)) (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (+.f64 (/.f64 -3 v) (/.f64 3/2 (.f64 (pow.f64 v 3) -6)))))
(+.f64 (.f64 -3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (+.f64 (.f64 -3 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) v))) (.f64 -3/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))))))
(fma.f64 -3 (.f64 v (.f64 (PI.f64) (sqrt.f64 -6))) (fma.f64 3/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3))) (fma.f64 -3 (/.f64 (PI.f64) (.f64 v (sqrt.f64 -6))) (.f64 -3/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5)))))))
(fma.f64 (.f64 (.f64 (PI.f64) v) (sqrt.f64 -6)) -3 (fma.f64 (/.f64 (PI.f64) (.f64 (.f64 (pow.f64 v 3) -6) (sqrt.f64 -6))) 3/2 (fma.f64 (/.f64 (/.f64 (PI.f64) v) (sqrt.f64 -6)) -3 (/.f64 (/.f64 (*.f64 (PI.f64) -3/2) (pow.f64 v 5)) (pow.f64 (sqrt.f64 -6) 5)))))
(+.f64 (.f64 -3 (fma.f64 (PI.f64) (.f64 v (sqrt.f64 -6)) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v))) (fma.f64 -3/2 (/.f64 (/.f64 (PI.f64) (pow.f64 v 5)) (pow.f64 (sqrt.f64 -6) 5)) (*.f64 (/.f64 (PI.f64) (pow.f64 v 3)) (/.f64 -1/4 (sqrt.f64 -6)))))
(fma.f64 v (.f64 (sqrt.f64 -6) (.f64 (PI.f64) -3)) (fma.f64 -3/2 (/.f64 (/.f64 (PI.f64) (pow.f64 v 5)) (pow.f64 (sqrt.f64 -6) 5)) (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (+.f64 (/.f64 -3 v) (/.f64 3/2 (.f64 (pow.f64 v 3) -6))))))
2
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(fma.f64 v (*.f64 v -6) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(fma.f64 v (*.f64 v -6) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(fma.f64 v (*.f64 v -6) 2)
(*.f64 -6 (pow.f64 v 2))
(.f64 (.f64 v v) -6)
(.f64 v (.f64 v -6))
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(fma.f64 v (*.f64 v -6) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(fma.f64 v (*.f64 v -6) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(fma.f64 v (*.f64 v -6) 2)
(*.f64 -6 (pow.f64 v 2))
(.f64 (.f64 v v) -6)
(.f64 v (.f64 v -6))
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(fma.f64 v (*.f64 v -6) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(fma.f64 v (*.f64 v -6) 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(fma.f64 v (*.f64 v -6) 2)

localize59.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 v v) -6 2)
✓	0.0b	(*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1))
✓	0.0b	(.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))
✓	1.0b	(/.f64 4 (+.f64 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))

Compiler

Compiled 111 to 66 computations (40.5% saved)

series8.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

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

rewrite210.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

708×	`log-prod_binary64`
374×	`pow2_binary64`
260×	`pow1/3_binary64`
260×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	74
1	396	65
2	4495	65

Stop Event

1×	node limit

Counts

4 → 133

Calls

Call 1

Inputs
(/.f64 4 (+.f64 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))
(.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))
(*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1))
(fma.f64 (*.f64 v v) -6 2)

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

simplify83.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

496×	`associate-+l+_binary64`
455×	`associate-+r+_binary64`
396×	`associate-*l/_binary64`
372×	`*-commutative_binary64`
365×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	1915
1	589	1829
2	2277	1711
3	7807	1711

Stop Event

1×	node limit

Counts

181 → 190

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

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 (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 (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 (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 (.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)) (fma.f64 (pow.f64 v 4) (+.f64 (/.f64 (/.f64 3/4 (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 (sqrt.f64 1/2) (PI.f64)))) (.f64 (.f64 v 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 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (/.f64 1/2 (PI.f64)))) (+.f64 (.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))) (+.f64 (pow.f64 v 4) (*.f64 v v))) (/.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))))))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 4/3 (.f64 (pow.f64 v 6) (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 (/.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 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 (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 (.f64 v v) (+.f64 (/.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 (fma.f64 (pow.f64 v 4) (+.f64 (/.f64 (/.f64 3/4 (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 (sqrt.f64 1/2) (PI.f64)))) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64))))) (.f64 (pow.f64 v 6) (+.f64 (fma.f64 1/2 (/.f64 (+.f64 27/2 (.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) 1/2) -3/4)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (/.f64 3/4 (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 (sqrt.f64 1/2) (PI.f64))))))))
(.f64 4/3 (+.f64 (+.f64 (.f64 (pow.f64 v 4) (.f64 (-.f64 (/.f64 9/2 (sqrt.f64 1/2)) (/.f64 (/.f64 9/16 (sqrt.f64 1/2)) 1/2)) (/.f64 1/2 (PI.f64)))) (+.f64 (.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (PI.f64)) (sqrt.f64 1/2))) (+.f64 (pow.f64 v 4) (.f64 v v))) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (.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 (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 (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 4/3 (/.f64 (pow.f64 v 5) (-.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (/.f64 (sqrt.f64 -1/6) (PI.f64))))))
(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 (/.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 (.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 (sqrt.f64 -1/6)) (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (PI.f64)))) (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)))))))
(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))) (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 (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))) (-.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 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 (+.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 (.f64 (/.f64 1/2 (sqrt.f64 -1/6)) (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (PI.f64)) (/.f64 (+.f64 1/162 (.f64 -1/6 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)))) (PI.f64)))) (/.f64 (sqrt.f64 -1/6) (PI.f64)))) (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 (+.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 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (PI.f64)))) (pow.f64 v 7)) (*.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -4/3 (pow.f64 v 3))))))
(.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 (PI.f64) (pow.f64 v 3)) (sqrt.f64 -1/6)))
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(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)))))
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(+.f64 (.f64 -3 (.f64 v (+.f64 (.f64 -1 (/.f64 (PI.f64) (sqrt.f64 -6))) (.f64 (sqrt.f64 -6) (PI.f64))))) (+.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 -1 (/.f64 (PI.f64) (sqrt.f64 -6)) (.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 (+.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (.f64 -1/12 (/.f64 (PI.f64) (sqrt.f64 -6)))) v) (.f64 3 (.f64 (pow.f64 v 3) (*.f64 (PI.f64) (sqrt.f64 -6)))))))
(+.f64 (.f64 (PI.f64) (.f64 3 (.f64 (pow.f64 v 3) (sqrt.f64 -6)))) (.f64 -3 (+.f64 (+.f64 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (/.f64 (fma.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (/.f64 (/.f64 (PI.f64) 12) (sqrt.f64 -6))) (pow.f64 v 3))) (/.f64 (*.f64 11/12 (/.f64 (PI.f64) (sqrt.f64 -6))) 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))
(fma.f64 (neg.f64 (*.f64 v v)) (PI.f64) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(fma.f64 (neg.f64 (*.f64 v v)) (PI.f64) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(fma.f64 (neg.f64 (*.f64 v v)) (PI.f64) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(.f64 -1 (.f64 (pow.f64 v 2) (PI.f64)))
(neg.f64 (.f64 (PI.f64) (.f64 v v)))
(.f64 (PI.f64) (neg.f64 (.f64 v v)))
(.f64 (PI.f64) (.f64 v (neg.f64 v)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(fma.f64 (neg.f64 (*.f64 v v)) (PI.f64) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(fma.f64 (neg.f64 (*.f64 v v)) (PI.f64) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(fma.f64 (neg.f64 (*.f64 v v)) (PI.f64) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(.f64 -1 (.f64 (pow.f64 v 2) (PI.f64)))
(neg.f64 (.f64 (PI.f64) (.f64 v v)))
(.f64 (PI.f64) (neg.f64 (.f64 v v)))
(.f64 (PI.f64) (.f64 v (neg.f64 v)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(fma.f64 (neg.f64 (*.f64 v v)) (PI.f64) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(fma.f64 (neg.f64 (*.f64 v v)) (PI.f64) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
(+.f64 (.f64 -1 (.f64 (pow.f64 v 2) (PI.f64))) (PI.f64))
(fma.f64 -1 (.f64 (PI.f64) (.f64 v v)) (PI.f64))
(fma.f64 (neg.f64 (*.f64 v v)) (PI.f64) (PI.f64))
(-.f64 (PI.f64) (.f64 (PI.f64) (.f64 v v)))
2
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(*.f64 -6 (pow.f64 v 2))
(.f64 (.f64 v v) -6)
(.f64 v (.f64 v -6))
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(*.f64 -6 (pow.f64 v 2))
(.f64 (.f64 v v) -6)
(.f64 v (.f64 v -6))
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)
(+.f64 (*.f64 -6 (pow.f64 v 2)) 2)
(fma.f64 -6 (*.f64 v v) 2)
(fma.f64 (*.f64 v v) -6 2)

eval197.0ms (4.6%)

Compiler: Compiled 9930 to 7749 computations (22% saved)

prune50.0ms (1.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	394	1	395
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	395	6	401

Error

Counts

401 → 6

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))))))
▶	1.0b	(/.f64 4 (+.f64 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (+.f64 (.f64 (*.f64 v v) -6) 2))))))
✓	1.6b	(/.f64 4 (.f64 (.f64 (PI.f64) 3) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
✓	0.7b	(/.f64 -4/3 (*.f64 (PI.f64) (neg.f64 (sqrt.f64 2))))
✓	0.0b	(/.f64 -4/3 (.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (fma.f64 v v -1)))
✓	1.6b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Compiler

Compiled 91 to 76 computations (16.5% saved)

localize92.0ms (2.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1))
✓	0.0b	(.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (+.f64 (.f64 (*.f64 v v) -6) 2))))
✓	0.2b	(.f64 (.f64 v v) -6)
✓	1.0b	(/.f64 4 (+.f64 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (+.f64 (.f64 (*.f64 v v) -6) 2))))))

Compiler

Compiled 122 to 74 computations (39.3% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite122.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

811×	`log-prod_binary64`
293×	`fma-def_binary64`
290×	`expm1-udef_binary64`
290×	`log1p-udef_binary64`
235×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	62
1	428	55
2	5035	55

Stop Event

1×	node limit

Counts

3 → 91

Calls

Call 1

Inputs

(/.f64 4 (+.f64 0 (*.f64 3 (*.f64 (*.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (+.f64 (*.f64 (*.f64 v v) -6) 2))))))

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

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

Outputs

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

((#(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 (*.f64 v v) 3)) 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 (*.f64 v v) 3)))))) (#(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 (log.f64 (*.f64 v (*.f64 v -6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 v (*.f64 v -6))) 1))))))

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simplify94.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

508×	`associate-+l+_binary64`
488×	`associate-+r+_binary64`
397×	`associate-*l/_binary64`
373×	`*-commutative_binary64`
366×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	1767
1	580	1697
2	2270	1579
3	7929	1579

Stop Event

1×	node limit

Counts

127 → 140

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

eval120.0ms (2.8%)

Compiler: Compiled 5444 to 4289 computations (21.2% saved)

prune26.0ms (0.6%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	168	7	175

Error

Counts

175 → 7

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))))))
✓	1.0b	(/.f64 4 (+.f64 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (+.f64 (.f64 (*.f64 v v) -6) 2))))))
▶	1.6b	(/.f64 4 (+.f64 0 (.f64 3 (.f64 (PI.f64) (sqrt.f64 (+.f64 (.f64 (.f64 v v) -6) 2))))))
✓	1.6b	(/.f64 4 (.f64 (.f64 (PI.f64) 3) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
✓	0.7b	(/.f64 -4/3 (*.f64 (PI.f64) (neg.f64 (sqrt.f64 2))))
✓	0.0b	(/.f64 -4/3 (.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (fma.f64 v v -1)))
✓	1.6b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Compiler

Compiled 108 to 91 computations (15.7% saved)

localize53.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (PI.f64) (sqrt.f64 (+.f64 (.f64 (*.f64 v v) -6) 2)))
✓	0.0b	(.f64 3 (.f64 (PI.f64) (sqrt.f64 (+.f64 (.f64 (.f64 v v) -6) 2))))
	0.2b	(.f64 (.f64 v v) -6)
✓	1.0b	(/.f64 4 (+.f64 0 (.f64 3 (.f64 (PI.f64) (sqrt.f64 (+.f64 (.f64 (.f64 v v) -6) 2))))))

Compiler

Compiled 83 to 55 computations (33.7% saved)

series8.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

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

rewrite114.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

662×	`log-prod_binary64`
357×	`pow2_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
245×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	51
1	352	48
2	4069	48

Stop Event

1×	node limit

Counts

3 → 96

Calls

Call 1

Inputs

(/.f64 4 (+.f64 0 (*.f64 3 (*.f64 (PI.f64) (sqrt.f64 (+.f64 (*.f64 (*.f64 v v) -6) 2))))))

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

(*.f64 (PI.f64) (sqrt.f64 (+.f64 (*.f64 (*.f64 v v) -6) 2)))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (PI.f64)) 2)) (*.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 (*.f64 3 (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 3 (PI.f64))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 0 (*.f64 (*.f64 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simplify114.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

745×	`times-frac_binary64`
707×	`associate-/r*_binary64`
500×	`associate-/l*_binary64`
466×	`fma-neg_binary64`
399×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	1448
1	566	1390
2	1971	1332
3	7678	1330

Stop Event

1×	node limit

Counts

132 → 167

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 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 2/3 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (*.f64 (sqrt.f64 1/2) (PI.f64))))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 2/3 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 2/3 (/.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))))) (*.f64 (sqrt.f64 1/2) (PI.f64)))))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64))))
(-.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -1/6) (PI.f64))))))
(-.f64 (+.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))))
(-.f64 (+.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (+.f64 (.f64 -2/3 (/.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) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64))))))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))))
(.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64))))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -1/6) (PI.f64))))))
(+.f64 (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64)))))))
(+.f64 (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (+.f64 (.f64 2/3 (/.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) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64))))))))
(.f64 3 (.f64 (sqrt.f64 2) (PI.f64)))
(+.f64 (.f64 -9 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (.f64 3 (.f64 (sqrt.f64 2) (PI.f64))))
(+.f64 (.f64 -9 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (+.f64 (.f64 -27/2 (/.f64 (.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (.f64 3 (.f64 (sqrt.f64 2) (PI.f64)))))
(+.f64 (.f64 -9 (/.f64 (.f64 (pow.f64 v 2) (PI.f64)) (sqrt.f64 2))) (+.f64 (.f64 -27/2 (/.f64 (.f64 (pow.f64 v 4) (PI.f64)) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (.f64 3 (.f64 (sqrt.f64 2) (PI.f64))) (.f64 -81/2 (/.f64 (.f64 (pow.f64 v 6) (PI.f64)) (pow.f64 (sqrt.f64 2) 5))))))
(.f64 3 (.f64 v (*.f64 (sqrt.f64 -6) (PI.f64))))
(+.f64 (.f64 3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))))
(+.f64 (.f64 -3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (+.f64 (.f64 3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v)))))
(+.f64 (.f64 -3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (+.f64 (.f64 3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 3 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) v))) (.f64 3/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))))))
(.f64 -3 (.f64 v (*.f64 (sqrt.f64 -6) (PI.f64))))
(+.f64 (.f64 -3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 -3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v))))
(+.f64 (.f64 -3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (.f64 -3 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) v)))))
(+.f64 (.f64 -3 (.f64 v (.f64 (sqrt.f64 -6) (PI.f64)))) (+.f64 (.f64 3/2 (/.f64 (PI.f64) (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))) (+.f64 (.f64 -3 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) v))) (.f64 -3/2 (/.f64 (PI.f64) (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))))))
(*.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)))))))

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 v v) (.f64 (sqrt.f64 1/2) (PI.f64))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 (*.f64 v v) (sqrt.f64 1/2)) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))) (.f64 2/3 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (*.f64 (sqrt.f64 1/2) (PI.f64))))))
(+.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 v v) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 2/3 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 4)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 2/3 (.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (/.f64 (pow.f64 v 4) (PI.f64))) (/.f64 (/.f64 (.f64 v v) (sqrt.f64 1/2)) (PI.f64))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 2/3 (.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 v v) (sqrt.f64 1/2)) (PI.f64))))
(+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (/.f64 (pow.f64 v 2) (.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 2/3 (/.f64 (.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 v 4)) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 2/3 (/.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))))) (*.f64 (sqrt.f64 1/2) (PI.f64)))))))
(+.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (.f64 v v) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 2/3 (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (.f64 (sqrt.f64 1/2) (PI.f64)) (pow.f64 v 4))) (/.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))))) (*.f64 (sqrt.f64 1/2) (PI.f64))))))
(fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 2/3 (fma.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (sqrt.f64 1/2)) (/.f64 (pow.f64 v 4) (PI.f64)) (.f64 (/.f64 (pow.f64 v 6) (.f64 (sqrt.f64 1/2) (PI.f64))) (-.f64 27/2 (/.f64 3/4 (/.f64 1/2 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2))))))) (/.f64 (/.f64 (*.f64 v v) (sqrt.f64 1/2)) (PI.f64))))
(+.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 (.f64 v v) (sqrt.f64 1/2)) (PI.f64))) (.f64 (/.f64 2/3 (sqrt.f64 1/2)) (+.f64 (*.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (/.f64 (pow.f64 v 4) (PI.f64))) (/.f64 (pow.f64 v 6) (/.f64 (PI.f64) 135/16)))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64))))
(.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)))
(-.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -1/6) (PI.f64))))))
(-.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v))) (/.f64 1/27 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -1/6)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (/.f64 -1/27 (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) v)) (/.f64 (/.f64 (/.f64 -1/27 (pow.f64 v 3)) (PI.f64)) (sqrt.f64 -1/6)))
(-.f64 (+.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64)))))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))))
(-.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 5))))) (/.f64 1/27 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -1/6)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (fma.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5)))) (/.f64 -1/27 (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (fma.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))) (/.f64 (/.f64 (/.f64 -1/27 (pow.f64 v 3)) (PI.f64)) (sqrt.f64 -1/6))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (fma.f64 (/.f64 -2/3 (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))) (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (/.f64 (/.f64 (/.f64 -1/27 (pow.f64 v 3)) (PI.f64)) (sqrt.f64 -1/6))))
(-.f64 (+.f64 (.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (+.f64 (.f64 -2/3 (/.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) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 -2/3 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64))))))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -1/6) (PI.f64))))))
(-.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (.f64 -2/3 (+.f64 (/.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 (.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 7))) (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 5)))))) (/.f64 1/27 (.f64 (pow.f64 v 3) (*.f64 (PI.f64) (sqrt.f64 -1/6)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (fma.f64 -2/3 (+.f64 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5)))) (/.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) (.f64 (sqrt.f64 -1/6) (pow.f64 v 7))))) (/.f64 -1/27 (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3))))))
(+.f64 (fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (/.f64 (/.f64 (/.f64 -1/27 (pow.f64 v 3)) (PI.f64)) (sqrt.f64 -1/6))) (.f64 (/.f64 -2/3 (.f64 (PI.f64) (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)))))
(fma.f64 4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (fma.f64 (/.f64 -2/3 (.f64 (PI.f64) (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))) (/.f64 (/.f64 (/.f64 -1/27 (pow.f64 v 3)) (PI.f64)) (sqrt.f64 -1/6))))
(.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64))))
(.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) -4/3)
(*.f64 (/.f64 (sqrt.f64 -1/6) v) (/.f64 -4/3 (PI.f64)))
(+.f64 (.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 v (PI.f64)))) (.f64 1/27 (/.f64 1 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -1/6) (PI.f64))))))
(fma.f64 -4/3 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) (/.f64 1/27 (.f64 (pow.f64 v 3) (*.f64 (PI.f64) (sqrt.f64 -1/6)))))
(fma.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) v)) -4/3 (/.f64 1/27 (.f64 (PI.f64) (*.f64 (sqrt.f64 -1/6) (pow.f64 v 3)))))
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(.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (neg.f64 v))
(.f64 (PI.f64) (neg.f64 (.f64 v (sqrt.f64 -6))))
(+.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 v (.f64 (PI.f64) (sqrt.f64 -6))) (/.f64 (PI.f64) (.f64 v (sqrt.f64 -6)))))
(neg.f64 (fma.f64 (*.f64 v (sqrt.f64 -6)) (PI.f64) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v)))
(neg.f64 (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (.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 v (.f64 (PI.f64) (sqrt.f64 -6))) (fma.f64 -1 (/.f64 (PI.f64) (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 (PI.f64) (*.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3))))))
(fma.f64 -1 (fma.f64 (.f64 v (sqrt.f64 -6)) (PI.f64) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v)) (.f64 1/2 (/.f64 (/.f64 (PI.f64) (*.f64 (sqrt.f64 -6) -6)) (pow.f64 v 3))))
(-.f64 (.f64 (/.f64 -1/12 (sqrt.f64 -6)) (/.f64 (PI.f64) (pow.f64 v 3))) (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (*.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 v (.f64 (PI.f64) (sqrt.f64 -6))) (fma.f64 -1 (/.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))) (.f64 1/2 (/.f64 (PI.f64) (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))))))
(fma.f64 -1 (fma.f64 (.f64 v (sqrt.f64 -6)) (PI.f64) (/.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) v)) (fma.f64 1/2 (/.f64 (/.f64 (PI.f64) (.f64 (sqrt.f64 -6) -6)) (pow.f64 v 3)) (*.f64 (/.f64 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (pow.f64 v 5)) -1/2)))
(-.f64 (fma.f64 (/.f64 (/.f64 (PI.f64) (pow.f64 v 5)) (pow.f64 (sqrt.f64 -6) 5)) -1/2 (.f64 (/.f64 -1/12 (sqrt.f64 -6)) (/.f64 (PI.f64) (pow.f64 v 3)))) (fma.f64 v (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (*.f64 v (sqrt.f64 -6)))))

eval95.0ms (2.2%)

Compiler: Compiled 4380 to 3564 computations (18.6% saved)

prune27.0ms (0.6%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	185	7	192

Error

Counts

192 → 7

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))))))
✓	1.0b	(/.f64 4 (+.f64 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (+.f64 (.f64 (*.f64 v v) -6) 2))))))
✓	1.6b	(/.f64 4 (+.f64 0 (.f64 3 (.f64 (PI.f64) (sqrt.f64 (+.f64 (.f64 (.f64 v v) -6) 2))))))
✓	1.6b	(/.f64 4 (.f64 (.f64 (PI.f64) 3) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
✓	0.7b	(/.f64 -4/3 (*.f64 (PI.f64) (neg.f64 (sqrt.f64 2))))
✓	0.0b	(/.f64 -4/3 (.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (fma.f64 v v -1)))
✓	1.6b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Compiler

Compiled 108 to 91 computations (15.7% saved)

regimes35.0ms (0.8%)

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 -4/3 (*.f64 (PI.f64) (neg.f64 (sqrt.f64 2))))
(/.f64 4 (.f64 (.f64 (PI.f64) 3) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 4 (+.f64 0 (.f64 3 (.f64 (PI.f64) (sqrt.f64 (+.f64 (.f64 (.f64 v v) -6) 2))))))
(/.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 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (+.f64 (.f64 (*.f64 v v) -6) 2))))))
(/.f64 -4/3 (.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (fma.f64 v v -1)))
(/.f64 4 (+.f64 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (fma.f64 (.f64 v v) -6 2))))))

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

Calls

7 calls:

8.0ms	v
5.0ms	(*.f64 v v)
4.0ms	(*.f64 v 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 4 (.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 213 to 155 computations (27.2% saved)

regimes54.0ms (1.3%)

Accuracy

Total -1.0b remaining (-149.9%)

Threshold costs -1.0b (-149.9%)

Counts

6 → 1

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 -4/3 (*.f64 (PI.f64) (neg.f64 (sqrt.f64 2))))
(/.f64 4 (.f64 (.f64 (PI.f64) 3) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 4 (+.f64 0 (.f64 3 (.f64 (PI.f64) (sqrt.f64 (+.f64 (.f64 (.f64 v v) -6) 2))))))
(/.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 0 (.f64 3 (.f64 (.f64 (PI.f64) (fma.f64 v (neg.f64 v) 1)) (sqrt.f64 (+.f64 (.f64 (*.f64 v v) -6) 2))))))

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

Calls

4 calls:

25.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
12.0ms	v
7.0ms	(*.f64 v v)
5.0ms	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Results

Error	Segments	Branch
0.7b	1	`v`
0.7b	1	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
0.7b	1	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
0.7b	1	`(*.f64 v v)`

Compiler

Compiled 132 to 98 computations (25.8% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	46
1	33	46
2	41	46
3	47	46
4	50	46
5	51	46

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 32 to 28 computations (12.5% saved)

soundness231.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

1332×	`fma-def_binary64`
576×	`fma-neg_binary64`
530×	`distribute-rgt-in_binary64`
496×	`unsub-neg_binary64`
430×	`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	967	26
5	1747	24
6	3707	24
7	6458	24

Stop Event

1×	node limit

Compiler

Compiled 611 to 485 computations (20.6% saved)

end56.0ms (1.3%)

Compiler: Compiled 30 to 24 computations (20% saved)

Details

analyze4.0ms (0.1%)

sample1.1s (27%)

preprocess68.0ms (1.6%)

simplify70.0ms (1.6%)

eval1.0ms (0%)

prune2.0ms (0%)

localize62.0ms (1.4%)

series11.0ms (0.3%)

rewrite127.0ms (3%)

simplify69.0ms (1.6%)

localize29.0ms (0.7%)

series10.0ms (0.2%)

rewrite133.0ms (3.1%)

simplify63.0ms (1.5%)

eval278.0ms (6.5%)

prune35.0ms (0.8%)

localize8.0ms (0.2%)

series0.0ms (0%)

rewrite75.0ms (1.8%)

simplify14.0ms (0.3%)

localize11.0ms (0.3%)

localize20.0ms (0.5%)

series5.0ms (0.1%)

rewrite77.0ms (1.8%)

simplify68.0ms (1.6%)

localize59.0ms (1.4%)

series8.0ms (0.2%)

rewrite210.0ms (4.9%)

simplify83.0ms (1.9%)

eval197.0ms (4.6%)

prune50.0ms (1.2%)

localize92.0ms (2.2%)

series5.0ms (0.1%)

rewrite122.0ms (2.9%)

simplify94.0ms (2.2%)

eval120.0ms (2.8%)

prune26.0ms (0.6%)

localize53.0ms (1.2%)

series8.0ms (0.2%)

rewrite114.0ms (2.7%)

simplify114.0ms (2.7%)

eval95.0ms (2.2%)

prune27.0ms (0.6%)

regimes35.0ms (0.8%)

regimes54.0ms (1.3%)

simplify8.0ms (0.2%)

soundness231.0ms (5.4%)

end56.0ms (1.3%)

Profiling