Details

analyze12.0ms (0.2%)

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)

sample1.7s (24.4%)

Results

1.7s	8256×	body	256	valid
1.0ms	4×	body	256	invalid

preprocess88.0ms (1.2%)

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)

simplify76.0ms (1.1%)

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)))

eval2.0ms (0%)

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

prune3.0ms (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)

localize52.0ms (0.7%)

Local error

Found 4 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	(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)

series22.0ms (0.3%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	v	@	0	(/.f64 -4/3 (.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (fma.f64 v v -1)))
4.0ms	v	@	inf	(/.f64 -4/3 (.f64 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))) (fma.f64 v v -1)))
3.0ms	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	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
1.0ms	v	@	0	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))

rewrite108.0ms (1.5%)

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	69
1	288	69
2	3355	69

Stop Event

1×	node limit

Counts

4 → 93

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

simplify129.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

683×	`associate-/r*_binary64`
604×	`times-frac_binary64`
503×	`associate-/l*_binary64`
344×	`associate-*r/_binary64`
334×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	2376
1	835	2244
2	2961	2107

Stop Event

1×	node limit

Counts

141 → 187

Calls

Call 1

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

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))
✓	0.0b	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
✓	0.1b	(.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)

series36.0ms (0.5%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
26.0ms	v	@	-inf	(sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))
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)))))

rewrite106.0ms (1.5%)

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	78
1	375	75
2	4681	69

Stop Event

1×	node limit

Counts

4 → 88

Calls

Call 1

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

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

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

513×	`associate-+l+_binary64`
464×	`associate-+r+_binary64`
445×	`associate-/r*_binary64`
404×	`associate-*l/_binary64`
383×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	2088
1	677	1998
2	2584	1890

Stop Event

1×	node limit

Counts

136 → 160

Calls

Call 1

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

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 4/3 (/.f64 (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))))))))
(.f64 4/3 (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 (.f64 v v) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64))))) (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (*.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64)))))))
(.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))))))))
(+.f64 (.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))))) (+.f64 (.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 4/3 (.f64 (pow.f64 v 6) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))) (+.f64 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 1/2 (/.f64 (-.f64 27/2 (.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64))))))))) (.f64 4/3 (.f64 (pow.f64 v 2) (+.f64 (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 (sqrt.f64 1/2) (PI.f64))))))))
(fma.f64 4/3 (.f64 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (fma.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 4/3 (+.f64 (.f64 (pow.f64 v 6) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (+.f64 (fma.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 1/2 (/.f64 (-.f64 27/2 (.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64))))))) (.f64 (.f64 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 (pow.f64 v 4) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (/.f64 3/4 (sqrt.f64 1/2)) (PI.f64))))) (.f64 4/3 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 (pow.f64 v 6) (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (fma.f64 1/2 (/.f64 (+.f64 27/2 (/.f64 (.f64 -3/4 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2))) 1/2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (/.f64 3/4 (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 (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 (fma.f64 (pow.f64 v 6) (+.f64 (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 (/.f64 1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (PI.f64)) (/.f64 135/16 (PI.f64))))) (.f64 v (.f64 v (+.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(.f64 -4/3 (/.f64 (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)))))
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(+.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)))))))))
(fma.f64 3 (.f64 (pow.f64 v 6) (fma.f64 -27/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 2) 5)) (/.f64 (.f64 9/2 (PI.f64)) (pow.f64 (sqrt.f64 2) 3)))) (fma.f64 3 (.f64 (pow.f64 v 4) (fma.f64 3 (/.f64 (PI.f64) (sqrt.f64 2)) (.f64 -9/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 2) 3))))) (.f64 3 (+.f64 (.f64 (PI.f64) (sqrt.f64 2)) (.f64 (.f64 v v) (fma.f64 -3 (/.f64 (PI.f64) (sqrt.f64 2)) (neg.f64 (*.f64 (PI.f64) (sqrt.f64 2)))))))))
(fma.f64 3 (.f64 (pow.f64 v 6) (fma.f64 -27/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 2) 5)) (.f64 9/4 (/.f64 (PI.f64) (sqrt.f64 2))))) (.f64 3 (+.f64 (fma.f64 (PI.f64) (sqrt.f64 2) (.f64 (.f64 v v) (-.f64 (.f64 -3 (/.f64 (PI.f64) (sqrt.f64 2))) (.f64 (PI.f64) (sqrt.f64 2))))) (.f64 (pow.f64 v 4) (fma.f64 3 (/.f64 (PI.f64) (sqrt.f64 2)) (*.f64 -9/4 (/.f64 (PI.f64) (sqrt.f64 2))))))))
(.f64 3 (+.f64 (fma.f64 (PI.f64) (sqrt.f64 2) (.f64 v (.f64 v (fma.f64 (neg.f64 (sqrt.f64 2)) (PI.f64) (.f64 (/.f64 -3 (sqrt.f64 2)) (PI.f64)))))) (+.f64 (.f64 (pow.f64 v 6) (fma.f64 -27/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 2) 5)) (.f64 (/.f64 (PI.f64) (sqrt.f64 2)) 9/4))) (.f64 (pow.f64 v 4) (.f64 (/.f64 (PI.f64) (sqrt.f64 2)) 3/4)))))
(.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 (pow.f64 v 3) (.f64 (*.f64 (PI.f64) (sqrt.f64 -6)) -3))
(.f64 (.f64 (pow.f64 v 3) (sqrt.f64 -6)) (*.f64 (PI.f64) -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 (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 (.f64 (pow.f64 v 3) (sqrt.f64 -6)) (*.f64 (PI.f64) -3)))
(+.f64 (.f64 3 (/.f64 (+.f64 (.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3))) (/.f64 (PI.f64) (sqrt.f64 -6))) v)) (+.f64 (.f64 -3 (.f64 (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 (.f64 (pow.f64 v 3) (sqrt.f64 -6)) (.f64 (PI.f64) -3))))
(+.f64 (.f64 3 (/.f64 (+.f64 (.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3))) (/.f64 (PI.f64) (sqrt.f64 -6))) v)) (+.f64 (.f64 3 (/.f64 (+.f64 (.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5))) (.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)))) (pow.f64 v 3))) (+.f64 (.f64 -3 (.f64 (pow.f64 v 3) (.f64 (sqrt.f64 -6) (PI.f64)))) (.f64 3 (.f64 v (+.f64 (.f64 (sqrt.f64 -6) (PI.f64)) (.f64 -1 (/.f64 (PI.f64) (sqrt.f64 -6)))))))))
(fma.f64 3 (/.f64 (fma.f64 1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)) (/.f64 (PI.f64) (sqrt.f64 -6))) v) (fma.f64 3 (/.f64 (.f64 -1/2 (+.f64 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 3)))) (pow.f64 v 3)) (fma.f64 -3 (.f64 (pow.f64 v 3) (.f64 (PI.f64) (sqrt.f64 -6))) (.f64 3 (*.f64 v (fma.f64 (sqrt.f64 -6) (PI.f64) (neg.f64 (/.f64 (PI.f64) (sqrt.f64 -6)))))))))
(fma.f64 3 (/.f64 (+.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (.f64 -1/12 (/.f64 (PI.f64) (sqrt.f64 -6)))) v) (fma.f64 3 (/.f64 (fma.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (.f64 1/12 (/.f64 (PI.f64) (sqrt.f64 -6)))) (pow.f64 v 3)) (fma.f64 3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (.f64 (pow.f64 v 3) (.f64 (*.f64 (PI.f64) (sqrt.f64 -6)) -3)))))
(fma.f64 3 (/.f64 (.f64 11/12 (/.f64 (PI.f64) (sqrt.f64 -6))) v) (fma.f64 3 (/.f64 (fma.f64 -1/2 (/.f64 (PI.f64) (pow.f64 (sqrt.f64 -6) 5)) (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) 1/12)) (pow.f64 v 3)) (fma.f64 3 (.f64 v (-.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (/.f64 (PI.f64) (sqrt.f64 -6)))) (.f64 (.f64 (pow.f64 v 3) (sqrt.f64 -6)) (*.f64 (PI.f64) -3)))))
(.f64 3 (.f64 (pow.f64 v 3) (*.f64 (sqrt.f64 -6) (PI.f64))))
(.f64 3 (.f64 (pow.f64 v 3) (*.f64 (PI.f64) (sqrt.f64 -6))))
(.f64 3 (.f64 (PI.f64) (*.f64 (pow.f64 v 3) (sqrt.f64 -6))))
(.f64 (.f64 (PI.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 (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 (.f64 (PI.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 (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)))))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 -3 (/.f64 (pow.f64 v 2) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (.f64 -3 (/.f64 (.f64 v v) (sqrt.f64 2))))
(fma.f64 -3 (/.f64 (*.f64 v v) (sqrt.f64 2)) (sqrt.f64 2))
(fma.f64 -3 (/.f64 v (/.f64 (sqrt.f64 2) v)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (/.f64 (pow.f64 v 2) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (/.f64 (.f64 v v) (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -3 (/.f64 (.f64 v v) (sqrt.f64 2)) (.f64 -9/4 (/.f64 (pow.f64 v 4) (sqrt.f64 2)))))
(+.f64 (fma.f64 -3 (/.f64 v (/.f64 (sqrt.f64 2) v)) (sqrt.f64 2)) (*.f64 -9/4 (/.f64 (pow.f64 v 4) (sqrt.f64 2))))
(+.f64 (.f64 -27/2 (/.f64 (pow.f64 v 6) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (+.f64 (.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3))) (*.f64 -3 (/.f64 (pow.f64 v 2) (sqrt.f64 2))))))
(fma.f64 -27/2 (/.f64 (pow.f64 v 6) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) (fma.f64 -9/2 (/.f64 (pow.f64 v 4) (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (/.f64 (.f64 v v) (sqrt.f64 2))))))
(fma.f64 -27/2 (/.f64 (pow.f64 v 6) (pow.f64 (sqrt.f64 2) 5)) (+.f64 (sqrt.f64 2) (fma.f64 -3 (/.f64 (.f64 v v) (sqrt.f64 2)) (.f64 -9/4 (/.f64 (pow.f64 v 4) (sqrt.f64 2))))))
(+.f64 (fma.f64 -3 (/.f64 v (/.f64 (sqrt.f64 2) v)) (*.f64 -9/4 (/.f64 (pow.f64 v 4) (sqrt.f64 2)))) (fma.f64 -27/2 (/.f64 (pow.f64 v 6) (pow.f64 (sqrt.f64 2) 5)) (sqrt.f64 2)))
(*.f64 (sqrt.f64 -6) v)
(*.f64 v (sqrt.f64 -6))
(+.f64 (/.f64 1 (.f64 (sqrt.f64 -6) v)) (.f64 (sqrt.f64 -6) v))
(+.f64 (.f64 v (sqrt.f64 -6)) (/.f64 1 (.f64 v (sqrt.f64 -6))))
(fma.f64 v (sqrt.f64 -6) (/.f64 1 (*.f64 v (sqrt.f64 -6))))
(-.f64 (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (.f64 (sqrt.f64 -6) v)) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))))
(-.f64 (+.f64 (.f64 v (sqrt.f64 -6)) (/.f64 1 (.f64 v (sqrt.f64 -6)))) (/.f64 1/2 (*.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3))))
(+.f64 (fma.f64 v (sqrt.f64 -6) (/.f64 1 (.f64 v (sqrt.f64 -6)))) (.f64 -1/2 (/.f64 (/.f64 -1/6 (sqrt.f64 -6)) (pow.f64 v 3))))
(+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (fma.f64 v (sqrt.f64 -6) (/.f64 1/12 (.f64 (pow.f64 v 3) (sqrt.f64 -6)))))
(-.f64 (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5)))) (.f64 (sqrt.f64 -6) v))) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3)))))
(+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (-.f64 (+.f64 (.f64 v (sqrt.f64 -6)) (/.f64 1/2 (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5)))) (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))))
(+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (+.f64 (/.f64 1/2 (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))) (fma.f64 v (sqrt.f64 -6) (*.f64 -1/2 (/.f64 (/.f64 -1/6 (sqrt.f64 -6)) (pow.f64 v 3))))))
(+.f64 (fma.f64 v (sqrt.f64 -6) (/.f64 1 (.f64 v (sqrt.f64 -6)))) (+.f64 (/.f64 1/2 (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))) (/.f64 1/12 (*.f64 (pow.f64 v 3) (sqrt.f64 -6)))))
(.f64 -1 (.f64 v (sqrt.f64 -6)))
(neg.f64 (*.f64 v (sqrt.f64 -6)))
(*.f64 v (neg.f64 (sqrt.f64 -6)))
(-.f64 (.f64 -1 (.f64 v (sqrt.f64 -6))) (/.f64 1 (*.f64 (sqrt.f64 -6) v)))
(-.f64 (neg.f64 (.f64 v (sqrt.f64 -6))) (/.f64 1 (.f64 v (sqrt.f64 -6))))
(fma.f64 (neg.f64 v) (sqrt.f64 -6) (/.f64 -1 (*.f64 v (sqrt.f64 -6))))
(-.f64 (/.f64 -1 (.f64 v (sqrt.f64 -6))) (.f64 v (sqrt.f64 -6)))
(-.f64 (+.f64 (.f64 -1 (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))) (/.f64 1 (*.f64 v (sqrt.f64 -6))))
(-.f64 (fma.f64 -1 (.f64 v (sqrt.f64 -6)) (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))) (/.f64 1 (*.f64 v (sqrt.f64 -6))))
(fma.f64 (neg.f64 v) (sqrt.f64 -6) (fma.f64 1/2 (/.f64 (/.f64 -1/6 (sqrt.f64 -6)) (pow.f64 v 3)) (/.f64 -1 (*.f64 v (sqrt.f64 -6)))))
(-.f64 (/.f64 -1/12 (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (fma.f64 v (sqrt.f64 -6) (/.f64 1 (.f64 v (sqrt.f64 -6)))))
(-.f64 (+.f64 (.f64 -1 (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -6) 3) (pow.f64 v 3))))) (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -6) 5) (pow.f64 v 5))))))
(-.f64 (fma.f64 -1 (.f64 v (sqrt.f64 -6)) (/.f64 1/2 (.f64 (pow.f64 v 3) (pow.f64 (sqrt.f64 -6) 3)))) (+.f64 (/.f64 1 (.f64 v (sqrt.f64 -6))) (/.f64 1/2 (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5)))))
(-.f64 (fma.f64 (neg.f64 v) (sqrt.f64 -6) (fma.f64 1/2 (/.f64 (/.f64 -1/6 (sqrt.f64 -6)) (pow.f64 v 3)) (/.f64 -1 (.f64 v (sqrt.f64 -6))))) (/.f64 1/2 (.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))))
(+.f64 (-.f64 (/.f64 -1/12 (.f64 (pow.f64 v 3) (sqrt.f64 -6))) (fma.f64 v (sqrt.f64 -6) (/.f64 1 (.f64 v (sqrt.f64 -6))))) (/.f64 -1/2 (*.f64 (pow.f64 v 5) (pow.f64 (sqrt.f64 -6) 5))))

eval309.0ms (4.3%)

Compiler: Compiled 10331 to 7985 computations (22.7% saved)

prune52.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	342	5	347
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	342	7	349

Error

Counts

349 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (sqrt.f64 (fma.f64 v (.f64 v -6) 2))) (/.f64 1 (fma.f64 v v -1)))
▶	0.0b	(.f64 (/.f64 1 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (.f64 (PI.f64) (fma.f64 v v -1)))) -4/3)
▶	1.9b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 2)))
✓	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
▶	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (neg.f64 (sqrt.f64 2))))
▶	2.0b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
✓	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 174 to 145 computations (16.7% saved)

localize34.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 82 to 56 computations (31.7% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite75.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log-prod_binary64`
398×	`pow-prod-down_binary64`
327×	`pow2_binary64`
231×	`pow1/3_binary64`
226×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	54
1	278	52
2	3187	52

Stop Event

1×	node limit

Counts

3 → 97

Calls

Call 1

Inputs

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

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

(*.f64 (PI.f64) (fma.f64 v v -1))

Outputs

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

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

simplify89.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-/r*_binary64`
477×	`associate-l_binary64`
450×	`times-frac_binary64`
439×	`associate-r_binary64`
369×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	1781
1	697	1687
2	2661	1562

Stop Event

1×	node limit

Counts

133 → 151

Calls

Call 1

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

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

localize18.0ms (0.3%)

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

rewrite68.0ms (1%)

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))))))))

simplify12.0ms (0.2%)

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

localize21.0ms (0.3%)

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

localize96.0ms (1.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 55 to 36 computations (34.5% saved)

series12.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	v	@	0	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 2))
2.0ms	v	@	inf	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 2)))
1.0ms	v	@	0	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 2)))
1.0ms	v	@	inf	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 2))
1.0ms	v	@	-inf	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 2)))

rewrite108.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

648×	`log-prod_binary64`
344×	`pow2_binary64`
239×	`pow1/3_binary64`
237×	`pow-unpow_binary64`
235×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	297	52
2	3584	52

Stop Event

1×	node limit

Counts

3 → 98

Calls

Call 1

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

Outputs

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

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

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

768×	`times-frac_binary64`
571×	`associate-/l*_binary64`
429×	`associate-*l/_binary64`
298×	`cancel-sign-sub-inv_binary64`
294×	`associate-*r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	943
1	202	908
2	645	800
3	2255	744
4	7484	744

Stop Event

1×	node limit

Counts

134 → 125

Calls

Call 1

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

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

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 66 to 47 computations (28.8% saved)

series6.0ms (0.1%)

Counts

3 → 24

Calls

6 calls:

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

rewrite92.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`log-prod_binary64`
401×	`pow2_binary64`
283×	`pow1/3_binary64`
276×	`expm1-udef_binary64`
276×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	338	46
2	4285	46

Stop Event

1×	node limit

Counts

3 → 145

Calls

Call 1

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

Outputs

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simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
519×	`associate-/r*_binary64`
452×	`times-frac_binary64`
418×	`associate-r_binary64`
416×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	1628
1	507	1558
2	1855	1459

Stop Event

1×	node limit

Counts

169 → 192

Calls

Call 1

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

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

eval485.0ms (6.8%)

Compiler: Compiled 15033 to 11733 computations (22% saved)

prune96.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	593	5	598
Fresh	0	0	0
Picked	1	0	1
Done	3	3	6
Total	597	8	605

Error

Counts

605 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.0b	(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (pow.f64 2 -1/2))
▶	1.0b	(/.f64 4/3 (*.f64 (sqrt.f64 2) (PI.f64)))
▶	1.9b	(.f64 (/.f64 (pow.f64 2 -1/2) (.f64 (PI.f64) (.f64 3 (-.f64 1 (.f64 v v))))) 4)
✓	1.9b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 2)))
▶	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (fma.f64 v v -1))
▶	0.0b	(.f64 (/.f64 1 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (.f64 (PI.f64) (+.f64 -1 (*.f64 v v))))) -4/3)
✓	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
✓	2.0b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Compiler

Compiled 191 to 160 computations (16.2% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 63 to 44 computations (30.2% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite93.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

660×	`log-prod_binary64`
398×	`pow-prod-down_binary64`
361×	`pow2_binary64`
254×	`pow1/3_binary64`
251×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	294	41
2	3599	41

Stop Event

1×	node limit

Counts

2 → 73

Calls

Call 1

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

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
519×	`associate-/r*_binary64`
452×	`times-frac_binary64`
418×	`associate-r_binary64`
416×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	1628
1	507	1558
2	1853	1459

Stop Event

1×	node limit

Counts

97 → 120

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

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

localize20.0ms (0.3%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

localize86.0ms (1.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 47 to 29 computations (38.3% saved)

series14.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	v	@	-inf	(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (pow.f64 2 -1/2))
3.0ms	v	@	0	(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (pow.f64 2 -1/2))
1.0ms	v	@	inf	(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (pow.f64 2 -1/2))
1.0ms	v	@	inf	(/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v))))
1.0ms	v	@	0	(/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v))))

rewrite114.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

578×	`log-prod_binary64`
341×	`pow-prod-down_binary64`
334×	`pow2_binary64`
231×	`pow1/3_binary64`
230×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	283	44
2	3428	44

Stop Event

1×	node limit

Counts

3 → 95

Calls

Call 1

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

Outputs

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

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

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

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

707×	`associate-/l*_binary64`
422×	`distribute-lft-out_binary64`
382×	`associate-/l/_binary64`
358×	`associate-*l/_binary64`
316×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	928
1	260	900
2	784	825
3	2599	770
4	7529	770

Stop Event

1×	node limit

Counts

131 → 130

Calls

Call 1

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

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

localize56.0ms (0.8%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 63 to 42 computations (33.3% saved)

series7.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite221.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

628×	`log-prod_binary64`
348×	`pow-prod-down_binary64`
334×	`pow2_binary64`
229×	`pow1/3_binary64`
228×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	281	43
2	3517	43

Stop Event

1×	node limit

Counts

3 → 101

Calls

Call 1

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

Outputs

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

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

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

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-def_binary64`
731×	`times-frac_binary64`
671×	`associate-/r*_binary64`
570×	`associate-l_binary64`
509×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	723
1	157	662
2	444	598
3	1401	549
4	7659	549

Stop Event

1×	node limit

Counts

137 → 127

Calls

Call 1

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

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

localize75.0ms (1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 90 to 57 computations (36.7% saved)

series9.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite236.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

691×	`log-prod_binary64`
374×	`pow2_binary64`
262×	`pow1/3_binary64`
255×	`expm1-udef_binary64`
255×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	60
1	314	52
2	3896	52

Stop Event

1×	node limit

Counts

3 → 130

Calls

Call 1

Inputs

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

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

(*.f64 (PI.f64) (+.f64 -1 (*.f64 v v)))

Outputs

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

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-/r*_binary64`
477×	`associate-l_binary64`
450×	`times-frac_binary64`
439×	`associate-r_binary64`
369×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	1781
1	697	1687
2	2661	1562

Stop Event

1×	node limit

Counts

166 → 184

Calls

Call 1

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

Outputs
(*.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 (neg.f64 (sqrt.f64 1/2)) (PI.f64))
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (.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)))))))
(fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.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 (.f64 (.f64 v v) (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))) (/.f64 (sqrt.f64 1/2) (PI.f64)))
(fma.f64 (*.f64 v v) (-.f64 (/.f64 (/.f64 -3/4 (PI.f64)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (neg.f64 (sqrt.f64 1/2)) (PI.f64)))
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.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 (+.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))))) (pow.f64 v 4))))
(fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.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 (-.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)))) (pow.f64 v 4))))
(-.f64 (fma.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (pow.f64 v 4) (.f64 (.f64 v v) (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64)))))) (/.f64 (sqrt.f64 1/2) (PI.f64)))
(-.f64 (fma.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 (PI.f64)) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (pow.f64 v 4) (.f64 v (*.f64 v (-.f64 (/.f64 (/.f64 -3/4 (PI.f64)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (PI.f64)))))) (/.f64 (sqrt.f64 1/2) (PI.f64)))
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 (pow.f64 v 6) (-.f64 (+.f64 (.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 27/2 (.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))))) (.f64 3/4 (/.f64 1 (.f64 (sqrt.f64 1/2) (PI.f64)))))) (+.f64 (.f64 (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 (+.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))))) (pow.f64 v 4)))))
(fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 (pow.f64 v 6) (-.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (.f64 -1/2 (+.f64 (/.f64 (+.f64 27/2 (.f64 -3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (pow.f64 (sqrt.f64 1/2) 2)))) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64)))))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (fma.f64 (.f64 v v) (-.f64 (neg.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 3/4 (.f64 (sqrt.f64 1/2) (PI.f64)))) (.f64 (-.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)))) (pow.f64 v 4)))))
(-.f64 (fma.f64 (pow.f64 v 6) (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 -1/2 (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 (-.f64 27/2 (.f64 3/4 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) 1/2))) (.f64 (sqrt.f64 1/2) (PI.f64)))) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (fma.f64 (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (fma.f64 -1/2 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (.f64 (sqrt.f64 1/2) (PI.f64))) (/.f64 -3/4 (.f64 (sqrt.f64 1/2) (PI.f64))))) (pow.f64 v 4) (.f64 (.f64 v v) (fma.f64 -1 (/.f64 (sqrt.f64 1/2) (PI.f64)) (/.f64 -3/4 (*.f64 (sqrt.f64 1/2) (PI.f64))))))) (/.f64 (sqrt.f64 1/2) (PI.f64)))
(-.f64 (fma.f64 (pow.f64 v 6) (+.f64 (.f64 (/.f64 -1/2 (sqrt.f64 1/2)) (+.f64 (/.f64 (-.f64 9/2 (pow.f64 (/.f64 3/4 (sqrt.f64 1/2)) 2)) (PI.f64)) (/.f64 135/16 (PI.f64)))) (-.f64 (/.f64 (/.f64 -3/4 (PI.f64)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (PI.f64)))) (fma.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 (PI.f64)) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (PI.f64))) (pow.f64 v 4) (.f64 v (.f64 v (-.f64 (/.f64 (/.f64 -3/4 (PI.f64)) (sqrt.f64 1/2)) (/.f64 (sqrt.f64 1/2) (PI.f64))))))) (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))
(/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3)))
(/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 3))
(-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))) (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 5) (PI.f64)))) (/.f64 1/36 (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64)))))
(-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5)))) (/.f64 1/36 (.f64 (pow.f64 v 5) (.f64 (PI.f64) (sqrt.f64 -1/6)))))
(+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)))
(+.f64 (/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 3)) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)))
(-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 7) (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 7) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))) (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 5) (PI.f64)))))) (+.f64 (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 7) (.f64 (sqrt.f64 -1/6) (PI.f64)))))))
(+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 7))) (-.f64 (fma.f64 -1/2 (/.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 7))) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5))))) (+.f64 (/.f64 1/36 (.f64 (pow.f64 v 5) (.f64 (PI.f64) (sqrt.f64 -1/6)))) (/.f64 1/36 (.f64 (*.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 7))))))
(-.f64 (+.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 7))) (.f64 -1/2 (/.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 7)))))) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)))) (/.f64 1/36 (.f64 (PI.f64) (.f64 (sqrt.f64 -1/6) (pow.f64 v 7)))))
(+.f64 (+.f64 (+.f64 (/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 7)) (.f64 -1/2 (/.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 7))))) (+.f64 (/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 3)) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)))) (/.f64 (/.f64 -1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6))) (pow.f64 v 7)))
(-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 7) (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 9) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 9) (PI.f64))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2))) 1/162) (.f64 (pow.f64 v 9) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (.f64 (pow.f64 v 7) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 5) (PI.f64))))))))) (+.f64 (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 7) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (+.f64 (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 5) (.f64 (sqrt.f64 -1/6) (PI.f64))))) (.f64 1/36 (/.f64 1 (.f64 (pow.f64 v 9) (*.f64 (sqrt.f64 -1/6) (PI.f64))))))))
(+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (-.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 7))) (fma.f64 -1/2 (/.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 9))) (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 9))) (fma.f64 -1/2 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) (pow.f64 (sqrt.f64 -1/6) 2)) 1/162) (.f64 (.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 9))) (fma.f64 -1/2 (/.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 7))) (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5)))))))) (+.f64 (/.f64 1/36 (.f64 (.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 7))) (+.f64 (/.f64 1/36 (.f64 (pow.f64 v 5) (.f64 (PI.f64) (sqrt.f64 -1/6)))) (/.f64 1/36 (.f64 (.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 9)))))))
(+.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 7)))) (-.f64 (+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 1/36 (/.f64 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2)) -1/6) 1/162) (.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 9)))) (fma.f64 -1/2 (/.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 7)))) (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5))))) (fma.f64 -1/2 (/.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 9)))) (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 9))))) (+.f64 (/.f64 1/36 (.f64 (PI.f64) (.f64 (sqrt.f64 -1/6) (pow.f64 v 5)))) (+.f64 (/.f64 1/36 (.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 9)))) (/.f64 1/36 (.f64 (PI.f64) (.f64 (sqrt.f64 -1/6) (pow.f64 v 7))))))))
(+.f64 (/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 3)) (+.f64 (+.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 5))) (.f64 (/.f64 -1/2 (.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 7)) (/.f64 (+.f64 (.f64 -1/6 (+.f64 1/54 (pow.f64 (/.f64 -1/36 (sqrt.f64 -1/6)) 2))) 1/162) (pow.f64 v 9))))) (fma.f64 -1/2 (/.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 9)))) (/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 9)))) (-.f64 (/.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (pow.f64 v 7)) (+.f64 (/.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (pow.f64 v 5)) (+.f64 (/.f64 (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6))) (pow.f64 v 9)) (/.f64 1/36 (.f64 (.f64 (PI.f64) (sqrt.f64 -1/6)) (pow.f64 v 7))))))))
(.f64 -1 (/.f64 (sqrt.f64 -1/6) (.f64 (pow.f64 v 3) (PI.f64))))
(neg.f64 (/.f64 (sqrt.f64 -1/6) (*.f64 (PI.f64) (pow.f64 v 3))))
(/.f64 (neg.f64 (sqrt.f64 -1/6)) (*.f64 (PI.f64) (pow.f64 v 3)))
(/.f64 (/.f64 (neg.f64 (sqrt.f64 -1/6)) (pow.f64 v 3)) (PI.f64))
(+.f64 (.f64 -1 (/.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 -1 (/.f64 (sqrt.f64 -1/6) (*.f64 (pow.f64 v 3) (PI.f64)))))
(fma.f64 -1 (/.f64 (-.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)) (neg.f64 (/.f64 (sqrt.f64 -1/6) (.f64 (PI.f64) (pow.f64 v 3)))))
(-.f64 (/.f64 (neg.f64 (sqrt.f64 -1/6)) (.f64 (PI.f64) (pow.f64 v 3))) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)))
(-.f64 (/.f64 (/.f64 (neg.f64 (sqrt.f64 -1/6)) (pow.f64 v 3)) (PI.f64)) (/.f64 (+.f64 (/.f64 (sqrt.f64 -1/6) (PI.f64)) (/.f64 -1/36 (*.f64 (PI.f64) (sqrt.f64 -1/6)))) (pow.f64 v 5)))
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(-.f64 (-.f64 (neg.f64 (fma.f64 v (-.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) (.f64 (PI.f64) (sqrt.f64 -6))) (.f64 (PI.f64) (.f64 (pow.f64 v 3) (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 (-.f64 (/.f64 (neg.f64 (.f64 (/.f64 (PI.f64) (sqrt.f64 -6)) -11/12)) v) (+.f64 (.f64 (.f64 (PI.f64) (sqrt.f64 -6)) (+.f64 (pow.f64 v 3) (neg.f64 v))) (/.f64 v (/.f64 (sqrt.f64 -6) (PI.f64))))) (.f64 (/.f64 (PI.f64) (pow.f64 v 3)) (+.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 -6) 5)) (/.f64 -1/12 (sqrt.f64 -6)))))
(*.f64 -1 (PI.f64))
(neg.f64 (PI.f64))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(*.f64 (pow.f64 v 2) (PI.f64))
(.f64 (PI.f64) (.f64 v v))
(.f64 (.f64 (PI.f64) v) v)
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(*.f64 (pow.f64 v 2) (PI.f64))
(.f64 (PI.f64) (.f64 v v))
(.f64 (.f64 (PI.f64) v) v)
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))
(+.f64 (.f64 -1 (PI.f64)) (.f64 (pow.f64 v 2) (PI.f64)))
(.f64 (PI.f64) (+.f64 -1 (.f64 v v)))

eval534.0ms (7.5%)

Compiler: Compiled 17478 to 13259 computations (24.1% saved)

prune190.0ms (2.7%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	701	1	702
Fresh	0	0	0
Picked	0	1	1
Done	2	5	7
Total	703	7	710

Error

Counts

710 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.9b	(/.f64 (/.f64 (.f64 4/3 (sqrt.f64 1/2)) (PI.f64)) (-.f64 1 (.f64 v v)))
✓	2.0b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (fma.f64 v v -1))
✓	0.0b	(.f64 (/.f64 1 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (.f64 (PI.f64) (+.f64 -1 (*.f64 v v))))) -4/3)
✓	1.0b	(/.f64 4/3 (*.f64 (sqrt.f64 2) (PI.f64)))
✓	1.9b	(.f64 (/.f64 (pow.f64 2 -1/2) (.f64 (PI.f64) (.f64 3 (-.f64 1 (.f64 v v))))) 4)
✓	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 101 to 84 computations (16.8% saved)

localize21.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 38 to 27 computations (28.9% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

0.0ms

-inf

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

rewrite79.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	262	23
2	3528	23

Stop Event

1×	node limit

Counts

2 → 101

Calls

Call 1

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

Outputs

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

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
731×	`times-frac_binary64`
668×	`associate-/r*_binary64`
503×	`associate-l_binary64`
486×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	447
1	146	440
2	421	376
3	1332	327
4	7510	327

Stop Event

1×	node limit

Counts

113 → 115

Calls

Call 1

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

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

eval105.0ms (1.5%)

Compiler: Compiled 1875 to 1326 computations (29.3% saved)

prune33.0ms (0.5%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	114	8	122

Error

Counts

122 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.9b	(/.f64 (/.f64 (.f64 4/3 (sqrt.f64 1/2)) (PI.f64)) (-.f64 1 (.f64 v v)))
✓	2.0b	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))) (fma.f64 v v -1))
✓	0.0b	(.f64 (/.f64 1 (.f64 (sqrt.f64 (fma.f64 v (.f64 v -6) 2)) (.f64 (PI.f64) (+.f64 -1 (*.f64 v v))))) -4/3)
✓	1.0b	(/.f64 4/3 (*.f64 (sqrt.f64 2) (PI.f64)))
	1.9b	(.f64 (/.f64 (sqrt.f64 8/9) (PI.f64)) (/.f64 1 (-.f64 1 (.f64 v v))))
✓	1.9b	(.f64 (/.f64 (pow.f64 2 -1/2) (.f64 (PI.f64) (.f64 3 (-.f64 1 (.f64 v v))))) 4)
✓	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 114 to 95 computations (16.7% saved)

regimes153.0ms (2.2%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

7 calls:

21.0ms	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
15.0ms	v
8.0ms	(*.f64 v v)
7.0ms	(*.f64 v v)
6.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))

Results

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

Compiler

Compiled 283 to 204 computations (27.9% saved)

regimes63.0ms (0.9%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

7 calls:

14.0ms	(*.f64 v v)
12.0ms	v
7.0ms	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
6.0ms	(*.f64 v v)
5.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))

Results

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

Compiler

Compiled 215 to 156 computations (27.4% saved)

regimes29.0ms (0.4%)

Counts

9 → 1

Calls

Call 1

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

Calls

4 calls:

8.0ms	v
5.0ms	(*.f64 v v)
3.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
3.0ms	(/.f64 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
1.0b	1	`v`
1.0b	1	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
1.0b	1	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
1.0b	1	`(*.f64 v v)`

Compiler

Compiled 152 to 111 computations (27% saved)

regimes14.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Error	Segments	Branch
1.0b	1	`v`
1.0b	1	`(*.f64 v v)`

Compiler

Compiled 92 to 68 computations (26.1% saved)

regimes9.0ms (0.1%)

Accuracy

Total -1.0b remaining (-95.6%)

Threshold costs -1.0b (-95.6%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	v
3.0ms	(*.f64 v v)

Results

Error	Segments	Branch
1.0b	1	`v`
1.0b	1	`(*.f64 v v)`

Compiler

Compiled 50 to 38 computations (24% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`distribute-rgt-neg-in_binary64`
3×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	114
1	66	114
2	79	114
3	85	114
4	88	114

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 79 to 64 computations (19% saved)

soundness222.0ms (3.1%)

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)

end54.0ms (0.8%)

Compiler: Compiled 75 to 54 computations (28% saved)

Details

analyze12.0ms (0.2%)

sample1.7s (24.4%)

preprocess88.0ms (1.2%)

simplify76.0ms (1.1%)

eval2.0ms (0%)

prune3.0ms (0%)

localize52.0ms (0.7%)

series22.0ms (0.3%)

rewrite108.0ms (1.5%)

simplify129.0ms (1.8%)

localize31.0ms (0.4%)

series36.0ms (0.5%)

rewrite106.0ms (1.5%)

simplify76.0ms (1.1%)

eval309.0ms (4.3%)

prune52.0ms (0.7%)

localize34.0ms (0.5%)

series6.0ms (0.1%)

rewrite75.0ms (1.1%)

simplify89.0ms (1.2%)

localize18.0ms (0.3%)

series0.0ms (0%)

rewrite68.0ms (1%)

simplify12.0ms (0.2%)

localize21.0ms (0.3%)

localize96.0ms (1.3%)

series12.0ms (0.2%)

rewrite108.0ms (1.5%)

simplify104.0ms (1.5%)

localize30.0ms (0.4%)

series6.0ms (0.1%)

rewrite92.0ms (1.3%)

simplify61.0ms (0.9%)

eval485.0ms (6.8%)

prune96.0ms (1.3%)

localize29.0ms (0.4%)

series4.0ms (0%)

rewrite93.0ms (1.3%)

simplify91.0ms (1.3%)

localize20.0ms (0.3%)

localize86.0ms (1.2%)

series14.0ms (0.2%)

rewrite114.0ms (1.6%)

simplify97.0ms (1.4%)

localize56.0ms (0.8%)

series7.0ms (0.1%)

rewrite221.0ms (3.1%)

simplify81.0ms (1.1%)

localize75.0ms (1%)

series9.0ms (0.1%)

rewrite236.0ms (3.3%)

simplify71.0ms (1%)

eval534.0ms (7.5%)

prune190.0ms (2.7%)

localize21.0ms (0.3%)

series2.0ms (0%)

rewrite79.0ms (1.1%)

simplify56.0ms (0.8%)

eval105.0ms (1.5%)

prune33.0ms (0.5%)

regimes153.0ms (2.2%)

regimes63.0ms (0.9%)

regimes29.0ms (0.4%)

regimes14.0ms (0.2%)

regimes9.0ms (0.1%)

simplify10.0ms (0.1%)

soundness222.0ms (3.1%)

end54.0ms (0.8%)

Profiling