Details

analyze291.0ms (4.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample2.7s (37.6%)

Results

1.4s	6364×	body	256	valid
538.0ms	781×	body	2048	valid
345.0ms	530×	body	1024	valid
216.0ms	291×	body	4096	valid
163.0ms	290×	body	512	valid

preprocess18.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

18×	`fma-def_binary64`
12×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	48
1	50	48
2	70	44
3	84	44
4	88	44
5	92	44
6	94	44
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 p (sqrt.f64 (+.f64 (.f64 (.f64 4 x) x) (.f64 p p)))))))

Outputs
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
(sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 (.f64 4 p) p (*.f64 x x)))))))
(sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))))))
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 p (sqrt.f64 (+.f64 (.f64 (.f64 4 x) x) (.f64 p p)))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 p (sqrt.f64 (fma.f64 (.f64 x 4) x (*.f64 p p)))) 1/2)))
(sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 p (sqrt.f64 (fma.f64 4 (.f64 x x) (*.f64 p p)))))))
(sqrt.f64 (fma.f64 1/2 (/.f64 p (sqrt.f64 (fma.f64 4 (.f64 x x) (.f64 p p)))) 1/2))

Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	24
2	41	22
3	48	22
4	50	22
5	52	22
6	53	22

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Outputs
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
(sqrt.f64 (+.f64 1/2 (.f64 (/.f64 x (sqrt.f64 (fma.f64 (.f64 4 p) p (*.f64 x x)))) 1/2)))
(sqrt.f64 (+.f64 1/2 (.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (*.f64 p p))))))))
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))

eval1.0ms (0%)

Compiler: Compiled 34 to 24 computations (29.4% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

13.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	13.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

localize34.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	16.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
	0.5b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
	0.2b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
	0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
✓	0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
✓	0.2b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
✓	0.5b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
✓	16.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 96 to 55 computations (42.7% saved)

series25.0ms (0.4%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
2.0ms	x	@	-inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
2.0ms	p	@	0	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
2.0ms	x	@	0	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
2.0ms	x	@	-inf	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))

rewrite78.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

740×	`log-prod_binary64`
492×	`fma-def_binary64`
264×	`pow1/3_binary64`
264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	72
1	325	48
2	4204	46

Stop Event

1×	node limit

Counts

4 → 150

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 x (.f64 2 p)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p)))) (cbrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p)))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (.f64 2 p)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (hypot.f64 x (.f64 2 p)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2)) (cbrt.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 x (.f64 2 p))) (sqrt.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2)) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (hypot.f64 x (.f64 2 p)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2)) 2) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 4 (.f64 p p)) 2) (pow.f64 x 4))) (sqrt.f64 (-.f64 (.f64 4 (.f64 p p)) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 (pow.f64 x 3) (pow.f64 (.f64 2 p) 3)) (hypot.f64 (.f64 4 (.f64 p p)) (sqrt.f64 (-.f64 (pow.f64 x 4) (.f64 4 (.f64 (.f64 p p) (.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (.f64 2 p)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x (.f64 2 p))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (.f64 2 p)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (.f64 2 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (.f64 2 p))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (.f64 2 p) x)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 x (.f64 2 p)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 x (.f64 2 p))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) (/.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2) (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) 2) (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) (sqrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3)) (/.f64 1 (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2)) (/.f64 1 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1) (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3)) (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3)) (+.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2) (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2)) (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3))) (neg.f64 (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2))) (neg.f64 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2) 1) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1) (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (/.f64 1 (hypot.f64 x (.f64 2 p))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) (pow.f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) 2) (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) (sqrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) (/.f64 1 (neg.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (hypot.f64 x (.f64 2 p))) x 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (hypot.f64 x (.f64 2 p))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (hypot.f64 x (.f64 2 p))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2))) (/.f64 x (cbrt.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2))) (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2))) (/.f64 (sqrt.f64 x) (cbrt.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 (hypot.f64 x (.f64 2 p)))) (/.f64 x (sqrt.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (hypot.f64 x (.f64 2 p)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (/.f64 x (hypot.f64 x (*.f64 2 p)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 x (hypot.f64 x (.f64 2 p))))) (cbrt.f64 (exp.f64 (/.f64 x (hypot.f64 x (.f64 2 p))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (/.f64 1 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) (pow.f64 (cbrt.f64 (/.f64 x (hypot.f64 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simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-*l/_binary64`
458×	`distribute-rgt-in_binary64`
455×	`distribute-lft-in_binary64`
335×	`associate-/r/_binary64`
321×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	3860
1	1076	3666
2	4074	3286

Stop Event

1×	node limit

Counts

246 → 285

Calls

Call 1

Inputs
x
(+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) x)) x))
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 4 (/.f64 (pow.f64 p 6) (pow.f64 x 5))) (+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)))
(*.f64 2 p)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (.f64 2 p))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (*.f64 2 p)))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5))) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (.f64 2 p))))
(*.f64 -2 p)
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 x 2) p)) (.f64 -2 p))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (*.f64 -2 p)))
(+.f64 (.f64 -1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (.f64 -2 p))))
(*.f64 2 p)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (.f64 2 p))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (*.f64 2 p)))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5))) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (.f64 2 p))))
x
(+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) x)) x))
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 4 (/.f64 (pow.f64 p 6) (pow.f64 x 5))) (+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)))
(*.f64 -1 x)
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) x)) (.f64 -1 x))
(+.f64 (.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) x)) (*.f64 -1 x)))
(+.f64 (.f64 -4 (/.f64 (pow.f64 p 6) (pow.f64 x 5))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) x)) (.f64 -1 x))))
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 p 6))) (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2)) (.f64 (pow.f64 x 5) p)) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
2
(+.f64 2 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4)))))
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4))) (.f64 -1/2 (/.f64 (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2)))) (pow.f64 x 6))))))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4))) (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2)))) (pow.f64 x 6))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4))) (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2)))) (pow.f64 x 6))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 2 (.f64 (pow.f64 p 2) (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2)))))) (+.f64 (.f64 -256 (pow.f64 p 8)) (pow.f64 (.f64 -1/2 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2))) 2))) (pow.f64 x 8))) (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))))
2
(+.f64 2 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 2 (+.f64 (.f64 1/2 (.f64 (pow.f64 p 4) (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2)))) (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -2 (/.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (.f64 64 (/.f64 1 (pow.f64 x 8)))) (.f64 (pow.f64 x 2) (pow.f64 p 6)))) (+.f64 2 (+.f64 (.f64 1/2 (.f64 (pow.f64 p 4) (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2)))) (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))))
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 (.f64 -1/64 (pow.f64 x 4)) (pow.f64 (.f64 -1/16 (pow.f64 x 2)) 2)) x) (pow.f64 p 5))) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
1
(+.f64 (*.f64 -1/2 (/.f64 x p)) 1)
(+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 1 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 1 (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (/.f64 (.f64 (+.f64 (.f64 -1/64 (pow.f64 x 4)) (pow.f64 (*.f64 -1/16 (pow.f64 x 2)) 2)) x) (pow.f64 p 5)))))
(*.f64 1/2 (/.f64 x p))
(+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 p 6))) (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2)) (.f64 (pow.f64 x 5) p)) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/256 (/.f64 1 (pow.f64 p 8))) (.f64 -1/8 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 p 6))) (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2)) (pow.f64 p 2)))) (.f64 p (pow.f64 x 7)))) (+.f64 (.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 p 6))) (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2)) (.f64 (pow.f64 x 5) p)) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
1
(+.f64 1 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4)))))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4))) (.f64 -1/2 (/.f64 (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2)))) (pow.f64 x 6))))))
-1
(-.f64 (*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) 1)
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4)))) 1)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2)))) (pow.f64 x 6))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/2 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4))))) 1)
1
(+.f64 1 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 1/2 (.f64 (pow.f64 p 4) (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2)))) (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))))
(+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -2 (/.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (.f64 64 (/.f64 1 (pow.f64 x 8)))) (.f64 (pow.f64 x 2) (pow.f64 p 6)))) (+.f64 1 (+.f64 (.f64 1/2 (.f64 (pow.f64 p 4) (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2)))) (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))))
(*.f64 1/2 (/.f64 x p))
(+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 -1 (/.f64 (.f64 (+.f64 (.f64 -1/64 (pow.f64 x 4)) (pow.f64 (.f64 -1/16 (pow.f64 x 2)) 2)) x) (pow.f64 p 5)))))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 (.f64 -1/64 (pow.f64 x 4)) (pow.f64 (.f64 -1/16 (pow.f64 x 2)) 2)) x) (pow.f64 p 5))) (.f64 -1 (/.f64 (.f64 (+.f64 (.f64 1/8 (.f64 (+.f64 (.f64 -1/64 (pow.f64 x 4)) (pow.f64 (.f64 -1/16 (pow.f64 x 2)) 2)) (pow.f64 x 2))) (*.f64 1/256 (pow.f64 x 6))) x) (pow.f64 p 7))))))
(*.f64 -1/2 (/.f64 x p))
(+.f64 (.f64 -1/2 (/.f64 x p)) (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))
(+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (/.f64 (.f64 (+.f64 (.f64 -1/64 (pow.f64 x 4)) (pow.f64 (*.f64 -1/16 (pow.f64 x 2)) 2)) x) (pow.f64 p 5))))
(+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/8 (.f64 (+.f64 (.f64 -1/64 (pow.f64 x 4)) (pow.f64 (.f64 -1/16 (pow.f64 x 2)) 2)) (pow.f64 x 2))) (.f64 1/256 (pow.f64 x 6))) x) (pow.f64 p 7)) (/.f64 (.f64 (+.f64 (.f64 -1/64 (pow.f64 x 4)) (pow.f64 (*.f64 -1/16 (pow.f64 x 2)) 2)) x) (pow.f64 p 5)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -3/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/2 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2))) (pow.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (sqrt.f64 2))) 2))) (*.f64 (sqrt.f64 2) (pow.f64 x 4))))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 (.f64 -1/2 (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2))))) (.f64 -1 (/.f64 (.f64 (-.f64 (.f64 -1/2 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2))) (pow.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (sqrt.f64 2))) 2)) (pow.f64 p 2)) (pow.f64 (sqrt.f64 2) 2)))) (sqrt.f64 1/2)) (.f64 (sqrt.f64 2) (pow.f64 x 6)))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 1/2)) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/2 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2))) (pow.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (sqrt.f64 2))) 2))) (.f64 (sqrt.f64 2) (pow.f64 x 4)))))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (sqrt.f64 1/2)) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) p)))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x)))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (sqrt.f64 1/2)) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) p)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (.f64 1/2 (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2))))) (pow.f64 (.f64 1/4 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (.f64 (sqrt.f64 2) p))) 2))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 5) p)))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (sqrt.f64 1/2)) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) p)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (-.f64 (.f64 1/2 (+.f64 (.f64 2 (.f64 (pow.f64 p 2) (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2)))))) (+.f64 (.f64 -256 (pow.f64 p 8)) (pow.f64 (.f64 -1/2 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2))) 2)))) (.f64 1/4 (/.f64 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (-.f64 (.f64 1/2 (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2))))) (pow.f64 (.f64 1/4 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (.f64 (sqrt.f64 2) p))) 2))) (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 p 2))))) (sqrt.f64 1/2)) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 7) p)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (.f64 1/2 (+.f64 (.f64 64 (pow.f64 p 6)) (.f64 2 (.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 p 2))))) (pow.f64 (.f64 1/4 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (.f64 (sqrt.f64 2) p))) 2))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 5) p)))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p)) x)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 1/2 (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (pow.f64 p 4))) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -2 (/.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (.f64 64 (/.f64 1 (pow.f64 x 8)))) (pow.f64 x 2))) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))))) (pow.f64 p 6))) (sqrt.f64 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 1/2 (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (pow.f64 p 4))) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/16 (pow.f64 x 3)) (.f64 -1/64 (pow.f64 x 3)))) (pow.f64 p 3))) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/16 (pow.f64 x 3)) (.f64 -1/64 (pow.f64 x 3)))) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))

Outputs
x
(+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)
(fma.f64 2 (/.f64 (*.f64 p p) x) x)
(fma.f64 2 (/.f64 p (/.f64 x p)) x)
(fma.f64 2 (*.f64 (/.f64 p x) p) x)
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) x)) x))
(fma.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (fma.f64 2 (/.f64 (*.f64 p p) x) x))
(fma.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (fma.f64 2 (/.f64 p (/.f64 x p)) x))
(fma.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (fma.f64 2 (*.f64 (/.f64 p x) p) x))
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 4 (/.f64 (pow.f64 p 6) (pow.f64 x 5))) (+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)))
(fma.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (fma.f64 4 (/.f64 (pow.f64 p 6) (pow.f64 x 5)) (fma.f64 2 (/.f64 (*.f64 p p) x) x)))
(fma.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (fma.f64 4 (/.f64 (pow.f64 p 6) (pow.f64 x 5)) (fma.f64 2 (/.f64 p (/.f64 x p)) x)))
(fma.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (fma.f64 4 (/.f64 (pow.f64 p 6) (pow.f64 x 5)) (fma.f64 2 (*.f64 (/.f64 p x) p) x)))
(*.f64 2 p)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (.f64 2 p))
(fma.f64 1/4 (/.f64 (.f64 x x) p) (.f64 2 p))
(fma.f64 2 p (*.f64 1/4 (/.f64 x (/.f64 p x))))
(fma.f64 2 p (/.f64 1/4 (/.f64 p (*.f64 x x))))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (*.f64 2 p)))
(fma.f64 1/4 (/.f64 (.f64 x x) p) (fma.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3)) (.f64 2 p)))
(fma.f64 1/4 (/.f64 x (/.f64 p x)) (fma.f64 2 p (*.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3)))))
(fma.f64 1/4 (.f64 (/.f64 x p) x) (fma.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3)) (.f64 2 p)))
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(*.f64 -2 p)
(*.f64 p -2)
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(fma.f64 p -2 (.f64 (/.f64 -1/4 p) (.f64 x x)))
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(*.f64 2 p)
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(fma.f64 2 p (*.f64 1/4 (/.f64 x (/.f64 p x))))
(fma.f64 2 p (/.f64 1/4 (/.f64 p (*.f64 x x))))
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x
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(fma.f64 2 (/.f64 p (/.f64 x p)) x)
(fma.f64 2 (*.f64 (/.f64 p x) p) x)
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(*.f64 -1 x)
(neg.f64 x)
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(fma.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (-.f64 (.f64 (/.f64 -2 x) (.f64 p p)) x))
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1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(fma.f64 1/2 (/.f64 x p) 1)
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2
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(fma.f64 2 (.f64 (/.f64 p (.f64 x x)) p) (.f64 (/.f64 1/2 (pow.f64 x 4)) (.f64 (pow.f64 p 4) -12)))
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2
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(fma.f64 -2 (*.f64 (/.f64 p x) (/.f64 p x)) 2)
(fma.f64 -2 (.f64 (/.f64 p (.f64 x x)) p) 2)
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(fma.f64 -1/4 (/.f64 (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2)) (/.f64 (.f64 (sqrt.f64 2) (.f64 p (pow.f64 x 3))) (sqrt.f64 1/2))) (fma.f64 -1/2 (.f64 (/.f64 (+.f64 (.f64 1/2 (fma.f64 2 (.f64 (.f64 p p) (fma.f64 64 (pow.f64 p 6) (.f64 2 (.f64 (.f64 p p) (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2)))))) (fma.f64 -256 (pow.f64 p 8) (pow.f64 (.f64 -1/2 (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2))) 2)))) (.f64 -1/4 (/.f64 (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2)) (/.f64 (.f64 (.f64 p p) (pow.f64 (sqrt.f64 2) 2)) (-.f64 (.f64 1/2 (fma.f64 64 (pow.f64 p 6) (.f64 2 (.f64 (.f64 p p) (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2)))))) (pow.f64 (.f64 1/4 (/.f64 (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2)) (.f64 p (sqrt.f64 2)))) 2)))))) (sqrt.f64 2)) (/.f64 (sqrt.f64 1/2) (.f64 p (pow.f64 x 7)))) (fma.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (-.f64 (.f64 1/2 (fma.f64 64 (pow.f64 p 6) (.f64 2 (.f64 (.f64 p p) (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2)))))) (pow.f64 (.f64 1/4 (/.f64 (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2)) (.f64 p (sqrt.f64 2)))) 2)) (.f64 p (pow.f64 x 5)))) (neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2))))))))
(fma.f64 -1/4 (.f64 (/.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (.f64 (pow.f64 x 3) (sqrt.f64 2))) (/.f64 (sqrt.f64 1/2) p)) (-.f64 (.f64 -1/2 (+.f64 (.f64 (/.f64 (-.f64 (.f64 1/2 (fma.f64 2 (+.f64 (.f64 (.f64 2 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4)))) (pow.f64 p 4)) (.f64 64 (pow.f64 p 8))) (fma.f64 -256 (pow.f64 p 8) (pow.f64 (.f64 -1/2 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4)))) 2)))) (.f64 1/8 (/.f64 (.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (-.f64 (+.f64 (.f64 (pow.f64 p 6) 32) (.f64 1 (.f64 p (.f64 p (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))))))) (pow.f64 (.f64 1/4 (/.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (.f64 p (sqrt.f64 2)))) 2))) (.f64 p p)))) (.f64 (pow.f64 x 7) (sqrt.f64 2))) (/.f64 (sqrt.f64 1/2) p)) (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (-.f64 (+.f64 (.f64 (pow.f64 p 6) 32) (.f64 1 (.f64 p (.f64 p (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))))))) (pow.f64 (.f64 1/4 (/.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (.f64 p (sqrt.f64 2)))) 2)) (*.f64 p (pow.f64 x 5)))))) (/.f64 (sqrt.f64 2) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))))
(fma.f64 -1/4 (.f64 (/.f64 (.f64 (pow.f64 p 4) -12) (sqrt.f64 2)) (/.f64 (sqrt.f64 1/2) (.f64 p (pow.f64 x 3)))) (-.f64 (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (+.f64 (/.f64 (+.f64 (+.f64 (.f64 (.f64 2 (.f64 (pow.f64 p 4) -12)) (pow.f64 p 4)) (.f64 64 (pow.f64 p 8))) (fma.f64 1/2 (fma.f64 -256 (pow.f64 p 8) (pow.f64 (.f64 -1/2 (.f64 (pow.f64 p 4) -12)) 2)) (.f64 -1/8 (/.f64 (.f64 (.f64 (pow.f64 p 4) -12) (+.f64 (.f64 (pow.f64 p 6) 32) (-.f64 (.f64 p (.f64 p (.f64 (pow.f64 p 4) -12))) (pow.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 p 4) -12) (.f64 p (sqrt.f64 2)))) 2)))) (.f64 p p))))) (.f64 p (pow.f64 x 7))) (/.f64 (+.f64 (.f64 (pow.f64 p 6) 32) (-.f64 (.f64 p (.f64 p (.f64 (pow.f64 p 4) -12))) (pow.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 p 4) -12) (.f64 p (sqrt.f64 2)))) 2))) (.f64 p (pow.f64 x 5)))))) (.f64 (/.f64 (sqrt.f64 2) x) (*.f64 p (sqrt.f64 1/2)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
(*.f64 (sqrt.f64 1/2) (sqrt.f64 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(fma.f64 -1 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (.f64 p p) (.f64 x x))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2)))
(-.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (*.f64 (/.f64 p x) (/.f64 p x)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2))))
(-.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (.f64 (/.f64 p (.f64 x x)) p) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 1/2 (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (pow.f64 p 4))) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2))))
(fma.f64 -1 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (.f64 p p) (.f64 x x))) (fma.f64 1/2 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (fma.f64 1/2 (.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) (neg.f64 (pow.f64 (/.f64 -1 (.f64 (.f64 x x) (sqrt.f64 2))) 2)))) (pow.f64 p 4)) (sqrt.f64 2)) (.f64 (sqrt.f64 1/2) (sqrt.f64 2))))
(-.f64 (fma.f64 (sqrt.f64 1/2) (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 1/2) 1/2) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 p 4)) (fma.f64 1/2 (.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) (neg.f64 (pow.f64 (/.f64 -1 (.f64 x (.f64 x (sqrt.f64 2)))) 2)))))) (.f64 (*.f64 (/.f64 p x) (/.f64 p x)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2))))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (pow.f64 p 4) (fma.f64 (.f64 x x) (.f64 1/2 (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) (neg.f64 (pow.f64 (/.f64 -1 (.f64 x (.f64 x (sqrt.f64 2)))) 2))))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2))) (.f64 (.f64 (/.f64 p (.f64 x x)) p) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -2 (/.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (.f64 64 (/.f64 1 (pow.f64 x 8)))) (pow.f64 x 2))) (.f64 -1 (/.f64 (-.f64 (.f64 1/2 (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2))))) (pow.f64 p 6))) (sqrt.f64 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 1/2 (.f64 (-.f64 (.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (pow.f64 x 2))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (pow.f64 p 4))) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))))
(fma.f64 1/2 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (fma.f64 -1/2 (.f64 (.f64 x x) (fma.f64 -2 (/.f64 (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (.f64 x x)) (/.f64 64 (pow.f64 x 8)))) (neg.f64 (neg.f64 (/.f64 (fma.f64 1/2 (.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) (neg.f64 (pow.f64 (/.f64 -1 (.f64 (.f64 x x) (sqrt.f64 2))) 2))) (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 2))))))) (pow.f64 p 6)) (sqrt.f64 2)) (fma.f64 -1 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (.f64 p p) (.f64 x x))) (fma.f64 1/2 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (fma.f64 1/2 (.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) (neg.f64 (pow.f64 (/.f64 -1 (.f64 (.f64 x x) (sqrt.f64 2))) 2)))) (pow.f64 p 4)) (sqrt.f64 2)) (*.f64 (sqrt.f64 1/2) (sqrt.f64 2)))))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (pow.f64 p 6) (fma.f64 -1/2 (.f64 x (.f64 x (fma.f64 -2 (-.f64 (/.f64 16 (pow.f64 x 8)) (/.f64 (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2) (.f64 x x))) (/.f64 64 (pow.f64 x 8))))) (/.f64 (fma.f64 1/2 (.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) (neg.f64 (pow.f64 (/.f64 -1 (.f64 x (.f64 x (sqrt.f64 2)))) 2))) (.f64 2 (.f64 x x)))))) (-.f64 (fma.f64 (sqrt.f64 1/2) (sqrt.f64 2) (/.f64 (.f64 (sqrt.f64 1/2) 1/2) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 p 4)) (fma.f64 1/2 (.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) (neg.f64 (pow.f64 (/.f64 -1 (.f64 x (.f64 x (sqrt.f64 2)))) 2)))))) (.f64 (.f64 (/.f64 p x) (/.f64 p x)) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (pow.f64 p 6) (fma.f64 (.f64 x x) (+.f64 (/.f64 1 (/.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)))) (/.f64 -32 (pow.f64 x 8))) (-.f64 (.f64 (/.f64 (.f64 1/2 (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) 2) 1) (/.f64 (pow.f64 (/.f64 -1 (.f64 x (.f64 x (sqrt.f64 2)))) 2) (.f64 2 (.f64 x x))))))) (-.f64 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (pow.f64 p 4) (fma.f64 (.f64 x x) (.f64 1/2 (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) (neg.f64 (pow.f64 (/.f64 -1 (.f64 x (.f64 x (sqrt.f64 2)))) 2))))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2))) (.f64 (.f64 (/.f64 p (.f64 x x)) p) (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x))))
(fma.f64 1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (/.f64 (.f64 -1/32 (.f64 (.f64 x x) (sqrt.f64 1/2))) (.f64 p p))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (.f64 -1/32 (*.f64 (/.f64 x (/.f64 p x)) (/.f64 (sqrt.f64 1/2) p)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 (.f64 (.f64 -1/32 (sqrt.f64 1/2)) (.f64 x x)) (*.f64 p p))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/16 (pow.f64 x 3)) (.f64 -1/64 (pow.f64 x 3)))) (pow.f64 p 3))) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 p 3) (.f64 (pow.f64 x 3) -3/64))) (/.f64 (.f64 -1/32 (.f64 (.f64 x x) (sqrt.f64 1/2))) (*.f64 p p)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 x 3) -3/64) (/.f64 (pow.f64 p 3) (sqrt.f64 1/2))) (.f64 -1/32 (.f64 (/.f64 x (/.f64 p x)) (/.f64 (sqrt.f64 1/2) p))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) -3/64) (/.f64 (.f64 (.f64 -1/32 (sqrt.f64 1/2)) (.f64 x x)) (.f64 p p)))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2)) (/.f64 (.f64 -1/32 (.f64 (.f64 x x) (sqrt.f64 1/2))) (.f64 p p)))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/32 (.f64 (/.f64 x (/.f64 p x)) (/.f64 (sqrt.f64 1/2) p)) (sqrt.f64 1/2)))
(fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) x) (/.f64 (sqrt.f64 1/2) p)) (sqrt.f64 1/2)))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (.f64 -1/16 (pow.f64 x 3)) (.f64 -1/64 (pow.f64 x 3)))) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (fma.f64 -1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 p 3) (.f64 (pow.f64 x 3) -3/64))) (+.f64 (sqrt.f64 1/2) (/.f64 (.f64 -1/32 (.f64 (.f64 x x) (sqrt.f64 1/2))) (*.f64 p p)))))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/2 (/.f64 (.f64 (pow.f64 x 3) -3/64) (/.f64 (pow.f64 p 3) (sqrt.f64 1/2))) (fma.f64 -1/32 (*.f64 (/.f64 x (/.f64 p x)) (/.f64 (sqrt.f64 1/2) p)) (sqrt.f64 1/2))))
(fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) -3/64) (fma.f64 -1/32 (.f64 (.f64 (/.f64 x p) x) (/.f64 (sqrt.f64 1/2) p)) (sqrt.f64 1/2))))

eval210.0ms (3%)

Compiler: Compiled 7980 to 6180 computations (22.6% saved)

prune49.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	274	11	285
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	275	11	286

Error

3.2b

Counts

286 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	54.3b	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
▶	26.3b	(sqrt.f64 1/2)
▶	60.0b	(sqrt.f64 (*.f64 1/2 (+.f64 1 -1)))
	52.6b	(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))
▶	29.2b	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))
	54.9b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))))
	14.0b	(pow.f64 (pow.f64 (fma.f64 (/.f64 x (hypot.f64 x (*.f64 2 p))) 1/2 1/2) 1/4) 2)
	28.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
	42.9b	(sqrt.f64 (*.f64 1/2 2))
	54.3b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
▶	13.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))

Compiler

Compiled 250 to 210 computations (16% saved)

localize22.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.5b	(+.f64 1 (/.f64 x (hypot.f64 x (*.f64 2 p))))
	0.2b	(/.f64 x (hypot.f64 x (*.f64 2 p)))
	0.0b	(hypot.f64 x (*.f64 2 p))
	0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))
✓	0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))
✓	0.0b	(hypot.f64 x (*.f64 2 p))
✓	0.2b	(/.f64 x (hypot.f64 x (*.f64 2 p)))
✓	0.5b	(+.f64 1 (/.f64 x (hypot.f64 x (*.f64 2 p))))

Compiler

Compiled 54 to 37 computations (31.5% saved)

series22.0ms (0.3%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
3.0ms	p	@	0	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))
2.0ms	x	@	-inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))
2.0ms	x	@	0	(+.f64 1 (/.f64 x (hypot.f64 x (*.f64 2 p))))
2.0ms	p	@	inf	(hypot.f64 x (*.f64 2 p))
2.0ms	x	@	-inf	(+.f64 1 (/.f64 x (hypot.f64 x (*.f64 2 p))))

rewrite75.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

554×	`log-prod_binary64`
395×	`prod-diff_binary64`
310×	`pow-prod-down_binary64`
301×	`pow2_binary64`
252×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	48
1	255	48
2	3135	46

Stop Event

1×	node limit

Counts

4 → 145

Calls

Call 1

Inputs
(+.f64 1 (/.f64 x (hypot.f64 x (*.f64 2 p))))
(/.f64 x (hypot.f64 x (*.f64 2 p)))
(hypot.f64 x (*.f64 2 p))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))

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

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

625×	`associate-*l/_binary64`
421×	`distribute-rgt-in_binary64`
418×	`distribute-lft-in_binary64`
399×	`fma-def_binary64`
329×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	3165
1	1133	3012
2	4374	2904

Stop Event

1×	node limit

Counts

241 → 277

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 (.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
2
(+.f64 2 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4)))))
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 x 6))) (.f64 -1 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4))))))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -4 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (*.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(+.f64 (.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)) (pow.f64 x 6))) (+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (.f64 -4 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 16 (pow.f64 p 8)) (pow.f64 (.f64 -2 (pow.f64 p 4)) 2)) (pow.f64 x 8))) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 4)) (pow.f64 x 8))) (+.f64 (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 p 2)) (pow.f64 x 8))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (+.f64 (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)) (pow.f64 x 6))) (+.f64 (.f64 -8 (/.f64 (pow.f64 p 8) (pow.f64 x 8))) (+.f64 (.f64 -4 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (*.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))))))))
2
(+.f64 2 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(+.f64 (.f64 -20 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (*.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (.f64 -1/128 (pow.f64 x 5))) (pow.f64 p 5))) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
1
(+.f64 (*.f64 -1/2 (/.f64 x p)) 1)
(+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 1 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 1 (+.f64 (.f64 -1/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))))
(*.f64 1/2 (/.f64 x p))
(+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))
(+.f64 (.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 1/2 (/.f64 x p)) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 (.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 -5/2048 (/.f64 (pow.f64 x 7) (pow.f64 p 7))) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
1
(+.f64 1 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4)))))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 x 6))) (.f64 -1 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4))))))
-1
(-.f64 (*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) 1)
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 x 4)))) 1)
(-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 x 6))) (.f64 -1 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 x 4))))) 1)
1
(+.f64 1 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(+.f64 (.f64 -20 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (+.f64 1 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (*.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
(*.f64 1/2 (/.f64 x p))
(+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 -1 (/.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (*.f64 -1/128 (pow.f64 x 5))) (pow.f64 p 5)))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/8 (.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (.f64 -1/128 (pow.f64 x 5))) (pow.f64 x 2))) (.f64 1/1024 (pow.f64 x 7))) (pow.f64 p 7))) (+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 -1 (/.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (*.f64 -1/128 (pow.f64 x 5))) (pow.f64 p 5))))))
(*.f64 -1/2 (/.f64 x p))
(+.f64 (.f64 -1/2 (/.f64 x p)) (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))
(+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 (.f64 -1/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
(+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 (.f64 -1/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 (.f64 1/1024 (/.f64 (pow.f64 x 7) (pow.f64 p 7))) (.f64 -1/8 (/.f64 (.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (*.f64 -1/128 (pow.f64 x 5))) (pow.f64 x 2)) (pow.f64 p 7))))))))
(*.f64 2 p)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (.f64 2 p))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (*.f64 2 p)))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5))) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (.f64 2 p))))
x
(+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) x)) x))
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 4 (/.f64 (pow.f64 p 6) (pow.f64 x 5))) (+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)))
(*.f64 -1 x)
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) x)) (.f64 -1 x))
(+.f64 (.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) x)) (*.f64 -1 x)))
(+.f64 (.f64 -4 (/.f64 (pow.f64 p 6) (pow.f64 x 5))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) x)) (.f64 -1 x))))
x
(+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) x)) x))
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 3))) (+.f64 (.f64 4 (/.f64 (pow.f64 p 6) (pow.f64 x 5))) (+.f64 (*.f64 2 (/.f64 (pow.f64 p 2) x)) x)))
(*.f64 2 p)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (.f64 2 p))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (*.f64 2 p)))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5))) (+.f64 (.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (.f64 2 p))))
(*.f64 -2 p)
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 x 2) p)) (.f64 -2 p))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (*.f64 -2 p)))
(+.f64 (.f64 -1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 x 2) p)) (+.f64 (.f64 1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))) (.f64 -2 p))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -3/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (sqrt.f64 2))) 2) (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (.f64 (sqrt.f64 2) (pow.f64 x 4)))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 8 (pow.f64 p 6)) (+.f64 (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2))) (/.f64 (.f64 (+.f64 (pow.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (sqrt.f64 2))) 2) (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4)))) (pow.f64 p 2)) (pow.f64 (sqrt.f64 2) 2))))) (.f64 (sqrt.f64 2) (pow.f64 x 6)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (sqrt.f64 2))) 2) (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (.f64 (sqrt.f64 2) (pow.f64 x 4)))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (sqrt.f64 1/2)) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) p)))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (sqrt.f64 1/2)) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) p)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (.f64 (sqrt.f64 2) p))) 2))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 5) p)))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p)) x))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (sqrt.f64 1/2)) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) p)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (.f64 2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 4))) (+.f64 (.f64 -1/2 (+.f64 (.f64 16 (pow.f64 p 8)) (pow.f64 (.f64 -2 (pow.f64 p 4)) 2))) (+.f64 (.f64 -2 (.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 p 2))) (.f64 -8 (pow.f64 p 8))))) (.f64 1/2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (-.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (.f64 (sqrt.f64 2) p))) 2))) (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 p 2)))))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 7) p)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (.f64 (sqrt.f64 2) p))) 2))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 5) p)))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 6 (/.f64 1 (pow.f64 x 4))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (pow.f64 p 4))) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 6 (/.f64 1 (pow.f64 x 4))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (pow.f64 p 4))) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 6 (/.f64 1 (pow.f64 x 4))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2)))) (.f64 20 (/.f64 1 (pow.f64 x 6)))) (.f64 (sqrt.f64 1/2) (pow.f64 p 6))) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/64 (pow.f64 x 3)) (.f64 1/16 (pow.f64 x 3)))) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/64 (pow.f64 x 3)) (.f64 1/16 (pow.f64 x 3)))) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))

Outputs
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 1 (fma.f64 1/2 (/.f64 x p) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 (fma.f64 1/2 (/.f64 x p) 1) (/.f64 -1/16 (pow.f64 (/.f64 p x) 3)))
(+.f64 (.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
(fma.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) (+.f64 1 (fma.f64 1/2 (/.f64 x p) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
(+.f64 1 (fma.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) (fma.f64 1/2 (/.f64 x p) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
(fma.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) (+.f64 (fma.f64 1/2 (/.f64 x p) 1) (/.f64 -1/16 (pow.f64 (/.f64 p x) 3))))
2
(+.f64 2 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 2 (/.f64 (.f64 -2 (.f64 p p)) (*.f64 x x)))
(fma.f64 -2 (/.f64 p (/.f64 (*.f64 x x) p)) 2)
(fma.f64 -2 (.f64 (/.f64 p (.f64 x x)) p) 2)
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -2 (/.f64 (.f64 p p) (.f64 x x)) (neg.f64 (/.f64 (*.f64 (pow.f64 p 4) -6) (pow.f64 x 4)))))
(-.f64 (fma.f64 -2 (/.f64 p (/.f64 (.f64 x x) p)) 2) (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))
(+.f64 (fma.f64 -2 (.f64 (/.f64 p (.f64 x x)) p) 2) (/.f64 (pow.f64 p 4) (/.f64 (pow.f64 x 4) 6)))
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 x 6))) (.f64 -1 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4))))))
(+.f64 2 (fma.f64 -2 (/.f64 (.f64 p p) (.f64 x x)) (fma.f64 -1 (/.f64 (fma.f64 8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) -6)))) (pow.f64 x 6)) (neg.f64 (/.f64 (*.f64 (pow.f64 p 4) -6) (pow.f64 x 4))))))
(+.f64 (fma.f64 -2 (/.f64 p (/.f64 (.f64 x x) p)) 2) (-.f64 (/.f64 (neg.f64 (.f64 (pow.f64 p 4) -6)) (pow.f64 x 4)) (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6))) (pow.f64 x 6))))
(+.f64 (fma.f64 -2 (.f64 (/.f64 p (.f64 x x)) p) 2) (-.f64 (/.f64 (pow.f64 p 4) (/.f64 (pow.f64 x 4) 6)) (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6))) (pow.f64 x 6))))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (/.f64 p (/.f64 (.f64 x x) p)))
(.f64 2 (.f64 (/.f64 p (*.f64 x x)) p))
(+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -4 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (*.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(fma.f64 2 (/.f64 (.f64 p p) (.f64 x x)) (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))
(fma.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6 (.f64 2 (/.f64 p (/.f64 (.f64 x x) p))))
(fma.f64 2 (.f64 (/.f64 p (.f64 x x)) p) (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))
(+.f64 (.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)) (pow.f64 x 6))) (+.f64 (.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (.f64 -4 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))))
(fma.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 2 (/.f64 (.f64 p p) (.f64 x x)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 p 4) -6) (/.f64 (pow.f64 x 6) (.f64 p p))) (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))))
(fma.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 2 (/.f64 p (/.f64 (.f64 x x) p)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 p 6) -6) (pow.f64 x 6)) (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))))
(fma.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 2 (.f64 (/.f64 p (.f64 x x)) p) (fma.f64 -2 (/.f64 (.f64 (pow.f64 p 6) -6) (pow.f64 x 6)) (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 16 (pow.f64 p 8)) (pow.f64 (.f64 -2 (pow.f64 p 4)) 2)) (pow.f64 x 8))) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 4)) (pow.f64 x 8))) (+.f64 (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 p 2)) (pow.f64 x 8))) (+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (+.f64 (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)) (pow.f64 x 6))) (+.f64 (.f64 -8 (/.f64 (pow.f64 p 8) (pow.f64 x 8))) (+.f64 (.f64 -4 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (*.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))))))))
(fma.f64 -1/2 (/.f64 (fma.f64 16 (pow.f64 p 8) (pow.f64 (.f64 -2 (pow.f64 p 4)) 2)) (pow.f64 x 8)) (fma.f64 2 (/.f64 (.f64 (pow.f64 p 4) -6) (/.f64 (pow.f64 x 8) (pow.f64 p 4))) (fma.f64 -2 (/.f64 (fma.f64 8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) -6)))) (/.f64 (pow.f64 x 8) (.f64 p p))) (fma.f64 2 (/.f64 (.f64 p p) (.f64 x x)) (fma.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 p 4) -6) (/.f64 (pow.f64 x 6) (.f64 p p))) (fma.f64 -8 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))))))))
(fma.f64 -1/2 (/.f64 (fma.f64 16 (pow.f64 p 8) (.f64 4 (pow.f64 p 8))) (pow.f64 x 8)) (fma.f64 2 (/.f64 (.f64 (pow.f64 p 8) -6) (pow.f64 x 8)) (fma.f64 -2 (.f64 (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6))) (pow.f64 x 8)) (.f64 p p)) (fma.f64 2 (/.f64 p (/.f64 (.f64 x x) p)) (fma.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 p 6) -6) (pow.f64 x 6)) (fma.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6 (*.f64 -8 (/.f64 (pow.f64 p 8) (pow.f64 x 8))))))))))
(fma.f64 -1/2 (/.f64 (.f64 (pow.f64 p 8) 20) (pow.f64 x 8)) (fma.f64 2 (.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -6) (fma.f64 -2 (.f64 (/.f64 (.f64 p p) (pow.f64 x 8)) (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6)))) (fma.f64 2 (.f64 (/.f64 p (.f64 x x)) p) (fma.f64 8 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 p 6) -6) (pow.f64 x 6)) (fma.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6 (/.f64 (.f64 (pow.f64 p 8) -8) (pow.f64 x 8)))))))))
2
(+.f64 2 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 2 (/.f64 (.f64 -2 (.f64 p p)) (*.f64 x x)))
(fma.f64 -2 (/.f64 p (/.f64 (*.f64 x x) p)) 2)
(fma.f64 -2 (.f64 (/.f64 p (.f64 x x)) p) 2)
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -2 (/.f64 (.f64 p p) (.f64 x x)) (neg.f64 (/.f64 (*.f64 (pow.f64 p 4) -6) (pow.f64 x 4)))))
(-.f64 (fma.f64 -2 (/.f64 p (/.f64 (.f64 x x) p)) 2) (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))
(+.f64 (fma.f64 -2 (.f64 (/.f64 p (.f64 x x)) p) 2) (/.f64 (pow.f64 p 4) (/.f64 (pow.f64 x 4) 6)))
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(fma.f64 -20 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (+.f64 2 (fma.f64 -2 (/.f64 (.f64 p p) (.f64 x x)) (*.f64 6 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
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x
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x
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(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (sqrt.f64 1/2)) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) p)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (.f64 2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 4))) (+.f64 (.f64 -1/2 (+.f64 (.f64 16 (pow.f64 p 8)) (pow.f64 (.f64 -2 (pow.f64 p 4)) 2))) (+.f64 (.f64 -2 (.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 p 2))) (.f64 -8 (pow.f64 p 8))))) (.f64 1/2 (/.f64 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (-.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (.f64 (sqrt.f64 2) p))) 2))) (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 p 2)))))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 7) p)))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (.f64 (sqrt.f64 2) p))) 2))) (.f64 (sqrt.f64 2) (.f64 (pow.f64 x 5) p)))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x)))))
(fma.f64 -1/2 (.f64 (/.f64 (.f64 (pow.f64 p 4) -6) (sqrt.f64 2)) (/.f64 (sqrt.f64 1/2) (.f64 p (pow.f64 x 3)))) (fma.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (+.f64 (fma.f64 2 (.f64 (pow.f64 p 4) (.f64 (pow.f64 p 4) -6)) (fma.f64 -1/2 (fma.f64 16 (pow.f64 p 8) (pow.f64 (.f64 -2 (pow.f64 p 4)) 2)) (fma.f64 -2 (.f64 (.f64 p p) (fma.f64 8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) -6))))) (.f64 (pow.f64 p 8) -8)))) (.f64 -1/2 (.f64 (/.f64 (.f64 (pow.f64 p 4) -6) (pow.f64 (sqrt.f64 2) 2)) (/.f64 (-.f64 (fma.f64 8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) -6)))) (pow.f64 (/.f64 (.f64 1/2 (.f64 (pow.f64 p 4) -6)) (.f64 p (sqrt.f64 2))) 2)) (.f64 p p))))) (.f64 p (pow.f64 x 7)))) (fma.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (-.f64 (fma.f64 8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) -6)))) (pow.f64 (/.f64 (.f64 1/2 (.f64 (pow.f64 p 4) -6)) (.f64 p (sqrt.f64 2))) 2)) (.f64 p (pow.f64 x 5)))) (neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (.f64 p (sqrt.f64 1/2))))))))
(fma.f64 -1/2 (.f64 (/.f64 (pow.f64 p 4) (/.f64 (sqrt.f64 2) -6)) (/.f64 (sqrt.f64 1/2) (.f64 p (pow.f64 x 3)))) (-.f64 (.f64 -1/2 (+.f64 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 (pow.f64 x 7) (sqrt.f64 2))) (/.f64 (+.f64 (fma.f64 2 (.f64 (pow.f64 p 8) -6) (fma.f64 -1/2 (fma.f64 16 (pow.f64 p 8) (.f64 4 (pow.f64 p 8))) (fma.f64 -2 (.f64 (.f64 p p) (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6)))) (.f64 (pow.f64 p 8) -8)))) (.f64 -1/2 (.f64 (/.f64 (pow.f64 p 4) -1/3) (/.f64 (-.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6))) (pow.f64 (.f64 1/2 (.f64 (/.f64 (pow.f64 p 4) p) (/.f64 -6 (sqrt.f64 2)))) 2)) (.f64 p p))))) p)) (/.f64 (-.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6))) (pow.f64 (.f64 1/2 (.f64 (/.f64 (pow.f64 p 4) p) (/.f64 -6 (sqrt.f64 2)))) 2)) (/.f64 (.f64 p (*.f64 (pow.f64 x 5) (sqrt.f64 2))) (sqrt.f64 1/2))))) (/.f64 (sqrt.f64 2) (/.f64 (/.f64 x (sqrt.f64 1/2)) p))))
(-.f64 (.f64 -1/2 (+.f64 (/.f64 (pow.f64 p 4) (/.f64 (.f64 p (pow.f64 x 3)) (.f64 -6 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2))))) (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (+.f64 (/.f64 (+.f64 (fma.f64 -1/2 (.f64 (pow.f64 p 8) 20) (fma.f64 -2 (.f64 (.f64 p p) (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6)))) (.f64 (pow.f64 p 8) -8))) (fma.f64 2 (.f64 (pow.f64 p 8) -6) (.f64 -1/2 (/.f64 (.f64 (/.f64 (pow.f64 p 4) -1/3) (-.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6))) (pow.f64 (.f64 1/2 (.f64 (/.f64 (pow.f64 p 4) p) (/.f64 -6 (sqrt.f64 2)))) 2))) (.f64 p p))))) (.f64 p (pow.f64 x 7))) (/.f64 (-.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6))) (pow.f64 (.f64 1/2 (.f64 (/.f64 (pow.f64 p 4) p) (/.f64 -6 (sqrt.f64 2)))) 2)) (.f64 p (pow.f64 x 5))))))) (*.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 2) (sqrt.f64 1/2))
(*.f64 (sqrt.f64 1/2) (sqrt.f64 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(fma.f64 -1 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (.f64 p p) (.f64 x x))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2)))
(-.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) (.f64 p p))) (*.f64 x x)))
(-.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (.f64 p p) (.f64 (.f64 x x) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 6 (/.f64 1 (pow.f64 x 4))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (pow.f64 p 4))) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2))))
(fma.f64 -1 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (.f64 p p) (.f64 x x))) (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 p 4) (-.f64 (/.f64 6 (pow.f64 x 4)) (pow.f64 (/.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 x x)) 2))))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2))))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (pow.f64 p 4) (-.f64 (/.f64 6 (pow.f64 x 4)) (pow.f64 (/.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 x x)) 2)))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2))) (/.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) (.f64 p p))) (.f64 x x)))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (pow.f64 p 4) (-.f64 (/.f64 6 (pow.f64 x 4)) (pow.f64 (/.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 x x)) 2)))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2))) (/.f64 (.f64 p p) (.f64 (*.f64 x x) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 p 2)) (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (-.f64 (.f64 6 (/.f64 1 (pow.f64 x 4))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (pow.f64 p 4))) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 -1 (/.f64 (-.f64 (.f64 6 (/.f64 1 (pow.f64 x 4))) (pow.f64 (/.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 2))) 2)) (.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 x 2)))) (.f64 20 (/.f64 1 (pow.f64 x 6)))) (.f64 (sqrt.f64 1/2) (pow.f64 p 6))) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (sqrt.f64 1/2)))))
(fma.f64 -1 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (/.f64 (.f64 p p) (.f64 x x))) (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 p 4) (-.f64 (/.f64 6 (pow.f64 x 4)) (pow.f64 (/.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 x x)) 2))))) (fma.f64 -1/2 (/.f64 (fma.f64 -1 (/.f64 (-.f64 (/.f64 6 (pow.f64 x 4)) (pow.f64 (/.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 x x)) 2)) (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 2))) (/.f64 20 (pow.f64 x 6))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 p 6) (sqrt.f64 1/2)))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2)))))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (pow.f64 p 4) (-.f64 (/.f64 6 (pow.f64 x 4)) (pow.f64 (/.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 x x)) 2)))) (fma.f64 -1/2 (.f64 (/.f64 (+.f64 (.f64 -1/2 (/.f64 (-.f64 (/.f64 6 (pow.f64 x 4)) (pow.f64 (/.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 x x)) 2)) (.f64 x x))) (/.f64 20 (pow.f64 x 6))) (sqrt.f64 2)) (.f64 (pow.f64 p 6) (sqrt.f64 1/2))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2)))) (/.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) (.f64 p p))) (*.f64 x x)))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 2)) (.f64 (pow.f64 p 4) (-.f64 (/.f64 6 (pow.f64 x 4)) (pow.f64 (/.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 x x)) 2)))) (fma.f64 -1/2 (.f64 (/.f64 (-.f64 (/.f64 20 (pow.f64 x 6)) (/.f64 (-.f64 (/.f64 6 (pow.f64 x 4)) (pow.f64 (/.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 x x)) 2)) (.f64 x (.f64 x 2)))) (sqrt.f64 2)) (.f64 (pow.f64 p 6) (sqrt.f64 1/2))) (.f64 (sqrt.f64 1/2) (sqrt.f64 2)))) (/.f64 (.f64 p p) (.f64 (.f64 x x) (/.f64 (sqrt.f64 2) (sqrt.f64 1/2)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x))))
(fma.f64 1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (/.f64 (.f64 -1/32 (.f64 (.f64 x x) (sqrt.f64 1/2))) (.f64 p p))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (.f64 -1/32 (.f64 (/.f64 (.f64 x x) p) (/.f64 (sqrt.f64 1/2) p)))))
(+.f64 (.f64 1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x)) (fma.f64 -1/32 (/.f64 (.f64 (.f64 x x) (/.f64 (sqrt.f64 1/2) p)) p) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/64 (pow.f64 x 3)) (.f64 1/16 (pow.f64 x 3)))) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 p 3) (.f64 (pow.f64 x 3) 3/64))) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (/.f64 (.f64 -1/32 (.f64 (.f64 x x) (sqrt.f64 1/2))) (*.f64 p p)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/2 (/.f64 (.f64 (pow.f64 x 3) (.f64 3/64 (sqrt.f64 1/2))) (pow.f64 p 3)) (fma.f64 1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (.f64 -1/32 (.f64 (/.f64 (.f64 x x) p) (/.f64 (sqrt.f64 1/2) p))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) 3/64) (fma.f64 1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (.f64 -1/32 (/.f64 (.f64 (*.f64 x x) (/.f64 (sqrt.f64 1/2) p)) p)))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2)) (/.f64 (.f64 -1/32 (.f64 (.f64 x x) (sqrt.f64 1/2))) (.f64 p p)))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/32 (.f64 (/.f64 (*.f64 x x) p) (/.f64 (sqrt.f64 1/2) p)) (sqrt.f64 1/2)))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/32 (/.f64 (.f64 (*.f64 x x) (/.f64 (sqrt.f64 1/2) p)) p) (sqrt.f64 1/2)))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/64 (pow.f64 x 3)) (.f64 1/16 (pow.f64 x 3)))) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 p 3) (.f64 (pow.f64 x 3) 3/64))) (+.f64 (sqrt.f64 1/2) (/.f64 (.f64 -1/32 (.f64 (.f64 x x) (sqrt.f64 1/2))) (*.f64 p p)))))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 x 3) (.f64 3/64 (sqrt.f64 1/2))) (pow.f64 p 3)) (fma.f64 -1/32 (.f64 (/.f64 (*.f64 x x) p) (/.f64 (sqrt.f64 1/2) p)) (sqrt.f64 1/2))))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) 3/64) (fma.f64 -1/32 (/.f64 (.f64 (.f64 x x) (/.f64 (sqrt.f64 1/2) p)) p) (sqrt.f64 1/2))))

localize3.0ms (0%)

Compiler: Compiled 5 to 5 computations (0% saved)

localize10.0ms (0.1%)

Compiler: Compiled 19 to 19 computations (0% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	1.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))
✓	1.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))

Compiler

Compiled 41 to 25 computations (39% saved)

series5.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))
1.0ms	p	@	0	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))
1.0ms	x	@	0	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))
1.0ms	x	@	-inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))
1.0ms	p	@	inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))

rewrite46.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

520×	`log-prod_binary64`
337×	`prod-diff_binary64`
290×	`pow-prod-down_binary64`
276×	`pow2_binary64`
267×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	235	12
2	2935	10

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

Inputs
(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))

Outputs

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

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

990×	`distribute-rgt-out_binary64`
646×	`associate-/r*_binary64`
546×	`fma-def_binary64`
543×	`associate-r_binary64`
518×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	318
1	80	306
2	251	297
3	1203	255
4	6561	255

Stop Event

1×	node limit

Counts

46 → 41

Calls

Call 1

Inputs
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 -1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 -1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 -1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))

Outputs
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (sqrt.f64 1/2) (/.f64 x p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (.f64 p p))))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) p) (/.f64 (*.f64 x x) p)) (sqrt.f64 1/2)))
(fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 -1/4 (*.f64 (/.f64 -1/32 p) x))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 -1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (fma.f64 -1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (*.f64 p p))))))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/128 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (pow.f64 x 3)) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) p) (/.f64 (.f64 x x) p)) (sqrt.f64 1/2))))
(fma.f64 -1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 -1/4 (*.f64 (/.f64 -1/32 p) x)))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (sqrt.f64 1/2) (/.f64 x p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (.f64 p p))))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) p) (/.f64 (*.f64 x x) p)) (sqrt.f64 1/2)))
(fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 -1/4 (*.f64 (/.f64 -1/32 p) x))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 -1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (fma.f64 -1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (*.f64 p p))))))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/128 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (pow.f64 x 3)) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) p) (/.f64 (.f64 x x) p)) (sqrt.f64 1/2))))
(fma.f64 -1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 -1/4 (*.f64 (/.f64 -1/32 p) x)))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (sqrt.f64 1/2) (/.f64 x p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (.f64 p p))))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) p) (/.f64 (*.f64 x x) p)) (sqrt.f64 1/2)))
(fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 -1/4 (*.f64 (/.f64 -1/32 p) x))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 -1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (fma.f64 -1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3)) (+.f64 (sqrt.f64 1/2) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (*.f64 p p))))))
(fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (fma.f64 -1/128 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (pow.f64 x 3)) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) p) (/.f64 (.f64 x x) p)) (sqrt.f64 1/2))))
(fma.f64 -1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 -1/4 (*.f64 (/.f64 -1/32 p) x)))))

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
	0.4b	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
✓	0.4b	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
✓	0.6b	(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))

Compiler

Compiled 33 to 23 computations (30.3% saved)

series10.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
1.0ms	p	@	0	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
1.0ms	x	@	0	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
1.0ms	x	@	inf	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
1.0ms	p	@	0	(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))

rewrite119.0ms (1.7%)

Algorithm

2×	egg-rewrite-iter-limit
2×	egg-rewrite
1×	batch-egg-rewrite

Rules

117×	`add-sqr-sqrt_binary64`
117×	`add-sqr-sqrt_binary64`
111×	`*-un-lft-identity_binary64`
111×	`pow1_binary64`
111×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	239	27
2	3249	27
0	8	11
1	178	11
2	2585	11
0	8	11
0	11	16
1	239	16
2	3249	16
0	11	16

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

2 → 19

Calls

Call 1

Inputs
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))

Outputs

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

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

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
269×	`fma-neg_binary64`
67×	`associate-/l*_binary64`
62×	`div-sub_binary64`
59×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	648
1	32	648
2	77	648
3	185	648
4	350	648
5	556	648
6	763	648
7	920	648
8	1091	648
9	1587	648
10	2030	648
11	2031	648

Stop Event

1×

saturated

Counts

67 → 23

Calls

Call 1

Inputs
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))

Outputs
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) (.f64 p (sqrt.f64 1/2)))
(.f64 p (neg.f64 (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 2) x))))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))

eval184.0ms (2.6%)

Compiler: Compiled 7986 to 5346 computations (33.1% saved)

prune57.0ms (0.8%)

Pruning

16 alts after pruning (11 fresh and 5 done)

	Pruned	Kept	Total
New	331	10	341
Fresh	5	1	6
Picked	0	1	1
Done	0	4	4
Total	336	16	352

Error

3.2b

Counts

352 → 16

Alt Table

Click to see full alt table

Status	Error	Program
▶	54.3b	(.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p) (sqrt.f64 1/2))
▶	42.9b	(sqrt.f64 (*.f64 1/2 2))
▶	28.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
✓	54.3b	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
✓	26.3b	(sqrt.f64 1/2)
	54.3b	(.f64 (.f64 -1 (/.f64 (*.f64 (sqrt.f64 2) p) x)) (sqrt.f64 1/2))
▶	29.7b	(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)
	52.6b	(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))
	55.0b	(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p)) (sqrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p))) (sqrt.f64 1/2))
	54.4b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p)) (cbrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p))) (cbrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p))) (sqrt.f64 1/2))
	54.3b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
▶	54.3b	(/.f64 (.f64 (.f64 p (sqrt.f64 2)) (neg.f64 (sqrt.f64 1/2))) x)
✓	13.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))
	54.9b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))))
✓	60.0b	(sqrt.f64 (*.f64 1/2 (+.f64 1 -1)))
✓	29.2b	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))

Compiler

Compiled 370 to 307 computations (17% saved)

localize16.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	2.4b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
	0.2b	(/.f64 x (*.f64 2 p))
	0.0b	(+.f64 1 (/.f64 x (*.f64 2 p)))
✓	0.0b	(+.f64 1 (/.f64 x (*.f64 2 p)))
✓	0.2b	(/.f64 x (*.f64 2 p))
✓	2.4b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))

Compiler

Compiled 41 to 30 computations (26.8% saved)

series8.0ms (0.1%)

Counts

3 → 60

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
1.0ms	p	@	0	(/.f64 x (*.f64 2 p))
1.0ms	x	@	0	(/.f64 x (*.f64 2 p))
1.0ms	x	@	inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
0.0ms	x	@	-inf	(/.f64 x (*.f64 2 p))

rewrite67.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

531×	`log-prod_binary64`
407×	`prod-diff_binary64`
298×	`pow-prod-down_binary64`
278×	`pow2_binary64`
242×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	236	28
2	2996	28

Stop Event

1×	node limit

Counts

3 → 146

Calls

Call 1

Inputs
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
(/.f64 x (*.f64 2 p))
(+.f64 1 (/.f64 x (*.f64 2 p)))

Outputs

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

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

990×	`distribute-rgt-out_binary64`
660×	`associate-/r*_binary64`
573×	`fma-def_binary64`
551×	`associate-r_binary64`
533×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	696
1	87	654
2	259	633
3	1232	591
4	6714	591

Stop Event

1×	node limit

Counts

206 → 155

Calls

Call 1

Inputs
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
(*.f64 1/2 (/.f64 x p))
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(*.f64 1/2 (/.f64 x p))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(*.f64 1/2 (/.f64 x p))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(*.f64 1/2 (/.f64 x p))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))

Outputs
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x))))
(fma.f64 1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(fma.f64 1/4 (*.f64 (sqrt.f64 1/2) (/.f64 x p)) (sqrt.f64 1/2))
(*.f64 (+.f64 (/.f64 1/4 (/.f64 p x)) 1) (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (.f64 p p)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x)) (/.f64 (.f64 (sqrt.f64 1/2) 1/4) (/.f64 p x))))
(fma.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 1/4 (*.f64 (/.f64 -1/32 p) x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3)) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (*.f64 p p))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/128 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (pow.f64 x 3)) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x)) (/.f64 (*.f64 (sqrt.f64 1/2) 1/4) (/.f64 p x)))))
(fma.f64 1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (fma.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2))))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 1/4 (*.f64 (/.f64 -1/32 p) x))) (fma.f64 1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (sqrt.f64 1/2)))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 1/4 (.f64 (/.f64 -1/32 p) x))) (.f64 (+.f64 (/.f64 1/128 (pow.f64 (/.f64 p x) 3)) 1) (sqrt.f64 1/2)))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x))))
(fma.f64 1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(fma.f64 1/4 (*.f64 (sqrt.f64 1/2) (/.f64 x p)) (sqrt.f64 1/2))
(*.f64 (+.f64 (/.f64 1/4 (/.f64 p x)) 1) (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (.f64 p p)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x)) (/.f64 (.f64 (sqrt.f64 1/2) 1/4) (/.f64 p x))))
(fma.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 1/4 (*.f64 (/.f64 -1/32 p) x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3)) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (*.f64 p p))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/128 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (pow.f64 x 3)) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x)) (/.f64 (*.f64 (sqrt.f64 1/2) 1/4) (/.f64 p x)))))
(fma.f64 1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (fma.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2))))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 1/4 (*.f64 (/.f64 -1/32 p) x))) (fma.f64 1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (sqrt.f64 1/2)))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 1/4 (.f64 (/.f64 -1/32 p) x))) (.f64 (+.f64 (/.f64 1/128 (pow.f64 (/.f64 p x) 3)) 1) (sqrt.f64 1/2)))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)))
(+.f64 (sqrt.f64 1/2) (*.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x))))
(fma.f64 1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(fma.f64 1/4 (*.f64 (sqrt.f64 1/2) (/.f64 x p)) (sqrt.f64 1/2))
(*.f64 (+.f64 (/.f64 1/4 (/.f64 p x)) 1) (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (.f64 p p)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x)) (/.f64 (.f64 (sqrt.f64 1/2) 1/4) (/.f64 p x))))
(fma.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 1/4 (*.f64 (/.f64 -1/32 p) x))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/128 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 3)) (pow.f64 p 3)) (fma.f64 1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (.f64 -1/32 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x x)) (*.f64 p p))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/128 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (pow.f64 x 3)) (fma.f64 -1/32 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x)) (/.f64 (*.f64 (sqrt.f64 1/2) 1/4) (/.f64 p x)))))
(fma.f64 1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (fma.f64 1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (fma.f64 -1/32 (.f64 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (/.f64 x p)) (sqrt.f64 1/2))))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 1/4 (*.f64 (/.f64 -1/32 p) x))) (fma.f64 1/128 (/.f64 (sqrt.f64 1/2) (pow.f64 (/.f64 p x) 3)) (sqrt.f64 1/2)))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (/.f64 x p)) (+.f64 1/4 (.f64 (/.f64 -1/32 p) x))) (.f64 (+.f64 (/.f64 1/128 (pow.f64 (/.f64 p x) 3)) 1) (sqrt.f64 1/2)))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(*.f64 1/2 (/.f64 x p))
(*.f64 x (/.f64 1/2 p))
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(+.f64 (*.f64 1/2 (/.f64 x p)) 1)
(fma.f64 1/2 (/.f64 x p) 1)

localize5.0ms (0.1%)

Compiler: Compiled 11 to 11 computations (0% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 p (sqrt.f64 2))
	0.4b	(.f64 (.f64 p (sqrt.f64 2)) (neg.f64 (sqrt.f64 1/2)))
✓	0.4b	(.f64 (.f64 p (sqrt.f64 2)) (neg.f64 (sqrt.f64 1/2)))
✓	0.5b	(*.f64 p (sqrt.f64 2))

Compiler

Compiled 35 to 29 computations (17.1% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	p	@	inf	(.f64 (.f64 p (sqrt.f64 2)) (neg.f64 (sqrt.f64 1/2)))
1.0ms	p	@	0	(.f64 (.f64 p (sqrt.f64 2)) (neg.f64 (sqrt.f64 1/2)))
1.0ms	p	@	inf	(*.f64 p (sqrt.f64 2))
0.0ms	p	@	-inf	(*.f64 p (sqrt.f64 2))
0.0ms	p	@	0	(*.f64 p (sqrt.f64 2))

rewrite82.0ms (1.2%)

Algorithm

1×	egg-rewrite-iter-limit
2×	egg-rewrite
1×	batch-egg-rewrite

Rules

417×	`pow1_binary64`
403×	`add-sqr-sqrt_binary64`
395×	`*-un-lft-identity_binary64`
386×	`add-log-exp_binary64`
386×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	186	19
2	2123	19
0	5	6
1	100	6
2	1075	6
0	9	13
1	186	13
2	2123	13
0	9	13

Stop Event

1×	iter limit
1×	unsound
1×	node limit
1×	unsound

Counts

2 → 22

Calls

Call 1

Inputs
(*.f64 p (sqrt.f64 2))
(.f64 (.f64 p (sqrt.f64 2)) (neg.f64 (sqrt.f64 1/2)))

Outputs

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

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

simplify22.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

244×	`fma-def_binary64`
21×	`sub-neg_binary64`
20×	`distribute-rgt-in_binary64`
18×	`associate-l_binary64`
18×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	228
1	20	228
2	50	228
3	95	228
4	109	228
5	157	228
6	229	228
7	266	228
8	308	228
9	477	228
10	505	228

Stop Event

1×

saturated

Counts

46 → 25

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))

Outputs
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 p (neg.f64 (sqrt.f64 2))))

localize18.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.5b	(/.f64 (neg.f64 (sqrt.f64 2)) x)
	0.4b	(.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p) (sqrt.f64 1/2))
	0.2b	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p)
✓	0.2b	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p)
✓	0.4b	(.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p) (sqrt.f64 1/2))
✓	0.5b	(/.f64 (neg.f64 (sqrt.f64 2)) x)

Compiler

Compiled 35 to 28 computations (20% saved)

series6.0ms (0.1%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p) (sqrt.f64 1/2))
1.0ms	x	@	0	(/.f64 (neg.f64 (sqrt.f64 2)) x)
1.0ms	p	@	inf	(.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p) (sqrt.f64 1/2))
1.0ms	x	@	inf	(/.f64 (neg.f64 (sqrt.f64 2)) x)
1.0ms	p	@	inf	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p)

rewrite115.0ms (1.6%)

Algorithm

3×	egg-rewrite-iter-limit
3×	egg-rewrite
1×	batch-egg-rewrite

Rules

113×	`add-sqr-sqrt_binary64`
113×	`add-sqr-sqrt_binary64`
107×	`*-un-lft-identity_binary64`
107×	`pow1_binary64`
107×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	233	35
2	2959	35
0	6	8
1	131	8
2	1746	8
0	6	8
0	11	16
1	233	16
2	2959	16
0	11	16
0	8	11
1	172	11
2	2302	11
0	8	11

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

3 → 24

Calls

Call 1

Inputs
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p) (sqrt.f64 1/2))
(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p)

Outputs

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

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

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

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1002×	`fma-def_binary64`
269×	`fma-neg_binary64`
67×	`associate-/l*_binary64`
58×	`sub-neg_binary64`
58×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	744
1	38	744
2	82	744
3	178	744
4	332	744
5	549	744
6	805	744
7	969	744
8	1236	744
9	1688	744
10	2131	744
11	2132	744

Stop Event

1×

saturated

Counts

84 → 30

Calls

Call 1

Inputs
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))

Outputs
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(*.f64 -1 (/.f64 (sqrt.f64 2) x))
(neg.f64 (/.f64 (sqrt.f64 2) x))
(/.f64 (neg.f64 (sqrt.f64 2)) x)
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
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(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
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(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
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(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
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(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
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(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) (.f64 (sqrt.f64 1/2) p))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (neg.f64 (/.f64 p x)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
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(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
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(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
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(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
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(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 (/.f64 p x) (neg.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.0b	(pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4)
	0.6b	(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)
✓	0.6b	(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)
✓	3.0b	(pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4)

Compiler

Compiled 35 to 22 computations (37.1% saved)

series23.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	(pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4)
3.0ms	p	@	0	(pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4)
2.0ms	p	@	inf	(pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4)
2.0ms	x	@	inf	(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)
2.0ms	x	@	inf	(pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4)

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

970×	`pow1_binary64`
902×	`add-log-exp_binary64`
902×	`log1p-expm1-u_binary64`
902×	`expm1-log1p-u_binary64`
108×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	235	21
2	2566	21

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4)
(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)

Outputs

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

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

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Rules

755×	`associate-/r*_binary64`
430×	`distribute-rgt-in_binary64`
425×	`distribute-lft-in_binary64`
315×	`fma-def_binary64`
249×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	2926
1	933	2567
2	3721	2225

Stop Event

1×	node limit

Counts

87 → 107

Calls

Call 1

Inputs
(pow.f64 1/2 1/4)
(+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4))
(+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (+.f64 (pow.f64 1/2 1/4) (.f64 -3/128 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 p 2)) (pow.f64 1/2 1/4)))))
(+.f64 (.f64 -7/1024 (.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (pow.f64 1/2 1/4))) (+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (+.f64 (pow.f64 1/2 1/4) (.f64 -3/128 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 p 2)) (pow.f64 1/2 1/4))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (*.f64 -1 (log.f64 (/.f64 1 x))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) p) x)) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) p) x)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2))) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x))))))) (pow.f64 x 2)) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x))))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) p) x)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2))) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x))))))) (pow.f64 x 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 p 3)) (+.f64 (.f64 -1/48 (pow.f64 p 3)) (.f64 -2/3 (pow.f64 p 3)))) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x))))))) (pow.f64 x 3)) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (*.f64 -1 (log.f64 (/.f64 1 x)))))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) p) x)) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) p) x)) (+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) (+.f64 (.f64 1/8 (pow.f64 p 2)) (*.f64 -1/2 (pow.f64 p 2)))) (pow.f64 x 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) p) x)) (+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) (+.f64 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2)))) (pow.f64 x 2)) (.f64 -1 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) (+.f64 (.f64 1/48 (pow.f64 p 3)) (+.f64 (.f64 2/3 (pow.f64 p 3)) (.f64 -1/4 (pow.f64 p 3))))) (pow.f64 x 3))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (*.f64 -1/4 x)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (.f64 -1/4 x))))) p) x)) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (.f64 -1/4 x))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (.f64 -1/4 x))))) p) x)) (+.f64 (.f64 -3/8 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (.f64 -1/4 x))))) (pow.f64 p 2)) (pow.f64 x 2))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (*.f64 -1/4 x)))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (.f64 -1/4 x))))) p) x)) (+.f64 (.f64 -3/8 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (.f64 -1/4 x))))) (pow.f64 p 2)) (pow.f64 x 2))) (+.f64 (.f64 -7/16 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (.f64 -1/4 x))))) (pow.f64 p 3)) (pow.f64 x 3))) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 p)) (log.f64 (.f64 -1/4 x))))))))
(pow.f64 1/2 1/4)
(+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4))
(+.f64 (.f64 (pow.f64 1/2 1/4) (/.f64 (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))) (pow.f64 p 2))) (+.f64 (.f64 -1/8 (*.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4)))
(+.f64 (.f64 (pow.f64 1/2 1/4) (/.f64 (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))) (pow.f64 p 2))) (+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (+.f64 (.f64 (/.f64 (+.f64 (.f64 1/256 (pow.f64 x 3)) (+.f64 (.f64 -1/3072 (pow.f64 x 3)) (*.f64 -1/96 (pow.f64 x 3)))) (pow.f64 p 3)) (pow.f64 1/2 1/4)) (pow.f64 1/2 1/4))))
(pow.f64 1/2 1/4)
(+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4))
(+.f64 (.f64 (pow.f64 1/2 1/4) (/.f64 (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))) (pow.f64 p 2))) (+.f64 (.f64 -1/8 (*.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4)))
(+.f64 (.f64 (pow.f64 1/2 1/4) (/.f64 (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))) (pow.f64 p 2))) (+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (+.f64 (.f64 -1 (.f64 (/.f64 (+.f64 (.f64 1/96 (pow.f64 x 3)) (+.f64 (.f64 -1/256 (pow.f64 x 3)) (.f64 1/3072 (pow.f64 x 3)))) (pow.f64 p 3)) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 (+.f64 (.f64 -3/64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 2))) (*.f64 1/64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 2)))) (pow.f64 x 2)) (sqrt.f64 1/2)))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (.f64 (+.f64 (.f64 -3/64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 2))) (.f64 1/64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 2)))) (pow.f64 x 2)) (+.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -7/512 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3))) (.f64 3/512 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)))) (pow.f64 x 3)))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (*.f64 -1 (log.f64 (/.f64 1 x)))))) 2)
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2) p) x)) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2) p) x)) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2)) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2) (.f64 1/4 (/.f64 (.f64 (pow.f64 p 2) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2)) (pow.f64 x 2))))))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2) p) x)) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 p 3)) (+.f64 (.f64 -1/48 (pow.f64 p 3)) (.f64 -2/3 (pow.f64 p 3)))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2)) (pow.f64 x 3))) (+.f64 (.f64 2 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2))) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2)) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2) (+.f64 (.f64 -1 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2))) (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2) p)) (pow.f64 x 3))) (.f64 1/4 (/.f64 (.f64 (pow.f64 p 2) (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) 2)) (pow.f64 x 2))))))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) (.f64 -1 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) p) x)))
(+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) (pow.f64 p 2)) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) p) x)) (.f64 2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2)))) (pow.f64 x 2))))))
(+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) (pow.f64 p 2)) (pow.f64 x 2))) (+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) (+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) p) x)) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) (.f64 (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2))) p)) (.f64 2 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) (+.f64 (.f64 1/48 (pow.f64 p 3)) (+.f64 (.f64 2/3 (pow.f64 p 3)) (.f64 -1/4 (pow.f64 p 3))))))) (pow.f64 x 3))) (.f64 2 (/.f64 (.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) 2) (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2)))) (pow.f64 x 2)))))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (*.f64 -1 (log.f64 p))))) 2)
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (.f64 -1 (/.f64 (.f64 p (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2)) x)))
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (+.f64 (.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 2))) (.f64 -3/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 2)))) (pow.f64 p 2)) (.f64 -1 (/.f64 (.f64 p (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (*.f64 -1 (log.f64 p))))) 2)) x))))
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (+.f64 (.f64 (+.f64 (.f64 -7/8 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 3))) (.f64 3/8 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 3)))) (pow.f64 p 3)) (+.f64 (.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 2))) (.f64 -3/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 2)))) (pow.f64 p 2)) (.f64 -1 (/.f64 (.f64 p (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2)) x)))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))) (pow.f64 p 2))) (.f64 1/64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))) (pow.f64 p 2))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))) x)) (pow.f64 p 3))) (+.f64 (.f64 1/64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))))) (pow.f64 p 3))) (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/256 (pow.f64 x 3)) (+.f64 (.f64 -1/3072 (pow.f64 x 3)) (*.f64 -1/96 (pow.f64 x 3))))) (pow.f64 p 3)))))))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))) (pow.f64 p 2))) (.f64 1/64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))) (pow.f64 p 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/96 (pow.f64 x 3)) (+.f64 (.f64 -1/256 (pow.f64 x 3)) (.f64 1/3072 (pow.f64 x 3)))))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))) x))) (.f64 1/8 (.f64 (sqrt.f64 1/2) (.f64 x (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))))))) (pow.f64 p 3))) (.f64 1/64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))))

Outputs
(pow.f64 1/2 1/4)
(+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (pow.f64 1/2 1/4))
(fma.f64 -1/8 (/.f64 (*.f64 x (pow.f64 1/2 1/4)) p) (pow.f64 1/2 1/4))
(.f64 (+.f64 (.f64 -1/8 (/.f64 x p)) 1) (pow.f64 1/2 1/4))
(.f64 (+.f64 (/.f64 (.f64 -1/8 x) p) 1) (pow.f64 1/2 1/4))
(+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (+.f64 (pow.f64 1/2 1/4) (.f64 -3/128 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 p 2)) (pow.f64 1/2 1/4)))))
(+.f64 (fma.f64 -1/8 (/.f64 (.f64 x (pow.f64 1/2 1/4)) p) (pow.f64 1/2 1/4)) (.f64 -3/128 (/.f64 (.f64 (.f64 x x) (pow.f64 1/2 1/4)) (*.f64 p p))))
(+.f64 (pow.f64 1/2 1/4) (.f64 (pow.f64 1/2 1/4) (+.f64 (.f64 -3/128 (.f64 (/.f64 x p) (/.f64 x p))) (.f64 -1/8 (/.f64 x p)))))
(.f64 (pow.f64 1/2 1/4) (+.f64 (+.f64 (/.f64 (.f64 -1/8 x) p) 1) (.f64 -3/128 (.f64 (/.f64 x p) (/.f64 x p)))))
(+.f64 (.f64 -7/1024 (.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (pow.f64 1/2 1/4))) (+.f64 (.f64 -1/8 (.f64 (/.f64 x p) (pow.f64 1/2 1/4))) (+.f64 (pow.f64 1/2 1/4) (.f64 -3/128 (.f64 (/.f64 (pow.f64 x 2) (pow.f64 p 2)) (pow.f64 1/2 1/4))))))
(fma.f64 -7/1024 (/.f64 (.f64 (pow.f64 x 3) (pow.f64 1/2 1/4)) (pow.f64 p 3)) (+.f64 (fma.f64 -1/8 (/.f64 (.f64 x (pow.f64 1/2 1/4)) p) (pow.f64 1/2 1/4)) (.f64 -3/128 (/.f64 (.f64 (.f64 x x) (pow.f64 1/2 1/4)) (.f64 p p)))))
(+.f64 (.f64 (+.f64 (.f64 -3/128 (.f64 (/.f64 x p) (/.f64 x p))) 1) (pow.f64 1/2 1/4)) (.f64 (pow.f64 1/2 1/4) (+.f64 (.f64 -7/1024 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 -1/8 (/.f64 x p)))))
(+.f64 (.f64 (pow.f64 1/2 1/4) (+.f64 (+.f64 (.f64 -7/1024 (pow.f64 (/.f64 x p) 3)) (/.f64 (.f64 -1/8 x) p)) (.f64 -3/128 (*.f64 (/.f64 x p) (/.f64 x p))))) (pow.f64 1/2 1/4))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (*.f64 -1 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x)))
(*.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) p) x)) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x))))) (/.f64 x p)) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x))))))
(fma.f64 -1/2 (*.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x))) x) p) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x))))
(fma.f64 -1/2 (/.f64 p (/.f64 (/.f64 x (pow.f64 p -1/4)) (pow.f64 (.f64 x -1/4) 1/4))) (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) p) x)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2))) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x))))))) (pow.f64 x 2)) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x))))))))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x))))) (/.f64 x p)) (+.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x))))) (/.f64 (.f64 (.f64 p p) -3/8) (/.f64 (*.f64 x x) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x)))))))))
(fma.f64 -1/2 (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x))) x) p) (+.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x))) (.f64 (/.f64 (.f64 p (.f64 p -3/8)) (*.f64 x x)) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x))))))
(fma.f64 -1/2 (/.f64 p (/.f64 (/.f64 x (pow.f64 p -1/4)) (pow.f64 (.f64 x -1/4) 1/4))) (.f64 (+.f64 (/.f64 (.f64 p (.f64 p -3/8)) (.f64 x x)) 1) (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x)))))) p) x)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 p 2)) (.f64 -1/2 (pow.f64 p 2))) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x))))))) (pow.f64 x 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 p 3)) (+.f64 (.f64 -1/48 (pow.f64 p 3)) (.f64 -2/3 (pow.f64 p 3)))) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (.f64 -1 (log.f64 (/.f64 1 x))))))) (pow.f64 x 3)) (exp.f64 (.f64 1/4 (+.f64 (log.f64 (neg.f64 (.f64 1/4 (/.f64 1 p)))) (*.f64 -1 (log.f64 (/.f64 1 x)))))))))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x))))) (/.f64 x p)) (+.f64 (/.f64 (.f64 (.f64 p p) -3/8) (/.f64 (.f64 x x) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x))))))) (+.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x))))) (/.f64 (fma.f64 1/4 (pow.f64 p 3) (.f64 (pow.f64 p 3) -11/16)) (/.f64 (pow.f64 x 3) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (/.f64 1/4 p))) (neg.f64 (neg.f64 (log.f64 x))))))))))
(+.f64 (+.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x))) (.f64 (/.f64 (.f64 (pow.f64 p 3) -7/16) (pow.f64 x 3)) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x))))) (fma.f64 -1/2 (.f64 (/.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x))) x) p) (.f64 (/.f64 (.f64 p (.f64 p -3/8)) (*.f64 x x)) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (/.f64 -1/4 p)) (log.f64 x))))))
(fma.f64 -1/2 (/.f64 p (/.f64 (/.f64 x (pow.f64 p -1/4)) (pow.f64 (.f64 x -1/4) 1/4))) (+.f64 (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)) (.f64 (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)) (+.f64 (/.f64 (.f64 p (.f64 p -3/8)) (.f64 x x)) (/.f64 (.f64 (pow.f64 p 3) -7/16) (pow.f64 x 3))))))
(exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p)))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (/.f64 1/4 p))))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (/.f64 1/4 p)) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 (/.f64 1/4 p) 1/4))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) p) x)) (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (/.f64 1/4 p)))) (/.f64 x p)) (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (/.f64 1/4 p)))))
(fma.f64 -1/2 (/.f64 p (/.f64 x (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (/.f64 1/4 p)) (log.f64 (/.f64 -1 x)))))) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (/.f64 1/4 p)) (log.f64 (/.f64 -1 x)))))
(fma.f64 -1/2 (.f64 (/.f64 p x) (.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 (/.f64 1/4 p) 1/4))) (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 (/.f64 1/4 p) 1/4)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) p) x)) (+.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) (/.f64 (.f64 (exp.f64 (.f64 1/4 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 1/4 p))))) (+.f64 (.f64 1/8 (pow.f64 p 2)) (*.f64 -1/2 (pow.f64 p 2)))) (pow.f64 x 2))))
(+.f64 (fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (/.f64 1/4 p)))) (/.f64 x p)) (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (/.f64 1/4 p))))) (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 (/.f64 1/4 p)))) (/.f64 (.f64 x x) (.f64 (*.f64 p p) -3/8))))
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(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 p) (log.f64 (.f64 x -1/4)))) 2) (fma.f64 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 p) (log.f64 (.f64 x -1/4)))) 2) (.f64 x x)) -1/2) (.f64 p p) (neg.f64 (/.f64 p (/.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 p) (log.f64 (.f64 x -1/4)))) 2))))))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 x -1/4)) (log.f64 p))) 2) (-.f64 (.f64 (.f64 p p) (.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 x -1/4)) (log.f64 p))) 2) (.f64 x x)))) (.f64 (/.f64 p x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 x -1/4)) (log.f64 p))) 2))))
(+.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)) 2) (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)) 2) (.f64 x x)) (.f64 p (.f64 p -1/2))) (.f64 (/.f64 p x) (pow.f64 (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)) 2))))
(+.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (+.f64 (.f64 (+.f64 (.f64 -7/8 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 3))) (.f64 3/8 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 3)))) (pow.f64 p 3)) (+.f64 (.f64 (+.f64 (.f64 1/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 2))) (.f64 -3/4 (/.f64 (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2) (pow.f64 x 2)))) (pow.f64 p 2)) (.f64 -1 (/.f64 (.f64 p (pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1/4 x)) (.f64 -1 (log.f64 p))))) 2)) x)))))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 p) (log.f64 (.f64 x -1/4)))) 2) (fma.f64 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 p) (log.f64 (.f64 x -1/4)))) 2) (pow.f64 x 3)) -1/2) (pow.f64 p 3) (fma.f64 (.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 p) (log.f64 (.f64 x -1/4)))) 2) (.f64 x x)) -1/2) (.f64 p p) (neg.f64 (/.f64 p (/.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 p) (log.f64 (.f64 x -1/4)))) 2)))))))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 x -1/4)) (log.f64 p))) 2) (-.f64 (fma.f64 (pow.f64 p 3) (.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 x -1/4)) (log.f64 p))) 2) (pow.f64 x 3))) (.f64 (.f64 p p) (.f64 -1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 x -1/4)) (log.f64 p))) 2) (.f64 x x))))) (.f64 (/.f64 p x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 x -1/4)) (log.f64 p))) 2))))
(+.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)) 2) (-.f64 (.f64 (.f64 p p) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)) 2) (.f64 x x))) (.f64 p (.f64 -1/2 (/.f64 (pow.f64 (.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)) 2) (pow.f64 x 3)))))) (.f64 (/.f64 p x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1/4 p) 1/4) (pow.f64 x 1/4)) 2))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))) (pow.f64 p 2))) (.f64 1/64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(+.f64 (fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2)) (fma.f64 2 (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 p p) (.f64 (.f64 x x) -3/128))) (.f64 1/64 (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 p p) (.f64 x x))))))
(+.f64 (fma.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x (.f64 x -3/128))) (.f64 1/64 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x)))) (fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2)))
(+.f64 (fma.f64 1/64 (.f64 (.f64 (/.f64 x p) (/.f64 x p)) (sqrt.f64 1/2)) (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 x x) -3/64)) (.f64 p p))) (fma.f64 -1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2)))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))) (pow.f64 p 2))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))) x)) (pow.f64 p 3))) (+.f64 (.f64 1/64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 x (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))))) (pow.f64 p 3))) (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/256 (pow.f64 x 3)) (+.f64 (.f64 -1/3072 (pow.f64 x 3)) (*.f64 -1/96 (pow.f64 x 3))))) (pow.f64 p 3)))))))))
(+.f64 (fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2)) (fma.f64 2 (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 p p) (.f64 (.f64 x x) -3/128))) (fma.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 p 3) (.f64 x (.f64 (.f64 x x) -3/128)))) (fma.f64 1/64 (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 p p) (.f64 x x))) (fma.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 p 3) (.f64 x (.f64 (.f64 x x) -3/128)))) (.f64 2 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 p 3) (fma.f64 1/256 (pow.f64 x 3) (*.f64 (pow.f64 x 3) -11/1024))))))))))
(+.f64 (fma.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x (.f64 x -3/128))) (fma.f64 -1/8 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (.f64 (pow.f64 x 3) -3/128)) (fma.f64 1/64 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x)) (fma.f64 -1/8 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (.f64 (pow.f64 x 3) -3/128)) (.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (.f64 (pow.f64 x 3) -7/1024))))))) (fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2)))
(+.f64 (+.f64 (fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2)) (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 x x) -3/64)) (.f64 p p))) (fma.f64 -1/8 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (.f64 (pow.f64 x 3) -3/128)) (fma.f64 1/64 (.f64 (.f64 (/.f64 x p) (/.f64 x p)) (sqrt.f64 1/2)) (fma.f64 -1/8 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (.f64 (pow.f64 x 3) -3/128)) (.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 p 3)) (.f64 (pow.f64 x 3) -7/1024)))))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (sqrt.f64 1/2))
(fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2))
(fma.f64 -1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))) (pow.f64 p 2))) (.f64 1/64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2))))))
(+.f64 (fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2)) (fma.f64 2 (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 p p) (.f64 (.f64 x x) -3/128))) (.f64 1/64 (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 p p) (.f64 x x))))))
(+.f64 (fma.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x (.f64 x -3/128))) (.f64 1/64 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x)))) (fma.f64 -1/4 (*.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2)))
(+.f64 (fma.f64 1/64 (.f64 (.f64 (/.f64 x p) (/.f64 x p)) (sqrt.f64 1/2)) (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 x x) -3/64)) (.f64 p p))) (fma.f64 -1/4 (*.f64 (/.f64 x p) (sqrt.f64 1/2)) (sqrt.f64 1/2)))
(+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 1/2) x) p)) (+.f64 (sqrt.f64 1/2) (+.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))) (pow.f64 p 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 2 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/96 (pow.f64 x 3)) (+.f64 (.f64 -1/256 (pow.f64 x 3)) (.f64 1/3072 (pow.f64 x 3)))))) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2))) x))) (.f64 1/8 (.f64 (sqrt.f64 1/2) (.f64 x (+.f64 (.f64 1/128 (pow.f64 x 2)) (.f64 -1/32 (pow.f64 x 2)))))))) (pow.f64 p 3))) (.f64 1/64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 x 2)) (pow.f64 p 2)))))))
(+.f64 (fma.f64 -1/4 (/.f64 (sqrt.f64 1/2) (/.f64 p x)) (sqrt.f64 1/2)) (fma.f64 2 (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 p p) (.f64 (.f64 x x) -3/128))) (fma.f64 -1 (/.f64 (fma.f64 2 (.f64 (fma.f64 1/96 (pow.f64 x 3) (.f64 (pow.f64 x 3) -11/3072)) (sqrt.f64 1/2)) (.f64 1/8 (+.f64 (.f64 (sqrt.f64 1/2) (.f64 x (.f64 (.f64 x x) -3/128))) (.f64 (sqrt.f64 1/2) (.f64 x (.f64 (.f64 x x) -3/128)))))) (pow.f64 p 3)) (.f64 1/64 (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 p p) (*.f64 x x)))))))
(+.f64 (fma.f64 2 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x (.f64 x -3/128))) (-.f64 (.f64 1/64 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 p p)) (.f64 x x))) (/.f64 (fma.f64 2 (.f64 (.f64 (pow.f64 x 3) 7/1024) (sqrt.f64 1/2)) (.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 x 3) -3/128)) 1/4)) (pow.f64 p 3)))) (fma.f64 -1/4 (.f64 (/.f64 (sqrt.f64 1/2) p) x) (sqrt.f64 1/2)))
(fma.f64 -1/4 (.f64 (/.f64 x p) (sqrt.f64 1/2)) (-.f64 (+.f64 (sqrt.f64 1/2) (fma.f64 1/64 (.f64 (.f64 (/.f64 x p) (/.f64 x p)) (sqrt.f64 1/2)) (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 x x) -3/64)) (.f64 p p)))) (/.f64 (fma.f64 2 (.f64 (.f64 (pow.f64 x 3) 7/1024) (sqrt.f64 1/2)) (.f64 1/8 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 x 3) -3/64)))) (pow.f64 p 3))))

eval163.0ms (2.3%)

Compiler: Compiled 7263 to 5634 computations (22.4% saved)

prune52.0ms (0.7%)

Pruning

15 alts after pruning (6 fresh and 9 done)

	Pruned	Kept	Total
New	312	5	317
Fresh	5	1	6
Picked	1	0	1
Done	0	9	9
Total	318	15	333

Error

2.3b

Counts

333 → 15

Alt Table

Click to see full alt table

Status	Error	Program
▶	53.1b	(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 p p))) (neg.f64 (sqrt.f64 1/2))) x)
✓	54.3b	(.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p) (sqrt.f64 1/2))
✓	42.9b	(sqrt.f64 (*.f64 1/2 2))
✓	28.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
▶	54.3b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
✓	54.3b	(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
✓	26.3b	(sqrt.f64 1/2)
▶	54.3b	(.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) p) x) (sqrt.f64 1/2))
	56.7b	(/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 p (sqrt.f64 2))) 2) (neg.f64 (sqrt.f64 1/2))) x)
▶	26.8b	(pow.f64 (pow.f64 1/2 1/4) 2)
✓	54.3b	(/.f64 (.f64 (.f64 p (sqrt.f64 2)) (neg.f64 (sqrt.f64 1/2))) x)
✓	13.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))
▶	52.6b	(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))
✓	60.0b	(sqrt.f64 (*.f64 1/2 (+.f64 1 -1)))
✓	29.2b	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))

Compiler

Compiled 240 to 201 computations (16.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	1.0b	(pow.f64 (pow.f64 1/2 1/4) 2)
✓	1.0b	(pow.f64 (pow.f64 1/2 1/4) 2)

Compiler

Compiled 13 to 13 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite35.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

414×	`pow1_binary64`
405×	`add-sqr-sqrt_binary64`
393×	`*-un-lft-identity_binary64`
390×	`add-log-exp_binary64`
390×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	130	3
2	1221	3

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(pow.f64 (pow.f64 1/2 1/4) 2)

Outputs

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

25 → 25

Calls

Call 1

Inputs

Outputs

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	25.6b	(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))
	0.2b	(/.f64 p (*.f64 x x))
	0.2b	(.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p)))
	0.1b	(.f64 (/.f64 p (.f64 x x)) p)
✓	0.1b	(.f64 (/.f64 p (.f64 x x)) p)
✓	0.2b	(.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p)))
✓	0.2b	(/.f64 p (*.f64 x x))
✓	25.6b	(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))

Compiler

Compiled 53 to 18 computations (66% saved)

series10.0ms (0.1%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
1.0ms	p	@	inf	(/.f64 p (*.f64 x x))
1.0ms	p	@	0	(/.f64 p (*.f64 x x))
1.0ms	p	@	inf	(.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p)))
1.0ms	x	@	0	(.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p)))
1.0ms	p	@	0	(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))

rewrite73.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

532×	`log-prod_binary64`
407×	`prod-exp_binary64`
389×	`exp-prod_binary64`
322×	`pow-prod-down_binary64`
282×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	234	25
2	2642	25

Stop Event

1×	node limit

Counts

4 → 242

Calls

Call 1

Inputs
(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))
(/.f64 p (*.f64 x x))
(.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p)))
(.f64 (/.f64 p (.f64 x x)) p)

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

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Rules

879×	`fma-def_binary64`
754×	`unswap-sqr_binary64`
696×	`times-frac_binary64`
347×	`fma-neg_binary64`
336×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	760
1	23	760
2	44	760
3	112	760
4	460	760
5	3484	760
6	5329	760
7	6141	760

Stop Event

1×	node limit

Counts

338 → 189

Calls

Call 1

Inputs
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(*.f64 -1 (/.f64 p x))
(*.f64 -1 (/.f64 p x))
(*.f64 -1 (/.f64 p x))
(*.f64 -1 (/.f64 p x))
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(*.f64 -1 (/.f64 p x))
(*.f64 -1 (/.f64 p x))
(*.f64 -1 (/.f64 p x))
(*.f64 -1 (/.f64 p x))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 p (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))

Outputs
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(*.f64 -1 (/.f64 p x))
(neg.f64 (/.f64 p x))
(/.f64 (neg.f64 p) x)
(*.f64 -1 (/.f64 p x))
(neg.f64 (/.f64 p x))
(/.f64 (neg.f64 p) x)
(*.f64 -1 (/.f64 p x))
(neg.f64 (/.f64 p x))
(/.f64 (neg.f64 p) x)
(*.f64 -1 (/.f64 p x))
(neg.f64 (/.f64 p x))
(/.f64 (neg.f64 p) x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(/.f64 p x)
(*.f64 -1 (/.f64 p x))
(neg.f64 (/.f64 p x))
(/.f64 (neg.f64 p) x)
(*.f64 -1 (/.f64 p x))
(neg.f64 (/.f64 p x))
(/.f64 (neg.f64 p) x)
(*.f64 -1 (/.f64 p x))
(neg.f64 (/.f64 p x))
(/.f64 (neg.f64 p) x)
(*.f64 -1 (/.f64 p x))
(neg.f64 (/.f64 p x))
(/.f64 (neg.f64 p) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 p (pow.f64 x 2))
(/.f64 p (*.f64 x x))
(/.f64 (/.f64 p x) x)
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))

localize17.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (neg.f64 (sqrt.f64 2)) p)
	0.4b	(.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) p) x) (sqrt.f64 1/2))
	0.3b	(/.f64 (*.f64 (neg.f64 (sqrt.f64 2)) p) x)
✓	0.3b	(/.f64 (*.f64 (neg.f64 (sqrt.f64 2)) p) x)
✓	0.4b	(.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) p) x) (sqrt.f64 1/2))
✓	0.5b	(*.f64 (neg.f64 (sqrt.f64 2)) p)

Compiler

Compiled 35 to 28 computations (20% saved)

series4.0ms (0.1%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	p	@	0	(*.f64 (neg.f64 (sqrt.f64 2)) p)
0.0ms	p	@	0	(/.f64 (*.f64 (neg.f64 (sqrt.f64 2)) p) x)
0.0ms	p	@	inf	(.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) p) x) (sqrt.f64 1/2))
0.0ms	p	@	0	(.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) p) x) (sqrt.f64 1/2))
0.0ms	p	@	-inf	(.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) p) x) (sqrt.f64 1/2))

rewrite111.0ms (1.6%)

Algorithm

3×	egg-rewrite-iter-limit
3×	egg-rewrite
1×	batch-egg-rewrite

Rules

113×	`add-sqr-sqrt_binary64`
113×	`add-sqr-sqrt_binary64`
107×	`*-un-lft-identity_binary64`
107×	`pow1_binary64`
107×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	233	35
2	2971	35
0	6	8
1	125	8
2	1469	8
0	6	8
0	11	16
1	233	16
2	2971	16
0	11	16
0	8	11
1	172	11
2	2302	11
0	8	11

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

3 → 24

Calls

Call 1

Inputs
(*.f64 (neg.f64 (sqrt.f64 2)) p)
(.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) p) x) (sqrt.f64 1/2))
(/.f64 (*.f64 (neg.f64 (sqrt.f64 2)) p) x)

Outputs

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

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

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

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary64`
185×	`fma-neg_binary64`
67×	`associate-/l*_binary64`
57×	`div-sub_binary64`
56×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	744
1	36	744
2	84	744
3	191	744
4	356	744
5	569	744
6	731	744
7	878	744
8	1197	744
9	1559	744
10	1675	744
11	1676	744

Stop Event

1×

saturated

Counts

84 → 30

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))

Outputs
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(*.f64 p (neg.f64 (sqrt.f64 2)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 p (sqrt.f64 1/2)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 p (sqrt.f64 1/2))))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 p (sqrt.f64 1/2)) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 1/2) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
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(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
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(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
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(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p))
(*.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 p))
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 p x))

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
✓	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))
✓	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))

Compiler

Compiled 34 to 19 computations (44.1% saved)

series5.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
0.0ms	p	@	0	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
0.0ms	x	@	inf	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
0.0ms	p	@	-inf	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
0.0ms	p	@	inf	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))

rewrite50.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

897×	`pow1_binary64`
832×	`add-log-exp_binary64`
831×	`log1p-expm1-u_binary64`
831×	`expm1-log1p-u_binary64`
815×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	232	13
2	2837	13

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

Inputs
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x)))

Outputs

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

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

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
269×	`fma-neg_binary64`
67×	`associate-/l*_binary64`
62×	`div-sub_binary64`
59×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	648
1	32	648
2	77	648
3	185	648
4	350	648
5	556	648
6	762	648
7	919	648
8	1090	648
9	1586	648
10	2029	648
11	2030	648

Stop Event

1×

saturated

Counts

108 → 64

Calls

Call 1

Inputs
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))

Outputs
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 (sqrt.f64 1/2) p) (/.f64 (neg.f64 (sqrt.f64 2)) x))
(/.f64 (sqrt.f64 1/2) (/.f64 (/.f64 x (sqrt.f64 2)) (neg.f64 p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x (*.f64 (sqrt.f64 1/2) p))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 (neg.f64 p) (sqrt.f64 1/2)))
(.f64 (.f64 (sqrt.f64 1/2) p) (/.f64 (neg.f64 (sqrt.f64 2)) x))
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(neg.f64 (*.f64 (/.f64 (sqrt.f64 2) x) p))
(*.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) p)
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(neg.f64 (*.f64 (/.f64 (sqrt.f64 2) x) p))
(*.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) p)
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(neg.f64 (*.f64 (/.f64 (sqrt.f64 2) x) p))
(*.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) p)
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) p) x))
(neg.f64 (/.f64 (sqrt.f64 2) (/.f64 x p)))
(neg.f64 (*.f64 (/.f64 (sqrt.f64 2) x) p))
(*.f64 (neg.f64 (/.f64 (sqrt.f64 2) x)) p)
(*.f64 p (/.f64 (neg.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 p) x))

localize19.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	30.9b	(sqrt.f64 (.f64 2 (.f64 p p)))
	0.4b	(.f64 (sqrt.f64 (.f64 2 (*.f64 p p))) (neg.f64 (sqrt.f64 1/2)))
	0.0b	(.f64 2 (.f64 p p))
✓	0.0b	(.f64 2 (.f64 p p))
✓	0.4b	(.f64 (sqrt.f64 (.f64 2 (*.f64 p p))) (neg.f64 (sqrt.f64 1/2)))
✓	30.9b	(sqrt.f64 (.f64 2 (.f64 p p)))

Compiler

Compiled 47 to 30 computations (36.2% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	p	@	0	(.f64 2 (.f64 p p))
0.0ms	p	@	inf	(.f64 2 (.f64 p p))
0.0ms	p	@	0	(sqrt.f64 (.f64 2 (.f64 p p)))
0.0ms	p	@	-inf	(.f64 (sqrt.f64 (.f64 2 (*.f64 p p))) (neg.f64 (sqrt.f64 1/2)))
0.0ms	p	@	inf	(sqrt.f64 (.f64 2 (.f64 p p)))

rewrite120.0ms (1.7%)

Algorithm

3×	egg-rewrite
1×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	206	32
2	2349	32
0	6	9
1	122	6
2	1363	6
0	10	16
1	206	16
2	2349	16
0	10	16
0	5	7
1	101	7
2	1124	7

Stop Event

1×	node limit
1×	iter limit
1×	unsound
1×	node limit
1×	unsound

Counts

3 → 46

Calls

Call 1

Inputs
(sqrt.f64 (.f64 2 (.f64 p p)))
(.f64 (sqrt.f64 (.f64 2 (*.f64 p p))) (neg.f64 (sqrt.f64 1/2)))
(.f64 2 (.f64 p p))

Outputs

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

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

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

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1403×	`fma-def_binary64`
543×	`fma-neg_binary64`
472×	`distribute-rgt-neg-in_binary64`
365×	`distribute-lft-neg-in_binary64`
331×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	312
1	32	312
2	78	312
3	161	312
4	400	312
5	1161	312
6	1806	312
7	2854	312
8	3550	312
9	4017	312
10	4384	312
11	4924	312
12	5838	312
13	7363	312

Stop Event

1×	node limit

Counts

82 → 54

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))
(*.f64 2 (pow.f64 p 2))

Outputs
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(*.f64 (sqrt.f64 2) p)
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(.f64 -1 (.f64 (sqrt.f64 2) p))
(neg.f64 (*.f64 (sqrt.f64 2) p))
(*.f64 (sqrt.f64 2) (neg.f64 p))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 p (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 2) (.f64 p (neg.f64 (sqrt.f64 1/2))))
(.f64 p (.f64 (sqrt.f64 1/2) (neg.f64 (sqrt.f64 2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 p (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 2) (.f64 p (neg.f64 (sqrt.f64 1/2))))
(.f64 p (.f64 (sqrt.f64 1/2) (neg.f64 (sqrt.f64 2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 p (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 2) (.f64 p (neg.f64 (sqrt.f64 1/2))))
(.f64 p (.f64 (sqrt.f64 1/2) (neg.f64 (sqrt.f64 2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 p (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 2) (.f64 p (neg.f64 (sqrt.f64 1/2))))
(.f64 p (.f64 (sqrt.f64 1/2) (neg.f64 (sqrt.f64 2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 p (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 2) (.f64 p (neg.f64 (sqrt.f64 1/2))))
(.f64 p (.f64 (sqrt.f64 1/2) (neg.f64 (sqrt.f64 2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 p (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 2) (.f64 p (neg.f64 (sqrt.f64 1/2))))
(.f64 p (.f64 (sqrt.f64 1/2) (neg.f64 (sqrt.f64 2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 p (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 2) (.f64 p (neg.f64 (sqrt.f64 1/2))))
(.f64 p (.f64 (sqrt.f64 1/2) (neg.f64 (sqrt.f64 2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 p)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2))))
(.f64 (.f64 p (sqrt.f64 1/2)) (neg.f64 (sqrt.f64 2)))
(.f64 p (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 2) (.f64 p (neg.f64 (sqrt.f64 1/2))))
(.f64 p (.f64 (sqrt.f64 1/2) (neg.f64 (sqrt.f64 2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 p)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p))
(.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2)))
(.f64 p (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p))
(.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2)))
(.f64 p (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p))
(.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2)))
(.f64 p (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) p))
(.f64 (sqrt.f64 2) (.f64 p (sqrt.f64 1/2)))
(.f64 p (.f64 (sqrt.f64 2) (sqrt.f64 1/2)))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))
(*.f64 2 (pow.f64 p 2))
(.f64 2 (.f64 p p))
(.f64 p (.f64 p 2))
(.f64 p (.f64 2 p))

eval93.0ms (1.3%)

Compiler: Compiled 4167 to 2764 computations (33.7% saved)

prune63.0ms (0.9%)

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	356	6	362
Fresh	1	0	1
Picked	1	0	1
Done	8	5	13
Total	366	11	377

Error

Counts

377 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	52.7b	(/.f64 1 (/.f64 x p))
✓	42.9b	(sqrt.f64 (*.f64 1/2 2))
	54.2b	(/.f64 (neg.f64 p) x)
✓	28.9b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
	52.5b	(*.f64 p (/.f64 1 x))
	52.5b	(/.f64 p x)
✓	26.3b	(sqrt.f64 1/2)
	54.2b	(/.f64 -1 (/.f64 x p))
✓	13.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))
	26.8b	(-.f64 (+.f64 1 (sqrt.f64 1/2)) 1)
✓	29.2b	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))

Compiler

Compiled 88 to 71 computations (19.3% saved)

regimes256.0ms (3.6%)

Counts

33 → 2

Calls

Call 1

Inputs
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 1 (/.f64 x p))
(*.f64 p (/.f64 1 x))
(/.f64 -1 (/.f64 x p))
(sqrt.f64 1/2)
(sqrt.f64 (*.f64 1/2 2))
(sqrt.f64 (*.f64 1/2 2))
(-.f64 (+.f64 1 (sqrt.f64 1/2)) 1)
(sqrt.f64 (*.f64 1/2 (+.f64 1 -1)))
(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))
(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))
(pow.f64 (pow.f64 1/2 1/4) 2)
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) p) x) (sqrt.f64 1/2))
(.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p) (sqrt.f64 1/2))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(/.f64 (.f64 (.f64 p (sqrt.f64 2)) (neg.f64 (sqrt.f64 1/2))) x)
(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
(.f64 (.f64 -1 (/.f64 (*.f64 (sqrt.f64 2) p) x)) (sqrt.f64 1/2))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 p p))) (neg.f64 (sqrt.f64 1/2))) x)
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)
(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))))
(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))))
(/.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 p (sqrt.f64 2))) 2) (neg.f64 (sqrt.f64 1/2))) x)
(pow.f64 (pow.f64 (fma.f64 (/.f64 x (hypot.f64 x (*.f64 2 p))) 1/2 1/2) 1/4) 2)
(.f64 (.f64 (sqrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p)) (sqrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p))) (sqrt.f64 1/2))
(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p)) (cbrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p))) (cbrt.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p))) (sqrt.f64 1/2))

Outputs
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 p p))) (neg.f64 (sqrt.f64 1/2))) x)
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))

Calls

12 calls:

82.0ms	p
73.0ms	x
14.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
13.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
13.0ms	(.f64 (.f64 4 p) p)

Results

Error	Segments	Branch
9.6b	5	`p`
9.5b	4	`x`
6.0b	2	`(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))`
6.0b	2	`(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))`
6.0b	2	`(.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))`
6.0b	2	`(.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))`
6.0b	2	`(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))`
6.0b	2	`(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))`
6.0b	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))`
6.0b	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))`
13.5b	1	`(.f64 (.f64 4 p) p)`
13.5b	1	`(.f64 (.f64 4 p) p)`

Compiler

Compiled 482 to 355 computations (26.3% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-1.991252423464601e-9

Compiler

Compiled 24 to 18 computations (25% saved)

regimes140.0ms (2%)

Counts

24 → 6

Calls

Call 1

Inputs
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 1 (/.f64 x p))
(*.f64 p (/.f64 1 x))
(/.f64 -1 (/.f64 x p))
(sqrt.f64 1/2)
(sqrt.f64 (*.f64 1/2 2))
(sqrt.f64 (*.f64 1/2 2))
(-.f64 (+.f64 1 (sqrt.f64 1/2)) 1)
(sqrt.f64 (*.f64 1/2 (+.f64 1 -1)))
(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 -1/2 (/.f64 x p)))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))
(sqrt.f64 (.f64 1/2 (.f64 2 (.f64 (/.f64 p (.f64 x x)) p))))
(pow.f64 (pow.f64 1/2 1/4) 2)
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(.f64 (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) p) x) (sqrt.f64 1/2))
(.f64 (.f64 (/.f64 (neg.f64 (sqrt.f64 2)) x) p) (sqrt.f64 1/2))
(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 1/2) (/.f64 (neg.f64 p) x)))
(/.f64 (.f64 (.f64 p (sqrt.f64 2)) (neg.f64 (sqrt.f64 1/2))) x)
(*.f64 (/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x p)) (sqrt.f64 1/2))
(.f64 (.f64 -1 (/.f64 (*.f64 (sqrt.f64 2) p) x)) (sqrt.f64 1/2))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 p p))) (neg.f64 (sqrt.f64 1/2))) x)

Outputs
(sqrt.f64 1/2)
(/.f64 p x)
(sqrt.f64 (*.f64 1/2 2))
(/.f64 (neg.f64 p) x)
(sqrt.f64 (*.f64 1/2 2))
(sqrt.f64 1/2)

Calls

2 calls:

71.0ms	p
62.0ms	x

Results

Error	Segments	Branch
12.7b	6	`p`
18.6b	5	`x`

Compiler

Compiled 195 to 143 computations (26.7% saved)

bsearch289.0ms (4.1%)

Algorithm

5×	binary-search

Steps

Time	Left	Right
48.0ms	8.640475694562824e-85	4.9724960893072815e-74
54.0ms	4.971237565362955e-121	3.687962994762444e-120
59.0ms	6.794751093088959e-165	1.326440113130313e-164
82.0ms	9.596726413784006e-304	3.1046041899476636e-302
46.0ms	-1.7224308668959296e-51	-9.93464044228702e-55

Compiler

Compiled 24 to 18 computations (25% saved)

regimes36.0ms (0.5%)

Counts

6 → 4

Calls

Call 1

Inputs
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 1 (/.f64 x p))
(*.f64 p (/.f64 1 x))
(/.f64 -1 (/.f64 x p))
(sqrt.f64 1/2)

Outputs
(sqrt.f64 1/2)
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(sqrt.f64 1/2)

Calls

2 calls:

19.0ms	p
15.0ms	x

Results

Error	Segments	Branch
17.0b	4	`p`
21.5b	3	`x`

Compiler

Compiled 32 to 19 computations (40.6% saved)

bsearch167.0ms (2.4%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
49.0ms	4.971237565362955e-121	3.687962994762444e-120
74.0ms	1.2009860048556524e-292	1.0406135645039503e-282
43.0ms	-1.7224308668959296e-51	-9.93464044228702e-55

Compiler

Compiled 24 to 18 computations (25% saved)

regimes25.0ms (0.4%)

Accuracy

Total -14.3b remaining (-30.5%)

Threshold costs -14.3b (-30.5%)

Counts

5 → 2

Calls

Call 1

Inputs
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 1 (/.f64 x p))
(*.f64 p (/.f64 1 x))
(/.f64 -1 (/.f64 x p))

Outputs
(/.f64 p x)
(/.f64 (neg.f64 p) x)

Calls

2 calls:

16.0ms	x
8.0ms	p

Results

Error	Segments	Branch
46.8b	2	`p`
50.3b	3	`x`

Compiler

Compiled 30 to 17 computations (43.3% saved)

bsearch67.0ms (1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
67.0ms	1.2009860048556524e-292	1.0406135645039503e-282

Compiler

Compiled 24 to 18 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
8×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	162
1	73	162
2	87	162
3	98	162
4	104	162
5	106	162

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))) -1) (/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 p p))) (neg.f64 (sqrt.f64 1/2))) x) (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))))
(if (<=.f64 p -46436644309368304/26959946667150639794667015087019630673637144422540572481103610249216) (sqrt.f64 1/2) (if (<=.f64 p 5927731477428189/6176826577981891429214335532193521333299458305790469920559733826520701280761576748411876944013584121557222835214746457256769065471978560695404461668113357846725995613908885539687100455996497080726311269484641878313049544782247701984195048695347886851221010025401573777842206256568313675909006576801941109109732291903488) (/.f64 p x) (if (<=.f64 p 7217900914545607680/1062275985633534197379176413104937254659186235454063846398888276400807119721704485478325004530458571337778658972493002030693158675305414478819039957533174703887662541670786438063456256) (sqrt.f64 (.f64 1/2 2)) (if (<=.f64 p 2890630376143047/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248) (/.f64 (neg.f64 p) x) (if (<=.f64 p 3779777345080507/4374501449566023848745004454235242730706338861786424872851541212819905998398751846447026354046107648) (sqrt.f64 (.f64 1/2 2)) (sqrt.f64 1/2))))))
(if (<=.f64 p -46436644309368304/26959946667150639794667015087019630673637144422540572481103610249216) (sqrt.f64 1/2) (if (<=.f64 p 21590042959947264/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216) (/.f64 p x) (if (<=.f64 p 2890630376143047/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248) (/.f64 (neg.f64 p) x) (sqrt.f64 1/2))))
(if (<=.f64 p 21590042959947264/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216) (/.f64 p x) (/.f64 (neg.f64 p) x))
(/.f64 p x)

Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))) -1) (/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 p p))) (neg.f64 (sqrt.f64 1/2))) x) (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) -1) (/.f64 (.f64 (sqrt.f64 (.f64 2 (.f64 p p))) (neg.f64 (sqrt.f64 1/2))) x) (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 p 2)))))))
(if (<=.f64 p -46436644309368304/26959946667150639794667015087019630673637144422540572481103610249216) (sqrt.f64 1/2) (if (<=.f64 p 5927731477428189/6176826577981891429214335532193521333299458305790469920559733826520701280761576748411876944013584121557222835214746457256769065471978560695404461668113357846725995613908885539687100455996497080726311269484641878313049544782247701984195048695347886851221010025401573777842206256568313675909006576801941109109732291903488) (/.f64 p x) (if (<=.f64 p 7217900914545607680/1062275985633534197379176413104937254659186235454063846398888276400807119721704485478325004530458571337778658972493002030693158675305414478819039957533174703887662541670786438063456256) (sqrt.f64 (.f64 1/2 2)) (if (<=.f64 p 2890630376143047/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248) (/.f64 (neg.f64 p) x) (if (<=.f64 p 3779777345080507/4374501449566023848745004454235242730706338861786424872851541212819905998398751846447026354046107648) (sqrt.f64 (.f64 1/2 2)) (sqrt.f64 1/2))))))
(if (<=.f64 p -2902290269335519/1684996666696914987166688442938726917102321526408785780068975640576) (sqrt.f64 1/2) (if (<=.f64 p 5927731477428189/6176826577981891429214335532193521333299458305790469920559733826520701280761576748411876944013584121557222835214746457256769065471978560695404461668113357846725995613908885539687100455996497080726311269484641878313049544782247701984195048695347886851221010025401573777842206256568313675909006576801941109109732291903488) (/.f64 p x) (if (<=.f64 p 7048731361860945/1037378892220248239628101965922790287753111558060609224998914332422663202853227036599926762236775948572049471652825197295598787768852943826971718708528490921765295450850377380921344) 1 (if (<=.f64 p 2890630376143047/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248) (/.f64 (neg.f64 p) x) (if (<=.f64 p 3779777345080507/4374501449566023848745004454235242730706338861786424872851541212819905998398751846447026354046107648) 1 (sqrt.f64 1/2))))))
(if (<=.f64 p -46436644309368304/26959946667150639794667015087019630673637144422540572481103610249216) (sqrt.f64 1/2) (if (<=.f64 p 21590042959947264/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216) (/.f64 p x) (if (<=.f64 p 2890630376143047/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248) (/.f64 (neg.f64 p) x) (sqrt.f64 1/2))))
(if (<=.f64 p -2902290269335519/1684996666696914987166688442938726917102321526408785780068975640576) (sqrt.f64 1/2) (if (<=.f64 p 42168052656147/351111940402796075728379920075981393284761128699669252487168127261196632432619068618571244770327218791250222421623815151677323767215657465806342637967722899175327916845440400930277772658683777577056802640791026892262013051450122815378736544025053197584668966180832613749896964723593195907881555331297312768) (/.f64 p x) (if (<=.f64 p 2890630376143047/5814709794364855124394590463104036274829130885498544482251921593445114304907183386609528405710108524486100172850129423468276813028917248) (/.f64 (neg.f64 p) x) (sqrt.f64 1/2))))
(if (<=.f64 p 21590042959947264/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216) (/.f64 p x) (/.f64 (neg.f64 p) x))
(if (<=.f64 p 42168052656147/351111940402796075728379920075981393284761128699669252487168127261196632432619068618571244770327218791250222421623815151677323767215657465806342637967722899175327916845440400930277772658683777577056802640791026892262013051450122815378736544025053197584668966180832613749896964723593195907881555331297312768) (/.f64 p x) (/.f64 (neg.f64 p) x))
(/.f64 p x)

end60.0ms (0.8%)

Stop Event

1×

fuel

Compiler

Compiled 230 to 155 computations (32.6% saved)

Iter	Nodes	Cost
0	11	228
1	20	228
2	50	228
3	95	228
4	109	228
5	157	228
6	229	228
7	266	228
8	308	228
9	477	228
10	505	228

Iter	Nodes	Cost
0	11	228
1	20	228
2	50	228
3	95	228
4	109	228
5	157	228
6	229	228
7	266	228
8	308	228
9	477	228
10	505	228

Iter	Nodes	Cost
0	11	228
1	20	228
2	50	228
3	95	228
4	109	228
5	157	228
6	229	228
7	266	228
8	308	228
9	477	228
10	505	228