Details

analyze363.0ms (6.7%)

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 (50.2%)

Results

1.1s	6182×	body	64	valid
690.0ms	826×	body	2048	valid
378.0ms	528×	body	1024	valid
317.0ms	277×	body	4096	valid
132.0ms	256×	body	512	valid
58.0ms	130×	body	256	valid
17.0ms	57×	body	128	valid

preprocess25.0ms (0.5%)

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 19 to 14 computations (26.3% saved)

simplify8.0ms (0.2%)

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))

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

12.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p)))))
✓	0.0b	(.f64 4 (.f64 p p))
✓	0.4b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)
✓	14.9b	(sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))

series23.0ms (0.4%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
4.0ms	p	@	inf	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p)))))
2.0ms	x	@	-inf	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)
2.0ms	x	@	inf	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)
1.0ms	p	@	0	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)
1.0ms	p	@	inf	(.f64 4 (.f64 p p))

rewrite77.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

507×	`log-prod_binary64`
396×	`exp-prod_binary64`
295×	`pow-prod-down_binary64`
277×	`pow2_binary64`
192×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	56
1	228	38
2	2692	38

Stop Event

1×	node limit

Counts

4 → 148

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 x (.f64 p 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (.f64 p 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (.f64 p 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (.f64 p 2))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (.f64 p 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 x (.f64 p 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (.f64 p 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (hypot.f64 x (.f64 p 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 x (.f64 p 2))) (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 2)) (cbrt.f64 (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 x (.f64 p 2))) (sqrt.f64 (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (.f64 p 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (.f64 2 (log.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 6) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x (.f64 p 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 2)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x (.f64 p 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 x (.f64 p 2)))) 2)) (cbrt.f64 (log.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 x (.f64 p 2))))) (sqrt.f64 (log.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (.f64 p 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 x (.f64 p 2)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 x (.f64 p 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (hypot.f64 x (.f64 p 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (hypot.f64 x (.f64 p 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 x (.f64 p 2)))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 x (.f64 p 2)))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 x (.f64 p 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (.f64 p 2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (.f64 p 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (*.f64 p 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2)))) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)) (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)) 2) (cbrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)) (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2)))) 3) 1/8) (+.f64 (pow.f64 (.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2)))) 2) (-.f64 1/4 (.f64 (.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2)))) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2)))) 2) 1/4) (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))) 2)) (cbrt.f64 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (sqrt.f64 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 p (.f64 4 p)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 4) (.f64 p p))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 4) (.f64 p p)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4) (.f64 p p)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4) (.f64 p p)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 p (.f64 4 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 p (.f64 4 p)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 p 4) 16) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 p 2) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (.f64 p 2)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 p 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (.f64 p (.f64 4 p))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 p (.f64 4 p)))) 2)) (cbrt.f64 (log.f64 (.f64 p (.f64 4 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 p (.f64 4 p))))) (sqrt.f64 (log.f64 (.f64 p (.f64 4 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 p 4) 16))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 4) (.f64 p p)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 p (.f64 4 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 p 2) 6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 p (.f64 4 p))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 p (.f64 4 p))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (.f64 p 2) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (cbrt.f64 (.f64 p 2)) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 p 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 p (.f64 4 p))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 p (.f64 4 p))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 p (.f64 4 p))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2)))) (.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (hypot.f64 x (.f64 p 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (hypot.f64 x (.f64 p 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (/.f64 1 (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 x (hypot.f64 x (.f64 p 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 x (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))) (pow.f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))) 2) (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))) (sqrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 x) (/.f64 1 (neg.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (hypot.f64 x (.f64 p 2))) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (hypot.f64 x (.f64 p 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 p 2))) -2) (/.f64 x (cbrt.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 2))) (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (hypot.f64 x (.f64 p 2)) 2))) (/.f64 (sqrt.f64 x) (cbrt.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 x (.f64 p 2)) -1/2) (/.f64 x (sqrt.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (hypot.f64 x (.f64 p 2)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (hypot.f64 x (.f64 p 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 p 2))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 p 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 x (.f64 p 2)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 x (.f64 p 2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (hypot.f64 x (.f64 p 2)) x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 x (hypot.f64 x (.f64 p 2))))) 2)) (cbrt.f64 (log.f64 (/.f64 x (hypot.f64 x (.f64 p 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))) (sqrt.f64 (log.f64 (/.f64 x (hypot.f64 x (.f64 p 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 p 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (hypot.f64 x (.f64 p 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 p 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 x (.f64 p 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 x (hypot.f64 x (.f64 p 2))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 x (hypot.f64 x (.f64 p 2))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (hypot.f64 x (.f64 p 2)) x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (.f64 (log.f64 x) 1) (log.f64 (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (.f64 (.f64 2 (log.f64 (hypot.f64 x (.f64 p 2)))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (.f64 (log.f64 x) 1) (.f64 (.f64 2 (log.f64 (hypot.f64 x (.f64 p 2)))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (.f64 (log.f64 (hypot.f64 x (.f64 p 2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (.f64 (log.f64 x) 1) (.f64 (log.f64 (hypot.f64 x (.f64 p 2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (hypot.f64 x (.f64 p 2)))))))))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

632×	`times-frac_binary64`
511×	`associate-/r*_binary64`
467×	`associate-/l*_binary64`
424×	`*-commutative_binary64`
376×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	2375
1	726	2264
2	2520	2074

Stop Event

1×	node limit

Counts

232 → 250

Calls

Call 1

Inputs
(*.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))))
1/2
(+.f64 1/2 (*.f64 1/4 (/.f64 x p)))
(+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 1/4 (/.f64 x p))))
(+.f64 (.f64 1/2 (.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 p 6))) (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2)) (.f64 p (pow.f64 x 5)))) (+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 1/4 (/.f64 x p)))))
1
(+.f64 1 (*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 (.f64 -1/4 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4))) (+.f64 1 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))))
(+.f64 (.f64 -1/4 (/.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 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1/4 (/.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 (pow.f64 p 2) (pow.f64 x 2))
(+.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (.f64 1/4 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (*.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4))))
(+.f64 (.f64 1/4 (/.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 (pow.f64 p 2) (pow.f64 x 2)) (.f64 1/4 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (*.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4)))))
(+.f64 (.f64 1/4 (/.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 (.f64 1/4 (/.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 (pow.f64 p 2) (pow.f64 x 2)) (.f64 1/4 (/.f64 (+.f64 (.f64 -16 (pow.f64 p 4)) (pow.f64 (*.f64 -2 (pow.f64 p 2)) 2)) (pow.f64 x 4))))))
1
(+.f64 1 (*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (pow.f64 p 4) (.f64 (pow.f64 x 2) (-.f64 (*.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)))))))
(+.f64 1 (+.f64 (.f64 -1/4 (.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 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (pow.f64 p 4) (.f64 (pow.f64 x 2) (-.f64 (*.f64 16 (/.f64 1 (pow.f64 x 6))) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))))))))
1/2
(+.f64 1/2 (*.f64 1/4 (/.f64 x p)))
(+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 1/4 (/.f64 x p))))
(+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 (.f64 1/4 (/.f64 x p)) (.f64 -1/2 (/.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))))))
1/2
(+.f64 1/2 (*.f64 -1/4 (/.f64 x p)))
(+.f64 (.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 1/2 (.f64 -1/4 (/.f64 x p))))
(+.f64 (.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 1/2 (+.f64 (.f64 -1/4 (/.f64 x p)) (.f64 1/2 (/.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 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 2))
(*.f64 4 (pow.f64 p 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 (-.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)))))

Outputs
(*.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))))
(+.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 x (/.f64 p x)) (fma.f64 2 p (/.f64 -1/64 (/.f64 (pow.f64 p 3) (pow.f64 x 4)))))
(+.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))))
(fma.f64 1/4 (/.f64 (.f64 x x) p) (fma.f64 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5)) (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 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5)) (fma.f64 2 p (*.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))))))
(fma.f64 1/4 (/.f64 x (/.f64 p x)) (fma.f64 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5)) (fma.f64 2 p (/.f64 -1/64 (/.f64 (pow.f64 p 3) (pow.f64 x 4))))))
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 -1 x)
(neg.f64 x)
(+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) x)) (.f64 -1 x))
(fma.f64 -2 (/.f64 (*.f64 p p) x) (neg.f64 x))
(-.f64 (*.f64 (/.f64 p (/.f64 x p)) -2) x)
(-.f64 (.f64 (.f64 (/.f64 p x) p) -2) 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)))
(fma.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (fma.f64 -2 (/.f64 (*.f64 p p) x) (neg.f64 x)))
(-.f64 (fma.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (*.f64 (/.f64 p (/.f64 x p)) -2)) x)
(fma.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (-.f64 (.f64 (.f64 (/.f64 p x) p) -2) 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))))
(fma.f64 -4 (/.f64 (pow.f64 p 6) (pow.f64 x 5)) (fma.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (fma.f64 -2 (/.f64 (*.f64 p p) x) (neg.f64 x))))
(fma.f64 (/.f64 (pow.f64 p 6) (pow.f64 x 5)) -4 (-.f64 (fma.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (*.f64 (/.f64 p (/.f64 x p)) -2)) x))
(fma.f64 (/.f64 (pow.f64 p 6) (pow.f64 x 5)) -4 (fma.f64 2 (/.f64 (pow.f64 p 4) (pow.f64 x 3)) (-.f64 (.f64 (.f64 (/.f64 p x) p) -2) x)))
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))))
(+.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 x (/.f64 p x)) (fma.f64 2 p (/.f64 -1/64 (/.f64 (pow.f64 p 3) (pow.f64 x 4)))))
(+.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))))
(fma.f64 1/4 (/.f64 (.f64 x x) p) (fma.f64 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5)) (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 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5)) (fma.f64 2 p (*.f64 -1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3))))))
(fma.f64 1/4 (/.f64 x (/.f64 p x)) (fma.f64 1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5)) (fma.f64 2 p (/.f64 -1/64 (/.f64 (pow.f64 p 3) (pow.f64 x 4))))))
(*.f64 -2 p)
(*.f64 p -2)
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 x 2) p)) (.f64 -2 p))
(fma.f64 -1/4 (/.f64 (.f64 x x) p) (.f64 p -2))
(fma.f64 p -2 (*.f64 (/.f64 x (/.f64 p x)) -1/4))
(fma.f64 (/.f64 x (/.f64 p x)) -1/4 (*.f64 p -2))
(+.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 p -2)))
(fma.f64 (/.f64 x (/.f64 p x)) -1/4 (fma.f64 p -2 (/.f64 (*.f64 (pow.f64 x 4) 1/64) (pow.f64 p 3))))
(+.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))))
(fma.f64 -1/512 (/.f64 (pow.f64 x 6) (pow.f64 p 5)) (fma.f64 -1/4 (/.f64 (.f64 x x) p) (fma.f64 1/64 (/.f64 (pow.f64 x 4) (pow.f64 p 3)) (.f64 p -2))))
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1/2
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1
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1
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1/2
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1/2
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(+.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))))))
(fma.f64 1/2 (/.f64 x p) (fma.f64 -1 (.f64 (+.f64 (/.f64 1/256 (pow.f64 p 8)) (.f64 -1/8 (/.f64 (-.f64 (/.f64 1/64 (pow.f64 p 6)) (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2)) (.f64 p p)))) (.f64 p (pow.f64 x 7))) (fma.f64 (-.f64 (/.f64 1/64 (pow.f64 p 6)) (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2)) (.f64 p (pow.f64 x 5)) (.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/16))))
(fma.f64 1/2 (/.f64 x p) (-.f64 (fma.f64 (-.f64 (/.f64 1/64 (pow.f64 p 6)) (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2)) (.f64 p (pow.f64 x 5)) (.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/16)) (.f64 (fma.f64 -1/8 (-.f64 (/.f64 1/64 (pow.f64 p 8)) (/.f64 (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2) (.f64 p p))) (/.f64 1/256 (pow.f64 p 8))) (*.f64 p (pow.f64 x 7)))))
(-.f64 (fma.f64 1/2 (/.f64 x p) (fma.f64 (-.f64 (/.f64 1/64 (pow.f64 p 6)) (pow.f64 (/.f64 -1/16 (pow.f64 p 3)) 2)) (.f64 p (pow.f64 x 5)) (.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/16))) (.f64 p (.f64 (fma.f64 -1/8 (+.f64 (/.f64 1/64 (pow.f64 p 8)) (/.f64 -1/256 (pow.f64 p 8))) (/.f64 1/256 (pow.f64 p 8))) (pow.f64 x 7))))
1
(+.f64 1 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (.f64 -2 (/.f64 (.f64 p p) (*.f64 x x))))
(fma.f64 -2 (*.f64 (/.f64 p x) (/.f64 p x)) 1)
(+.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 (fma.f64 -2 (/.f64 (.f64 p p) (.f64 x x)) (.f64 (/.f64 (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (*.f64 p p) -2) 2)) (pow.f64 x 4)) -1/2)))
(+.f64 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) 1) (/.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (/.f64 (pow.f64 x 4) -1/2)))
(+.f64 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) 1) (/.f64 (.f64 (pow.f64 p 4) -12) (/.f64 (pow.f64 x 4) -1/2)))
(+.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))))))
(+.f64 1 (fma.f64 -2 (/.f64 (.f64 p p) (.f64 x x)) (.f64 -1/2 (+.f64 (/.f64 (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2)) (pow.f64 x 4)) (/.f64 (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 x 6))))))
(+.f64 1 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) (.f64 -1/2 (+.f64 (/.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (pow.f64 x 4)) (/.f64 (fma.f64 (pow.f64 p 6) 64 (.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (.f64 2 (*.f64 p p)))) (pow.f64 x 6))))))
(+.f64 1 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) (.f64 -1/2 (+.f64 (/.f64 (.f64 (pow.f64 p 4) -12) (pow.f64 x 4)) (/.f64 (fma.f64 2 (.f64 p (.f64 p (.f64 (pow.f64 p 4) -12))) (*.f64 (pow.f64 p 6) 64)) (pow.f64 x 6))))))
-1
(-.f64 (*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) 1)
(fma.f64 2 (/.f64 (.f64 p p) (.f64 x x)) -1)
(fma.f64 2 (*.f64 (/.f64 p x) (/.f64 p x)) -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 (fma.f64 2 (/.f64 (.f64 p p) (.f64 x x)) (.f64 1/2 (/.f64 (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (*.f64 p p) -2) 2)) (pow.f64 x 4)))) -1)
(fma.f64 2 (.f64 (/.f64 p x) (/.f64 p x)) (fma.f64 1/2 (/.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (pow.f64 x 4)) -1))
(fma.f64 2 (.f64 (/.f64 p x) (/.f64 p x)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 p 4) -12) (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)
(+.f64 (fma.f64 1/2 (/.f64 (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 x 6)) (fma.f64 2 (/.f64 (.f64 p p) (.f64 x x)) (.f64 1/2 (/.f64 (fma.f64 -16 (pow.f64 p 4) (pow.f64 (.f64 (.f64 p p) -2) 2)) (pow.f64 x 4))))) -1)
(fma.f64 1/2 (/.f64 (fma.f64 (pow.f64 p 6) 64 (.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (.f64 2 (.f64 p p)))) (pow.f64 x 6)) (fma.f64 2 (.f64 (/.f64 p x) (/.f64 p x)) (fma.f64 1/2 (/.f64 (fma.f64 (pow.f64 p 4) -16 (.f64 4 (pow.f64 p 4))) (pow.f64 x 4)) -1)))
(fma.f64 1/2 (/.f64 (fma.f64 2 (.f64 p (.f64 p (.f64 (pow.f64 p 4) -12))) (.f64 (pow.f64 p 6) 64)) (pow.f64 x 6)) (fma.f64 2 (.f64 (/.f64 p x) (/.f64 p x)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 p 4) -12) (pow.f64 x 4)) -1)))
1
(+.f64 1 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (.f64 -2 (/.f64 (.f64 p p) (*.f64 x x))))
(fma.f64 -2 (*.f64 (/.f64 p x) (/.f64 p x)) 1)
(+.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 (fma.f64 1/2 (.f64 (pow.f64 p 4) (.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)))) (.f64 -2 (/.f64 (.f64 p p) (.f64 x x)))))
(+.f64 1 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) (.f64 (pow.f64 p 4) (.f64 (.f64 (*.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) 1/2))))
(+.f64 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) 1) (.f64 (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (.f64 1/2 (.f64 (*.f64 x x) (pow.f64 p 4)))))
(+.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))))))
(fma.f64 -1/2 (.f64 (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))) (.f64 (.f64 x x) (pow.f64 p 6))) (+.f64 1 (fma.f64 1/2 (.f64 (pow.f64 p 4) (.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)))) (.f64 -2 (/.f64 (.f64 p p) (.f64 x x))))))
(+.f64 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) (.f64 (pow.f64 p 4) (.f64 (.f64 (.f64 x x) (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2))) 1/2))) (fma.f64 -1/2 (.f64 (.f64 x x) (.f64 (pow.f64 p 6) (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))))) 1))
(+.f64 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) (.f64 (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) (.f64 1/2 (.f64 (.f64 x x) (pow.f64 p 4))))) (fma.f64 (+.f64 (/.f64 1 (/.f64 x (/.f64 (-.f64 (/.f64 16 (pow.f64 x 6)) (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2)) x))) (/.f64 -32 (pow.f64 x 8))) (.f64 x (*.f64 x (pow.f64 p 6))) 1))
(*.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))))
(fma.f64 1/2 (/.f64 x p) (*.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/16))
(fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/16 (*.f64 1/2 (/.f64 x p)))
(+.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)))))
(fma.f64 1/2 (/.f64 x p) (fma.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (neg.f64 (/.f64 (fma.f64 -1/64 (pow.f64 x 4) (pow.f64 (.f64 (.f64 x x) -1/16) 2)) (/.f64 (pow.f64 p 5) x)))))
(-.f64 (fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/16 (.f64 1/2 (/.f64 x p))) (.f64 (/.f64 (fma.f64 -1/64 (pow.f64 x 4) (*.f64 (pow.f64 x 4) 1/256)) (pow.f64 p 5)) x))
(-.f64 (fma.f64 1/2 (/.f64 x p) (.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/16)) (.f64 x (/.f64 (*.f64 (pow.f64 x 4) -3/256) (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))))))
(fma.f64 1/2 (/.f64 x p) (fma.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (.f64 -1 (+.f64 (/.f64 (fma.f64 -1/64 (pow.f64 x 4) (pow.f64 (.f64 (.f64 x x) -1/16) 2)) (/.f64 (pow.f64 p 5) x)) (/.f64 (fma.f64 1/8 (.f64 (.f64 x x) (fma.f64 -1/64 (pow.f64 x 4) (pow.f64 (.f64 (.f64 x x) -1/16) 2))) (.f64 (pow.f64 x 6) 1/256)) (/.f64 (pow.f64 p 7) x))))))
(fma.f64 1/2 (/.f64 x p) (fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/16 (-.f64 (/.f64 (.f64 (neg.f64 x) (fma.f64 (pow.f64 x 6) 1/256 (.f64 (fma.f64 -1/64 (pow.f64 x 4) (.f64 (pow.f64 x 4) 1/256)) (.f64 (.f64 x x) 1/8)))) (pow.f64 p 7)) (.f64 (/.f64 (fma.f64 -1/64 (pow.f64 x 4) (*.f64 (pow.f64 x 4) 1/256)) (pow.f64 p 5)) x))))
(-.f64 (fma.f64 1/2 (/.f64 x p) (.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/16)) (.f64 x (+.f64 (/.f64 (.f64 (pow.f64 x 4) -3/256) (pow.f64 p 5)) (/.f64 (fma.f64 (pow.f64 x 6) 1/256 (.f64 (.f64 (pow.f64 x 4) -3/256) (.f64 (*.f64 x x) 1/8))) (pow.f64 p 7)))))
(*.f64 -1/2 (/.f64 x p))
(*.f64 (/.f64 x p) -1/2)
(*.f64 (/.f64 -1/2 p) x)
(+.f64 (.f64 -1/2 (/.f64 x p)) (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))
(fma.f64 -1/2 (/.f64 x p) (*.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/16))
(fma.f64 (/.f64 x p) -1/2 (/.f64 1/16 (/.f64 (pow.f64 p 3) (pow.f64 x 3))))
(fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/16 (*.f64 (/.f64 -1/2 p) x))
(+.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))))
(fma.f64 -1/2 (/.f64 x p) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (/.f64 (fma.f64 -1/64 (pow.f64 x 4) (pow.f64 (.f64 (.f64 x x) -1/16) 2)) (/.f64 (pow.f64 p 5) x))))
(fma.f64 (/.f64 x p) -1/2 (fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/16 (.f64 (/.f64 (fma.f64 -1/64 (pow.f64 x 4) (.f64 (pow.f64 x 4) 1/256)) (pow.f64 p 5)) x)))
(fma.f64 (/.f64 x p) -1/2 (fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/16 (.f64 x (/.f64 (.f64 (pow.f64 x 4) -3/256) (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)))))
(fma.f64 -1/2 (/.f64 x p) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (+.f64 (/.f64 (fma.f64 -1/64 (pow.f64 x 4) (pow.f64 (.f64 (.f64 x x) -1/16) 2)) (/.f64 (pow.f64 p 5) x)) (/.f64 (fma.f64 1/8 (.f64 (.f64 x x) (fma.f64 -1/64 (pow.f64 x 4) (pow.f64 (.f64 (.f64 x x) -1/16) 2))) (*.f64 (pow.f64 x 6) 1/256)) (/.f64 (pow.f64 p 7) x)))))
(+.f64 (fma.f64 (/.f64 x p) -1/2 (fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/16 (.f64 (/.f64 (fma.f64 -1/64 (pow.f64 x 4) (.f64 (pow.f64 x 4) 1/256)) (pow.f64 p 5)) x))) (.f64 (/.f64 (fma.f64 (pow.f64 x 6) 1/256 (.f64 (fma.f64 -1/64 (pow.f64 x 4) (.f64 (pow.f64 x 4) 1/256)) (.f64 (*.f64 x x) 1/8))) (pow.f64 p 7)) x))
(fma.f64 (/.f64 x p) -1/2 (fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/16 (.f64 x (+.f64 (/.f64 (.f64 (pow.f64 x 4) -3/256) (pow.f64 p 5)) (/.f64 (fma.f64 (pow.f64 x 6) 1/256 (.f64 (.f64 (pow.f64 x 4) -3/256) (.f64 (.f64 x x) 1/8))) (pow.f64 p 7))))))

prune1.0s (18.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	248	2	250
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	2	251

Error

4.9b

Counts

251 → 2

Alt Table

Status	Error	Program
	52.4b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))
▶	12.5b	(sqrt.f64 (exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)))

Compiler

Compiled 5756 to 4374 computations (24% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3))
✓	0.2b	(log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))
✓	0.4b	(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)
✓	0.5b	(.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)

series26.0ms (0.5%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
9.0ms	x	@	-inf	(.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)
4.0ms	x	@	inf	(.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)
2.0ms	p	@	0	(.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)
1.0ms	x	@	0	(.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)
1.0ms	p	@	inf	(.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)

rewrite99.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

593×	`log-prod_binary64`
326×	`pow2_binary64`
278×	`pow-prod-down_binary64`
231×	`expm1-udef_binary64`
231×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	72
1	306	60
2	3565	60

Stop Event

1×	node limit

Counts

4 → 227

Calls

Call 1

Inputs
(.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)
(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)
(log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))
(exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3))

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

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-/r*_binary64`
606×	`associate-/l*_binary64`
561×	`associate-+l+_binary64`
513×	`distribute-rgt-in_binary64`
511×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	3708
1	785	3358
2	2928	3170

Stop Event

1×	node limit

Counts

323 → 198

Calls

Call 1

Inputs
(log.f64 1/2)
(+.f64 (*.f64 1/2 (/.f64 x p)) (log.f64 1/2))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2)))))
(+.f64 (.f64 -1/48 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2))))))
(*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (pow.f64 p 4)) (.f64 -12 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (pow.f64 x 4))))
(+.f64 (.f64 1/720 (/.f64 (+.f64 (.f64 -240 (pow.f64 p 6)) (+.f64 (.f64 -360 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2))) (.f64 -360 (+.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 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (pow.f64 p 4)) (.f64 -12 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (pow.f64 x 4)))))
(+.f64 (.f64 1/720 (/.f64 (+.f64 (.f64 -240 (pow.f64 p 6)) (+.f64 (.f64 -360 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2))) (.f64 -360 (+.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 (.f64 1/40320 (/.f64 (+.f64 (.f64 -20160 (.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 (.f64 -20160 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 4))) (+.f64 (.f64 -10080 (pow.f64 p 8)) (+.f64 (.f64 -5040 (pow.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) 2)) (.f64 -20160 (+.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)))))))))) (pow.f64 x 8))) (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (pow.f64 p 4)) (.f64 -12 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (pow.f64 x 4))))))
(+.f64 (*.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2)))
(+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (*.f64 (pow.f64 p 2) (pow.f64 x 2)))) (log.f64 (pow.f64 p 2))))
(+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (.f64 (pow.f64 p 2) (pow.f64 x 2)))) (+.f64 (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (/.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 p 2))) (.f64 -3 (/.f64 (pow.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (*.f64 2 (pow.f64 p 4))) 2) (pow.f64 p 4)))) (pow.f64 x 4))) (log.f64 (pow.f64 p 2)))))
(+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (.f64 (pow.f64 p 2) (pow.f64 x 2)))) (+.f64 (.f64 1/720 (/.f64 (+.f64 (.f64 -360 (/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (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 8 (pow.f64 p 8)) (.f64 -2 (.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 p 2)))))) (pow.f64 p 2))) (+.f64 (.f64 -30 (/.f64 (pow.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) 3) (pow.f64 p 6))) (.f64 -180 (/.f64 (.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (+.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 p 4))))) (pow.f64 x 6))) (+.f64 (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (/.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 p 2))) (.f64 -3 (/.f64 (pow.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) 2) (pow.f64 p 4)))) (pow.f64 x 4))) (log.f64 (pow.f64 p 2))))))
(*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(+.f64 (.f64 5/2 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 (.f64 5/2 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (*.f64 -22/3 (/.f64 (pow.f64 p 6) (pow.f64 x 6)))))
(+.f64 (.f64 1/40320 (.f64 (-.f64 (.f64 20160 (-.f64 (.f64 60 (/.f64 1 (pow.f64 x 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2) (.f64 16 (/.f64 1 (pow.f64 x 6)))) (pow.f64 x 2))))) (.f64 473760 (/.f64 1 (pow.f64 x 8)))) (pow.f64 p 8))) (+.f64 (.f64 5/2 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -22/3 (/.f64 (pow.f64 p 6) (pow.f64 x 6))))))
(log.f64 1/2)
(+.f64 (*.f64 1/2 (/.f64 x p)) (log.f64 1/2))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2)))))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 1/6 (/.f64 (+.f64 (.f64 -3/8 (pow.f64 x 3)) (.f64 1/4 (pow.f64 x 3))) (pow.f64 p 3))) (+.f64 (log.f64 1/2) (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2))))))
(log.f64 1/2)
(+.f64 (*.f64 -1/2 (/.f64 x p)) (log.f64 1/2))
(+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2)))))
(+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 -3/8 (pow.f64 x 3)) (.f64 1/4 (pow.f64 x 3))) (pow.f64 p 3))) (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2))))))
1/2
(+.f64 1/2 (*.f64 1/4 (/.f64 x p)))
(+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 1/4 (/.f64 x p))))
(+.f64 1/2 (+.f64 (.f64 3/512 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (*.f64 1/4 (/.f64 x p)))))
1
(+.f64 1 (*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4)))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4))) (.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 x 6))))))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (*.f64 2 (pow.f64 p 4))) (pow.f64 x 4))) (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 x 4))) (+.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (.f64 -1/2 (/.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 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 x 4))) (+.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (+.f64 (.f64 -1/2 (/.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 -1/2 (/.f64 (+.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 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 p 4))) (+.f64 (.f64 8 (pow.f64 p 8)) (.f64 -2 (.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 p 2)))))) (pow.f64 x 8))))))
1
(+.f64 1 (*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (*.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
1/2
(+.f64 1/2 (*.f64 1/4 (/.f64 x p)))
(+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 1/4 (/.f64 x p))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (.f64 -1/128 (pow.f64 x 5))) (pow.f64 p 5))) (+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (*.f64 1/4 (/.f64 x p)))))
1/2
(+.f64 1/2 (*.f64 -1/4 (/.f64 x p)))
(+.f64 (.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 1/2 (.f64 -1/4 (/.f64 x p))))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (.f64 -1/128 (pow.f64 x 5))) (pow.f64 p 5))) (+.f64 (.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 1/2 (*.f64 -1/4 (/.f64 x p)))))
(log.f64 1/2)
(+.f64 (*.f64 1/2 (/.f64 x p)) (log.f64 1/2))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2)))))
(+.f64 (.f64 -1/48 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2))))))
(*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (pow.f64 p 4)) (.f64 -12 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (pow.f64 x 4))))
(+.f64 (.f64 1/720 (/.f64 (+.f64 (.f64 -240 (pow.f64 p 6)) (+.f64 (.f64 -360 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2))) (.f64 -360 (+.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 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (pow.f64 p 4)) (.f64 -12 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (pow.f64 x 4)))))
(+.f64 (.f64 1/720 (/.f64 (+.f64 (.f64 -240 (pow.f64 p 6)) (+.f64 (.f64 -360 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2))) (.f64 -360 (+.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 (.f64 1/40320 (/.f64 (+.f64 (.f64 -20160 (.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 (.f64 -20160 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 4))) (+.f64 (.f64 -10080 (pow.f64 p 8)) (+.f64 (.f64 -5040 (pow.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) 2)) (.f64 -20160 (+.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)))))))))) (pow.f64 x 8))) (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (pow.f64 p 4)) (.f64 -12 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (pow.f64 x 4))))))
(+.f64 (*.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2)))
(+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (*.f64 (pow.f64 p 2) (pow.f64 x 2)))) (log.f64 (pow.f64 p 2))))
(+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (.f64 (pow.f64 p 2) (pow.f64 x 2)))) (+.f64 (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (/.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 p 2))) (.f64 -3 (/.f64 (pow.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (*.f64 2 (pow.f64 p 4))) 2) (pow.f64 p 4)))) (pow.f64 x 4))) (log.f64 (pow.f64 p 2)))))
(+.f64 (.f64 2 (log.f64 (/.f64 -1 x))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (.f64 (pow.f64 p 2) (pow.f64 x 2)))) (+.f64 (.f64 1/720 (/.f64 (+.f64 (.f64 -360 (/.f64 (+.f64 (.f64 2 (.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (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 8 (pow.f64 p 8)) (.f64 -2 (.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 p 2)))))) (pow.f64 p 2))) (+.f64 (.f64 -30 (/.f64 (pow.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) 3) (pow.f64 p 6))) (.f64 -180 (/.f64 (.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (+.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 p 4))))) (pow.f64 x 6))) (+.f64 (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (/.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 p 2))) (.f64 -3 (/.f64 (pow.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) 2) (pow.f64 p 4)))) (pow.f64 x 4))) (log.f64 (pow.f64 p 2))))))
(*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(+.f64 (.f64 5/2 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 (.f64 5/2 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (*.f64 -22/3 (/.f64 (pow.f64 p 6) (pow.f64 x 6)))))
(+.f64 (.f64 1/40320 (.f64 (-.f64 (.f64 20160 (-.f64 (.f64 60 (/.f64 1 (pow.f64 x 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -2 (pow.f64 x 3)) 2) (.f64 16 (/.f64 1 (pow.f64 x 6)))) (pow.f64 x 2))))) (.f64 473760 (/.f64 1 (pow.f64 x 8)))) (pow.f64 p 8))) (+.f64 (.f64 5/2 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -22/3 (/.f64 (pow.f64 p 6) (pow.f64 x 6))))))
(log.f64 1/2)
(+.f64 (*.f64 1/2 (/.f64 x p)) (log.f64 1/2))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2)))))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (.f64 1/6 (/.f64 (+.f64 (.f64 -3/8 (pow.f64 x 3)) (.f64 1/4 (pow.f64 x 3))) (pow.f64 p 3))) (+.f64 (log.f64 1/2) (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2))))))
(log.f64 1/2)
(+.f64 (*.f64 -1/2 (/.f64 x p)) (log.f64 1/2))
(+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2)))))
(+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 -3/8 (pow.f64 x 3)) (.f64 1/4 (pow.f64 x 3))) (pow.f64 p 3))) (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2))))))
1/2
(+.f64 1/2 (*.f64 1/4 (/.f64 x p)))
(+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 1/4 (/.f64 x p))))
(+.f64 1/2 (+.f64 (.f64 3/512 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (*.f64 1/4 (/.f64 x p)))))
1
(+.f64 1 (*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4)))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4))) (.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 x 6))))))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (*.f64 2 (pow.f64 p 4))) (pow.f64 x 4))) (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 x 4))) (+.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (.f64 -1/2 (/.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 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 x 4))) (+.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (+.f64 (.f64 -1/2 (/.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 -1/2 (/.f64 (+.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 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 p 4))) (+.f64 (.f64 8 (pow.f64 p 8)) (.f64 -2 (.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 p 2)))))) (pow.f64 x 8))))))
1
(+.f64 1 (*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (*.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
1/2
(+.f64 1/2 (*.f64 1/4 (/.f64 x p)))
(+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 1/4 (/.f64 x p))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (.f64 -1/128 (pow.f64 x 5))) (pow.f64 p 5))) (+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (*.f64 1/4 (/.f64 x p)))))
1/2
(+.f64 1/2 (*.f64 -1/4 (/.f64 x p)))
(+.f64 (.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 1/2 (.f64 -1/4 (/.f64 x p))))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (.f64 -1/128 (pow.f64 x 5))) (pow.f64 p 5))) (+.f64 (.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 1/2 (*.f64 -1/4 (/.f64 x p)))))

Outputs
(log.f64 1/2)
(+.f64 (*.f64 1/2 (/.f64 x p)) (log.f64 1/2))
(fma.f64 1/2 (/.f64 x p) (log.f64 1/2))
(+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2)))))
(+.f64 (fma.f64 1/2 (/.f64 x p) (log.f64 1/2)) (.f64 -1/8 (/.f64 (.f64 x x) (*.f64 p p))))
(fma.f64 1/2 (/.f64 x p) (fma.f64 -1/8 (*.f64 (/.f64 x p) (/.f64 x p)) (log.f64 1/2)))
(+.f64 (.f64 -1/48 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 (.f64 1/2 (/.f64 x p)) (+.f64 (log.f64 1/2) (*.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 p 2))))))
(fma.f64 -1/48 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (+.f64 (fma.f64 1/2 (/.f64 x p) (log.f64 1/2)) (.f64 -1/8 (/.f64 (.f64 x x) (*.f64 p p)))))
(fma.f64 -1/48 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (fma.f64 1/2 (/.f64 x p) (fma.f64 -1/8 (*.f64 (/.f64 x p) (/.f64 x p)) (log.f64 1/2))))
(fma.f64 -1/48 (pow.f64 (/.f64 x p) 3) (fma.f64 1/2 (/.f64 x p) (fma.f64 -1/8 (*.f64 (/.f64 x p) (/.f64 x p)) (log.f64 1/2))))
(*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(neg.f64 (/.f64 (.f64 p p) (.f64 x x)))
(/.f64 (neg.f64 (.f64 p p)) (.f64 x x))
(*.f64 (/.f64 p x) (neg.f64 (/.f64 p x)))
(+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (pow.f64 p 4)) (.f64 -12 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (pow.f64 x 4))))
(fma.f64 -1 (/.f64 (.f64 p p) (.f64 x x)) (.f64 1/24 (/.f64 (.f64 -12 (+.f64 (pow.f64 p 4) (*.f64 (pow.f64 p 4) -6))) (pow.f64 x 4))))
(-.f64 (/.f64 (.f64 -1/2 (+.f64 (pow.f64 p 4) (.f64 (pow.f64 p 4) -6))) (pow.f64 x 4)) (*.f64 (/.f64 p x) (/.f64 p x)))
(-.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 p 4) 60) (pow.f64 x 4))) (*.f64 (/.f64 p x) (/.f64 p x)))
(+.f64 (.f64 1/720 (/.f64 (+.f64 (.f64 -240 (pow.f64 p 6)) (+.f64 (.f64 -360 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2))) (.f64 -360 (+.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 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (pow.f64 p 4)) (.f64 -12 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (pow.f64 x 4)))))
(fma.f64 1/720 (/.f64 (fma.f64 -240 (pow.f64 p 6) (.f64 -360 (+.f64 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) -6)) (fma.f64 8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) -6))))))) (pow.f64 x 6)) (fma.f64 -1 (/.f64 (.f64 p p) (.f64 x x)) (.f64 1/24 (/.f64 (.f64 -12 (+.f64 (pow.f64 p 4) (*.f64 (pow.f64 p 4) -6))) (pow.f64 x 4)))))
(fma.f64 1/720 (/.f64 (fma.f64 -240 (pow.f64 p 6) (.f64 -360 (+.f64 (.f64 (pow.f64 p 6) -6) (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 (pow.f64 p 6) 8))))) (pow.f64 x 6)) (-.f64 (/.f64 (.f64 -1/2 (+.f64 (pow.f64 p 4) (.f64 (pow.f64 p 4) -6))) (pow.f64 x 4)) (*.f64 (/.f64 p x) (/.f64 p x))))
(fma.f64 1/720 (/.f64 (fma.f64 -240 (pow.f64 p 6) (+.f64 (.f64 (pow.f64 p 6) -2880) (.f64 (.f64 (pow.f64 p 6) -6) 360))) (pow.f64 x 6)) (-.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 p 4) 60) (pow.f64 x 4))) (.f64 (/.f64 p x) (/.f64 p x))))
(+.f64 (.f64 1/720 (/.f64 (+.f64 (.f64 -240 (pow.f64 p 6)) (+.f64 (.f64 -360 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2))) (.f64 -360 (+.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 (.f64 1/40320 (/.f64 (+.f64 (.f64 -20160 (.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 (.f64 -20160 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 4))) (+.f64 (.f64 -10080 (pow.f64 p 8)) (+.f64 (.f64 -5040 (pow.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) 2)) (.f64 -20160 (+.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)))))))))) (pow.f64 x 8))) (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 1/24 (/.f64 (+.f64 (.f64 -12 (pow.f64 p 4)) (.f64 -12 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))))) (pow.f64 x 4))))))
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(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4))) (.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 x 6))))))
(+.f64 1 (fma.f64 -1 (/.f64 (.f64 p p) (.f64 x x)) (.f64 -1/2 (+.f64 (/.f64 (.f64 (pow.f64 p 4) -6) (pow.f64 x 4)) (/.f64 (fma.f64 8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) -6)))) (pow.f64 x 6))))))
(+.f64 1 (-.f64 (.f64 -1/2 (+.f64 (/.f64 (.f64 (pow.f64 p 4) -6) (pow.f64 x 4)) (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 (pow.f64 p 6) 8)) (pow.f64 x 6)))) (*.f64 (/.f64 p x) (/.f64 p x))))
(+.f64 1 (fma.f64 -1/2 (+.f64 (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6) (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 (pow.f64 p 6) 8)) (pow.f64 x 6))) (.f64 (/.f64 p x) (neg.f64 (/.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 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (*.f64 2 (pow.f64 p 4))) (pow.f64 x 4))) (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(fma.f64 -1/2 (/.f64 (.f64 (pow.f64 p 4) 6) (pow.f64 x 4)) (/.f64 (.f64 p p) (*.f64 x x)))
(fma.f64 -1/2 (/.f64 (.f64 (pow.f64 p 4) 6) (pow.f64 x 4)) (.f64 (/.f64 p x) (/.f64 p x)))
(fma.f64 -1/2 (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) 6) (.f64 (/.f64 p x) (/.f64 p x)))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 x 4))) (+.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (.f64 -1/2 (/.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 (fma.f64 -1/2 (/.f64 (.f64 (pow.f64 p 4) 6) (pow.f64 x 4)) (/.f64 (.f64 p p) (.f64 x x))) (.f64 -1/2 (/.f64 (fma.f64 -8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) 6)))) (pow.f64 x 6))))
(fma.f64 -1/2 (/.f64 (.f64 (pow.f64 p 4) 6) (pow.f64 x 4)) (fma.f64 -1/2 (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) 6) (.f64 (pow.f64 p 6) -8)) (pow.f64 x 6)) (.f64 (/.f64 p x) (/.f64 p x))))
(fma.f64 -1/2 (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) 6) (fma.f64 -1/2 (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) 6) (.f64 (pow.f64 p 6) -8)) (pow.f64 x 6)) (.f64 (/.f64 p x) (/.f64 p x))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 x 4))) (+.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (+.f64 (.f64 -1/2 (/.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 -1/2 (/.f64 (+.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 4 (pow.f64 p 4)) (.f64 2 (pow.f64 p 4))) (pow.f64 p 4))) (+.f64 (.f64 8 (pow.f64 p 8)) (.f64 -2 (.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 p 2)))))) (pow.f64 x 8))))))
(+.f64 (fma.f64 -1/2 (/.f64 (.f64 (pow.f64 p 4) 6) (pow.f64 x 4)) (/.f64 (.f64 p p) (.f64 x x))) (.f64 -1/2 (+.f64 (/.f64 (fma.f64 -8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) 6)))) (pow.f64 x 6)) (/.f64 (fma.f64 1/2 (fma.f64 16 (pow.f64 p 8) (pow.f64 (.f64 (pow.f64 p 4) -2) 2)) (fma.f64 2 (.f64 (pow.f64 p 4) (.f64 (pow.f64 p 4) 6)) (fma.f64 8 (pow.f64 p 8) (.f64 (.f64 -2 (fma.f64 -8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) 6))))) (.f64 p p))))) (pow.f64 x 8)))))
(fma.f64 -1/2 (/.f64 (.f64 (pow.f64 p 4) 6) (pow.f64 x 4)) (fma.f64 -1/2 (+.f64 (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) 6) (.f64 (pow.f64 p 6) -8)) (pow.f64 x 6)) (/.f64 (fma.f64 1/2 (fma.f64 (pow.f64 p 8) 16 (.f64 4 (pow.f64 p 8))) (fma.f64 2 (.f64 (pow.f64 p 8) 6) (fma.f64 -2 (.f64 p (.f64 p (fma.f64 -2 (.f64 (pow.f64 p 6) 6) (.f64 (pow.f64 p 6) -8)))) (.f64 8 (pow.f64 p 8))))) (pow.f64 x 8))) (*.f64 (/.f64 p x) (/.f64 p x))))
(fma.f64 -1/2 (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) 6) (fma.f64 -1/2 (+.f64 (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) 6) (.f64 (pow.f64 p 6) -8)) (pow.f64 x 6)) (/.f64 (fma.f64 1/2 (.f64 (pow.f64 p 8) 20) (fma.f64 2 (.f64 (pow.f64 p 8) 6) (fma.f64 -2 (.f64 p (.f64 p (fma.f64 -2 (.f64 (pow.f64 p 6) 6) (.f64 (pow.f64 p 6) -8)))) (.f64 8 (pow.f64 p 8))))) (pow.f64 x 8))) (*.f64 (/.f64 p x) (/.f64 p x))))
1
(+.f64 1 (*.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 (neg.f64 (/.f64 (.f64 p p) (.f64 x x))) 1)
(-.f64 1 (*.f64 (/.f64 p x) (/.f64 p x)))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1 (/.f64 (.f64 p p) (.f64 x x)) (*.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(+.f64 1 (-.f64 (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (.f64 (/.f64 p x) (/.f64 p x))))
(+.f64 1 (+.f64 (.f64 -1 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (*.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
(+.f64 1 (fma.f64 -1 (/.f64 (.f64 p p) (.f64 x x)) (fma.f64 -10 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (*.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4))))))
(+.f64 1 (-.f64 (fma.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) (/.f64 (.f64 (pow.f64 p 6) -10) (pow.f64 x 6))) (.f64 (/.f64 p x) (/.f64 p x))))
(+.f64 (-.f64 1 (.f64 (/.f64 p x) (/.f64 p x))) (fma.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) (/.f64 (.f64 (pow.f64 p 6) -10) (pow.f64 x 6))))
1/2
(+.f64 1/2 (*.f64 1/4 (/.f64 x p)))
(+.f64 1/2 (*.f64 (/.f64 x p) 1/4))
(fma.f64 (/.f64 x p) 1/4 1/2)
(+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (.f64 1/4 (/.f64 x p))))
(+.f64 1/2 (fma.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (*.f64 (/.f64 x p) 1/4)))
(+.f64 1/2 (fma.f64 (/.f64 x p) 1/4 (*.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/32)))
(+.f64 1/2 (fma.f64 (pow.f64 (/.f64 x p) 3) -1/32 (*.f64 (/.f64 x p) 1/4)))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (.f64 -1/128 (pow.f64 x 5))) (pow.f64 p 5))) (+.f64 1/2 (+.f64 (.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (*.f64 1/4 (/.f64 x p)))))
(fma.f64 -1/2 (/.f64 (.f64 (pow.f64 x 5) -3/256) (pow.f64 p 5)) (+.f64 1/2 (fma.f64 -1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (.f64 (/.f64 x p) 1/4))))
(+.f64 (fma.f64 (/.f64 x p) 1/4 (*.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) -1/32)) (fma.f64 -1/2 (/.f64 (pow.f64 x 5) (/.f64 (pow.f64 p 5) -3/256)) 1/2))
(+.f64 (fma.f64 (pow.f64 (/.f64 x p) 3) -1/32 (.f64 (/.f64 x p) 1/4)) (fma.f64 -1/2 (.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -3/256) 1/2))
1/2
(+.f64 1/2 (*.f64 -1/4 (/.f64 x p)))
(+.f64 1/2 (*.f64 (/.f64 x p) -1/4))
(fma.f64 (/.f64 x p) -1/4 1/2)
(+.f64 (.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 1/2 (.f64 -1/4 (/.f64 x p))))
(fma.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (+.f64 1/2 (*.f64 (/.f64 x p) -1/4)))
(fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/32 (fma.f64 (/.f64 x p) -1/4 1/2))
(fma.f64 (pow.f64 (/.f64 x p) 3) 1/32 (fma.f64 (/.f64 x p) -1/4 1/2))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (.f64 -1/128 (pow.f64 x 5))) (pow.f64 p 5))) (+.f64 (.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 1/2 (*.f64 -1/4 (/.f64 x p)))))
(fma.f64 1/2 (/.f64 (.f64 (pow.f64 x 5) -3/256) (pow.f64 p 5)) (fma.f64 1/32 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (+.f64 1/2 (.f64 (/.f64 x p) -1/4))))
(fma.f64 1/2 (/.f64 (pow.f64 x 5) (/.f64 (pow.f64 p 5) -3/256)) (fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/32 (fma.f64 (/.f64 x p) -1/4 1/2)))
(fma.f64 1/2 (*.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -3/256) (fma.f64 (pow.f64 (/.f64 x p) 3) 1/32 (fma.f64 (/.f64 x p) -1/4 1/2)))

prune586.0ms (10.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	197	3	200

Error

4.9b

Counts

200 → 3

Alt Table

Status

Error

Program

▶

52.4b

(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

55.9b

(sqrt.f64 (exp.f64 (+.f64 (*.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2)))))

✓

12.5b

(sqrt.f64 (exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)))

Compiler

Compiled 6509 to 4448 computations (31.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 p x) (/.f64 p x))
✓	21.7b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

series6.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite47.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

605×	`pow1_binary64`
567×	`add-log-exp_binary64`
567×	`log1p-expm1-u_binary64`
567×	`expm1-log1p-u_binary64`
551×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	130	11
2	1588	11

Stop Event

1×	node limit

Counts

2 → 86

Calls

Call 1

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

Outputs

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

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
671×	`times-frac_binary64`
650×	`unswap-sqr_binary64`
343×	`div-sub_binary64`
326×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	352
1	22	352
2	42	352
3	106	352
4	434	352
5	3292	352
6	4926	352
7	5669	352
8	7661	352

Stop Event

1×	node limit

Counts

134 → 90

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 (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 (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))

prune51.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	90	3	93

Error

0.1b

Counts

93 → 3

Alt Table

Status

Error

Program

▶

47.1b

(fabs.f64 (/.f64 p x))

55.9b

(sqrt.f64 (exp.f64 (+.f64 (*.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2)))))

✓

12.5b

(sqrt.f64 (exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)))

Compiler

Compiled 793 to 381 computations (52% saved)

localize3.0ms (0.1%)

prune2.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.1b

Counts

3 → 3

Alt Table

Status

Error

Program

✓

47.1b

(fabs.f64 (/.f64 p x))

55.9b

(sqrt.f64 (exp.f64 (+.f64 (*.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2)))))

✓

12.5b

(sqrt.f64 (exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)))

Compiler

Compiled 42 to 35 computations (16.7% saved)

regimes73.0ms (1.4%)

Accuracy

Total -61.6b remaining (-95181.7%)

Threshold costs -61.6b (-95181.7%)

Counts

6 → 2

Calls

Call 1

Inputs
(fabs.f64 (/.f64 p x))
(sqrt.f64 (exp.f64 (+.f64 (*.f64 2 (log.f64 (/.f64 -1 x))) (log.f64 (pow.f64 p 2)))))
(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))
(sqrt.f64 (exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)))
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Outputs
(fabs.f64 (/.f64 p x))
(sqrt.f64 (exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3)))

Results

22.0ms	9.9b	`p`
27.0ms	6.2b	`x`
4.0ms	0.1b	`(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))`
4.0ms	0.1b	`(.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))`
5.0ms	0.1b	`(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))`
5.0ms	0.1b	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))`
4.0ms	12.5b	`(.f64 (.f64 4 p) p)`

Compiler

Compiled 156 to 109 computations (30.1% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))

Steps

Iters	Point		Range
-0.5	∈ [	-0.9999999999818008	,	-5.71851858486337e-10	]

Compiler

Compiled 24 to 18 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`fabs-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	55
1	38	55

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))) -2147483648/4294967296) (fabs.f64 (/.f64 p x)) (sqrt.f64 (exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3))))

Outputs

(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x)))) -2147483648/4294967296) (fabs.f64 (/.f64 p x)) (sqrt.f64 (exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3))))

(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (*.f64 p (*.f64 4 p)) (*.f64 x x)))) -1/2) (fabs.f64 (/.f64 p x)) (sqrt.f64 (exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))) 1/3))))

end28.0ms (0.5%)

Stop Event

1×

fuel

Compiler

Compiled 76 to 56 computations (26.3% saved)

Details

analyze363.0ms (6.7%)

sample2.7s (50.2%)

preprocess25.0ms (0.5%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize20.0ms (0.4%)

series23.0ms (0.4%)

rewrite77.0ms (1.4%)

simplify73.0ms (1.3%)

prune1.0s (18.7%)

localize14.0ms (0.3%)

series26.0ms (0.5%)

rewrite99.0ms (1.8%)

simplify79.0ms (1.5%)

prune586.0ms (10.9%)

localize4.0ms (0.1%)

series6.0ms (0.1%)

rewrite47.0ms (0.9%)

simplify64.0ms (1.2%)

prune51.0ms (0.9%)

localize3.0ms (0.1%)

prune2.0ms (0%)

regimes73.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end28.0ms (0.5%)

Profiling