Details

analyze488.0ms (8.1%)

Algorithm

1×

Search

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

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample1.9s (31.1%)

Results

951.0ms	6344×	body	256	valid
453.0ms	849×	body	2048	valid
196.0ms	530×	body	1024	valid
182.0ms	280×	body	4096	valid
70.0ms	253×	body	512	valid

preprocess17.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

15.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	15.8b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

localize35.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
✓	0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
✓	0.6b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
✓	14.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 96 to 55 computations (42.7% saved)

series23.0ms (0.4%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
3.0ms	p	@	0	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
1.0ms	x	@	-inf	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
1.0ms	x	@	inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
1.0ms	x	@	0	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite91.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	67
1	325	48
2	4211	46

Stop Event

1×	node limit

Counts

4 → 174

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 x (.f64 2 p)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p)))) (cbrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p)))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (.f64 2 p)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (hypot.f64 x (.f64 2 p)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 2) (cbrt.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 x (.f64 2 p))) (sqrt.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2) 2))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (hypot.f64 x (.f64 2 p)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2) 2)) 1/2) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 4 (.f64 p p)) 2) (pow.f64 x 4))) (sqrt.f64 (fma.f64 p (.f64 4 p) (.f64 (neg.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 (pow.f64 x 3) (pow.f64 (.f64 2 p) 3)) (hypot.f64 (.f64 4 (.f64 p p)) (sqrt.f64 (-.f64 (pow.f64 x 4) (.f64 4 (.f64 (.f64 p p) (.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (.f64 2 p)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x (.f64 2 p))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (.f64 2 p)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (.f64 2 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (.f64 2 p))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (.f64 2 p) x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (.f64 2 p))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 x (.f64 2 p)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 x (*.f64 2 p))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) (/.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2) (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) 2) (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) (sqrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3)) (/.f64 1 (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2)) (/.f64 1 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1) (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3)) (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3)) (+.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2) (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2)) (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3))) (neg.f64 (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2))) (neg.f64 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2) 1) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) (-.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1) 1) (+.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) (-.f64 1 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log1p.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (/.f64 1 (hypot.f64 x (.f64 2 p))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 x (hypot.f64 x (.f64 2 p))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) (cbrt.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (/.f64 x (hypot.f64 x (.f64 2 p))) 2)) (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (/.f64 1 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) (sqrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) (/.f64 1 (neg.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (hypot.f64 x (.f64 2 p))) x 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (hypot.f64 x (.f64 2 p))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (hypot.f64 x (.f64 2 p))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 2)) (/.f64 x (cbrt.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 2)) (cbrt.f64 (/.f64 x (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 (hypot.f64 x (.f64 2 p)))) (/.f64 x (sqrt.f64 (hypot.f64 x (.f64 2 p)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (hypot.f64 x (.f64 2 p)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (hypot.f64 x (*.f64 2 p)))) 1)))))
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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 4 (.f64 p p)) 2) (pow.f64 x 4))) (neg.f64 (fma.f64 p (.f64 4 p) (.f64 (neg.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (pow.f64 (.f64 4 (.f64 p p)) 2)) (-.f64 (.f64 x x) (.f64 4 (.f64 p p))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (.f64 2 p)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (hypot.f64 x (.f64 2 p)) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x (.f64 2 p))) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 4 (.f64 p p))) (pow.f64 (.f64 4 (.f64 p p)) 2)) (fma.f64 64 (pow.f64 (.f64 p p) 3) (pow.f64 x 6))) -1)))) 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p)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 p (.f64 (sqrt.f64 p) 2)) (.f64 (sqrt.f64 p) 2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 4 p) (pow.f64 (cbrt.f64 p) 2)) (cbrt.f64 p) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 4 p) (sqrt.f64 p)) (sqrt.f64 p) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 4 (.f64 p p)))))))

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

555×	`associate-*l/_binary64`
532×	`associate-*r/_binary64`
405×	`distribute-rgt-in_binary64`
404×	`distribute-lft-in_binary64`
317×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	3139
1	946	2992
2	3656	2729

Stop Event

1×	node limit

Counts

270 → 279

Calls

Call 1

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

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

eval149.0ms (2.5%)

Compiler: Compiled 7418 to 5603 computations (24.5% saved)

prune50.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	268	11	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	269	11	280

Error

2.0b

Counts

280 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	59.0b	(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (neg.f64 x)))))
	32.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
▶	49.0b	(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
▶	29.9b	(sqrt.f64 1/2)
▶	32.7b	(sqrt.f64 (.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 x p)) 1)))
	16.2b	(pow.f64 (pow.f64 (fma.f64 (/.f64 x (hypot.f64 x (*.f64 2 p))) 1/2 1/2) 1/4) 2)
	43.4b	(sqrt.f64 (*.f64 1/2 2))
	53.8b	(-.f64 (fma.f64 -1/4 (.f64 (/.f64 (.f64 (pow.f64 p 4) -12) (sqrt.f64 2)) (/.f64 (sqrt.f64 1/2) (.f64 p (pow.f64 x 3)))) (.f64 (/.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 p (pow.f64 x 5))) (/.f64 (+.f64 (.f64 (pow.f64 p 6) 32) (-.f64 (.f64 p (.f64 p (.f64 (pow.f64 p 4) -12))) (pow.f64 (.f64 (/.f64 1/4 p) (/.f64 (.f64 (pow.f64 p 4) -12) (sqrt.f64 2))) 2))) (sqrt.f64 2)))) (.f64 (/.f64 (sqrt.f64 2) x) (.f64 p (sqrt.f64 1/2))))
▶	15.8b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (.f64 2 p) x)))))
	48.8b	(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
	49.8b	(sqrt.f64 (.f64 1/2 (.f64 2 (*.f64 (/.f64 p x) (/.f64 p x)))))

Compiler

Compiled 378 to 310 computations (18% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (hypot.f64 (*.f64 2 p) x))
✓	0.0b	(hypot.f64 (*.f64 2 p) x)
✓	0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (.f64 2 p) x)))))
✓	0.6b	(+.f64 1 (/.f64 x (hypot.f64 (*.f64 2 p) x)))

Compiler

Compiled 54 to 37 computations (31.5% saved)

series19.0ms (0.3%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/.f64 x (hypot.f64 (*.f64 2 p) x))
2.0ms	x	@	-inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (.f64 2 p) x)))))
2.0ms	x	@	-inf	(+.f64 1 (/.f64 x (hypot.f64 (*.f64 2 p) x)))
1.0ms	p	@	-inf	(+.f64 1 (/.f64 x (hypot.f64 (*.f64 2 p) x)))
1.0ms	x	@	inf	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (.f64 2 p) x)))))

rewrite83.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	48
1	255	48
2	3141	46

Stop Event

1×	node limit

Counts

4 → 145

Calls

Call 1

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

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

simplify89.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	3165
1	1134	3012
2	4424	2904

Stop Event

1×	node limit

Counts

241 → 277

Calls

Call 1

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

Outputs
1
(+.f64 1 (*.f64 1/2 (/.f64 x p)))
(fma.f64 1/2 (/.f64 x p) 1)
(+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 1 (fma.f64 1/2 (/.f64 x p) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)))))
(+.f64 (fma.f64 1/2 (/.f64 x p) 1) (/.f64 -1/16 (pow.f64 (/.f64 p x) 3)))
(+.f64 (.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 1 (+.f64 (.f64 1/2 (/.f64 x p)) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
(fma.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) (+.f64 1 (fma.f64 1/2 (/.f64 x p) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
(+.f64 1 (fma.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) (fma.f64 1/2 (/.f64 x p) (*.f64 -1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))))))
(+.f64 1 (fma.f64 3/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) (fma.f64 1/2 (/.f64 x p) (/.f64 -1/16 (pow.f64 (/.f64 p x) 3)))))
2
(+.f64 2 (*.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))))
(+.f64 2 (/.f64 (.f64 -2 (.f64 p p)) (*.f64 x x)))
(fma.f64 -2 (*.f64 (/.f64 p x) (/.f64 p x)) 2)
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (.f64 -1 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4)))))
(+.f64 2 (fma.f64 -2 (/.f64 (.f64 p p) (.f64 x x)) (neg.f64 (/.f64 (*.f64 (pow.f64 p 4) -6) (pow.f64 x 4)))))
(-.f64 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) 2) (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))
(+.f64 2 (fma.f64 (/.f64 -2 x) (*.f64 (/.f64 p x) p) (/.f64 6 (/.f64 (pow.f64 x 4) (pow.f64 p 4)))))
(+.f64 2 (+.f64 (.f64 -2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 8 (pow.f64 p 6)) (.f64 -2 (.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 p 2)))) (pow.f64 x 6))) (.f64 -1 (/.f64 (+.f64 (.f64 -2 (pow.f64 p 4)) (.f64 -4 (pow.f64 p 4))) (pow.f64 x 4))))))
(+.f64 2 (fma.f64 -2 (/.f64 (.f64 p p) (.f64 x x)) (fma.f64 -1 (/.f64 (fma.f64 8 (pow.f64 p 6) (.f64 -2 (.f64 (.f64 p p) (.f64 (pow.f64 p 4) -6)))) (pow.f64 x 6)) (neg.f64 (/.f64 (*.f64 (pow.f64 p 4) -6) (pow.f64 x 4))))))
(+.f64 2 (-.f64 (-.f64 (.f64 -2 (.f64 (/.f64 p x) (/.f64 p x))) (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (.f64 8 (pow.f64 p 6))) (pow.f64 x 6))) (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6)))
(+.f64 (fma.f64 -2 (.f64 (/.f64 p x) (/.f64 p x)) 2) (-.f64 (/.f64 6 (/.f64 (pow.f64 x 4) (pow.f64 p 4))) (/.f64 (fma.f64 -2 (.f64 (pow.f64 p 6) -6) (*.f64 8 (pow.f64 p 6))) (pow.f64 x 6))))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(/.f64 (.f64 p (.f64 p 2)) (*.f64 x x))
(+.f64 (.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 -4 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (*.f64 -2 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
(fma.f64 2 (/.f64 (.f64 p p) (.f64 x x)) (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))
(fma.f64 2 (.f64 (/.f64 p x) (/.f64 p x)) (.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -6))
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2
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1
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1
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(sqrt.f64 1/2)
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(sqrt.f64 1/2)
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x
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(*.f64 2 p)
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x
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1
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-1
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1
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(fma.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -1/128 (fma.f64 (/.f64 x p) -1/2 (fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/16 (*.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -1/256))))
(fma.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -1/128 (fma.f64 (/.f64 x p) -1/2 (fma.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -1/256 (/.f64 1/16 (pow.f64 (/.f64 p x) 3)))))
(+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 -1/2 (/.f64 x p)) (+.f64 (.f64 -1/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3))) (+.f64 (.f64 1/1024 (/.f64 (pow.f64 x 7) (pow.f64 p 7))) (.f64 -1/8 (/.f64 (.f64 (+.f64 (.f64 -1/256 (pow.f64 x 5)) (*.f64 -1/128 (pow.f64 x 5))) (pow.f64 x 2)) (pow.f64 p 7))))))))
(fma.f64 -1/128 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) (fma.f64 -1/2 (/.f64 x p) (fma.f64 -1/256 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) (fma.f64 1/1024 (/.f64 (pow.f64 x 7) (pow.f64 p 7)) (.f64 -1/8 (/.f64 (.f64 (pow.f64 x 5) -3/256) (/.f64 (pow.f64 p 7) (*.f64 x x)))))))))
(fma.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -1/128 (fma.f64 (/.f64 x p) -1/2 (fma.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -1/256 (fma.f64 (/.f64 (pow.f64 x 3) (pow.f64 p 3)) 1/16 (fma.f64 (/.f64 (pow.f64 x 7) (pow.f64 p 7)) 1/1024 (.f64 -1/8 (/.f64 (pow.f64 x 5) (/.f64 (/.f64 (pow.f64 p 7) (.f64 x x)) -3/256))))))))
(+.f64 (fma.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -1/128 (fma.f64 (/.f64 x p) -1/2 (fma.f64 (/.f64 (pow.f64 x 5) (pow.f64 p 5)) -1/256 (/.f64 1/16 (pow.f64 (/.f64 p x) 3))))) (fma.f64 (/.f64 (pow.f64 x 7) (pow.f64 p 7)) 1/1024 (.f64 -1/8 (.f64 (/.f64 (pow.f64 x 5) (/.f64 (pow.f64 p 7) (*.f64 x x))) -3/256))))

localize3.0ms (0.1%)

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

localize11.0ms (0.2%)

Compiler: Compiled 34 to 17 computations (50% saved)

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -1/2 (/.f64 x p))
✓	2.9b	(sqrt.f64 (.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 x p)) 1)))

Compiler

Compiled 41 to 25 computations (39% saved)

series9.0ms (0.1%)

Counts

2 → 12

Calls

12 calls:

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

rewrite68.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`log-prod_binary64`
292×	`pow-prod-down_binary64`
280×	`prod-diff_binary64`
276×	`pow2_binary64`
191×	`pow1/3_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	237	19
2	2940	17

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

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

Outputs

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

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

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

990×	`distribute-rgt-out_binary64`
660×	`associate-/r*_binary64`
550×	`associate-r_binary64`
546×	`fma-def_binary64`
521×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	318
1	80	306
2	251	297
3	1203	255
4	6741	255

Stop Event

1×	node limit

Counts

87 → 82

Calls

Call 1

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

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

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (/.f64 x p) (sqrt.f64 1/2))
✓	0.8b	(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))

Compiler

Compiled 32 to 22 computations (31.3% saved)

series10.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

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

rewrite110.0ms (1.8%)

Algorithm

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

Rules

840×	`pow1_binary64`
784×	`add-log-exp_binary64`
784×	`log1p-expm1-u_binary64`
784×	`expm1-log1p-u_binary64`
767×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	245	25
2	3503	25
0	11	16
1	245	16
2	3503	16
0	11	16
0	7	9
1	152	9
2	2058	9

Stop Event

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

Counts

2 → 50

Calls

Call 1

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

Outputs

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

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

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-def_binary64`
228×	`fma-neg_binary64`
65×	`associate-/r/_binary64`
63×	`div-sub_binary64`
62×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	600
1	24	600
2	58	600
3	173	600
4	349	600
5	528	600
6	687	600
7	825	600
8	946	600
9	1343	600
10	1786	600
11	1788	600

Stop Event

1×

saturated

Counts

98 → 54

Calls

Call 1

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

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

eval211.0ms (3.5%)

Compiler: Compiled 9075 to 6142 computations (32.3% saved)

prune70.0ms (1.2%)

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	403	10	413
Fresh	4	2	6
Picked	0	1	1
Done	1	3	4
Total	408	16	424

Error

1.9b

Counts

424 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	49.0b	(/.f64 (neg.f64 (sqrt.f64 2)) (.f64 x (.f64 (/.f64 1 p) (pow.f64 1/2 -1/2))))
	49.0b	(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
✓	49.0b	(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
✓	29.9b	(sqrt.f64 1/2)
	59.0b	(sqrt.f64 (*.f64 1/2 (+.f64 1 -1)))
▶	48.8b	(.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 (.f64 p (sqrt.f64 1/2))))
	49.0b	(/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 x (pow.f64 1/2 1/4)) (/.f64 (/.f64 1 p) (pow.f64 1/2 1/4))))
▶	49.8b	(sqrt.f64 (.f64 1/2 (.f64 2 (*.f64 (/.f64 p x) (/.f64 p x)))))
	49.0b	(.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (/.f64 x (.f64 (sqrt.f64 1/2) p))))
▶	32.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 p 2)))))
✓	32.7b	(sqrt.f64 (.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 x p)) 1)))
	48.8b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
▶	43.4b	(sqrt.f64 (*.f64 1/2 2))
▶	49.0b	(/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (pow.f64 1/2 -1/2) (/.f64 x p)))
✓	15.8b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (.f64 2 p) x)))))
	33.2b	(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)

Compiler

Compiled 340 to 287 computations (15.6% saved)

localize22.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 p 2)))))

Compiler

Compiled 41 to 30 computations (26.8% saved)

series4.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

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

rewrite57.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

539×	`log-prod_binary64`
416×	`prod-diff_binary64`
292×	`pow-prod-down_binary64`
279×	`pow2_binary64`
242×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	236	13
2	3022	13

Stop Event

1×	node limit

Counts

1 → 29

Calls

Call 1

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

Outputs

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

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

990×	`distribute-rgt-out_binary64`
661×	`associate-/r*_binary64`
568×	`fma-def_binary64`
553×	`associate-r_binary64`
521×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	324
1	78	318
2	247	297
3	1203	255
4	6753	255

Stop Event

1×	node limit

Counts

41 → 36

Calls

Call 1

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

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

localize5.0ms (0.1%)

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

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
✓	0.2b	(*.f64 (/.f64 p x) (/.f64 p x))
✓	22.1b	(sqrt.f64 (.f64 1/2 (.f64 2 (*.f64 (/.f64 p x) (/.f64 p x)))))

Compiler

Compiled 48 to 17 computations (64.6% saved)

series9.0ms (0.2%)

Counts

3 → 72

Calls

18 calls:

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

rewrite67.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`pow1_binary64`
809×	`add-log-exp_binary64`
809×	`log1p-expm1-u_binary64`
809×	`expm1-log1p-u_binary64`
791×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	217	21
2	2454	21

Stop Event

1×	node limit

Counts

3 → 100

Calls

Call 1

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

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

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

924×	`fma-def_binary64`
724×	`associate-/l*_binary64`
453×	`associate-/r*_binary64`
366×	`unswap-sqr_binary64`
360×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	664
1	26	664
2	56	664
3	164	664
4	821	664
5	5064	664
6	6062	664
7	6820	664

Stop Event

1×	node limit

Counts

172 → 106

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))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(*.f64 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 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(/.f64 (pow.f64 p 2) (pow.f64 x 2))
(/.f64 (.f64 p p) (.f64 x x))
(*.f64 (/.f64 p x) (/.f64 p x))
(*.f64 p (/.f64 (/.f64 p x) x))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))
(*.f64 2 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
(.f64 2 (/.f64 (.f64 p p) (*.f64 x x)))
(.f64 2 (.f64 (/.f64 p x) (/.f64 p x)))
(.f64 (/.f64 p x) (.f64 (/.f64 p x) 2))
(.f64 p (.f64 2 (/.f64 (/.f64 p x) x)))

localize16.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 33 to 26 computations (21.2% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

12 calls:

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

rewrite70.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`log-prod_binary64`
405×	`exp-prod_binary64`
321×	`pow-prod-down_binary64`
269×	`pow-unpow_binary64`
258×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	235	26
2	2942	26

Stop Event

1×	node limit

Counts

3 → 121

Calls

Call 1

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

Outputs

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

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

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

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
228×	`fma-neg_binary64`
66×	`associate-/r/_binary64`
63×	`associate-/l*_binary64`
63×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	456
1	22	456
2	56	456
3	166	456
4	346	456
5	530	456
6	689	456
7	827	456
8	948	456
9	1345	456
10	1788	456
11	1790	456

Stop Event

1×

saturated

Counts

157 → 124

Calls

Call 1

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

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

localize18.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 1/2 -1/2) (/.f64 x p))
✓	0.8b	(/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (pow.f64 1/2 -1/2) (/.f64 x p)))

Compiler

Compiled 36 to 26 computations (27.8% saved)

series12.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (pow.f64 1/2 -1/2) (/.f64 x p)))
1.0ms	p	@	inf	(/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (pow.f64 1/2 -1/2) (/.f64 x p)))
1.0ms	x	@	0	(*.f64 (pow.f64 1/2 -1/2) (/.f64 x p))
1.0ms	p	@	0	(*.f64 (pow.f64 1/2 -1/2) (/.f64 x p))
1.0ms	x	@	-inf	(*.f64 (pow.f64 1/2 -1/2) (/.f64 x p))

rewrite115.0ms (1.9%)

Algorithm

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

Rules

810×	`pow1_binary64`
754×	`add-log-exp_binary64`
754×	`log1p-expm1-u_binary64`
754×	`expm1-log1p-u_binary64`
737×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	265	27
2	3682	27
0	12	17
1	265	17
2	3682	17
0	12	17
0	8	10
1	173	9
2	2097	9

Stop Event

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

Counts

2 → 33

Calls

Call 1

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

Outputs

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

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

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	360
1	16	360
2	27	360
3	35	360
4	42	360
5	50	360
6	58	360
7	68	360
8	78	360
9	97	360
10	98	360

Stop Event

1×

saturated

Counts

81 → 36

Calls

Call 1

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

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

eval88.0ms (1.5%)

Compiler: Compiled 3906 to 2886 computations (26.1% saved)

prune51.0ms (0.8%)

Pruning

13 alts after pruning (8 fresh and 5 done)

	Pruned	Kept	Total
New	295	7	302
Fresh	6	1	7
Picked	1	0	1
Done	3	5	8
Total	305	13	318

Error

0.1b

Counts

318 → 13

Alt Table

Click to see full alt table

Status	Error	Program
✓	43.4b	(sqrt.f64 (*.f64 1/2 2))
▶	58.7b	(-.f64 (+.f64 1 (/.f64 p x)) 1)
	48.6b	(/.f64 (neg.f64 p) x)
▶	53.8b	(*.f64 (/.f64 1 x) p)
✓	15.8b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (.f64 2 p) x)))))
✓	32.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 p 2)))))
	53.7b	(/.f64 1 (/.f64 x p))
✓	32.7b	(sqrt.f64 (.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 x p)) 1)))
▶	53.9b	(pow.f64 (cbrt.f64 (/.f64 p x)) 3)
	55.0b	(exp.f64 (log.f64 (/.f64 p x)))
✓	29.9b	(sqrt.f64 1/2)
▶	33.2b	(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)
▶	53.7b	(/.f64 p x)

Compiler

Compiled 170 to 131 computations (22.9% saved)

localize17.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)
✓	4.1b	(pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4)

Compiler

Compiled 35 to 22 computations (37.1% saved)

series18.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

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

rewrite59.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	235	21
2	2586	21

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

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

Outputs

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

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

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

755×	`associate-/r*_binary64`
423×	`distribute-rgt-in_binary64`
419×	`distribute-lft-in_binary64`
315×	`fma-def_binary64`
247×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

87 → 107

Calls

Call 1

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

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

localize4.0ms (0.1%)

Compiler: Compiled 7 to 3 computations (57.1% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 x) p)

Compiler

Compiled 13 to 8 computations (38.5% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite45.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`pow1_binary64`
511×	`add-sqr-sqrt_binary64`
492×	`add-log-exp_binary64`
492×	`log1p-expm1-u_binary64`
492×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	4
1	118	4
2	1386	4

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96

Stop Event

1×

saturated

Counts

45 → 21

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

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

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(-.f64 (+.f64 1 (/.f64 p x)) 1)

Compiler

Compiled 20 to 10 computations (50% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite55.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

842×	`pow1_binary64`
788×	`add-log-exp_binary64`
788×	`log1p-expm1-u_binary64`
788×	`expm1-log1p-u_binary64`
774×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	160	4
2	2358	4

Stop Event

1×	node limit

Counts

1 → 62

Calls

Call 1

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

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	96

Stop Event

1×

saturated

Counts

86 → 62

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

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

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (cbrt.f64 (/.f64 p x)) 3)
✓	7.7b	(cbrt.f64 (/.f64 p x))

Compiler

Compiled 18 to 7 computations (61.1% saved)

series9.0ms (0.2%)

Counts

2 → 0

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	p	@	0	(pow.f64 (cbrt.f64 (/.f64 p x)) 3)
1.0ms	p	@	-inf	(pow.f64 (cbrt.f64 (/.f64 p x)) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (/.f64 p x)) 3)
1.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (/.f64 p x)) 3)
1.0ms	p	@	-inf	(cbrt.f64 (/.f64 p x))

rewrite56.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`pow1_binary64`
599×	`add-log-exp_binary64`
599×	`log1p-expm1-u_binary64`
599×	`expm1-log1p-u_binary64`
584×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	153	10
2	1650	10

Stop Event

1×	node limit

Counts

2 → 71

Calls

Call 1

Inputs
(cbrt.f64 (/.f64 p x))
(pow.f64 (cbrt.f64 (/.f64 p x)) 3)

Outputs

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

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

71 → 71

Calls

Call 1

Inputs

Outputs

eval114.0ms (1.9%)

Compiler: Compiled 5562 to 3876 computations (30.3% saved)

prune42.0ms (0.7%)

Pruning

15 alts after pruning (7 fresh and 8 done)

	Pruned	Kept	Total
New	255	6	261
Fresh	2	1	3
Picked	0	1	1
Done	2	7	9
Total	259	15	274

Error

0.1b

Counts

274 → 15

Alt Table

Click to see full alt table

Status	Error	Program
	30.4b	(pow.f64 (pow.f64 1/2 1/4) 2)
	59.1b	(/.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 p x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 p x) -1) (+.f64 (/.f64 p x) -1)) (+.f64 (/.f64 p x) -1))))
	53.7b	(/.f64 1 (/.f64 x p))
✓	43.4b	(sqrt.f64 (*.f64 1/2 2))
	59.4b	(pow.f64 (log.f64 (exp.f64 (cbrt.f64 (/.f64 p x)))) 3)
	48.6b	(/.f64 (neg.f64 p) x)
✓	53.8b	(*.f64 (/.f64 1 x) p)
✓	15.8b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (.f64 2 p) x)))))
	58.7b	(+.f64 (+.f64 (/.f64 p x) -1) 1)
✓	29.9b	(sqrt.f64 1/2)
✓	32.7b	(sqrt.f64 (.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 x p)) 1)))
✓	53.9b	(pow.f64 (cbrt.f64 (/.f64 p x)) 3)
	58.9b	(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 p x) -1) (+.f64 (/.f64 p x) -1))) (-.f64 1 (+.f64 (/.f64 p x) -1)))
✓	53.7b	(/.f64 p x)
✓	32.5b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 p 2)))))

Compiler

Compiled 161 to 121 computations (24.8% saved)

regimes268.0ms (4.5%)

Counts

35 → 2

Calls

Call 1

Inputs
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 1 (/.f64 x p))
(*.f64 (/.f64 1 x) p)
(/.f64 1 (/.f64 x p))
(+.f64 (+.f64 (/.f64 p x) -1) 1)
(-.f64 (+.f64 1 (/.f64 p x)) 1)
(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 p x) -1) (+.f64 (/.f64 p x) -1))) (-.f64 1 (+.f64 (/.f64 p x) -1)))
(sqrt.f64 1/2)
(sqrt.f64 (*.f64 1/2 2))
(sqrt.f64 (*.f64 1/2 (+.f64 1 -1)))
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (neg.f64 x)))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 p 2)))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
(sqrt.f64 (.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 x p)) 1)))
(sqrt.f64 (.f64 1/2 (.f64 2 (*.f64 (/.f64 p x) (/.f64 p x)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 p x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 p x) -1) (+.f64 (/.f64 p x) -1)) (+.f64 (/.f64 p x) -1))))
(pow.f64 (pow.f64 1/2 1/4) 2)
(exp.f64 (log.f64 (/.f64 p x)))
(pow.f64 (cbrt.f64 (/.f64 p x)) 3)
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 (.f64 p (sqrt.f64 1/2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (pow.f64 1/2 -1/2) (/.f64 x p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (/.f64 x (.f64 (sqrt.f64 1/2) p))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (.f64 2 p) x)))))
(/.f64 (neg.f64 (sqrt.f64 2)) (.f64 x (.f64 (/.f64 1 p) (pow.f64 1/2 -1/2))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
(pow.f64 (pow.f64 (fma.f64 (/.f64 x p) -1/4 1/2) 1/4) 2)
(/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 x (pow.f64 1/2 1/4)) (/.f64 (/.f64 1 p) (pow.f64 1/2 1/4))))
(pow.f64 (log.f64 (exp.f64 (cbrt.f64 (/.f64 p x)))) 3)
(pow.f64 (pow.f64 (fma.f64 (/.f64 x (hypot.f64 x (*.f64 2 p))) 1/2 1/2) 1/4) 2)
(-.f64 (fma.f64 -1/4 (.f64 (/.f64 (.f64 (pow.f64 p 4) -12) (sqrt.f64 2)) (/.f64 (sqrt.f64 1/2) (.f64 p (pow.f64 x 3)))) (.f64 (/.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 p (pow.f64 x 5))) (/.f64 (+.f64 (.f64 (pow.f64 p 6) 32) (-.f64 (.f64 p (.f64 p (.f64 (pow.f64 p 4) -12))) (pow.f64 (.f64 (/.f64 1/4 p) (/.f64 (.f64 (pow.f64 p 4) -12) (sqrt.f64 2))) 2))) (sqrt.f64 2)))) (.f64 (/.f64 (sqrt.f64 2) x) (.f64 p (sqrt.f64 1/2))))

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

Calls

12 calls:

84.0ms	p
76.0ms	x
13.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
12.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
12.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

Results

Error	Segments	Branch
10.5b	5	`p`
12.6b	4	`x`
5.4b	2	`(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))`
5.4b	2	`(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))`
5.4b	2	`(.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))`
5.4b	2	`(.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x))))))`
5.4b	2	`(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))`
5.4b	2	`(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))`
5.4b	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))`
5.4b	2	`(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))`
15.8b	1	`(.f64 (.f64 4 p) p)`
15.8b	1	`(.f64 (.f64 4 p) p)`

Compiler

Compiled 559 to 402 computations (28.1% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-0.9999999999999476

Compiler

Compiled 24 to 18 computations (25% saved)

regimes120.0ms (2%)

Counts

27 → 5

Calls

Call 1

Inputs
(/.f64 p x)
(/.f64 (neg.f64 p) x)
(/.f64 1 (/.f64 x p))
(*.f64 (/.f64 1 x) p)
(/.f64 1 (/.f64 x p))
(+.f64 (+.f64 (/.f64 p x) -1) 1)
(-.f64 (+.f64 1 (/.f64 p x)) 1)
(/.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 p x) -1) (+.f64 (/.f64 p x) -1))) (-.f64 1 (+.f64 (/.f64 p x) -1)))
(sqrt.f64 1/2)
(sqrt.f64 (*.f64 1/2 2))
(sqrt.f64 (*.f64 1/2 (+.f64 1 -1)))
(sqrt.f64 (*.f64 1/2 (+.f64 1 (/.f64 x (neg.f64 x)))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 p 2)))))
(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (.f64 2 p)))))
(sqrt.f64 (.f64 1/2 (+.f64 (.f64 -1/2 (/.f64 x p)) 1)))
(sqrt.f64 (.f64 1/2 (.f64 2 (*.f64 (/.f64 p x) (/.f64 p x)))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 p x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 p x) -1) (+.f64 (/.f64 p x) -1)) (+.f64 (/.f64 p x) -1))))
(pow.f64 (pow.f64 1/2 1/4) 2)
(exp.f64 (log.f64 (/.f64 p x)))
(pow.f64 (cbrt.f64 (/.f64 p x)) 3)
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 x (*.f64 (sqrt.f64 1/2) p)))
(.f64 (/.f64 (sqrt.f64 2) x) (neg.f64 (.f64 p (sqrt.f64 1/2))))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 p x))))
(/.f64 (neg.f64 (sqrt.f64 2)) (/.f64 (/.f64 x p) (sqrt.f64 1/2)))
(/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (pow.f64 1/2 -1/2) (/.f64 x p)))
(.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 1/2) p)) x))
(.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (/.f64 x (.f64 (sqrt.f64 1/2) p))))

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

Calls

2 calls:

62.0ms	p
49.0ms	x

Results

Error	Segments	Branch
14.6b	5	`p`
23.7b	4	`x`

Compiler

Compiled 247 to 169 computations (31.6% saved)

bsearch215.0ms (3.6%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
36.0ms	1.8062527207981708e-19	9.829691545208197e-7
71.0ms	1.9822307214939477e-274	2.4547706122196443e-267
69.0ms	-5.4651664445348303e-216	-2.2660019902243004e-217
39.0ms	-4.9056321965133376e-27	-2.3596857107636277e-31

Compiler

Compiled 24 to 18 computations (25% saved)

regimes40.0ms (0.7%)

Counts

9 → 4

Calls

Call 1

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

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

Calls

2 calls:

21.0ms	p
16.0ms	x

Results

Error	Segments	Branch
16.8b	4	`p`
25.1b	2	`x`

Compiler

Compiled 67 to 39 computations (41.8% saved)

bsearch152.0ms (2.5%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
37.0ms	1.8062527207981708e-19	9.829691545208197e-7
76.0ms	-1.6982543834110598e-294	-8.587880788532667e-296
39.0ms	-4.9056321965133376e-27	-2.3596857107636277e-31

Compiler

Compiled 24 to 18 computations (25% saved)

regimes28.0ms (0.5%)

Accuracy

Total -16.9b remaining (-38.9%)

Threshold costs -16.9b (-38.9%)

Counts

8 → 2

Calls

Call 1

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

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

Calls

2 calls:

15.0ms	x
10.0ms	p

Results

Error	Segments	Branch
43.3b	2	`p`
47.6b	2	`x`

Compiler

Compiled 65 to 37 computations (43.1% saved)

bsearch76.0ms (1.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
75.0ms	-1.6982543834110598e-294	-8.587880788532667e-296

Compiler

Compiled 24 to 18 computations (25% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	142
1	57	142
2	61	142
3	64	142
4	65	142

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))) -1) (/.f64 (neg.f64 p) x) (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (*.f64 2 p) x))))))
(if (<=.f64 p -6837453353259503/1393796574908163946345982392040522594123776) (sqrt.f64 1/2) (if (<=.f64 p -8484769782575063/1552518092300708935148979488462502555256886017116696611139052038026050952686376886330878408828646477950487730697131073206171580044114814391444287275041181139204454976020849905550265285631598444825262999193716468750892846853816057856) (/.f64 p x) (if (<=.f64 p 7726984329600999/38981256045599996321413529551500753243504907430380030107471625828851794763065704409862460263528041036901219664925634672733836679460812376186311949185250613678125110799825892119483158621960214593411198373916873515494742391701579499782985454461875862451310955212417110188327314359967656443904) (sqrt.f64 (*.f64 1/2 2)) (if (<=.f64 p 3751440131168131/20769187434139310514121985316880384) (/.f64 (neg.f64 p) x) (sqrt.f64 1/2)))))
(if (<=.f64 p -6837453353259503/1393796574908163946345982392040522594123776) (sqrt.f64 1/2) (if (<=.f64 p -1221176098523159/719077253944926363091722076315609893447190791576922629093720324630930703222003852530833909289630144084480455519485573430635159075257666489971389722557896497511071573699461941105208878404984376477812331808340023075352602729369851525895652442163308948653402042738345192959788983753918865219341425318496896548864) (/.f64 p x) (if (<=.f64 p 3751440131168131/20769187434139310514121985316880384) (/.f64 (neg.f64 p) x) (sqrt.f64 1/2))))
(if (<=.f64 p -1221176098523159/719077253944926363091722076315609893447190791576922629093720324630930703222003852530833909289630144084480455519485573430635159075257666489971389722557896497511071573699461941105208878404984376477812331808340023075352602729369851525895652442163308948653402042738345192959788983753918865219341425318496896548864) (/.f64 p x) (/.f64 (neg.f64 p) x))
(/.f64 p x)

Outputs
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))) -1) (/.f64 (neg.f64 p) x) (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (*.f64 2 p) x))))))
(if (<=.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) -1) (/.f64 (neg.f64 p) x) (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (hypot.f64 (*.f64 p 2) x))))))
(if (<=.f64 p -6837453353259503/1393796574908163946345982392040522594123776) (sqrt.f64 1/2) (if (<=.f64 p -8484769782575063/1552518092300708935148979488462502555256886017116696611139052038026050952686376886330878408828646477950487730697131073206171580044114814391444287275041181139204454976020849905550265285631598444825262999193716468750892846853816057856) (/.f64 p x) (if (<=.f64 p 7726984329600999/38981256045599996321413529551500753243504907430380030107471625828851794763065704409862460263528041036901219664925634672733836679460812376186311949185250613678125110799825892119483158621960214593411198373916873515494742391701579499782985454461875862451310955212417110188327314359967656443904) (sqrt.f64 (*.f64 1/2 2)) (if (<=.f64 p 3751440131168131/20769187434139310514121985316880384) (/.f64 (neg.f64 p) x) (sqrt.f64 1/2)))))
(if (<=.f64 p -6837453353259503/1393796574908163946345982392040522594123776) (sqrt.f64 1/2) (if (<=.f64 p -8484769782575063/1552518092300708935148979488462502555256886017116696611139052038026050952686376886330878408828646477950487730697131073206171580044114814391444287275041181139204454976020849905550265285631598444825262999193716468750892846853816057856) (/.f64 p x) (if (<=.f64 p 7726984329600999/38981256045599996321413529551500753243504907430380030107471625828851794763065704409862460263528041036901219664925634672733836679460812376186311949185250613678125110799825892119483158621960214593411198373916873515494742391701579499782985454461875862451310955212417110188327314359967656443904) 1 (if (<=.f64 p 3751440131168131/20769187434139310514121985316880384) (/.f64 (neg.f64 p) x) (sqrt.f64 1/2)))))
(if (<=.f64 p -6837453353259503/1393796574908163946345982392040522594123776) (sqrt.f64 1/2) (if (<=.f64 p -1221176098523159/719077253944926363091722076315609893447190791576922629093720324630930703222003852530833909289630144084480455519485573430635159075257666489971389722557896497511071573699461941105208878404984376477812331808340023075352602729369851525895652442163308948653402042738345192959788983753918865219341425318496896548864) (/.f64 p x) (if (<=.f64 p 3751440131168131/20769187434139310514121985316880384) (/.f64 (neg.f64 p) x) (sqrt.f64 1/2))))
(if (<=.f64 p -1221176098523159/719077253944926363091722076315609893447190791576922629093720324630930703222003852530833909289630144084480455519485573430635159075257666489971389722557896497511071573699461941105208878404984376477812331808340023075352602729369851525895652442163308948653402042738345192959788983753918865219341425318496896548864) (/.f64 p x) (/.f64 (neg.f64 p) x))
(/.f64 p x)

Compiler

Compiled 106 to 74 computations (30.2% saved)

soundness77.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

555×	`associate-*l/_binary64`
532×	`associate-*r/_binary64`
405×	`distribute-rgt-in_binary64`
404×	`distribute-lft-in_binary64`
317×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	289	3139
1	946	2992
2	3656	2729
0	10	360
1	16	360
2	27	360
3	35	360
4	42	360
5	50	360
6	58	360
7	68	360
8	78	360
9	97	360
10	98	360

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 81 to 65 computations (19.8% saved)

end50.0ms (0.8%)

Compiler: Compiled 98 to 57 computations (41.8% saved)

Iter	Nodes	Cost
0	10	360
1	16	360
2	27	360
3	35	360
4	42	360
5	50	360
6	58	360
7	68	360
8	78	360
9	97	360
10	98	360

Iter	Nodes	Cost
0	10	360
1	16	360
2	27	360
3	35	360
4	42	360
5	50	360
6	58	360
7	68	360
8	78	360
9	97	360
10	98	360

Details

analyze488.0ms (8.1%)

sample1.9s (31.1%)

preprocess17.0ms (0.3%)

simplify8.0ms (0.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize35.0ms (0.6%)

series23.0ms (0.4%)

rewrite91.0ms (1.5%)

simplify85.0ms (1.4%)

eval149.0ms (2.5%)

prune50.0ms (0.8%)

localize22.0ms (0.4%)

series19.0ms (0.3%)

rewrite83.0ms (1.4%)

simplify89.0ms (1.5%)

localize3.0ms (0.1%)

localize11.0ms (0.2%)

localize15.0ms (0.2%)

series9.0ms (0.1%)

rewrite68.0ms (1.1%)

simplify54.0ms (0.9%)

localize16.0ms (0.3%)

series10.0ms (0.2%)

rewrite110.0ms (1.8%)

simplify59.0ms (1%)

eval211.0ms (3.5%)

prune70.0ms (1.2%)

localize22.0ms (0.4%)

series4.0ms (0.1%)

rewrite57.0ms (0.9%)

simplify52.0ms (0.9%)

localize5.0ms (0.1%)

localize13.0ms (0.2%)

series9.0ms (0.2%)

rewrite67.0ms (1.1%)

simplify78.0ms (1.3%)

localize16.0ms (0.3%)

series4.0ms (0.1%)

rewrite70.0ms (1.2%)

simplify56.0ms (0.9%)

localize18.0ms (0.3%)

series12.0ms (0.2%)

rewrite115.0ms (1.9%)

simplify26.0ms (0.4%)

eval88.0ms (1.5%)

prune51.0ms (0.8%)

localize17.0ms (0.3%)

series18.0ms (0.3%)

rewrite59.0ms (1%)

simplify76.0ms (1.3%)

localize4.0ms (0.1%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite45.0ms (0.8%)

simplify8.0ms (0.1%)

localize8.0ms (0.1%)

series2.0ms (0%)

rewrite55.0ms (0.9%)

simplify9.0ms (0.1%)

localize7.0ms (0.1%)

series9.0ms (0.2%)

rewrite56.0ms (0.9%)

simplify9.0ms (0.1%)

eval114.0ms (1.9%)

prune42.0ms (0.7%)

regimes268.0ms (4.5%)

bsearch1.0ms (0%)

regimes120.0ms (2%)

bsearch215.0ms (3.6%)

regimes40.0ms (0.7%)

bsearch152.0ms (2.5%)

regimes28.0ms (0.5%)

bsearch76.0ms (1.3%)

simplify9.0ms (0.2%)

soundness77.0ms (1.3%)

end50.0ms (0.8%)

Profiling

Iter	Nodes	Cost
0	10	360
1	16	360
2	27	360
3	35	360
4	42	360
5	50	360
6	58	360
7	68	360
8	78	360
9	97	360
10	98	360