Details

analyze178.0ms (4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
28.6%	25%	62.5%	0%	0%	0%	12.5%	4
30.8%	25%	56.2%	0%	0%	0%	18.7%	5
36%	28.1%	50%	0%	0%	0%	21.9%	6
38.8%	29.7%	46.9%	0%	0%	0%	23.4%	7
40.2%	30.5%	45.3%	0%	0%	0%	24.2%	8
40.7%	30.8%	44.9%	0%	0%	0%	24.2%	9
41.2%	31.2%	44.5%	0%	0%	0%	24.2%	10
41.4%	31.3%	44.4%	0%	0%	0%	24.2%	11
41.5%	31.4%	44.3%	0%	0%	0%	24.3%	12

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.0s (46.1%)

Results

1.0s	2790×	body	1024	valid
401.0ms	3819×	body	256	valid
385.0ms	1382×	body	512	valid
119.0ms	265×	body	2048	valid
6.0ms	50×	body	256	infinite
0.0ms	1×	body	256	unsamplable

Bogosity

preprocess39.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

1440×	`associate-/l*`
1382×	`associate-r`
1160×	`associate-/r*`
968×	`associate-l`
702×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	27	25
2	36	25
3	62	25
4	135	21
5	349	15
6	1238	15
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify34.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1440×	`associate-/l*`
1382×	`associate-r`
1160×	`associate-/r*`
968×	`associate-l`
702×	`fma-def`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	27	25
2	36	25
3	62	25
4	135	21
5	349	15
6	1238	15

Stop Event

1×	node limit

Counts

1 → 5

Calls

Call 1

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

Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (+.f64 1 (exp.f64 x)) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

eval1.0ms (0%)

Compiler: Compiled 41 to 29 computations (29.3% saved)

prune37.0ms (0.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	4	1	5
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	5	1	6

Error

0.0b

Counts

6 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 14 to 8 computations (42.9% saved)

series1.0ms (0%)

Counts

2 → 8

Calls

6 calls:

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

rewrite58.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1470×	`add-sqr-sqrt`
1452×	`*-un-lft-identity`
1352×	`add-cube-cbrt`
1340×	`add-cbrt-cube`
1328×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	156	26
2	1851	26

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 1 (exp.f64 x))

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

Outputs

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

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

simplify60.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1462×	`associate-/l*`
1180×	`distribute-lft-in`
1010×	`unswap-sqr`
814×	`associate-/r*`
662×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	2019
1	388	1795
2	1270	1463
3	4226	1417

Stop Event

1×	node limit

Counts

69 → 103

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (.f64 1/2 (pow.f64 x 2)) x)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (/.f64 1 (-.f64 1 (exp.f64 x))))
(.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x)))))
(.f64 (.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(.f64 (.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (pow.f64 (exp.f64 x) 3))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 2)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(exp.f64 (log1p.f64 (exp.f64 x)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(fma.f64 1 (exp.f64 x) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (/.f64 3/8 (sqrt.f64 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (/.f64 3/8 (sqrt.f64 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 x (fma.f64 x (*.f64 1/2 x) 2))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(+.f64 2 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 x (fma.f64 1/6 (pow.f64 x 3) (fma.f64 x (*.f64 1/2 x) 2)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) 1/2)
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) 1/2)
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 1))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) 1/2)
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))
(.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 4))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (/.f64 1 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(.f64 (.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(.f64 (.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))
(.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 4))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (pow.f64 (exp.f64 x) 3))))
(/.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(/.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) 1) (expm1.f64 x))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (neg.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 2)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(exp.f64 (log1p.f64 (exp.f64 x)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1))
(exp.f64 (log1p.f64 (exp.f64 x)))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(fma.f64 1 (exp.f64 x) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 1 (exp.f64 x))

eval26.0ms (0.6%)

Compiler: Compiled 1286 to 912 computations (29.1% saved)

prune30.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	5	104

Error

Counts

104 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
▶	0.6b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)
▶	23.5b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	19.1b	(sqrt.f64 2)

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize2.0ms (0%)

Compiler: Compiled 4 to 4 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 2 x))

Compiler

Compiled 10 to 7 computations (30% saved)

series1.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite49.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1482×	`add-sqr-sqrt`
1458×	`*-un-lft-identity`
1368×	`add-cube-cbrt`
1358×	`add-cbrt-cube`
1348×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	148	11
2	1810	11

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 2 x))

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

Outputs

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

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1128×	`associate-r`
968×	`associate-l`
764×	`associate-/l*`
682×	`fma-def`
672×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	800
1	191	672
2	505	560
3	1419	516
4	6085	516

Stop Event

1×	node limit

Counts

28 → 45

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2))
(/.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(pow.f64 (+.f64 2 x) 1/2)
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 3)
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (+.f64 2 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))
(exp.f64 (*.f64 (log.f64 (+.f64 2 x)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 -1/8 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3)) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (.f64 -1/16 (/.f64 (.f64 x x) (sqrt.f64 2)))) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (fma.f64 -1/16 (/.f64 x (/.f64 (sqrt.f64 2) x)) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5)) (*.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (/.f64 x -16)))))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) (cbrt.f64 (+.f64 2 x)))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 2 x))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (+.f64 2 x)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2)
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 2 x)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 2 x)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 2 x))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (+.f64 2 x)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2)
(/.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (+.f64 4 (*.f64 x (-.f64 x 2)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (+.f64 4 (*.f64 x (+.f64 x -2)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (fma.f64 x (+.f64 x -2) 4)))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(pow.f64 (+.f64 2 x) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 2 x))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(fabs.f64 (sqrt.f64 (+.f64 2 x)))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(cbrt.f64 (pow.f64 (+.f64 2 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (+.f64 2 x)) 1/2))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 2 x)) 1))
(+.f64 (sqrt.f64 (+.f64 2 x)) 0)
(sqrt.f64 (+.f64 2 x))

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 x))
	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	0.6b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)

Compiler

Compiled 30 to 20 computations (33.3% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite81.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1408×	`associate-*r/`
1078×	`associate-*l/`
884×	`distribute-lft-in`
808×	`*-commutative`
320×	`associate-+l+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	217	15
2	2979	15

Stop Event

1×	node limit

Counts

1 → 119

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 1)

Outputs

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

simplify105.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1588×	`associate-/l*`
1284×	`associate-/r*`
860×	`*-commutative`
800×	`associate-*r/`
640×	`associate-+r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	8013
1	896	7745
2	3120	7733

Stop Event

1×	node limit

Counts

131 → 191

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 1 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (*.f64 (pow.f64 1 1/2) 0))
(+.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1)
(+.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) 1)
(+.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 (.f64 (pow.f64 1 1/2) 1) (.f64 (pow.f64 1 1/2) (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))))
(+.f64 (.f64 (pow.f64 1 1/2) (expm1.f64 (.f64 (log1p.f64 (exp.f64 x)) 1/2))) (*.f64 (pow.f64 1 1/2) 1))
(+.f64 (.f64 (pow.f64 1 1/2) (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (.f64 (pow.f64 1 1/2) -1))
(+.f64 (.f64 (pow.f64 1 1/2) -1) (.f64 (pow.f64 1 1/2) (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 1 1/2))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))
(*.f64 (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))) (-.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) 1))
(*.f64 (-.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) 1) (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))))
(*.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1))
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(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 x))))
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(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3) 3) 1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))) (+.f64 (.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3))))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) 1) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) 1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1)
(fma.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) -1)

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (sqrt.f64 2))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (.f64 x x) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/6 (/.f64 (.f64 1/2 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2))) (pow.f64 (sqrt.f64 2) 2))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (.f64 x x) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)))) (*.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 1 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)))
(+.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x)))))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 0)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (*.f64 (pow.f64 1 1/2) 0))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2)) 1)
(+.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x)))))
(+.f64 -1 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (.f64 (pow.f64 1 1/2) 1) (.f64 (pow.f64 1 1/2) (expm1.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))))
(+.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x)))))
(+.f64 (.f64 (pow.f64 1 1/2) (expm1.f64 (.f64 (log1p.f64 (exp.f64 x)) 1/2))) (*.f64 (pow.f64 1 1/2) 1))
(+.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x)))))
(+.f64 (.f64 (pow.f64 1 1/2) (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (.f64 (pow.f64 1 1/2) -1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (.f64 (pow.f64 1 1/2) -1) (.f64 (pow.f64 1 1/2) (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 1 1/2))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (+.f64 2 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 2 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(*.f64 (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))) (-.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) 1))
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))) (+.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) -1))
(fma.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) -1)
(*.f64 (-.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) 1) (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))))
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))) (+.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) -1))
(fma.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) -1)
(*.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))) (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (+.f64 2 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 2 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2)) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2) (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2)) 1/2))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1)) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (-.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))) (-.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3))) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (-.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3))) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (neg.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3))) (-.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (-.f64 (.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2)) (*.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))) (-.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (-.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 4) (.f64 (+.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (+.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (-.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 4) (.f64 (+.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (-.f64 -2 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (-.f64 -2 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 (pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) 3) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2) 3))) (-.f64 (+.f64 (.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2)) (.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))) (.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))
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(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) -1) (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) 1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (+.f64 2 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 2 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (+.f64 2 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 2 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2) (+.f64 2 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (+.f64 2 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)) (+.f64 2 (+.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 2))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) 1/2)
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fma.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) -1)
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))) (+.f64 (hypot.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) -1))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) -1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
✓	0.2b	(sqrt.f64 (exp.f64 x))

Compiler

Compiled 13 to 6 computations (53.8% saved)

series2.0ms (0%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
0.0ms	x	@	-inf	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
0.0ms	x	@	inf	(sqrt.f64 (exp.f64 x))
0.0ms	x	@	0	(sqrt.f64 (exp.f64 x))
0.0ms	x	@	0	(hypot.f64 1 (sqrt.f64 (exp.f64 x)))

rewrite55.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1234×	`add-sqr-sqrt`
1222×	`*-un-lft-identity`
1152×	`pow1`
1124×	`add-cube-cbrt`
1112×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	147	24
2	1577	24

Stop Event

1×	node limit

Counts

2 → 37

Calls

Call 1

Inputs
(sqrt.f64 (exp.f64 x))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))

Outputs

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

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

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1566×	`fma-def`
918×	`*-commutative`
870×	`associate-r`
794×	`associate-/l*`
664×	`associate-l`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	1371
1	253	1129
2	942	947
3	3261	863

Stop Event

1×	node limit

Counts

53 → 73

Calls

Call 1

Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/48 (pow.f64 x 3)))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(-.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(*.f64 (sqrt.f64 (exp.f64 x)) 1)
(*.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (pow.f64 (exp.f64 x) 1/4) (pow.f64 (exp.f64 x) 1/4))
(*.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (exp.f64 x)))
(*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (sqrt.f64 (exp.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (exp.f64 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1/2) (pow.f64 (cbrt.f64 (exp.f64 x)) 1/2))
(pow.f64 (exp.f64 x) 1/2)
(pow.f64 (sqrt.f64 (exp.f64 x)) 1)
(pow.f64 (pow.f64 (exp.f64 x) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (exp.f64 x) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))
(cbrt.f64 (pow.f64 (exp.f64 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 x))))
(exp.f64 (*.f64 x 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (exp.f64 x))))
(-.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1)
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(*.f64 (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 (exp.f64 x) 1)))
(*.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(pow.f64 (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 2)
(pow.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 3)
(pow.f64 (+.f64 (exp.f64 x) 1) 1/2)
(pow.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3) 1/3)
(sqrt.f64 (+.f64 (exp.f64 x) 1))
(log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(cbrt.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(exp.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))

Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) 1))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/8) 1))
(fma.f64 x (fma.f64 x 1/8 1/2) 1)
(+.f64 (.f64 1/8 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (+.f64 1 (*.f64 1/48 (pow.f64 x 3)))))
(fma.f64 1/8 (.f64 x x) (+.f64 (fma.f64 1/2 x 1) (.f64 1/48 (pow.f64 x 3))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/48 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/8) (fma.f64 1/48 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/48 1/8)) 1))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x)))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (+.f64 1/6 (.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x)))) (/.f64 (.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(+.f64 (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))) (fma.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3) (sqrt.f64 2)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(-.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(*.f64 (sqrt.f64 (exp.f64 x)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(*.f64 1 (sqrt.f64 (exp.f64 x)))
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(*.f64 (pow.f64 (exp.f64 x) 1/4) (pow.f64 (exp.f64 x) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(*.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (exp.f64 x)))
(*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (sqrt.f64 (exp.f64 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) (cbrt.f64 (exp.f64 x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (fabs.f64 (cbrt.f64 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(pow.f64 (cbrt.f64 (exp.f64 x)) 3/2)
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (exp.f64 x)))
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1/2) (pow.f64 (cbrt.f64 (exp.f64 x)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (fabs.f64 (cbrt.f64 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(*.f64 (cbrt.f64 (exp.f64 x)) (sqrt.f64 (cbrt.f64 (exp.f64 x))))
(pow.f64 (cbrt.f64 (exp.f64 x)) 3/2)
(pow.f64 (exp.f64 x) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(pow.f64 (sqrt.f64 (exp.f64 x)) 1)
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(pow.f64 (pow.f64 (exp.f64 x) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(pow.f64 (cbrt.f64 (sqrt.f64 (exp.f64 x))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(pow.f64 (pow.f64 (exp.f64 x) 3/2) 1/3)
(cbrt.f64 (pow.f64 (exp.f64 x) 3/2))
(fabs.f64 (sqrt.f64 (exp.f64 x)))
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(log.f64 (exp.f64 (sqrt.f64 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(cbrt.f64 (pow.f64 (exp.f64 x) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(exp.f64 (*.f64 x 1/2))
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(log1p.f64 (expm1.f64 (sqrt.f64 (exp.f64 x))))
(+.f64 1 (-.f64 (sqrt.f64 (exp.f64 x)) 1))
(+.f64 (sqrt.f64 (exp.f64 x)) 0)
(sqrt.f64 (exp.f64 x))
(-.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 (exp.f64 x) 1)))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 (exp.f64 x) 1)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(pow.f64 (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 2)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(pow.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 3)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(pow.f64 (+.f64 (exp.f64 x) 1) 1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3) 1/3)
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 (exp.f64 x) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(cbrt.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(+.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1))
(+.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 0)
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))

eval203.0ms (4.6%)

Compiler: Compiled 8629 to 6731 computations (22% saved)

prune88.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	409	3	412
Fresh	0	0	0
Picked	1	0	1
Done	1	3	4
Total	411	6	417

Error

Counts

417 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	22.2b	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
▶	0.0b	(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))
▶	19.7b	(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
✓	23.5b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	19.1b	(sqrt.f64 2)

Compiler

Compiled 36 to 32 computations (11.1% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 15 to 15 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite54.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1504×	`add-sqr-sqrt`
1480×	`*-un-lft-identity`
1398×	`add-cube-cbrt`
1386×	`add-cbrt-cube`
1378×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	174	5
2	2198	5

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (sqrt.f64 2)) 1)

Outputs

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

simplify44.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1294×	`associate-r`
1134×	`associate-l`
968×	`fma-def`
938×	`distribute-lft-in`
758×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	994
1	252	682
2	1111	640

Stop Event

1×	node limit

Counts

40 → 53

Calls

Call 1

Inputs
(+.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1))
(+.f64 1 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) 1))
(+.f64 (+.f64 1 (sqrt.f64 2)) -1)
(+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 0)
(+.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) 1)
(+.f64 -1 (+.f64 1 (sqrt.f64 2)))
(*.f64 1 (-.f64 (+.f64 1 (sqrt.f64 2)) 1))
(*.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 1)
(*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4))
(*.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) (cbrt.f64 2))
(*.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(.f64 (.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) (/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2)))
(*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2))))
(*.f64 (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1))
(/.f64 1 (/.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)))
(/.f64 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2))
(/.f64 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) (-.f64 (+.f64 1 (sqrt.f64 2)) -1))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2)))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 2)) -1))))
(/.f64 (-.f64 1 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1))) (-.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1)) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1))))
(/.f64 (neg.f64 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1))) (neg.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2))))
(pow.f64 2 1/2)
(pow.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 1)
(pow.f64 (pow.f64 2 1/4) 2)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) 3)
(pow.f64 (pow.f64 2 3/2) 1/3)
(sqrt.f64 2)
(log.f64 (exp.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(cbrt.f64 (pow.f64 2 3/2))
(expm1.f64 (log1p.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(exp.f64 (log.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(exp.f64 (*.f64 (log.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) 1))
(exp.f64 (*.f64 (log.f64 2) 1/2))
(log1p.f64 (expm1.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(fma.f64 1 (+.f64 1 (sqrt.f64 2)) -1)
(fma.f64 (hypot.f64 1 (pow.f64 2 1/4)) (hypot.f64 1 (pow.f64 2 1/4)) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 2))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 2))) -1)

Outputs
(+.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(+.f64 1 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) 1))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(+.f64 (+.f64 1 (sqrt.f64 2)) -1)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 0)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(+.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) 1)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(+.f64 -1 (+.f64 1 (sqrt.f64 2)))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(*.f64 1 (-.f64 (+.f64 1 (sqrt.f64 2)) 1))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(*.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 1)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(*.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) (cbrt.f64 2))
(*.f64 (cbrt.f64 (+.f64 0 (sqrt.f64 2))) (cbrt.f64 2))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))
(*.f64 (cbrt.f64 2) (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(*.f64 (cbrt.f64 (+.f64 0 (sqrt.f64 2))) (cbrt.f64 2))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))
(.f64 (.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) (/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2)))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(*.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 1 (-.f64 (sqrt.f64 2) -1)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(*.f64 (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 2 1/4)) 1))
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 2 1/4))) (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) -1))
(fma.f64 (hypot.f64 1 (pow.f64 2 1/4)) (hypot.f64 1 (pow.f64 2 1/4)) -1)
(/.f64 1 (/.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1))))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2)) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 1 (-.f64 (sqrt.f64 2) -1)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(/.f64 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) (-.f64 (+.f64 1 (sqrt.f64 2)) -1))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 1 (-.f64 (sqrt.f64 2) -1)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (-.f64 1 (*.f64 (+.f64 1 (sqrt.f64 2)) -1))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 1 (-.f64 (sqrt.f64 2) -1)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(/.f64 (-.f64 1 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1))) (-.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1)))
(/.f64 (-.f64 1 (*.f64 (+.f64 (+.f64 0 (sqrt.f64 2)) -1) (+.f64 (+.f64 0 (sqrt.f64 2)) -1))) (-.f64 1 (+.f64 (+.f64 0 (sqrt.f64 2)) -1)))
(/.f64 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) (+.f64 (sqrt.f64 2) -1))) (-.f64 2 (sqrt.f64 2)))
(/.f64 (+.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 2) -2)) (-.f64 2 (sqrt.f64 2)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1)) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) -1))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (+.f64 0 (sqrt.f64 2)) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (+.f64 0 (sqrt.f64 2)) -1) (+.f64 (+.f64 0 (sqrt.f64 2)) -1)) (+.f64 (+.f64 0 (sqrt.f64 2)) -1))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (+.f64 1 (*.f64 (+.f64 (sqrt.f64 2) -1) (-.f64 (+.f64 (sqrt.f64 2) -1) 1))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (sqrt.f64 2) -1) 3)) (fma.f64 (+.f64 (sqrt.f64 2) -1) (+.f64 (sqrt.f64 2) -2) 1))
(/.f64 (neg.f64 (*.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2) (-.f64 (+.f64 1 (sqrt.f64 2)) 1))) (neg.f64 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2)))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 2)) 2) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (/.f64 1 (+.f64 (+.f64 1 (-.f64 (sqrt.f64 2) -1)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (sqrt.f64 2)) (pow.f64 (+.f64 1 (sqrt.f64 2)) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 2)) 3)) (+.f64 (+.f64 2 (pow.f64 2 3/2)) (+.f64 (sqrt.f64 2) 3)))
(pow.f64 2 1/2)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(pow.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1) 1)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(pow.f64 (pow.f64 2 1/4) 2)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(pow.f64 (cbrt.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) 3)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(pow.f64 (pow.f64 2 3/2) 1/3)
(cbrt.f64 (pow.f64 2 3/2))
(sqrt.f64 2)
(+.f64 0 (sqrt.f64 2))
(log.f64 (exp.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(cbrt.f64 (pow.f64 2 3/2))
(expm1.f64 (log1p.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(exp.f64 (log.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(exp.f64 (*.f64 (log.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)) 1))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(exp.f64 (*.f64 (log.f64 2) 1/2))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(log1p.f64 (expm1.f64 (-.f64 (+.f64 1 (sqrt.f64 2)) 1)))
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(fma.f64 1 (+.f64 1 (sqrt.f64 2)) -1)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)
(fma.f64 (hypot.f64 1 (pow.f64 2 1/4)) (hypot.f64 1 (pow.f64 2 1/4)) -1)
(*.f64 (+.f64 1 (hypot.f64 1 (pow.f64 2 1/4))) (+.f64 (hypot.f64 1 (pow.f64 2 1/4)) -1))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 2))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 2))) -1)
(+.f64 0 (sqrt.f64 2))
(sqrt.f64 2)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite75.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1416×	`add-sqr-sqrt`
1402×	`*-un-lft-identity`
1294×	`add-cube-cbrt`
1280×	`add-cbrt-cube`
1264×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	170	15
2	1796	15

Stop Event

1×	node limit

Counts

1 → 18

Calls

Call 1

Inputs
(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))

Outputs

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

simplify60.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1108×	`fma-def`
726×	`*-commutative`
724×	`associate-r`
718×	`associate-/l*`
626×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	968
1	172	592
2	698	580
3	2579	532
4	7582	532

Stop Event

1×	node limit

Counts

30 → 34

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(-.f64 (+.f64 1 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))) 1)
(.f64 1 (hypot.f64 1 (exp.f64 (.f64 x 1/2))))
(.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2))) 1)
(.f64 (sqrt.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2)))) (sqrt.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2)))))
(pow.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2))) 1)
(pow.f64 (sqrt.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))) 2)
(pow.f64 (cbrt.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))) 3)
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(pow.f64 (pow.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2))) 3) 1/3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))
(cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2))) 3))
(expm1.f64 (log1p.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))
(exp.f64 (log.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))
(exp.f64 (.f64 (log.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2)))) 1))
(log1p.f64 (expm1.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (/.f64 7/192 (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(+.f64 (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))) (fma.f64 (/.f64 7/192 (sqrt.f64 2)) (pow.f64 x 3) (sqrt.f64 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 (*.f64 1/2 x)) 2)))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(-.f64 (+.f64 1 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))) 1)
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(.f64 1 (hypot.f64 1 (exp.f64 (.f64 x 1/2))))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2))) 1)
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(.f64 (sqrt.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2)))) (sqrt.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(.f64 (cbrt.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2)))))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2))) 1)
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))) 2)
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (cbrt.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))) 3)
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2))) 3) 1/3)
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(log.f64 (exp.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2))) 3))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(expm1.f64 (log1p.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (log.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (.f64 (log.f64 (hypot.f64 1 (exp.f64 (.f64 x 1/2)))) 1))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (expm1.f64 (hypot.f64 1 (exp.f64 (*.f64 x 1/2)))))
(sqrt.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 1/2) x) 2)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 15 computations (21.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite55.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1554×	`add-sqr-sqrt`
1538×	`*-un-lft-identity`
1434×	`add-cube-cbrt`
1420×	`add-cbrt-cube`
1406×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	167	15
2	1942	15

Stop Event

1×	node limit

Counts

1 → 18

Calls

Call 1

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

Outputs

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

simplify50.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1052×	`associate-/r*`
904×	`*-commutative`
866×	`associate-/r/`
830×	`associate-*r/`
798×	`associate-r`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	884
1	199	760
2	790	640
3	3375	564

Stop Event

1×	node limit

Counts

30 → 58

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 x (sqrt.f64 2))) (.f64 -1/4 (/.f64 (*.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (pow.f64 (sqrt.f64 2) 3))))))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 x) (/.f64 1 x))) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) 1)
(-.f64 (*.f64 -1/2 x) (+.f64 1 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 1 (/.f64 1 x)))
(-.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 1)
(.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))
(.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 1)
(.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
(pow.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)
(pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)
(pow.f64 (pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 3) 1/3)
(pow.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 1/2 x) 1) 2)) 1/2)
(sqrt.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 1/2 x) 1) 2)))
(log.f64 (exp.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(cbrt.f64 (pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 3))
(expm1.f64 (log1p.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(exp.f64 (log.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(exp.f64 (.f64 (log.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 1))
(log1p.f64 (expm1.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 1/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 x (sqrt.f64 2))) (.f64 -1/4 (/.f64 (*.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (pow.f64 (sqrt.f64 2) 3))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/4 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (.f64 -1/8 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (sqrt.f64 2)))))
(fma.f64 1/2 (fma.f64 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (fma.f64 -1/8 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (sqrt.f64 2)))
(+.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2)) (.f64 (.f64 1/8 (/.f64 (.f64 x x) (sqrt.f64 2))) (+.f64 1/2 (.f64 x -1/8))))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(+.f64 1 (fma.f64 1/2 x (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 1/2 x 1))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 x) (/.f64 1 x))) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1 (-.f64 (fma.f64 1/2 x (/.f64 1 x)) (/.f64 2 (*.f64 x x))))
(+.f64 (fma.f64 1/2 x (/.f64 1 x)) (+.f64 1 (/.f64 -2 (*.f64 x x))))
(+.f64 1 (+.f64 (fma.f64 1/2 x (/.f64 1 x)) (/.f64 -2 (*.f64 x x))))
(+.f64 (-.f64 1 (/.f64 -1 x)) (fma.f64 1/2 x (/.f64 -2 (*.f64 x x))))
(*.f64 -1/2 x)
(*.f64 x -1/2)
(-.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x -1)
(fma.f64 x -1/2 -1)
(-.f64 (*.f64 -1/2 x) (+.f64 1 (/.f64 1 x)))
(-.f64 (fma.f64 -1/2 x -1) (/.f64 1 x))
(-.f64 (fma.f64 x -1/2 -1) (/.f64 1 x))
(+.f64 (fma.f64 x -1/2 -1) (/.f64 -1 x))
(-.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 1 (/.f64 1 x)))
(-.f64 (fma.f64 -1/2 x (/.f64 2 (*.f64 x x))) (+.f64 1 (/.f64 1 x)))
(+.f64 (/.f64 2 (*.f64 x x)) (-.f64 (fma.f64 x -1/2 -1) (/.f64 1 x)))
(+.f64 (/.f64 2 (*.f64 x x)) (+.f64 (fma.f64 x -1/2 -1) (/.f64 -1 x)))
(-.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 1)
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 1)
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 3) 1/3)
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 1/2 x) 1) 2)) 1/2)
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(sqrt.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 1/2 x) 1) 2)))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(log.f64 (exp.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(cbrt.f64 (pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 3))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(expm1.f64 (log1p.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(exp.f64 (log.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(exp.f64 (.f64 (log.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 1))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(log1p.f64 (expm1.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(+.f64 1 (-.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 1))
(+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))

eval95.0ms (2.1%)

Compiler: Compiled 2060 to 1863 computations (9.6% saved)

prune25.0ms (0.6%)

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	139	6	145
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	139	12	151

Error

Counts

151 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	22.2b	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
✓	0.0b	(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))
▶	22.8b	(-.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 1)
✓	19.7b	(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
▶	62.1b	(-.f64 (*.f64 -1/2 x) 1)
	62.3b	(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
▶	55.2b	(+.f64 1 (*.f64 1/2 x))
▶	61.3b	(*.f64 x -1/2)
▶	62.1b	(*.f64 1/2 x)
✓	23.5b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	19.1b	(sqrt.f64 2)

Compiler

Compiled 120 to 102 computations (15% saved)

localize14.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 39 to 33 computations (15.4% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite110.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1170×	`associate-*r/`
930×	`associate-*l/`
832×	`*-commutative`
702×	`distribute-lft-in`
660×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	228	15
2	3050	15

Stop Event

1×	node limit

Counts

1 → 87

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))) (-.f64 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))) 1) (+.f64 1 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))) (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1)) (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1) (-.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))) (-.f64 0 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3))) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) (-.f64 0 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)) (-.f64 (*.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)) (*.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2) (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))) (-.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)) (+.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) 3) (pow.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2) 3))) (+.f64 (*.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)) (-.f64 (*.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2) (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)) (*.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) (-.f64 1 (*.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) -1))) (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1) (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2) (/.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2) (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)) (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) (-.f64 1 (*.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1)) (/.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1))))))) (#(struct:change #<rule egg-rr> (2) 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simplify111.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1372×	`associate-/r*`
1270×	`associate-*r/`
898×	`*-commutative`
750×	`associate-*l/`
656×	`associate--r+`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	6353
1	756	6209
2	3540	6197

Stop Event

1×	node limit

Counts

99 → 166

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 x (sqrt.f64 2))) (.f64 -1/4 (/.f64 (*.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (pow.f64 (sqrt.f64 2) 3))))))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 x) (/.f64 1 x))) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(*.f64 -1/2 x)
(-.f64 (*.f64 -1/2 x) 1)
(-.f64 (*.f64 -1/2 x) (+.f64 1 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 1 (/.f64 1 x)))
(+.f64 1 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) -1))
(+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 0)
(+.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) -1)
(+.f64 0 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(+.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) -1) 1)
(+.f64 -1 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))
(.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 1)
(.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))
(.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))))
(.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))))) (-.f64 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))) 1))
(.f64 (-.f64 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) 1) (+.f64 1 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))))
(.f64 (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1))
(.f64 (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))) (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))
(.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1)) (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))
(.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (-.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))) (-.f64 0 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))))
(.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (-.f64 0 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (-.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))) (-.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (+.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) 3) (pow.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) 3))) (+.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (-.f64 (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)) (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))))
(/.f64 1 (/.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (-.f64 1 (.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) -1))) (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))))
(/.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
(/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2))
(/.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (/.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (-.f64 1 (.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) -1))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1)) (/.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1))))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (/.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))) (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))))
(/.f64 (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (-.f64 1 (.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) -1))) (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1)) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1))) (/.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1))))
(/.f64 (.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))) (/.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))))
(/.f64 (.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))) (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (-.f64 1 (.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) -1))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)))))
(/.f64 (-.f64 1 (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1))) (+.f64 (-.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 1))
(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) 1) (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))))
(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) 1) (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3))))
(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) 1) (.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (-.f64 1 (.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) -1))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1) 3)) (+.f64 1 (-.f64 (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1)) (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) -1))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) 3) 1) (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (+.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) 3) 1) (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))) (+.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) 3) 1) (.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (-.f64 1 (.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) -1))) (+.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1)) (neg.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))
(/.f64 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (neg.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))
(/.f64 (.f64 1 (-.f64 1 (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1)))) (+.f64 (-.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 1))
(/.f64 (.f64 1 (+.f64 1 (pow.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1) 3))) (+.f64 1 (-.f64 (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1)) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1))))
(/.f64 (.f64 1 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1))) (neg.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))
(/.f64 (.f64 1 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))) (neg.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))))
(/.f64 (.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1))) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))
(/.f64 (.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1))) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))
(/.f64 (.f64 (-.f64 1 (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1))) 1) (+.f64 (-.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 1))
(/.f64 (.f64 (+.f64 1 (pow.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1) 3)) 1) (+.f64 1 (-.f64 (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1)) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) -1))))
(/.f64 (.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1)) 1) (neg.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))
(/.f64 (.f64 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) 1) (neg.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1)) (sqrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))
(/.f64 (.f64 (sqrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (sqrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1)) (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))
(/.f64 (.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) 1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))
(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) 3) 1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2))) (+.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) 1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)))
(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) 3) 1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))))) (+.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) 1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2))) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) 1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))))) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))))) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))))
(pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
(pow.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)
(pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)
(pow.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 1/2 x) 1) 2)) 1/2)
(pow.f64 (pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 3) 1/3)
(sqrt.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 1/2 x) 1) 2)))
(log.f64 (exp.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(log.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))))
(cbrt.f64 (pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 3))
(expm1.f64 (log1p.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
(exp.f64 (log.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(log1p.f64 (expm1.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(fma.f64 1 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) -1)
(fma.f64 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) -1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) 2) (cbrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) -1)

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (sqrt.f64 2))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (.f64 x x) (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 x (sqrt.f64 2))) (.f64 -1/4 (/.f64 (*.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (pow.f64 (sqrt.f64 2) 3))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/4 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3)))))))
(+.f64 (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (sqrt.f64 2)) (.f64 -1/8 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (.f64 x x) (/.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)))) (.f64 (/.f64 (.f64 (-.f64 1/4 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 3)) (sqrt.f64 2)) -1/8)))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
(+.f64 1 (fma.f64 1/2 x (/.f64 1 x)))
(+.f64 (/.f64 1 x) (fma.f64 1/2 x 1))
(-.f64 (+.f64 1 (+.f64 (.f64 1/2 x) (/.f64 1 x))) (.f64 2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1 (-.f64 (fma.f64 1/2 x (/.f64 1 x)) (/.f64 2 (*.f64 x x))))
(+.f64 (fma.f64 1/2 x (/.f64 1 x)) (+.f64 1 (/.f64 -2 (*.f64 x x))))
(+.f64 (/.f64 1 x) (-.f64 (fma.f64 1/2 x 1) (/.f64 2 (*.f64 x x))))
(*.f64 -1/2 x)
(*.f64 x -1/2)
(-.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x -1)
(fma.f64 x -1/2 -1)
(-.f64 (*.f64 -1/2 x) (+.f64 1 (/.f64 1 x)))
(-.f64 (fma.f64 -1/2 x -1) (/.f64 1 x))
(-.f64 (fma.f64 x -1/2 -1) (/.f64 1 x))
(-.f64 (+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 (pow.f64 x 2)))) (+.f64 1 (/.f64 1 x)))
(-.f64 (fma.f64 -1/2 x (/.f64 2 (*.f64 x x))) (+.f64 1 (/.f64 1 x)))
(+.f64 (/.f64 2 (*.f64 x x)) (-.f64 (fma.f64 x -1/2 -1) (/.f64 1 x)))
(+.f64 1 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) -1))
(hypot.f64 1 (fma.f64 1/2 x 1))
(+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 0)
(hypot.f64 1 (fma.f64 1/2 x 1))
(+.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) -1)
(hypot.f64 1 (fma.f64 1/2 x 1))
(+.f64 0 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(hypot.f64 1 (fma.f64 1/2 x 1))
(+.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) -1) 1)
(hypot.f64 1 (fma.f64 1/2 x 1))
(+.f64 -1 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 1)
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (/.f64 1 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))
(.f64 (+.f64 1 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))))) (-.f64 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))) 1))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (-.f64 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) 1) (+.f64 1 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2) -1))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))) (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (/.f64 1 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))
(.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1)) (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (-.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))) (-.f64 0 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (-.f64 0 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))))
(/.f64 (*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) (neg.f64 (hypot.f64 1 (fma.f64 1/2 x 1))))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3))) (-.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) (hypot.f64 1 (fma.f64 1/2 x 1))))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (-.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))) (-.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (-.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 4) (.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1)))))) (-.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1)))))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 4) (.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (-.f64 -2 (hypot.f64 1 (fma.f64 1/2 x 1)))))) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) (-.f64 -2 (hypot.f64 1 (fma.f64 1/2 x 1)))))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (+.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) 3) (pow.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) 3))) (+.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (-.f64 (.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)) (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))))
(.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (+.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) 3) (pow.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) 3))) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 4) (.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (-.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)))))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (+.f64 (pow.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 6))) (fma.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (-.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 4)))
(/.f64 1 (/.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (-.f64 1 (.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) -1))) (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))))
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(/.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))) (/.f64 (cbrt.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1)))) (pow.f64 (cbrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)))
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(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) (/.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))) (cbrt.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))))))
(/.f64 (.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))) (pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))
(/.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) (/.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) (cbrt.f64 (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))) (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3))))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) (/.f64 (cbrt.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3))) (cbrt.f64 (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) 1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 4) -1) (*.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 4)) (*.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))
(*.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (/.f64 (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))
(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) 3) 1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2))) (+.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))))
(/.f64 (+.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) 3) -1) (*.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 4) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 6)) (*.f64 (+.f64 2 (hypot.f64 1 (fma.f64 1/2 x 1))) (+.f64 1 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 4)))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) 1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 6) -1) (*.f64 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 6)) (*.f64 (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3))))
(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) 3) 1) (/.f64 1 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))))) (+.f64 (.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3))))
(/.f64 (+.f64 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3) 3) -1) (*.f64 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))) (+.f64 (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 6))))
(/.f64 (+.f64 -1 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3) 3)) (*.f64 (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))) (+.f64 (+.f64 1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 6))))
(/.f64 (+.f64 -1 (pow.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3) 3)) (*.f64 (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))) (+.f64 1 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 6)))))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) 1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2))
(hypot.f64 1 (fma.f64 1/2 x 1))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2))) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))
(hypot.f64 1 (fma.f64 1/2 x 1))
(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2) -1) (.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) 2)))) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 2)))
(hypot.f64 1 (fma.f64 1/2 x 1))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) 1) (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (/.f64 1 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2))))) (sqrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (/.f64 1 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))
(/.f64 (/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 3)) (.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))))) (cbrt.f64 (+.f64 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1))) 2)))))
(*.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (/.f64 1 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (+.f64 2 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 3)) (+.f64 2 (+.f64 (hypot.f64 1 (fma.f64 1/2 x 1)) (pow.f64 (+.f64 1 (hypot.f64 1 (fma.f64 1/2 x 1))) 2))))
(pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (sqrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 2)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (cbrt.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 3)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 1/2 x) 1) 2)) 1/2)
(hypot.f64 1 (fma.f64 1/2 x 1))
(pow.f64 (pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 3) 1/3)
(hypot.f64 1 (fma.f64 1/2 x 1))
(sqrt.f64 (+.f64 1 (pow.f64 (+.f64 (*.f64 1/2 x) 1) 2)))
(hypot.f64 1 (fma.f64 1/2 x 1))
(log.f64 (exp.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(log.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(cbrt.f64 (pow.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1)) 3))
(hypot.f64 1 (fma.f64 1/2 x 1))
(expm1.f64 (log1p.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
(hypot.f64 1 (fma.f64 1/2 x 1))
(exp.f64 (log.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(log1p.f64 (expm1.f64 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))))
(hypot.f64 1 (fma.f64 1/2 x 1))
(fma.f64 1 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) -1)
(hypot.f64 1 (fma.f64 1/2 x 1))
(fma.f64 (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) (sqrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) -1)
(hypot.f64 1 (fma.f64 1/2 x 1))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) 2) (cbrt.f64 (+.f64 1 (hypot.f64 1 (+.f64 (.f64 1/2 x) 1)))) -1)
(hypot.f64 1 (fma.f64 1/2 x 1))

localize4.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize2.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.1%)

Compiler: Compiled 12 to 9 computations (25% saved)

localize5.0ms (0.1%)

Compiler: Compiled 12 to 9 computations (25% saved)

eval224.0ms (5.1%)

Compiler: Compiled 6551 to 5901 computations (9.9% saved)

prune33.0ms (0.7%)

Pruning

13 alts after pruning (2 fresh and 11 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	0	1	1
Picked	0	1	1
Done	0	10	10
Total	223	13	236

Error

Counts

236 → 13

Alt Table

Click to see full alt table

Status	Error	Program
✓	22.2b	(hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))
✓	0.0b	(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))
✓	22.8b	(-.f64 (+.f64 1 (hypot.f64 1 (+.f64 (*.f64 1/2 x) 1))) 1)
	55.2b	(-.f64 (+.f64 1 (+.f64 1 (*.f64 1/2 x))) 1)
✓	19.7b	(-.f64 (+.f64 1 (sqrt.f64 2)) 1)
✓	62.1b	(-.f64 (*.f64 -1/2 x) 1)
	62.3b	(+.f64 1 (+.f64 (*.f64 1/2 x) (/.f64 1 x)))
✓	55.2b	(+.f64 1 (*.f64 1/2 x))
✓	61.3b	(*.f64 x -1/2)
✓	62.1b	(*.f64 1/2 x)
✓	23.5b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	19.1b	(sqrt.f64 2)

Compiler

Compiled 88 to 76 computations (13.6% saved)

regimes22.0ms (0.5%)

Counts

16 → 1

Calls

Call 1

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

Outputs
(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))

Calls

3 calls:

11.0ms	x
3.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
3.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))`
0.0b	1	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`

Compiler

Compiled 129 to 105 computations (18.6% saved)

regimes9.0ms (0.2%)

Counts

12 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 72 to 60 computations (16.7% saved)

regimes47.0ms (1.1%)

Counts

11 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

44.0ms

Results

Error	Segments	Branch
19.1b	1	`x`

Compiler

Compiled 67 to 56 computations (16.4% saved)

regimes6.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

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

Outputs
(+.f64 1 (*.f64 1/2 x))

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
55.2b	1	`x`

Compiler

Compiled 37 to 29 computations (21.6% saved)

regimes5.0ms (0.1%)

Accuracy

Total -1.5b remaining (-2.5%)

Threshold costs -1.5b (-2.5%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(*.f64 x -1/2)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
61.3b	1	`x`

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative`
4×	`*-commutative`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	64
1	24	64

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

Outputs
(hypot.f64 1 (exp.f64 (*.f64 x 1/2)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 x 1/2))
(*.f64 x -1/2)
(*.f64 1/2 x)
(*.f64 x 1/2)

Compiler

Compiled 30 to 25 computations (16.7% saved)

soundness67.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1440×	`associate-/l*`
1382×	`associate-r`
1160×	`associate-/r*`
968×	`associate-l`
702×	`fma-def`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	27	25
2	36	25
3	62	25
4	135	21
5	349	15
6	1238	15

Stop Event

1×	node limit

Compiler

Compiled 85 to 56 computations (34.1% saved)

end56.0ms (1.3%)

Compiler: Compiled 25 to 20 computations (20% saved)

Details

analyze178.0ms (4%)

sample2.0s (46.1%)

preprocess39.0ms (0.9%)

simplify34.0ms (0.8%)

eval1.0ms (0%)

prune37.0ms (0.8%)

localize6.0ms (0.1%)

series1.0ms (0%)

rewrite58.0ms (1.3%)

simplify60.0ms (1.4%)

eval26.0ms (0.6%)

prune30.0ms (0.7%)

localize2.0ms (0%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite49.0ms (1.1%)

simplify57.0ms (1.3%)

localize11.0ms (0.2%)

series0.0ms (0%)

rewrite81.0ms (1.8%)

simplify105.0ms (2.4%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite55.0ms (1.2%)

simplify55.0ms (1.2%)

eval203.0ms (4.6%)

prune88.0ms (2%)

localize6.0ms (0.1%)

series0.0ms (0%)

rewrite54.0ms (1.2%)

simplify44.0ms (1%)

localize7.0ms (0.2%)

series2.0ms (0%)

rewrite75.0ms (1.7%)

simplify60.0ms (1.4%)

localize8.0ms (0.2%)

series1.0ms (0%)

rewrite55.0ms (1.2%)

simplify50.0ms (1.1%)

eval95.0ms (2.1%)

prune25.0ms (0.6%)

localize14.0ms (0.3%)

series0.0ms (0%)

rewrite110.0ms (2.5%)

simplify111.0ms (2.5%)

localize4.0ms (0.1%)

localize2.0ms (0.1%)

localize5.0ms (0.1%)

localize5.0ms (0.1%)

eval224.0ms (5.1%)

prune33.0ms (0.7%)

regimes22.0ms (0.5%)

regimes9.0ms (0.2%)

regimes47.0ms (1.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

simplify5.0ms (0.1%)

soundness67.0ms (1.5%)

end56.0ms (1.3%)

Profiling