Details

analyze173.0ms (3.4%)

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)

sample2.2s (43.3%)

Results

1.2s	2750×	body	1024	valid
411.0ms	1417×	body	512	valid
396.0ms	3782×	body	256	valid
140.0ms	307×	body	2048	valid
6.0ms	51×	body	256	infinite
0.0ms	3×	body	256	unsamplable

Bogosity

preprocess61.0ms (1.2%)

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)

simplify35.0ms (0.7%)

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)

prune1.0ms (0%)

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

Counts

6 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

series0.0ms (0%)

Counts

1 → 4

Calls

3 calls:

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

rewrite49.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1318×	`add-sqr-sqrt`
1302×	`*-un-lft-identity`
1212×	`add-cube-cbrt`
1200×	`add-cbrt-cube`
1188×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	137	11
2	1629	11

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

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

Outputs

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

simplify46.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1100×	`distribute-lft-in`
976×	`distribute-rgt-in`
936×	`associate-/l*`
798×	`associate-r`
784×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	840
1	200	790
2	709	616
3	2924	592

Stop Event

1×	node limit

Counts

34 → 51

Calls

Call 1

Inputs
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 (+.f64 1 (exp.f64 x))) 1)
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (/.f64 1 (-.f64 1 (exp.f64 x))))
(.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (/.f64 1 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (+.f64 x x)))))
(/.f64 1 (/.f64 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (exp.f64 (.f64 x 3)))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 (exp.f64 (+.f64 x x)) 1) (expm1.f64 x))
(/.f64 (neg.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (neg.f64 (+.f64 1 (exp.f64 (.f64 x 3)))) (neg.f64 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x)))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(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)))
(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 (cbrt.f64 (exp.f64 (+.f64 x x))) (cbrt.f64 (exp.f64 x)) 1)

Outputs
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 2 (fma.f64 x (*.f64 x 1/2) x))
(+.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 x (*.f64 x 1/2) x)))
(+.f64 (fma.f64 x (*.f64 x 1/2) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 2 (expm1.f64 x))
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(*.f64 1 (+.f64 1 (exp.f64 x)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 2 (expm1.f64 x))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 2 (expm1.f64 x))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 2 (expm1.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 2 (expm1.f64 x))
(*.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 2 (expm1.f64 x))
(*.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (/.f64 1 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(.f64 (+.f64 1 (exp.f64 (.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 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (+.f64 x x)))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 1 (/.f64 (+.f64 1 (.f64 (exp.f64 x) (expm1.f64 x))) (+.f64 1 (exp.f64 (.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 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (+.f64 1 (exp.f64 (.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 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 (exp.f64 (+.f64 x x)) (-.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 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (-.f64 (exp.f64 (+.f64 x x)) 1) (expm1.f64 x))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (neg.f64 (-.f64 1 (exp.f64 (+.f64 x x)))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (exp.f64 (+.f64 x x))) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 2 (expm1.f64 x)) 1)
(/.f64 (neg.f64 (+.f64 1 (exp.f64 (.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))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (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 2 (expm1.f64 x))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 2 (expm1.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 2 (expm1.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 2 (expm1.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 2 (expm1.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 2 (expm1.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 2 (expm1.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 2 (expm1.f64 x))
(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 2 (expm1.f64 x))
(fma.f64 1 (exp.f64 x) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (+.f64 (exp.f64 x) -1))
(+.f64 2 (expm1.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 2 (expm1.f64 x))
(fma.f64 (cbrt.f64 (exp.f64 (+.f64 x x))) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 2) x)) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (cbrt.f64 (exp.f64 x)) 1)

eval10.0ms (0.2%)

Compiler: Compiled 547 to 359 computations (34.4% saved)

prune31.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	3	52

Error

Counts

52 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	20.3b	(sqrt.f64 (+.f64 2 x))
✓	0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	16.8b	(sqrt.f64 2)

Compiler

Compiled 14 to 12 computations (14.3% 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
0.0ms	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))

rewrite53.0ms (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))))))))

simplify55.0ms (1.1%)

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))

eval11.0ms (0.2%)

Compiler: Compiled 510 to 426 computations (16.5% saved)

prune9.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	44	4	48

Error

Counts

48 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	20.9b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
✓	20.3b	(sqrt.f64 (+.f64 2 x))
✓	0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	16.8b	(sqrt.f64 2)

Compiler

Compiled 23 to 20 computations (13% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 2 x))
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 2 x)))
✓	0.7b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)

Compiler

Compiled 25 to 20 computations (20% saved)

series1.0ms (0%)

Counts

2 → 8

Calls

6 calls:

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

rewrite91.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1450×	`associate-*r/`
1116×	`associate-*l/`
848×	`distribute-lft-in`
812×	`*-commutative`
312×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	40
1	223	28
2	3006	28

Stop Event

1×	node limit

Counts

2 → 197

Calls

Call 1

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

Outputs

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

simplify134.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1188×	`associate-+r-`
1084×	`+-commutative`
1000×	`associate-+l-`
808×	`associate--l+`
568×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	508	10645
1	1434	10089
2	5598	10063

Stop Event

1×	node limit

Counts

205 → 313

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

eval217.0ms (4.2%)

Compiler: Compiled 8431 to 7336 computations (13% saved)

prune81.0ms (1.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	355	3	358
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	355	7	362

Error

Counts

362 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.6b	(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
▶	17.5b	(-.f64 (+.f64 (sqrt.f64 2) 1) 1)
✓	20.9b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
▶	21.6b	(-.f64 (*.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (-.f64 -1 x)) 1)
✓	20.3b	(sqrt.f64 (+.f64 2 x))
✓	0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	16.8b	(sqrt.f64 2)

Compiler

Compiled 58 to 51 computations (12.1% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x))))
	0.0b	(sqrt.f64 (+.f64 2 x))
✓	0.7b	(-.f64 (*.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (-.f64 -1 x)) 1)
✓	1.1b	(-.f64 1 (sqrt.f64 (+.f64 2 x)))

Compiler

Compiled 55 to 45 computations (18.2% saved)

series9.0ms (0.2%)

Counts

3 → 12

Calls

9 calls:

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

rewrite133.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1456×	`associate-/r*`
1118×	`associate-/r/`
856×	`associate-/l*`
320×	`add-sqr-sqrt`
308×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	316	51
2	4242	51

Stop Event

1×	node limit

Counts

3 → 263

Calls

Call 1

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

Outputs

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

simplify163.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1140×	`associate-r`
922×	`associate-/r*`
854×	`distribute-lft-in`
792×	`associate-l`
768×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	750	15101
1	2275	14915

Stop Event

1×	node limit

Counts

275 → 432

Calls

Call 1

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

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

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 15 to 15 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite53.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1462×	`add-sqr-sqrt`
1438×	`*-un-lft-identity`
1356×	`add-cube-cbrt`
1348×	`add-cbrt-cube`
1338×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	5
2	2183	5

Stop Event

1×	node limit

Counts

1 → 44

Calls

Call 1

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

Outputs

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

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1150×	`distribute-rgt-out`
968×	`associate-r`
842×	`associate-l`
706×	`distribute-lft-in`
658×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	688
1	227	638
2	895	618
3	6734	608

Stop Event

1×	node limit

Counts

44 → 51

Calls

Call 1

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

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

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x))))
	0.0b	(sqrt.f64 (+.f64 2 x))
✓	0.7b	(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
	1.1b	(-.f64 1 (sqrt.f64 (+.f64 2 x)))

Compiler

Compiled 43 to 34 computations (20.9% saved)

series5.0ms (0.1%)

Counts

2 → 8

Calls

6 calls:

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

rewrite87.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1428×	`associate-/l*`
1312×	`associate-/r/`
784×	`associate-/l/`
306×	`add-sqr-sqrt`
294×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	64
1	298	28
2	4160	28

Stop Event

1×	node limit

Counts

2 → 155

Calls

Call 1

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

Outputs

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

simplify208.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1244×	`associate-+r-`
866×	`distribute-lft-in`
828×	`associate-r`
802×	`distribute-rgt-in`
620×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	463	9505
1	1477	8885
2	7481	8855

Stop Event

1×	node limit

Counts

163 → 274

Calls

Call 1

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

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

eval642.0ms (12.6%)

Compiler: Compiled 28810 to 25108 computations (12.8% saved)

prune243.0ms (4.7%)

Pruning

12 alts after pruning (6 fresh and 6 done)

	Pruned	Kept	Total
New	1049	6	1055
Fresh	0	0	0
Picked	0	1	1
Done	1	5	6
Total	1050	12	1062

Error

Counts

1062 → 12

Alt Table

Click to see full alt table

Status	Error	Program
	17.5b	(/.f64 2 (sqrt.f64 2))
	21.6b	(-.f64 (/.f64 (-.f64 -1 x) (/.f64 (/.f64 (-.f64 -1 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x))))) (-.f64 -1 x))) 1)
✓	21.6b	(-.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (sqrt.f64 (+.f64 2 x)))) 1)
	20.9b	(-.f64 (/.f64 (-.f64 -1 x) (.f64 (/.f64 (-.f64 1 (.f64 x x)) (+.f64 1 (sqrt.f64 (+.f64 2 x)))) (/.f64 1 (+.f64 x -1)))) 1)
	21.6b	(-.f64 (/.f64 (-.f64 -1 x) (.f64 (-.f64 1 (sqrt.f64 (+.f64 2 x))) (.f64 (/.f64 (-.f64 -1 x) (-.f64 1 (*.f64 x x))) (+.f64 x -1)))) 1)
	18.1b	(-.f64 (/.f64 -1 (-.f64 1 (sqrt.f64 2))) 1)
✓	20.9b	(-.f64 (+.f64 1 (sqrt.f64 (+.f64 2 x))) 1)
✓	21.6b	(-.f64 (*.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 2 x)))) (-.f64 -1 x)) 1)
	20.9b	(-.f64 (.f64 (.f64 (/.f64 1 (-.f64 -1 x)) (+.f64 1 (sqrt.f64 (+.f64 2 x)))) (-.f64 -1 x)) 1)
✓	20.3b	(sqrt.f64 (+.f64 2 x))
✓	0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	16.8b	(sqrt.f64 2)

Compiler

Compiled 159 to 134 computations (15.7% saved)

regimes23.0ms (0.4%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

3 calls:

9.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
7.0ms	x
3.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))`
0b	1	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`

Compiler

Compiled 193 to 159 computations (17.6% saved)

regimes10.0ms (0.2%)

Accuracy

Total -5.4b remaining (-32%)

Threshold costs -5.4b (-32%)

Counts

12 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
16.8b	1	`x`

Compiler

Compiled 151 to 125 computations (17.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	13	20

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)

Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)

Compiler

Compiled 9 to 8 computations (11.1% saved)

soundness64.0ms (1.3%)

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)

end50.0ms (1%)

Compiler: Compiled 8 to 7 computations (12.5% saved)

Details

analyze173.0ms (3.4%)

sample2.2s (43.3%)

preprocess61.0ms (1.2%)

simplify35.0ms (0.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series0.0ms (0%)

rewrite49.0ms (1%)

simplify46.0ms (0.9%)

eval10.0ms (0.2%)

prune31.0ms (0.6%)

localize2.0ms (0%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite53.0ms (1%)

simplify55.0ms (1.1%)

eval11.0ms (0.2%)

prune9.0ms (0.2%)

localize10.0ms (0.2%)

series1.0ms (0%)

rewrite91.0ms (1.8%)

simplify134.0ms (2.6%)

eval217.0ms (4.2%)

prune81.0ms (1.6%)

localize22.0ms (0.4%)

series9.0ms (0.2%)

rewrite133.0ms (2.6%)

simplify163.0ms (3.2%)

localize7.0ms (0.1%)

series0.0ms (0%)

rewrite53.0ms (1%)

simplify78.0ms (1.5%)

localize17.0ms (0.3%)

series5.0ms (0.1%)

rewrite87.0ms (1.7%)

simplify208.0ms (4.1%)

eval642.0ms (12.6%)

prune243.0ms (4.7%)

regimes23.0ms (0.4%)

regimes10.0ms (0.2%)

simplify4.0ms (0.1%)

soundness64.0ms (1.3%)

end50.0ms (1%)

Profiling