Metrics for sqrtexp (problem 3.4.4)

analyze122.0ms (2.4%)

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
50%	50%	50%	0%	0%	0%	0%	3
50%	50%	50%	0%	0%	0%	0%	4
50%	50%	50%	0%	0%	0%	0%	5
53.1%	53.1%	46.9%	0%	0%	0%	0%	6
54.7%	54.7%	45.3%	0%	0%	0%	0%	7
55.5%	55.4%	44.5%	0%	0%	0%	0%	8
55.9%	55.8%	44.1%	0%	0%	0%	0%	9
56.1%	56%	43.9%	0%	0%	0%	0%	10
56.2%	56.1%	43.8%	0%	0%	0%	0%	11
56.2%	56.2%	43.8%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.5s (48.9%)

Results

1.2s	2825×	body	1024	valid
607.0ms	3770×	body	256	valid
254.0ms	1308×	body	512	valid
196.0ms	2647×	body	256	unsamplable
183.0ms	306×	body	2048	valid
5.0ms	47×	body	256	infinite

Bogosity

preprocess45.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

1382×	`associate-r`
1260×	`associate-/l*`
1064×	`associate-/r*`
1038×	`associate-l`
904×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	27	25
2	36	25
3	62	25
4	130	21
5	352	15
6	1351	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)

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1382×	`associate-r`
1260×	`associate-/l*`
1064×	`associate-/r*`
1038×	`associate-l`
904×	`fma-def`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	27	25
2	36	25
3	62	25
4	130	21
5	352	15
6	1351	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)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	3	2	5
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	3	6

Accurracy

100.0%

Counts

6 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	32.8%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
▶	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	32.8%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
▶	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 38 to 32 computations (15.8% saved)

localize152.0ms (3%)

Local Accuracy

Found 6 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
✓	99.3%	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
✓	36.4%	(-.f64 (exp.f64 (*.f64 2 x)) 1)
✓	36.3%	(-.f64 (exp.f64 x) 1)
✓	100.0%	(+.f64 1 (exp.f64 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 60 to 40 computations (33.3% saved)

series4.0ms (0.1%)

Counts

6 → 24

Calls

18 calls:

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

rewrite120.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1620×	`prod-diff`
1226×	`log-prod`
938×	`fma-def`
456×	`log1p-udef`
452×	`expm1-udef`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	68
1	323	68
2	4313	68

Stop Event

1×	node limit

Counts

6 → 388

Calls

Call 1

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

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

simplify195.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1108×	`times-frac`
890×	`fma-neg`
640×	`associate-r`
606×	`associate-l`
522×	`associate-/l*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	655	17774
1	1456	15348
2	6820	15054

Stop Event

1×	node limit

Counts

412 → 487

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (.f64 1/2 (pow.f64 x 2)) x)))
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(*.f64 2 x)
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (*.f64 2 x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (.f64 2 x))))
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)))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
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(*.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (+.f64 x x)))
(*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(*.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (/.f64 1 (-.f64 1 (exp.f64 x))))
(.f64 (.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (/.f64 (expm1.f64 (+.f64 x x)) (cbrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (expm1.f64 (+.f64 x x)) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) 1) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(*.f64 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (cbrt.f64 (expm1.f64 x))))
(.f64 (.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (.f64 x 3))) (+.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) (exp.f64 x)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) (+.f64 1 (exp.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)) 2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1)
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (exp.f64 x)))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) 3) (pow.f64 (expm1.f64 x) 3)))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(exp.f64 (log1p.f64 (exp.f64 x)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(fma.f64 1 (exp.f64 x) 1)
(fma.f64 1 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (exp.f64 x) 1 1)
(fma.f64 (pow.f64 (exp.f64 2) x) (/.f64 1 (expm1.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (*.f64 (cbrt.f64 (exp.f64 x)) 1) 1)
(fma.f64 (cbrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (*.f64 (sqrt.f64 (exp.f64 x)) 1) 1)
(fma.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x))) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x)))) (cbrt.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x))) (sqrt.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) x) 2))) (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2)) 1)
(fma.f64 (/.f64 1 (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (/.f64 (pow.f64 (exp.f64 2) x) (cbrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 (pow.f64 (exp.f64 2) x) (sqrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) x) 2)) 1) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (expm1.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) x) 2)) (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) x) 2)) (sqrt.f64 (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 x) 1) (/.f64 (exp.f64 x) (expm1.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (*.f64 x 3))) (+.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) (exp.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x))) (+.f64 1 (exp.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))
(+.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 1)
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 1 (expm1.f64 x)) 1/2))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))
(/.f64 1 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(/.f64 1 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 2) x))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (+.f64 1/6 (.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
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 (.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 2 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x)))
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x)))
(*.f64 2 x)
(+.f64 x x)
(+.f64 (.f64 2 (pow.f64 x 2)) (.f64 2 x))
(.f64 2 (+.f64 (.f64 x x) x))
(*.f64 2 (fma.f64 x x x))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (*.f64 2 x)))
(fma.f64 2 (*.f64 x x) (fma.f64 4/3 (pow.f64 x 3) (+.f64 x x)))
(+.f64 (.f64 (pow.f64 x 3) 4/3) (.f64 2 (fma.f64 x x x)))
(+.f64 (.f64 2 (pow.f64 x 2)) (+.f64 (.f64 2/3 (pow.f64 x 4)) (+.f64 (.f64 4/3 (pow.f64 x 3)) (.f64 2 x))))
(fma.f64 2 (*.f64 x x) (fma.f64 2/3 (pow.f64 x 4) (fma.f64 4/3 (pow.f64 x 3) (+.f64 x x))))
(+.f64 (fma.f64 (pow.f64 x 4) 2/3 (.f64 (pow.f64 x 3) 4/3)) (.f64 2 (fma.f64 x x x)))
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 (.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 2 (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x)))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (+.f64 1/6 (.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(+.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 1 (expm1.f64 x)) 1/2))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
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(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) x) 2)) (sqrt.f64 (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 2) x) 2)) (sqrt.f64 (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 -1 (expm1.f64 x)))
(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (exp.f64 2) (+.f64 x x))) (sqrt.f64 (expm1.f64 x))) (/.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 -1 (expm1.f64 x)))
(fma.f64 (/.f64 (exp.f64 x) 1) (/.f64 (exp.f64 x) (expm1.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 x)) (/.f64 -1 (expm1.f64 x)))
(*.f64 (/.f64 1 (expm1.f64 x)) (+.f64 (pow.f64 (exp.f64 2) x) -1))
(/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) -1) (expm1.f64 x))
(fma.f64 (/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (expm1.f64 x) 2))) (/.f64 (exp.f64 x) (cbrt.f64 (expm1.f64 x))) (/.f64 -1 (expm1.f64 x)))
(fma.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (/.f64 (exp.f64 x) (sqrt.f64 (expm1.f64 x))) (/.f64 -1 (expm1.f64 x)))
(fma.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (*.f64 x 3))) (+.f64 (+.f64 1 (pow.f64 (exp.f64 2) x)) (exp.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (*.f64 x 3))) (+.f64 1 (+.f64 (pow.f64 (exp.f64 2) x) (exp.f64 x))) (/.f64 -1 (expm1.f64 x)))
(fma.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (*.f64 x 3))) (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 2) x))) (/.f64 -1 (expm1.f64 x)))
(fma.f64 (+.f64 (exp.f64 x) (+.f64 1 (pow.f64 (exp.f64 x) 2))) (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 (*.f64 x 3))) (/.f64 -1 (expm1.f64 x)))
(fma.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x))) (+.f64 1 (exp.f64 x)) (neg.f64 (/.f64 1 (expm1.f64 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 2) x) (expm1.f64 (+.f64 x x))) (+.f64 1 (exp.f64 x)) (/.f64 -1 (expm1.f64 x)))
(fma.f64 (+.f64 1 (exp.f64 x)) (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 (+.f64 x x))) (/.f64 -1 (expm1.f64 x)))
(+.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 1 (expm1.f64 x)) 1/2))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 1 (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(/.f64 1 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(/.f64 1 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 1 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 2) x))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(*.f64 1 (/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 1))
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))

eval208.0ms (4.1%)

Compiler: Compiled 12439 to 7693 computations (38.2% saved)

prune66.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	484	3	487
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	485	4	489

Accurracy

100.0%

Counts

489 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(/.f64 1 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
▶	69.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	74.6%	(sqrt.f64 2)
▶	99.0%	(/.f64 1 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
▶	69.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	74.6%	(sqrt.f64 2)

Compiler

Compiled 48 to 42 computations (12.5% saved)

localize88.0ms (1.8%)

Local Accuracy

Found 5 expressions with local accuracy:

New	Accuracy	Program
	100.0%	(+.f64 1 (exp.f64 x))
✓	100.0%	(sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))
✓	100.0%	(/.f64 1 (+.f64 1 (exp.f64 x)))
✓	99.0%	(/.f64 1 (sqrt.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
✓	100.0%	(sqrt.f64 (+.f64 2 x))

Compiler

Compiled 44 to 31 computations (29.5% saved)

series4.0ms (0.1%)

Counts

4 → 24

Calls

12 calls:

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

rewrite83.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1096×	`log-prod`
682×	`pow-prod-down`
660×	`pow-exp`
632×	`pow-prod-up`
466×	`fma-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	76
1	278	60
2	3523	60

Stop Event

1×	node limit

Counts

4 → 188

Calls

Call 1

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

Outputs
(+.f64 0 (sqrt.f64 (+.f64 2 x)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x)))) 1)
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(*.f64 (cbrt.f64 (+.f64 2 x)) (pow.f64 (+.f64 2 x) 1/6))
(*.f64 (pow.f64 (+.f64 2 x) 1/6) (cbrt.f64 (+.f64 2 x)))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (fma.f64 x (-.f64 x 2) 4)))
(pow.f64 (+.f64 2 x) 1/2)
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2)
(pow.f64 (pow.f64 (+.f64 2 x) 1/6) 3)
(pow.f64 (pow.f64 (+.f64 2 x) 2) 1/4)
(pow.f64 (pow.f64 (+.f64 2 x) 3) 1/6)
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(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))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1) 1))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 2 x) 1/6)) 3))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (+.f64 2 x))) 1/3))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (+.f64 2 x))) 2))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 1)
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 -1 (/.f64 1 (/.f64 -1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -1)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) -3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) -3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) 3)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2) -1/4)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) -1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) -1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) -2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(pow.f64 (neg.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) -1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(exp.f64 (.f64 (.f64 -1/2 (log1p.f64 (exp.f64 x))) -1))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 1))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) -1/2))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) -1) -1/2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1) -1/2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2) -1))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) 1) -1))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) -1) 1))
(exp.f64 (.f64 (.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))) 1) 1))
(exp.f64 (.f64 (.f64 1/3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 2))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 0 (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))) (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))) 1)
(*.f64 1 (/.f64 1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2)))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 3/4))
(*.f64 -1 (/.f64 1 (neg.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 3/4) (pow.f64 (+.f64 1 (exp.f64 x)) -1/4))
(*.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 5/6) (pow.f64 (+.f64 1 (exp.f64 x)) -1/6))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(*.f64 (/.f64 1 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (-.f64 1 (exp.f64 x)))
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 2)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) -2)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) 6)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) 1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) 2/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) -1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) -1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) 4)
(pow.f64 (+.f64 1 (exp.f64 x)) -1)
(pow.f64 (neg.f64 (neg.f64 (+.f64 1 (exp.f64 x)))) -1)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2))
(log.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3))
(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(exp.f64 (neg.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) -1))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) -1) 1))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1) 1))
(exp.f64 (.f64 (.f64 -1/2 (log1p.f64 (exp.f64 x))) 2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2) 2))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) 1) 2))
(exp.f64 (.f64 (.f64 1/3 (neg.f64 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 -2 (log1p.f64 (exp.f64 x))) 1/2))
(exp.f64 (.f64 (.f64 3 (neg.f64 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) -1))
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(+.f64 0 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))) (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))) 1)
(*.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 1)
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (pow.f64 (+.f64 1 (exp.f64 x)) -1/6))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) -1/4))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2))) (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))))
(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(/.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(/.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 1)
(/.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(/.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(/.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(/.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1)
(/.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (+.f64 1 (exp.f64 x)))))
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 1)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) -1)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) -3)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2) 1/4)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) 1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) 1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) -1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) -1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) 2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) -2)
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(pow.f64 (/.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1) -1)
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(log.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2))
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))
(exp.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2))
(exp.f64 (.f64 (.f64 -1/2 (log1p.f64 (exp.f64 x))) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) -1) 1/2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1) 1/2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2) 1))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) 1) 1))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) -1))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) -1) -1))
(exp.f64 (.f64 (.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))) 1) -1))
(exp.f64 (.f64 (.f64 1/3 (*.f64 -1/2 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 3/2 (neg.f64 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 1/4 (neg.f64 (log1p.f64 (exp.f64 x)))) 2))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) -1/2))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) -1/2))
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))

simplify91.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

998×	`fma-def`
700×	`times-frac`
636×	`exp-prod`
634×	`sqr-pow`
594×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	458	5050
1	1037	4756
2	2710	4528

Stop Event

1×	node limit

Counts

212 → 271

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))))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
1/2
(+.f64 1/2 (*.f64 -1/4 x))
(+.f64 1/2 (+.f64 (.f64 -1/4 x) (.f64 1/48 (pow.f64 x 3))))
(+.f64 (.f64 -1/480 (pow.f64 x 5)) (+.f64 1/2 (+.f64 (.f64 -1/4 x) (*.f64 1/48 (pow.f64 x 3)))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/8 (/.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1/8 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/48 (.f64 1/512 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (pow.f64 x 3)) (sqrt.f64 1/2))) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 -1/8 (/.f64 x (sqrt.f64 1/2))))))
(+.f64 0 (sqrt.f64 (+.f64 2 x)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x)))) 1)
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(*.f64 (cbrt.f64 (+.f64 2 x)) (pow.f64 (+.f64 2 x) 1/6))
(*.f64 (pow.f64 (+.f64 2 x) 1/6) (cbrt.f64 (+.f64 2 x)))
(*.f64 (pow.f64 (+.f64 2 x) 1/4) (pow.f64 (+.f64 2 x) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(/.f64 (sqrt.f64 (-.f64 4 (*.f64 x x))) (sqrt.f64 (-.f64 2 x)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (fma.f64 x (-.f64 x 2) 4)))
(pow.f64 (+.f64 2 x) 1/2)
(pow.f64 (sqrt.f64 (+.f64 2 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 2 x)) 3/2)
(pow.f64 (pow.f64 (+.f64 2 x) 1/6) 3)
(pow.f64 (pow.f64 (+.f64 2 x) 2) 1/4)
(pow.f64 (pow.f64 (+.f64 2 x) 3) 1/6)
(pow.f64 (pow.f64 (+.f64 2 x) 3/2) 1/3)
(pow.f64 (pow.f64 (+.f64 2 x) 1/4) 2)
(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))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1) 1/2))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 2 x)) 1/2) 1))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 2 x))) 1) 1))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 2 x) 1/6)) 3))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (+.f64 2 x))) 1/3))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (+.f64 2 x))) 2))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 2 x))))
(+.f64 0 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))) 1)
(*.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 -1 (/.f64 1 (/.f64 -1 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -1)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) -3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) -3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) 3)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2) -1/4)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) -1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) -1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) -2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(pow.f64 (neg.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 (exp.f64 x))))) -1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fabs.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))))
(exp.f64 (.f64 (.f64 -1/2 (log1p.f64 (exp.f64 x))) -1))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 1))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) -1/2))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) -1) -1/2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1) -1/2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2) -1))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) 1) -1))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) -1) 1))
(exp.f64 (.f64 (.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))) 1) 1))
(exp.f64 (.f64 (.f64 1/3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 2))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1/2))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(+.f64 0 (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))) (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))) 1)
(*.f64 1 (/.f64 1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 1)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2)))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 3/4))
(*.f64 -1 (/.f64 1 (neg.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 3/4) (pow.f64 (+.f64 1 (exp.f64 x)) -1/4))
(*.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 5/6) (pow.f64 (+.f64 1 (exp.f64 x)) -1/6))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(*.f64 (/.f64 1 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (-.f64 1 (exp.f64 x)))
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 2)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) -2)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) 6)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) 1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) 2/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) -1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) -1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) 4)
(pow.f64 (+.f64 1 (exp.f64 x)) -1)
(pow.f64 (neg.f64 (neg.f64 (+.f64 1 (exp.f64 x)))) -1)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2))
(log.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3))
(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(exp.f64 (neg.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) -1))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) -1) 1))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1) 1))
(exp.f64 (.f64 (.f64 -1/2 (log1p.f64 (exp.f64 x))) 2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2) 2))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) 1) 2))
(exp.f64 (.f64 (.f64 1/3 (neg.f64 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 -2 (log1p.f64 (exp.f64 x))) 1/2))
(exp.f64 (.f64 (.f64 3 (neg.f64 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) -1))
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(+.f64 0 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))) (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))) 1)
(*.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 1)
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (pow.f64 (+.f64 1 (exp.f64 x)) -1/6))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) -1/4))
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2))) (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))))
(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(/.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(/.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 1)
(/.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(/.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(/.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(/.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1)
(/.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (+.f64 1 (exp.f64 x)))))
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 1)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) -1)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) -3)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2) 1/4)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) 1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) 1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) -1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) -1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) 2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) -2)
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(pow.f64 (/.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1) -1)
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(log.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2))
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))
(exp.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2))
(exp.f64 (.f64 (.f64 -1/2 (log1p.f64 (exp.f64 x))) 1))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) -1) 1/2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1) 1/2))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2) 1))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) 1) 1))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) -1))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) -1) -1))
(exp.f64 (.f64 (.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))) 1) -1))
(exp.f64 (.f64 (.f64 1/3 (*.f64 -1/2 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 3/2 (neg.f64 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 1/4 (neg.f64 (log1p.f64 (exp.f64 x)))) 2))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) -1/2))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) -1/2))
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (/.f64 (*.f64 1/2 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 (.f64 1/2 x) (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 x (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 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 (.f64 1/2 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 1/2 (/.f64 x (sqrt.f64 2)) (.f64 -1/16 (/.f64 (.f64 x x) (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))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (/.f64 (*.f64 1/2 x) (sqrt.f64 2)))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (/.f64 (sqrt.f64 2) x) x))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (+.f64 1/6 (.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (/.f64 (sqrt.f64 2) x) x))) (/.f64 (*.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 (/.f64 1/4 (sqrt.f64 2)) 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
1/2
(+.f64 1/2 (*.f64 -1/4 x))
(+.f64 1/2 (*.f64 x -1/4))
(fma.f64 x -1/4 1/2)
(+.f64 1/2 (+.f64 (.f64 -1/4 x) (.f64 1/48 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 -1/4 x (*.f64 (pow.f64 x 3) 1/48)))
(+.f64 1/2 (fma.f64 x -1/4 (*.f64 (pow.f64 x 3) 1/48)))
(fma.f64 (pow.f64 x 3) 1/48 (fma.f64 x -1/4 1/2))
(+.f64 (.f64 -1/480 (pow.f64 x 5)) (+.f64 1/2 (+.f64 (.f64 -1/4 x) (*.f64 1/48 (pow.f64 x 3)))))
(fma.f64 -1/480 (pow.f64 x 5) (+.f64 1/2 (fma.f64 -1/4 x (*.f64 (pow.f64 x 3) 1/48))))
(+.f64 (fma.f64 x -1/4 (*.f64 (pow.f64 x 3) 1/48)) (fma.f64 -1/480 (pow.f64 x 5) 1/2))
(fma.f64 -1/480 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) 1/48 (fma.f64 x -1/4 1/2)))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/8 (/.f64 x (sqrt.f64 1/2))))
(fma.f64 -1/8 (/.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1/8 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/128 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (.f64 -1/8 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (fma.f64 -1/8 (/.f64 x (sqrt.f64 1/2)) (.f64 -1/64 (/.f64 (.f64 x x) (sqrt.f64 1/2)))))
(fma.f64 -1/8 (/.f64 x (sqrt.f64 1/2)) (fma.f64 -1/64 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/48 (.f64 1/512 (/.f64 1 (pow.f64 (sqrt.f64 1/2) 4)))) (pow.f64 x 3)) (sqrt.f64 1/2))) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 -1/8 (/.f64 x (sqrt.f64 1/2))))))
(+.f64 (sqrt.f64 1/2) (fma.f64 1/2 (/.f64 (-.f64 1/48 (/.f64 1/512 (pow.f64 (sqrt.f64 1/2) 4))) (/.f64 (sqrt.f64 1/2) (pow.f64 x 3))) (fma.f64 -1/128 (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 1/2) 3)) (.f64 -1/8 (/.f64 x (sqrt.f64 1/2))))))
(+.f64 (sqrt.f64 1/2) (+.f64 (fma.f64 -1/8 (/.f64 x (sqrt.f64 1/2)) (.f64 -1/64 (/.f64 (.f64 x x) (sqrt.f64 1/2)))) (/.f64 (*.f64 5/768 (pow.f64 x 3)) (sqrt.f64 1/2))))
(+.f64 (fma.f64 -1/8 (/.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2)) (fma.f64 -1/64 (/.f64 x (/.f64 (sqrt.f64 1/2) x)) (*.f64 (/.f64 5/768 (sqrt.f64 1/2)) (pow.f64 x 3))))
(+.f64 0 (sqrt.f64 (+.f64 2 x)))
(sqrt.f64 (+.f64 2 x))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 2 x)))) 1)
(sqrt.f64 (+.f64 2 x))
(*.f64 (sqrt.f64 (+.f64 2 x)) 1)
(sqrt.f64 (+.f64 2 x))
(*.f64 1 (sqrt.f64 (+.f64 2 x)))
(sqrt.f64 (+.f64 2 x))
(*.f64 (cbrt.f64 (+.f64 2 x)) (pow.f64 (+.f64 2 x) 1/6))
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 (+.f64 2 x) 1/6) (cbrt.f64 (+.f64 2 x)))
(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 (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))))
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(+.f64 0 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))) (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))) 1)
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(*.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 1)
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (pow.f64 (+.f64 1 (exp.f64 x)) -1/6))
(/.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (pow.f64 (+.f64 1 (exp.f64 x)) -1/6))
(/.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) -1/4))
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(*.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2))) (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))))
(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(/.f64 1 (/.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1))
(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(/.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 1)
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(/.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(/.f64 1 (*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(/.f64 1 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/12) 6))
(/.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(/.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))
(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(/.f64 (/.f64 -1 (sqrt.f64 (+.f64 1 (exp.f64 x)))) -1)
(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (+.f64 1 (exp.f64 x)))))
(/.f64 (sqrt.f64 -1) (sqrt.f64 (+.f64 -1 (neg.f64 (exp.f64 x)))))
(/.f64 (sqrt.f64 -1) (sqrt.f64 (-.f64 -1 (exp.f64 x))))
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 1/2)
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 1)
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) -1)
(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/6) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) -3)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -3/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2) 1/4)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) 1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) -1/3)
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) -1/6) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) -1/6))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) -1/6)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/4) 2)
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) -2)
(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(pow.f64 (/.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 1) -1)
(/.f64 1 (sqrt.f64 (+.f64 1 (exp.f64 x))))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(log.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))))
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2))
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)
(exp.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (*.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 -1/2 (log1p.f64 (exp.f64 x))) 1))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) -1) 1/2))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1) 1/2))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 (neg.f64 (log1p.f64 (exp.f64 x))) 1/2) 1))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) 1) 1))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) -1))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 (*.f64 -1/2 (log1p.f64 (exp.f64 x))) -1) -1))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 (*.f64 1/2 (log1p.f64 (exp.f64 x))) 1) -1))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 1/3 (*.f64 -1/2 (log1p.f64 (exp.f64 x)))) 3))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 3/2 (neg.f64 (log1p.f64 (exp.f64 x)))) 1/3))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 1/4 (neg.f64 (log1p.f64 (exp.f64 x)))) 2))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) -1/2))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) 1) -1/2))
(pow.f64 (exp.f64 -1/2) (log1p.f64 (exp.f64 x)))
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))
(pow.f64 (+.f64 1 (exp.f64 x)) -1/2)

eval145.0ms (2.9%)

Compiler: Compiled 6663 to 4848 computations (27.2% saved)

prune75.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	424	3	427
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	425	6	431

Accurracy

100.0%

Counts

431 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
▶	70.5%	(/.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/4))))
▶	73.6%	(/.f64 1 (sqrt.f64 1/2))
✓	69.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.6%	(sqrt.f64 2)
▶	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
▶	70.5%	(/.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/4))))
▶	73.6%	(/.f64 1 (sqrt.f64 1/2))
✓	69.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.6%	(sqrt.f64 2)

Compiler

Compiled 74 to 66 computations (10.8% saved)

localize83.0ms (1.6%)

Local Accuracy

Found 6 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
	100.0%	(+.f64 1 (exp.f64 x))
	100.0%	(/.f64 1 (+.f64 1 (exp.f64 x)))
✓	100.0%	(sqrt.f64 (+.f64 1/2 (*.f64 x -1/4)))
✓	98.9%	(/.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/4))))
✓	98.4%	(/.f64 1 (sqrt.f64 1/2))

Compiler

Compiled 59 to 46 computations (22% saved)

series54.0ms (1.1%)

Counts

4 → 20

Calls

9 calls:

Time	Variable		Point	Expression
27.0ms	x	@	inf	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
23.0ms	x	@	-inf	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
2.0ms	x	@	0	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
1.0ms	x	@	inf	(/.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/4))))
1.0ms	x	@	-inf	(/.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/4))))

rewrite83.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1494×	`log-prod`
606×	`expm1-udef`
602×	`log1p-udef`
554×	`fma-def`
396×	`prod-diff`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	74
1	386	48
2	4659	48

Stop Event

1×	node limit

Counts

4 → 112

Calls

Call 1

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

Outputs
(+.f64 0 (sqrt.f64 2))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 2))) (cbrt.f64 (exp.f64 (sqrt.f64 2))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 2)))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 2)))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 2))) 1)
(*.f64 1 (sqrt.f64 2))
(*.f64 (sqrt.f64 2) 1)
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))
(*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2)))
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 1/2))))
(*.f64 (pow.f64 (cbrt.f64 1/2) -1) (pow.f64 (cbrt.f64 (sqrt.f64 1/2)) -1))
(*.f64 (pow.f64 (pow.f64 1/2 1/4) -1) (pow.f64 (pow.f64 1/2 1/4) -1))
(pow.f64 1/2 -1/2)
(pow.f64 (sqrt.f64 1/2) -1)
(pow.f64 (sqrt.f64 2) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 2)) 3)
(pow.f64 (/.f64 2 (sqrt.f64 1/2)) 1/3)
(pow.f64 (sqrt.f64 (sqrt.f64 2)) 2)
(sqrt.f64 2)
(log.f64 (exp.f64 (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 2))))
(cbrt.f64 (/.f64 2 (sqrt.f64 1/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 2)))
(exp.f64 (log.f64 (sqrt.f64 2)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 1/2)) -1))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 2)))
(+.f64 0 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))) (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))) 1)
(*.f64 1 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(*.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1)
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) (cbrt.f64 (/.f64 1 (fma.f64 x -1/4 1/2))))
(*.f64 (cbrt.f64 (/.f64 1 (fma.f64 x -1/4 1/2))) (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) (sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) -1) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) -1))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) -1) (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) -1))
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(pow.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) -1)
(pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1)
(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) 3)
(pow.f64 (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 3) 1/3)
(pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) 2)
(sqrt.f64 (/.f64 1 (fma.f64 x -1/4 1/2)))
(log.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))))
(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(exp.f64 (log.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) -1))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) 1))
(log1p.f64 (expm1.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(+.f64 0 (sqrt.f64 (fma.f64 x -1/4 1/2)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))) (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))) 1)
(*.f64 1 (sqrt.f64 (fma.f64 x -1/4 1/2)))
(*.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) (cbrt.f64 (fma.f64 x -1/4 1/2)))
(*.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) (cbrt.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(*.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) (pow.f64 (fma.f64 x -1/4 1/2) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x -1/4 1/2))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x -1/4 1/2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) 1/2))
(/.f64 1 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(/.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) 1)
(/.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(/.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) (sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) -1)
(/.f64 (sqrt.f64 (fma.f64 -1/64 (pow.f64 x 3) 1/8)) (sqrt.f64 (fma.f64 (*.f64 x -1/4) (fma.f64 x -1/4 -1/2) 1/4)))
(/.f64 (sqrt.f64 (-.f64 1/4 (.f64 1/16 (.f64 x x)))) (sqrt.f64 (-.f64 1/2 (*.f64 x -1/4))))
(pow.f64 (fma.f64 x -1/4 1/2) 1/2)
(pow.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) 3)
(pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) 2)
(fabs.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))))
(cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(exp.f64 (*.f64 (log.f64 (fma.f64 x -1/4 1/2)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(+.f64 0 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))) (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))) 1)
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 1 -1/2) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2)) -1/2) (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) -1/2))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -1/2) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -1/2))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fabs.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))
(cbrt.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(exp.f64 (*.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1732×	`times-frac`
900×	`associate-/r*`
696×	`unswap-sqr`
544×	`distribute-lft-in`
476×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	3034
1	650	2844
2	2448	2632

Stop Event

1×	node limit

Counts

132 → 175

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 x (sqrt.f64 2))) (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/8 (/.f64 x (sqrt.f64 1/2))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1/8 (/.f64 x (sqrt.f64 1/2)))))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/1024 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 1/2) 5))) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (*.f64 -1/8 (/.f64 x (sqrt.f64 1/2))))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (+.f64 (.f64 7/384 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 0 (sqrt.f64 2))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 2))) (cbrt.f64 (exp.f64 (sqrt.f64 2))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 2)))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 2)))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 2))) 1)
(*.f64 1 (sqrt.f64 2))
(*.f64 (sqrt.f64 2) 1)
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))
(*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (sqrt.f64 2)))
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 1/2))))
(*.f64 (pow.f64 (cbrt.f64 1/2) -1) (pow.f64 (cbrt.f64 (sqrt.f64 1/2)) -1))
(*.f64 (pow.f64 (pow.f64 1/2 1/4) -1) (pow.f64 (pow.f64 1/2 1/4) -1))
(pow.f64 1/2 -1/2)
(pow.f64 (sqrt.f64 1/2) -1)
(pow.f64 (sqrt.f64 2) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 2)) 3)
(pow.f64 (/.f64 2 (sqrt.f64 1/2)) 1/3)
(pow.f64 (sqrt.f64 (sqrt.f64 2)) 2)
(sqrt.f64 2)
(log.f64 (exp.f64 (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 2))))
(cbrt.f64 (/.f64 2 (sqrt.f64 1/2)))
(expm1.f64 (log1p.f64 (sqrt.f64 2)))
(exp.f64 (log.f64 (sqrt.f64 2)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 1/2)) -1))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 2)) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 2)))
(+.f64 0 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))) (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))))
(-.f64 (exp.f64 (log1p.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))) 1)
(*.f64 1 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(*.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1)
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) (cbrt.f64 (/.f64 1 (fma.f64 x -1/4 1/2))))
(*.f64 (cbrt.f64 (/.f64 1 (fma.f64 x -1/4 1/2))) (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) (sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(*.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) -1) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) -1))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) -1) (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) -1))
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(pow.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) -1)
(pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1)
(pow.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) 3)
(pow.f64 (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 3) 1/3)
(pow.f64 (sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) 2)
(sqrt.f64 (/.f64 1 (fma.f64 x -1/4 1/2)))
(log.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))))
(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(exp.f64 (log.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) -1))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) 1))
(log1p.f64 (expm1.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(+.f64 0 (sqrt.f64 (fma.f64 x -1/4 1/2)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))) (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))) 1)
(*.f64 1 (sqrt.f64 (fma.f64 x -1/4 1/2)))
(*.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) 1)
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) (cbrt.f64 (fma.f64 x -1/4 1/2)))
(*.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) (cbrt.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(*.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) (pow.f64 (fma.f64 x -1/4 1/2) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x -1/4 1/2))))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x -1/4 1/2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) 1/2))
(/.f64 1 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(/.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) 1)
(/.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(/.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) (sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) -1)
(/.f64 (sqrt.f64 (fma.f64 -1/64 (pow.f64 x 3) 1/8)) (sqrt.f64 (fma.f64 (*.f64 x -1/4) (fma.f64 x -1/4 -1/2) 1/4)))
(/.f64 (sqrt.f64 (-.f64 1/4 (.f64 1/16 (.f64 x x)))) (sqrt.f64 (-.f64 1/2 (*.f64 x -1/4))))
(pow.f64 (fma.f64 x -1/4 1/2) 1/2)
(pow.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) 3)
(pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) 1/4) 2)
(fabs.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)))))
(cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(exp.f64 (*.f64 (log.f64 (fma.f64 x -1/4 1/2)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x -1/4 1/2))))
(+.f64 0 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))) (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))) 1)
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 1 -1/2) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2)) -1/2) (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) -1/2))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -1/2) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -1/2))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fabs.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(log.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))
(cbrt.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(exp.f64 (*.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 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 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 x (sqrt.f64 2))) (.f64 1/2 (/.f64 (.f64 (-.f64 1/4 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/4 (*.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3)))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (.f64 x x))) (/.f64 (*.f64 5/64 (pow.f64 x 3)) (sqrt.f64 2))))
(+.f64 (.f64 3/16 (.f64 x (/.f64 x (sqrt.f64 2)))) (+.f64 (sqrt.f64 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 5/32 (pow.f64 x 3))))))
(sqrt.f64 1/2)
(+.f64 (sqrt.f64 1/2) (*.f64 -1/8 (/.f64 x (sqrt.f64 1/2))))
(fma.f64 -1/8 (/.f64 x (sqrt.f64 1/2)) (sqrt.f64 1/2))
(+.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/128 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 1/2) 3))) (.f64 -1/8 (/.f64 x (sqrt.f64 1/2)))))
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(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))))))
(-.f64 (exp.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 1 -1/2) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2)) -1/2) (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) -1/2))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -1/2) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -1/2))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -1)
(/.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fabs.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))

eval143.0ms (2.8%)

Compiler: Compiled 6211 to 4555 computations (26.7% saved)

prune61.0ms (1.2%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	403	1	404
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	403	7	410

Accurracy

100.0%

Counts

410 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
▶	71.5%	(pow.f64 (+.f64 1/2 (*.f64 x -1/4)) -1/2)
✓	70.5%	(/.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/4))))
✓	73.6%	(/.f64 1 (sqrt.f64 1/2))
✓	69.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.6%	(sqrt.f64 2)
✓	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
▶	71.5%	(pow.f64 (+.f64 1/2 (*.f64 x -1/4)) -1/2)
✓	70.5%	(/.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/4))))
✓	73.6%	(/.f64 1 (sqrt.f64 1/2))
✓	69.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.6%	(sqrt.f64 2)

Compiler

Compiled 90 to 80 computations (11.1% saved)

localize39.0ms (0.8%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(pow.f64 (+.f64 1/2 (*.f64 x -1/4)) -1/2)

Compiler

Compiled 21 to 17 computations (19% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(pow.f64 (+.f64 1/2 (*.f64 x -1/4)) -1/2)
1.0ms	x	@	inf	(pow.f64 (+.f64 1/2 (*.f64 x -1/4)) -1/2)
0.0ms	x	@	0	(pow.f64 (+.f64 1/2 (*.f64 x -1/4)) -1/2)

rewrite60.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1814×	`pow1`
1690×	`add-exp-log`
1690×	`log1p-expm1-u`
1690×	`expm1-log1p-u`
1662×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	197	15
2	2298	15

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

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

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1640×	`fma-def`
1184×	`times-frac`
854×	`associate-/l*`
584×	`associate-/r*`
502×	`distribute-lft-out`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	98	1409
1	233	1219
2	585	913
3	1836	781
4	6725	775

Stop Event

1×	node limit

Counts

27 → 63

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (.f64 5/128 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4))))
(+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) x) (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))))
(+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) (pow.f64 x 2))) (+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) x) (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4))))))
(+.f64 (.f64 5/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) (pow.f64 x 3))) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) (pow.f64 x 2))) (+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) x) (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4))))
(+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) x) (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))))
(+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) x) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) (pow.f64 x 2))) (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4))))))
(+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) x) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) (pow.f64 x 2))) (+.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) (.f64 5/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) (pow.f64 x 3))))))
(-.f64 (+.f64 1 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) 1)
(*.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1)
(*.f64 1 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1)) (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(*.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/4) (pow.f64 (fma.f64 x -1/4 1/2) -1/4))
(*.f64 (pow.f64 1 -1/2) (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) 2) -1/2) (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) -1/2))
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) -1/2))
(sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1))
(log.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(exp.f64 (*.f64 -1/2 (log.f64 (fma.f64 x -1/4 1/2))))
(log1p.f64 (expm1.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 (sqrt.f64 2) x)))
(fma.f64 1/4 (*.f64 (sqrt.f64 2) x) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 1/4 x 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 2) (.f64 (.f64 x x) 3/32))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/4 x) (.f64 3/32 (.f64 x x)))))
(fma.f64 (sqrt.f64 2) (.f64 x (+.f64 (.f64 x 3/32) 1/4)) (sqrt.f64 2))
(+.f64 (.f64 5/128 (.f64 (sqrt.f64 2) (pow.f64 x 3))) (+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2))) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(fma.f64 5/128 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (.f64 x x)) (.f64 1/4 (*.f64 (sqrt.f64 2) x)))))
(+.f64 (fma.f64 1/4 (.f64 (sqrt.f64 2) x) (.f64 (sqrt.f64 2) (.f64 (.f64 x x) 3/32))) (fma.f64 5/128 (*.f64 (sqrt.f64 2) (pow.f64 x 3)) (sqrt.f64 2)))
(+.f64 (sqrt.f64 2) (fma.f64 (sqrt.f64 2) (.f64 5/128 (pow.f64 x 3)) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/4 x) (.f64 3/32 (*.f64 x x))))))
(fma.f64 (fma.f64 1/4 x 1) (sqrt.f64 2) (.f64 (.f64 (sqrt.f64 2) (.f64 x x)) (+.f64 3/32 (.f64 x 5/128))))
(.f64 (sqrt.f64 2) (+.f64 (fma.f64 1/4 x 1) (.f64 (.f64 x x) (+.f64 (.f64 x 5/128) 3/32))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4))))
(pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4)))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4)))
(*.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2))
(pow.f64 (*.f64 x -1/4) -1/2)
(+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) x) (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))))
(+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) x))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) x))
(fma.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2) (/.f64 (*.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2)) x))
(+.f64 (pow.f64 (.f64 x -1/4) -1/2) (/.f64 (pow.f64 (.f64 x -1/4) -1/2) x))
(+.f64 (pow.f64 (*.f64 x -1/4) -1/2) (/.f64 (pow.f64 -1/4 -1/2) (pow.f64 x 3/2)))
(+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) (pow.f64 x 2))) (+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) x) (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4))))))
(fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) x)))
(fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) x)))
(fma.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2) (.f64 (+.f64 (/.f64 3/2 x) 1) (/.f64 (.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2)) x)))
(fma.f64 (+.f64 1 (/.f64 3/2 x)) (/.f64 (pow.f64 (.f64 x -1/4) -1/2) x) (pow.f64 (.f64 x -1/4) -1/2))
(fma.f64 (+.f64 1 (/.f64 3/2 x)) (/.f64 (pow.f64 -1/4 -1/2) (pow.f64 x 3/2)) (pow.f64 (*.f64 x -1/4) -1/2))
(+.f64 (.f64 5/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) (pow.f64 x 3))) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) (pow.f64 x 2))) (+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))) x) (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 -1/4)))))))
(fma.f64 5/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (pow.f64 x 3)) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) x))))
(fma.f64 5/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (pow.f64 x 3)) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) x))))
(+.f64 (fma.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2) (/.f64 (.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2)) x)) (.f64 (*.f64 (/.f64 (pow.f64 x -1/2) x) (/.f64 (pow.f64 -1/4 -1/2) x)) (+.f64 (/.f64 5/2 x) 3/2)))
(+.f64 (pow.f64 (.f64 x -1/4) -1/2) (.f64 (/.f64 (pow.f64 (.f64 x -1/4) -1/2) x) (+.f64 (/.f64 5/2 (.f64 x x)) (+.f64 1 (/.f64 3/2 x)))))
(+.f64 (pow.f64 (.f64 x -1/4) -1/2) (.f64 (/.f64 (pow.f64 -1/4 -1/2) (pow.f64 x 3/2)) (+.f64 (/.f64 5/2 (*.f64 x x)) (+.f64 1 (/.f64 3/2 x)))))
(exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4))))
(pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4)))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4)))
(*.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2))
(pow.f64 (*.f64 x -1/4) -1/2)
(+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) x) (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))))
(+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) x))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) x))
(fma.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2) (/.f64 (*.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2)) x))
(+.f64 (pow.f64 (.f64 x -1/4) -1/2) (/.f64 (pow.f64 (.f64 x -1/4) -1/2) x))
(+.f64 (pow.f64 (*.f64 x -1/4) -1/2) (/.f64 (pow.f64 -1/4 -1/2) (pow.f64 x 3/2)))
(+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) x) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) (pow.f64 x 2))) (exp.f64 (.f64 -1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4))))))
(fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) x)))
(fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) x)))
(fma.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2) (.f64 (+.f64 (/.f64 3/2 x) 1) (/.f64 (.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2)) x)))
(fma.f64 (+.f64 1 (/.f64 3/2 x)) (/.f64 (pow.f64 (.f64 x -1/4) -1/2) x) (pow.f64 (.f64 x -1/4) -1/2))
(fma.f64 (+.f64 1 (/.f64 3/2 x)) (/.f64 (pow.f64 -1/4 -1/2) (pow.f64 x 3/2)) (pow.f64 (*.f64 x -1/4) -1/2))
(+.f64 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) x) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) (pow.f64 x 2))) (+.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) (.f64 5/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 1/4)))) (pow.f64 x 3))))))
(fma.f64 5/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (pow.f64 x 3)) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (fma.f64 -1 (neg.f64 (log.f64 x)) (log.f64 -1/4))) x))))
(fma.f64 5/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (pow.f64 x 3)) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) (log.f64 -1/4))) x))))
(+.f64 (fma.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2) (/.f64 (.f64 (pow.f64 x -1/2) (pow.f64 -1/4 -1/2)) x)) (.f64 (*.f64 (/.f64 (pow.f64 x -1/2) x) (/.f64 (pow.f64 -1/4 -1/2) x)) (+.f64 (/.f64 5/2 x) 3/2)))
(+.f64 (pow.f64 (.f64 x -1/4) -1/2) (.f64 (/.f64 (pow.f64 (.f64 x -1/4) -1/2) x) (+.f64 (/.f64 5/2 (.f64 x x)) (+.f64 1 (/.f64 3/2 x)))))
(+.f64 (pow.f64 (.f64 x -1/4) -1/2) (.f64 (/.f64 (pow.f64 -1/4 -1/2) (pow.f64 x 3/2)) (+.f64 (/.f64 5/2 (*.f64 x x)) (+.f64 1 (/.f64 3/2 x)))))
(-.f64 (+.f64 1 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) 1)
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(*.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1)
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(*.f64 1 (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) (cbrt.f64 (/.f64 1 (fma.f64 x -1/4 1/2))))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1)) (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1)))
(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)) (cbrt.f64 (/.f64 1 (fma.f64 x -1/4 1/2))))
(*.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/4) (pow.f64 (fma.f64 x -1/4 1/2) -1/4))
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(*.f64 (pow.f64 1 -1/2) (pow.f64 (fma.f64 x -1/4 1/2) -1/2))
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) 2) -1/2) (pow.f64 (cbrt.f64 (fma.f64 x -1/4 1/2)) -1/2))
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) -1/2) (pow.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) -1/2))
(pow.f64 (sqrt.f64 (fma.f64 x -1/4 1/2)) -1)
(/.f64 1 (sqrt.f64 (fma.f64 x -1/4 1/2)))
(sqrt.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1))
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(log.f64 (exp.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(cbrt.f64 (pow.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 3))
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(expm1.f64 (log1p.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(exp.f64 (*.f64 -1/2 (log.f64 (fma.f64 x -1/4 1/2))))
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(log1p.f64 (expm1.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2)))
(+.f64 1 (-.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 1))
(+.f64 (pow.f64 (fma.f64 x -1/4 1/2) -1/2) 0)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)

eval45.0ms (0.9%)

Compiler: Compiled 1184 to 970 computations (18.1% saved)

prune15.0ms (0.3%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	63	7	70

Accurracy

100.0%

Counts

70 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
✓	71.5%	(pow.f64 (+.f64 1/2 (*.f64 x -1/4)) -1/2)
✓	70.5%	(/.f64 1 (sqrt.f64 (+.f64 1/2 (*.f64 x -1/4))))
✓	73.6%	(/.f64 1 (sqrt.f64 1/2))
✓	69.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.6%	(sqrt.f64 2)

Compiler

Compiled 105 to 89 computations (15.2% saved)

regimes12.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

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

Outputs
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)

Calls

3 calls:

5.0ms	x
2.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
2.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))`
100.0%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`

Compiler

Compiled 87 to 71 computations (18.4% saved)

regimes9.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 33 to 28 computations (15.2% saved)

regimes5.0ms (0.1%)

Accuracy

Total -4.5b remaining (-27.8%)

Threshold costs -4.5b (-27.8%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
74.6%	1	`x`

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	16	43

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 18 to 16 computations (11.1% saved)

soundness342.0ms (6.8%)

Rules

1620×	`prod-diff`
1382×	`associate-r`
1260×	`associate-/l*`
1226×	`log-prod`
1096×	`log-prod`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	27	25
2	36	25
3	62	25
4	130	21
5	352	15
6	1351	15
0	15	68
1	323	68
2	4313	68
0	13	76
1	278	60
2	3523	60

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 317 to 230 computations (27.4% saved)

end37.0ms (0.7%)

Compiler: Compiled 58 to 48 computations (17.2% saved)

analyze122.0ms (2.4%)

sample2.5s (48.9%)

preprocess45.0ms (0.9%)

simplify36.0ms (0.7%)

eval1.0ms (0%)

prune2.0ms (0%)

localize152.0ms (3%)

series4.0ms (0.1%)

rewrite120.0ms (2.4%)

simplify195.0ms (3.9%)

eval208.0ms (4.1%)

prune66.0ms (1.3%)

localize88.0ms (1.8%)

series4.0ms (0.1%)

rewrite83.0ms (1.7%)

simplify91.0ms (1.8%)

eval145.0ms (2.9%)

prune75.0ms (1.5%)

localize83.0ms (1.6%)

series54.0ms (1.1%)

rewrite83.0ms (1.7%)

simplify70.0ms (1.4%)

eval143.0ms (2.8%)

prune61.0ms (1.2%)

localize39.0ms (0.8%)

series1.0ms (0%)

rewrite60.0ms (1.2%)

simplify75.0ms (1.5%)

eval45.0ms (0.9%)

prune15.0ms (0.3%)

regimes12.0ms (0.2%)

regimes9.0ms (0.2%)

regimes5.0ms (0.1%)

simplify5.0ms (0.1%)

soundness342.0ms (6.8%)

end37.0ms (0.7%)

Profiling