Metrics for sqrtexp (problem 3.4.4)

analyze138.0ms (3.8%)

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)

sample2.0s (56.4%)

Results

919.0ms	2766×	body	1024	valid
399.0ms	3775×	body	256	valid
265.0ms	1360×	body	512	valid
195.0ms	2620×	body	256	unsamplable
144.0ms	309×	body	2048	valid
5.0ms	46×	body	256	infinite

Bogosity

preprocess165.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1354×	`associate-/l*`
1124×	`associate-r`
1042×	`associate-/r*`
892×	`associate-l`
684×	`fma-def`

Problems

180×	`(-.f64 (exp.f64 (*.f64 2 x)) 1)`
62×	No Errors
10×	`(-.f64 (exp.f64 x) 1)`
4×	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	24	144
1	53	136
2	85	136
3	165	136
4	387	108
5	1518	84

Stop Event

1×	node limit

Calls

Call 1

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

Compiler

Compiled 60 to 45 computations (25% saved)

eval1.0ms (0%)

Compiler: Compiled 21 to 16 computations (23.8% saved)

prune5.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
▶	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	98.4%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
▶	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 30 to 24 computations (20% saved)

localize53.0ms (1.5%)

Localize:

Found 4 expressions with local error:

New	Accuracy	Program
✓	100.0%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
✓	98.7%	(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	100.0%	(+.f64 1 (exp.f64 x))

Compiler

Compiled 41 to 25 computations (39% saved)

series4.0ms (0.1%)

Counts

4 → 32

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
1.0ms	x	@	-inf	(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
0.0ms	x	@	0	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0ms	x	@	inf	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))

rewrite135.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

758×	`log-prod`
733×	`log1p-expm1-u`
731×	`expm1-log1p-u`
516×	`pow-prod-down`
426×	`fma-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	64
1	197	64
2	2472	64

Stop Event

1×	node limit

Counts

4 → 239

Calls

Call 1

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

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

simplify95.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1366×	`fma-def`
1064×	`associate-/l*`
896×	`associate-/r*`
532×	`*-commutative`
488×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	333	7133
1	742	6806
2	2256	6673

Stop Event

1×	node limit

Counts

271 → 177

Calls

Call 1

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

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

eval47.0ms (1.3%)

Compiler: Compiled 2124 to 1554 computations (26.8% saved)

prune25.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	175	4	179

Accuracy

100.0%

Counts

179 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
▶	74.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	78.4%	(sqrt.f64 2)
▶	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
▶	74.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	78.4%	(sqrt.f64 2)

Compiler

Compiled 46 to 40 computations (13% saved)

localize54.0ms (1.5%)

Localize:

Found 3 expressions with local error:

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

Compiler

Compiled 37 to 26 computations (29.7% saved)

series52.0ms (1.4%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	x	@	inf	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
24.0ms	x	@	-inf	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
1.0ms	x	@	-inf	(/.f64 1 (+.f64 1 (exp.f64 x)))
0.0ms	x	@	inf	(/.f64 1 (+.f64 1 (exp.f64 x)))
0.0ms	x	@	0	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)

rewrite62.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`unpow-prod-down`
501×	`log1p-expm1-u`
501×	`expm1-log1p-u`
498×	`log-prod`
433×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	129	38
2	1529	38

Stop Event

1×	node limit

Counts

2 → 96

Calls

Call 1

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

Outputs
(+.f64 0 (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))) 2)) (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 (+.f64 1 (/.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 (/.f64 1 (+.f64 1 (exp.f64 x))) (log.f64 (E.f64)))
(*.f64 -1 (/.f64 1 (+.f64 -1 (neg.f64 (exp.f64 x)))))
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(*.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) 3))) (pow.f64 (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)) -1))
(.f64 (/.f64 1 (-.f64 1 (exp.f64 (.f64 2 x)))) (-.f64 1 (exp.f64 x)))
(.f64 (/.f64 1 (-.f64 1 (exp.f64 (.f64 2 x)))) (pow.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) -1))
(*.f64 (pow.f64 1 1/3) (/.f64 1 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) -1) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) -1))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) -1) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) -1))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/6) -1) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))) 2) 3) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))) 3) (pow.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3)) 1/3))
(.f64 (pow.f64 (.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2)) 1/3) (cbrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -5/2) 1/3) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))
(pow.f64 (+.f64 1 (exp.f64 x)) -1)
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) -2)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -3)
(pow.f64 (/.f64 1 (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)) -2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) 1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 2)
(pow.f64 (E.f64) (neg.f64 (log1p.f64 (exp.f64 x))))
(pow.f64 (neg.f64 (+.f64 -1 (neg.f64 (exp.f64 x)))) -1)
(pow.f64 (exp.f64 -1) (log1p.f64 (exp.f64 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log1p.f64 (exp.f64 x)))) 2)) (cbrt.f64 (neg.f64 (log1p.f64 (exp.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log1p.f64 (exp.f64 x))))) (sqrt.f64 (neg.f64 (log1p.f64 (exp.f64 x)))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2))
(log.f64 (exp.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 (.f64 1/3 (neg.f64 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 3 (neg.f64 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 -1/2 (log1p.f64 (exp.f64 x))) 2))
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(+.f64 0 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))) 2)) (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 (+.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1)
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (log.f64 (E.f64)))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (pow.f64 1 1/2))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/12) 2))
(*.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) (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2) 2) -1/4))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/8) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) -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 (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) 1/2))
(.f64 (sqrt.f64 (-.f64 1 (exp.f64 (.f64 2 x)))) (pow.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) 1/2))
(*.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (pow.f64 (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)) 1/2))
(*.f64 (pow.f64 1 1/3) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 1 1/2) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) 1/2) (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/6) 1/2) (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)))
(*.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 1 (+.f64 -1 (neg.f64 (exp.f64 x)))) -1/2))
(*.f64 (pow.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) 3))) -1/2) (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) -1/2))
(.f64 (pow.f64 (/.f64 1 (-.f64 1 (exp.f64 (.f64 2 x)))) -1/2) (pow.f64 (-.f64 1 (exp.f64 x)) -1/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)) 2) 3) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)) 3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)) 3))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2) 2) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/8))
(*.f64 (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 5) -1/4) (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/12))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4) 1/3) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/4) 1/3) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)))
(/.f64 (sqrt.f64 (-.f64 1 (exp.f64 (*.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)))
(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)))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (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 1/3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 -2 (log1p.f64 (exp.f64 x))) -1/4))
(exp.f64 (.f64 (.f64 3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 1/4 (log1p.f64 (exp.f64 x))) 2))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))

simplify82.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

982×	`distribute-lft-in`
948×	`sqr-pow`
650×	`fma-def`
568×	`unswap-sqr`
546×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	292	3664
1	708	3518
2	1740	3387
3	4718	3278

Stop Event

1×	node limit

Counts

112 → 168

Calls

Call 1

Inputs
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 1/2 (+.f64 (.f64 -1/4 x) (+.f64 (.f64 -1/480 (pow.f64 x 5)) (*.f64 1/48 (pow.f64 x 3)))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (pow.f64 x 2) (sqrt.f64 2))) (.f64 1/4 (.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 7/384 (.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 3/32 (.f64 (pow.f64 x 2) (sqrt.f64 2))) (.f64 1/4 (.f64 x (sqrt.f64 2))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 0 (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (exp.f64 x))))) 2)) (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 (+.f64 1 (/.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 (/.f64 1 (+.f64 1 (exp.f64 x))) (log.f64 (E.f64)))
(*.f64 -1 (/.f64 1 (+.f64 -1 (neg.f64 (exp.f64 x)))))
(*.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))
(*.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) 3))) (pow.f64 (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)) -1))
(.f64 (/.f64 1 (-.f64 1 (exp.f64 (.f64 2 x)))) (-.f64 1 (exp.f64 x)))
(.f64 (/.f64 1 (-.f64 1 (exp.f64 (.f64 2 x)))) (pow.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) -1))
(*.f64 (pow.f64 1 1/3) (/.f64 1 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) -1) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) -1))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) -1) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) -1))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/6) -1) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))) 2) 3) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))) 3) (pow.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3)) 1/3))
(.f64 (pow.f64 (.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2)) 1/3) (cbrt.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x))))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -5/2) 1/3) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2)))
(pow.f64 (+.f64 1 (exp.f64 x)) -1)
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) 1)
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) -2)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -3)
(pow.f64 (/.f64 1 (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)) -2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) 1/3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) 2)
(pow.f64 (E.f64) (neg.f64 (log1p.f64 (exp.f64 x))))
(pow.f64 (neg.f64 (+.f64 -1 (neg.f64 (exp.f64 x)))) -1)
(pow.f64 (exp.f64 -1) (log1p.f64 (exp.f64 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log1p.f64 (exp.f64 x)))) 2)) (cbrt.f64 (neg.f64 (log1p.f64 (exp.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log1p.f64 (exp.f64 x))))) (sqrt.f64 (neg.f64 (log1p.f64 (exp.f64 x)))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -2))
(log.f64 (exp.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 (.f64 1/3 (neg.f64 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 3 (neg.f64 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 -1/2 (log1p.f64 (exp.f64 x))) 2))
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (exp.f64 x)))))
(+.f64 0 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))) 2)) (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 (+.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1)
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (log.f64 (E.f64)))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (pow.f64 1 1/2))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/12) 2))
(*.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) (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2) 2) -1/4))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/8) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) -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 (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) 1/2))
(.f64 (sqrt.f64 (-.f64 1 (exp.f64 (.f64 2 x)))) (pow.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) 1/2))
(*.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (pow.f64 (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)) 1/2))
(*.f64 (pow.f64 1 1/3) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 1 1/2) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) 1/2) (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/6) 1/2) (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)))
(*.f64 (pow.f64 -1 -1/2) (pow.f64 (/.f64 1 (+.f64 -1 (neg.f64 (exp.f64 x)))) -1/2))
(*.f64 (pow.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) 3))) -1/2) (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) -1/2))
(.f64 (pow.f64 (/.f64 1 (-.f64 1 (exp.f64 (.f64 2 x)))) -1/2) (pow.f64 (-.f64 1 (exp.f64 x)) -1/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)) 2) 3) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)) 3) (pow.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)) 3))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2) 2) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/8))
(*.f64 (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 5) -1/4) (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/12))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4) 1/3) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/4) 1/3) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)))
(/.f64 (sqrt.f64 (-.f64 1 (exp.f64 (*.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)))
(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)))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (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 1/3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 3))
(exp.f64 (.f64 (.f64 -2 (log1p.f64 (exp.f64 x))) -1/4))
(exp.f64 (.f64 (.f64 3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 1/3))
(exp.f64 (.f64 (.f64 1/4 (log1p.f64 (exp.f64 x))) 2))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))

Outputs
1/2
(+.f64 1/2 (*.f64 -1/4 x))
(fma.f64 -1/4 x 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 1/48 (pow.f64 x 3))))
(+.f64 (fma.f64 -1/4 x 1/2) (*.f64 1/48 (pow.f64 x 3)))
(fma.f64 -1/4 x (fma.f64 1/48 (pow.f64 x 3) 1/2))
(+.f64 1/2 (+.f64 (.f64 -1/4 x) (+.f64 (.f64 -1/480 (pow.f64 x 5)) (*.f64 1/48 (pow.f64 x 3)))))
(+.f64 1/2 (fma.f64 -1/4 x (fma.f64 -1/480 (pow.f64 x 5) (*.f64 1/48 (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/4 x 1/2) (fma.f64 1/48 (pow.f64 x 3) (*.f64 -1/480 (pow.f64 x 5))))
(+.f64 1/2 (fma.f64 -1/4 x (fma.f64 1/48 (pow.f64 x 3) (*.f64 -1/480 (pow.f64 x 5)))))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 x (sqrt.f64 2))))
(fma.f64 1/4 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (pow.f64 x 2) (sqrt.f64 2))) (.f64 1/4 (.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)) (.f64 1/4 (*.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 x 1/4) (*.f64 3/32 (pow.f64 x 2)))))
(fma.f64 (sqrt.f64 2) (.f64 x (+.f64 (.f64 x 3/32) 1/4)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 7/384 (.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 3/32 (.f64 (pow.f64 x 2) (sqrt.f64 2))) (.f64 1/4 (.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 7/384 (.f64 (pow.f64 x 3) (sqrt.f64 2)) (fma.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)) (.f64 1/4 (.f64 x (sqrt.f64 2))))))
(+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) 7/384) (.f64 3/32 (pow.f64 x 2)))) (fma.f64 1/4 (.f64 x (sqrt.f64 2)) (sqrt.f64 2)))
(fma.f64 (sqrt.f64 2) (.f64 (pow.f64 x 2) (+.f64 (.f64 x 7/384) 3/32)) (*.f64 (sqrt.f64 2) (fma.f64 x 1/4 1)))
(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 (/.f64 1 (+.f64 1 (exp.f64 x))))
(/.f64 1 (+.f64 1 (exp.f64 x)))
(/.f64 -1 (-.f64 -1 (exp.f64 x)))
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(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -2) 2) -1/4))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) -4) -1/4))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) -1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/8))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/8) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3/2) -1/4))
(*.f64 (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 5) -1/4) (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/12))
(*.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/12) (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 5) -1/4))
(*.f64 (pow.f64 (/.f64 -1 (-.f64 -1 (exp.f64 x))) -1/12) (pow.f64 (pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) 5) -1/4))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4) 1/3) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6)) (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4)))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/4) 1/3) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/4)) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4)))
(/.f64 (sqrt.f64 (-.f64 1 (exp.f64 (*.f64 2 x)))) (sqrt.f64 (-.f64 1 (exp.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 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x 2)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(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)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (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 1/3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 3))
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (.f64 (.f64 -2 (log1p.f64 (exp.f64 x))) -1/4))
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (.f64 (.f64 3 (*.f64 1/2 (log1p.f64 (exp.f64 x)))) 1/3))
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(exp.f64 (.f64 (.f64 1/4 (log1p.f64 (exp.f64 x))) 2))
(pow.f64 (exp.f64 1/2) (log1p.f64 (exp.f64 x)))
(sqrt.f64 (exp.f64 (log1p.f64 (exp.f64 x))))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))

eval89.0ms (2.5%)

Compiler: Compiled 3643 to 2754 computations (24.4% saved)

prune36.0ms (1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	258	6	264

Accuracy

100.0%

Counts

264 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.4%	(pow.f64 (/.f64 1 (+.f64 2 x)) -1/2)
✓	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
▶	76.1%	(pow.f64 (+.f64 1/2 (*.f64 -1/4 x)) -1/2)
✓	74.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	78.4%	(sqrt.f64 2)
▶	74.4%	(pow.f64 (/.f64 1 (+.f64 2 x)) -1/2)
✓	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
▶	76.1%	(pow.f64 (+.f64 1/2 (*.f64 -1/4 x)) -1/2)
✓	74.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	78.4%	(sqrt.f64 2)

Compiler

Compiled 78 to 68 computations (12.8% saved)

localize53.0ms (1.5%)

Localize:

Found 3 expressions with local error:

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

Compiler

Compiled 40 to 32 computations (20% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite70.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

864×	`log1p-expm1-u`
864×	`expm1-log1p-u`
828×	`log-prod`
486×	`pow-exp`
374×	`fma-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	60
1	191	48
2	2447	48

Stop Event

1×	node limit

Counts

3 → 98

Calls

Call 1

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

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

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1706×	`fma-def`
912×	`unswap-sqr`
830×	`times-frac`
492×	`distribute-lft-in`
430×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	365	4640
1	823	4387
2	2187	3826

Stop Event

1×	node limit

Counts

134 → 233

Calls

Call 1

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

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/4 (.f64 x (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 (fma.f64 1/4 x 1) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 3/32 (.f64 (pow.f64 x 2) (sqrt.f64 2))) (.f64 1/4 (.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (fma.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)) (.f64 1/4 (*.f64 (sqrt.f64 2) x))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 1/4 x) (*.f64 3/32 (pow.f64 x 2)))))
(fma.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (.f64 3/32 x))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 5/128 (.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 3/32 (.f64 (pow.f64 x 2) (sqrt.f64 2))) (.f64 1/4 (.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 5/128 (.f64 (sqrt.f64 2) (pow.f64 x 3)) (fma.f64 3/32 (.f64 (sqrt.f64 2) (pow.f64 x 2)) (.f64 1/4 (.f64 (sqrt.f64 2) x)))))
(+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 1/4 x) (.f64 3/32 (pow.f64 x 2)))) (.f64 (+.f64 (*.f64 5/128 (pow.f64 x 3)) 1) (sqrt.f64 2)))
(fma.f64 (fma.f64 5/128 (pow.f64 x 3) 1) (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 x (+.f64 1/4 (*.f64 3/32 x)))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (.f64 -1 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x)))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x)))
(*.f64 (pow.f64 -1/4 -1/2) (pow.f64 x -1/2))
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (.f64 -1 (log.f64 (/.f64 1 x)))))) (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (.f64 -1 (log.f64 (/.f64 1 x)))))) x))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x))))) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x))))) x))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x))) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x))) x))
(fma.f64 (pow.f64 -1/4 -1/2) (pow.f64 x -1/2) (/.f64 (*.f64 (pow.f64 -1/4 -1/2) (pow.f64 x -1/2)) x))
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (.f64 -1 (log.f64 (/.f64 1 x)))))) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (.f64 -1 (log.f64 (/.f64 1 x)))))) (pow.f64 x 2))) (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (*.f64 -1 (log.f64 (/.f64 1 x)))))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x))))) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x))))) (pow.f64 x 2)) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x))))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x))) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x))) (pow.f64 x 2)) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x))) x)))
(fma.f64 (pow.f64 -1/4 -1/2) (pow.f64 x -1/2) (.f64 (+.f64 (/.f64 3/2 x) 1) (/.f64 (.f64 (pow.f64 -1/4 -1/2) (pow.f64 x -1/2)) x)))
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (.f64 -1 (log.f64 (/.f64 1 x)))))) (+.f64 (.f64 3/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (.f64 -1 (log.f64 (/.f64 1 x)))))) (pow.f64 x 2))) (+.f64 (.f64 5/2 (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (.f64 -1 (log.f64 (/.f64 1 x)))))) (pow.f64 x 3))) (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 -1/4) (.f64 -1 (log.f64 (/.f64 1 x)))))) x))))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x))))) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x))))) (pow.f64 x 2)) (fma.f64 5/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x))))) (pow.f64 x 3)) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (neg.f64 (neg.f64 (log.f64 x))))) x))))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x))) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x))) (pow.f64 x 2)) (fma.f64 5/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x))) (pow.f64 x 3)) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 -1/4) (log.f64 x))) x))))
(+.f64 (/.f64 (.f64 (pow.f64 -1/4 -1/2) (pow.f64 x -1/2)) x) (fma.f64 (pow.f64 -1/4 -1/2) (pow.f64 x -1/2) (.f64 (/.f64 (*.f64 (pow.f64 -1/4 -1/2) (pow.f64 x -1/2)) (pow.f64 x 2)) (+.f64 3/2 (/.f64 5/2 x)))))
(exp.f64 (.f64 -1/2 (+.f64 (log.f64 1/4) (.f64 -1 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 1/4) (neg.f64 (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 1/4) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 1/4 -1/2) (pow.f64 (/.f64 -1 x) 1/2))
(+.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 1/4) (.f64 -1 (log.f64 (/.f64 -1 x)))))) (/.f64 (exp.f64 (.f64 -1/2 (+.f64 (log.f64 1/4) (.f64 -1 (log.f64 (/.f64 -1 x)))))) x))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 1/4) (neg.f64 (log.f64 (/.f64 -1 x))))) (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 1/4) (neg.f64 (log.f64 (/.f64 -1 x))))) x))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 1/4) (log.f64 (/.f64 -1 x)))) (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 1/4) (log.f64 (/.f64 -1 x)))) x))
(fma.f64 (pow.f64 1/4 -1/2) (pow.f64 (/.f64 -1 x) 1/2) (/.f64 (*.f64 (pow.f64 1/4 -1/2) (pow.f64 (/.f64 -1 x) 1/2)) x))
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1/2
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(pow.f64 (fma.f64 -1/4 x 1/2) -1/2)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(exp.f64 (*.f64 (log.f64 (pow.f64 (pow.f64 (fma.f64 -1/4 x 1/2) -1/2) 3)) 1/3))
(pow.f64 (fma.f64 -1/4 x 1/2) -1/2)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(exp.f64 (.f64 (.f64 -1/4 (log.f64 (fma.f64 -1/4 x 1/2))) 2))
(pow.f64 (fma.f64 -1/4 x 1/2) -1/2)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 -1/4 x 1/2)) -1/4) 2))
(pow.f64 (fma.f64 -1/4 x 1/2) -1/2)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(log1p.f64 (expm1.f64 (pow.f64 (fma.f64 -1/4 x 1/2) -1/2)))
(pow.f64 (fma.f64 -1/4 x 1/2) -1/2)
(pow.f64 (fma.f64 x -1/4 1/2) -1/2)
(+.f64 0 (/.f64 1 (+.f64 x 2)))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 x 2)))) (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 x 2)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 x 2))))))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 2 x)))) (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 2 x)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 2 x))))))
(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (/.f64 -1 (-.f64 -2 x)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 -1 (-.f64 -2 x))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 -1 (-.f64 -2 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 x 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 x 2))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 2 x))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 -1 (-.f64 -2 x))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 x 2)))) 1)
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(*.f64 1 (/.f64 1 (+.f64 x 2)))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(*.f64 (/.f64 1 (+.f64 x 2)) 1)
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(*.f64 (/.f64 1 (+.f64 x 2)) (log.f64 (exp.f64 1)))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(*.f64 -1 (/.f64 1 (+.f64 (neg.f64 x) -2)))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(*.f64 (cbrt.f64 (/.f64 1 (+.f64 x 2))) (cbrt.f64 (pow.f64 (+.f64 x 2) -2)))
(*.f64 (cbrt.f64 (/.f64 1 (+.f64 2 x))) (cbrt.f64 (pow.f64 (+.f64 2 x) -2)))
(*.f64 (cbrt.f64 (/.f64 -1 (-.f64 -2 x))) (cbrt.f64 (pow.f64 (+.f64 2 x) -2)))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 x 2) -2)) (cbrt.f64 (/.f64 1 (+.f64 x 2))))
(*.f64 (cbrt.f64 (/.f64 1 (+.f64 2 x))) (cbrt.f64 (pow.f64 (+.f64 2 x) -2)))
(*.f64 (cbrt.f64 (/.f64 -1 (-.f64 -2 x))) (cbrt.f64 (pow.f64 (+.f64 2 x) -2)))
(*.f64 (pow.f64 (+.f64 x 2) -1/2) (pow.f64 (+.f64 x 2) -1/2))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 x 2)) 2)) (cbrt.f64 (/.f64 1 (+.f64 x 2))))
(*.f64 (cbrt.f64 (/.f64 1 (+.f64 2 x))) (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)))
(/.f64 (cbrt.f64 (/.f64 -1 (-.f64 -2 x))) (pow.f64 (cbrt.f64 (+.f64 2 x)) 2))
(*.f64 (/.f64 1 (+.f64 8 (pow.f64 x 3))) (fma.f64 x (-.f64 x 2) 4))
(*.f64 (/.f64 1 (+.f64 (pow.f64 x 3) 8)) (fma.f64 x (+.f64 x -2) 4))
(/.f64 (fma.f64 x (+.f64 x -2) 4) (+.f64 (pow.f64 x 3) 8))
(*.f64 (/.f64 1 (-.f64 4 (pow.f64 x 2))) (-.f64 2 x))
(/.f64 (-.f64 2 x) (-.f64 4 (pow.f64 x 2)))
(pow.f64 (+.f64 x 2) -1)
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(pow.f64 (/.f64 1 (+.f64 x 2)) 1)
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(pow.f64 (cbrt.f64 (/.f64 1 (+.f64 x 2))) 3)
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(pow.f64 (pow.f64 (/.f64 1 (+.f64 x 2)) 3) 1/3)
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(pow.f64 (pow.f64 (+.f64 x 2) -1/2) 2)
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(pow.f64 (neg.f64 (+.f64 (neg.f64 x) -2)) -1)
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(sqrt.f64 (pow.f64 (+.f64 x 2) -2))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(log.f64 (exp.f64 (/.f64 1 (+.f64 x 2))))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 x 2)))))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x 2)) 3))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 2))))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(exp.f64 (neg.f64 (log.f64 (+.f64 x 2))))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(exp.f64 (*.f64 (log.f64 (+.f64 x 2)) -1))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 x 2))) 1))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 x 2)) 1) -1))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 x 2)) -1) 1))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(exp.f64 (.f64 (.f64 (neg.f64 (log.f64 (+.f64 x 2))) 1) 1))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (cbrt.f64 (+.f64 x 2)))) 3))
(exp.f64 (*.f64 3 (neg.f64 (log.f64 (cbrt.f64 (+.f64 2 x))))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 2 x))) -3))
(pow.f64 (cbrt.f64 (+.f64 2 x)) -3)
(exp.f64 (.f64 (.f64 3 (neg.f64 (log.f64 (+.f64 x 2)))) 1/3))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(exp.f64 (.f64 (.f64 -1/2 (log.f64 (+.f64 x 2))) 2))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(log1p.f64 (expm1.f64 (/.f64 1 (+.f64 x 2))))
(/.f64 1 (+.f64 2 x))
(/.f64 -1 (-.f64 -2 x))
(+.f64 0 (sqrt.f64 (+.f64 x 2)))
(sqrt.f64 (+.f64 2 x))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 2)))) (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 2)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 2))))))
(+.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 x 2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 2))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 2 x))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 2)))) 1)
(sqrt.f64 (+.f64 2 x))
(*.f64 1 (sqrt.f64 (+.f64 x 2)))
(sqrt.f64 (+.f64 2 x))
(*.f64 (sqrt.f64 (+.f64 x 2)) 1)
(sqrt.f64 (+.f64 2 x))
(*.f64 (sqrt.f64 (+.f64 x 2)) (log.f64 (exp.f64 1)))
(sqrt.f64 (+.f64 2 x))
(*.f64 (cbrt.f64 (+.f64 x 2)) (cbrt.f64 (sqrt.f64 (+.f64 x 2))))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 2))) (cbrt.f64 (+.f64 x 2)))
(*.f64 (cbrt.f64 (+.f64 2 x)) (cbrt.f64 (sqrt.f64 (+.f64 2 x))))
(*.f64 (pow.f64 (+.f64 x 2) 1/4) (pow.f64 (+.f64 x 2) 1/4))
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 1 -1/2) (sqrt.f64 (+.f64 x 2)))
(sqrt.f64 (+.f64 2 x))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x 2) -2)) -1/2) (pow.f64 (cbrt.f64 (/.f64 1 (+.f64 x 2))) -1/2))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) -2)) -1/2) (pow.f64 (cbrt.f64 (/.f64 1 (+.f64 2 x))) -1/2))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 2 x) -2)) -1/2) (pow.f64 (cbrt.f64 (/.f64 -1 (-.f64 -2 x))) -1/2))
(*.f64 (pow.f64 (pow.f64 (+.f64 x 2) -1/2) -1/2) (pow.f64 (pow.f64 (+.f64 x 2) -1/2) -1/2))
(sqrt.f64 (+.f64 2 x))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 2)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 2))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 2 x))) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(*.f64 (cbrt.f64 (+.f64 2 x)) (sqrt.f64 (cbrt.f64 (+.f64 2 x))))
(/.f64 (sqrt.f64 (+.f64 8 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x (-.f64 x 2) 4)))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) 8)) (sqrt.f64 (fma.f64 x (+.f64 x -2) 4)))
(/.f64 (sqrt.f64 (-.f64 4 (pow.f64 x 2))) (sqrt.f64 (-.f64 2 x)))
(sqrt.f64 (+.f64 x 2))
(sqrt.f64 (+.f64 2 x))
(fabs.f64 (sqrt.f64 (+.f64 x 2)))
(sqrt.f64 (+.f64 2 x))
(log.f64 (exp.f64 (sqrt.f64 (+.f64 x 2))))
(sqrt.f64 (+.f64 2 x))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 2)))))
(sqrt.f64 (+.f64 2 x))
(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 x 2)) 3))
(sqrt.f64 (+.f64 2 x))
(expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 2))))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (log.f64 (sqrt.f64 (+.f64 x 2))))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 x 2))) 1))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (+.f64 x 2)) 1/2))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 x 2)) 1) 1/2))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 x 2)) -1) -1/2))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 (neg.f64 (log.f64 (+.f64 x 2))) 1) -1/2))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 x 2))) 1) 1))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 2)))) 3))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x 2) -2)) -1/4))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 3 (log.f64 (sqrt.f64 (+.f64 x 2)))) 1/3))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (+.f64 x 2))) 2))
(sqrt.f64 (+.f64 2 x))
(exp.f64 (.f64 (.f64 (neg.f64 (log.f64 (+.f64 x 2))) -1/4) 2))
(sqrt.f64 (+.f64 2 x))
(log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 2))))
(sqrt.f64 (+.f64 2 x))

eval90.0ms (2.5%)

Compiler: Compiled 3674 to 3144 computations (14.4% saved)

prune31.0ms (0.9%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	232	7	239

Accuracy

100.0%

Counts

239 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	74.4%	(pow.f64 (/.f64 1 (+.f64 2 x)) -1/2)
✓	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
✓	76.1%	(pow.f64 (+.f64 1/2 (*.f64 -1/4 x)) -1/2)
✓	74.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	3.0%	(sqrt.f64 x)
✓	78.4%	(sqrt.f64 2)
✓	74.4%	(pow.f64 (/.f64 1 (+.f64 2 x)) -1/2)
✓	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
✓	76.1%	(pow.f64 (+.f64 1/2 (*.f64 -1/4 x)) -1/2)
✓	74.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	3.0%	(sqrt.f64 x)
✓	78.4%	(sqrt.f64 2)

Compiler

Compiled 84 to 72 computations (14.3% saved)

localize11.0ms (0.3%)

Compiler: Compiled 5 to 3 computations (40% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune4.0ms (0.1%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	6	6
Total	7	7

Accuracy

100.0%

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	74.4%	(pow.f64 (/.f64 1 (+.f64 2 x)) -1/2)
✓	100.0%	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
✓	76.1%	(pow.f64 (+.f64 1/2 (*.f64 -1/4 x)) -1/2)
✓	74.4%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	3.0%	(sqrt.f64 x)
✓	78.4%	(sqrt.f64 2)

Compiler

Compiled 98 to 80 computations (18.4% saved)

regimes106.0ms (2.9%)

Counts

9 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 x)
(sqrt.f64 (+.f64 2 x))
(pow.f64 (+.f64 1/2 (*.f64 -1/4 x)) -1/2)
(pow.f64 (/.f64 1 (+.f64 2 x)) -1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1/2)
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

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

Calls

3 calls:

96.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
5.0ms	x
3.0ms	(/.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 83 to 66 computations (20.5% saved)

regimes5.0ms (0.1%)

Accuracy

Total -48.3b remaining (-349.5%)

Threshold costs -48.3b (-349.5%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
78.4%	1	`x`

Compiler

Compiled 25 to 20 computations (20% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	15	23

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

soundness58.0ms (1.6%)

Rules

1354×	`associate-/l*`
1124×	`associate-r`
1042×	`associate-/r*`
892×	`associate-l`
684×	`fma-def`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	24	144
1	53	136
2	85	136
3	165	136
4	387	108
5	1518	84

Stop Event

1×	node limit

Compiler

Compiled 85 to 56 computations (34.1% saved)

end0.0ms (0%)

preprocess28.0ms (0.8%)

Compiler: Compiled 42 to 36 computations (14.3% saved)

analyze138.0ms (3.8%)

sample2.0s (56.4%)

preprocess165.0ms (4.6%)

eval1.0ms (0%)

prune5.0ms (0.1%)

localize53.0ms (1.5%)

series4.0ms (0.1%)

rewrite135.0ms (3.7%)

simplify95.0ms (2.6%)

eval47.0ms (1.3%)

prune25.0ms (0.7%)

localize54.0ms (1.5%)

series52.0ms (1.4%)

rewrite62.0ms (1.7%)

simplify82.0ms (2.3%)

eval89.0ms (2.5%)

prune36.0ms (1%)

localize53.0ms (1.5%)

series3.0ms (0.1%)

rewrite70.0ms (2%)

simplify65.0ms (1.8%)

eval90.0ms (2.5%)

prune31.0ms (0.9%)

localize11.0ms (0.3%)

eval0.0ms (0%)

prune4.0ms (0.1%)

regimes106.0ms (2.9%)

regimes5.0ms (0.1%)

simplify2.0ms (0%)

soundness58.0ms (1.6%)

end0.0ms (0%)

preprocess28.0ms (0.8%)

Profiling