Metrics for sqrtexp (problem 3.4.4)

analyze127.0ms (4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
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)

sample2.1s (65.6%)

Results

1.0s	2673×	body	1024	valid
412.0ms	3879×	body	256	valid
280.0ms	1385×	body	512	valid
222.0ms	2650×	body	256	unsamplable
108.0ms	277×	body	2048	valid
5.0ms	42×	body	256	infinite

Bogosity

preprocess211.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

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

Problems

171×	`(-.f64 (exp.f64 (*.f64 2 x)) 1)`
80×	No Errors
4×	`(-.f64 (exp.f64 x) 1)`
1×	`(/.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)

prune2.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
▶	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	99.6%	(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)

localize57.0ms (1.8%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	99.7%	(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
✓	100.0%	(+.f64 1 (exp.f64 x))

Compiler

Compiled 41 to 25 computations (39% saved)

series2.0ms (0.1%)

Counts

2 → 16

Calls

6 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	(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
0.0ms	x	@	0	(+.f64 1 (exp.f64 x))
0.0ms	x	@	inf	(+.f64 1 (exp.f64 x))

rewrite122.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

986×	`unpow-prod-down`
672×	`log-prod`
654×	`log1p-expm1-u`
652×	`expm1-log1p-u`
426×	`pow-prod-down`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	157	28
2	2022	28

Stop Event

1×	node limit

Counts

2 → 195

Calls

Call 1

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

simplify90.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1174×	`fma-def`
932×	`distribute-lft-in`
902×	`distribute-rgt-in`
884×	`associate-*r/`
558×	`sqr-pow`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	6507
1	775	6356
2	2795	6245

Stop Event

1×	node limit

Counts

211 → 155

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

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

eval46.0ms (1.5%)

Compiler: Compiled 2343 to 1664 computations (29% saved)

prune20.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	152	5	157

Accuracy

100.0%

Counts

157 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	70.0%	(sqrt.f64 (+.f64 2 (+.f64 x (*.f64 1/2 (pow.f64 x 2)))))
▶	68.2%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	99.4%	(sqrt.f64 (.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (.f64 x 2))))
▶	74.2%	(sqrt.f64 2)
▶	70.0%	(sqrt.f64 (+.f64 2 (+.f64 x (*.f64 1/2 (pow.f64 x 2)))))
▶	68.2%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	99.4%	(sqrt.f64 (.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (.f64 x 2))))
▶	74.2%	(sqrt.f64 2)

Compiler

Compiled 72 to 60 computations (16.7% saved)

localize111.0ms (3.5%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 1 (expm1.f64 x))
✓	99.5%	(.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (.f64 x 2)))

Compiler

Compiled 86 to 62 computations (27.9% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/.f64 1 (expm1.f64 x))
0.0ms	x	@	-inf	(/.f64 1 (expm1.f64 x))
0.0ms	x	@	0	(.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (.f64 x 2)))
0.0ms	x	@	0	(/.f64 1 (expm1.f64 x))
0.0ms	x	@	inf	(.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (.f64 x 2)))

rewrite59.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

920×	`unpow-prod-down`
624×	`log-prod`
529×	`log1p-expm1-u`
527×	`expm1-log1p-u`
460×	`exp-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	129	41
2	1502	41

Stop Event

1×	node limit

Counts

2 → 76

Calls

Call 1

Inputs
(.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (.f64 x 2)))
(/.f64 1 (expm1.f64 x))

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

simplify74.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1594×	`fma-neg`
898×	`times-frac`
756×	`log-prod`
748×	`fma-def`
670×	`unswap-sqr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2534
1	517	2455
2	1456	2443
3	6843	2443

Stop Event

1×	node limit

Counts

100 → 111

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)))))
(/.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))
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1/2)
(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2)
(-.f64 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))) 1/2)
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(+.f64 0 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x))))))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))) 1)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 1 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x 2))))
(/.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 (expm1.f64 (*.f64 x 2)) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (.f64 (expm1.f64 (.f64 x 2)) -1) (neg.f64 (expm1.f64 x)))
(/.f64 (.f64 -1 (expm1.f64 (.f64 x 2))) (neg.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 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)) 1)
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))) 3)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))) 2)
(pow.f64 (E.f64) (log.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(pow.f64 (/.f64 (pow.f64 (expm1.f64 (*.f64 x 2)) 3) (pow.f64 (expm1.f64 x) 3)) 1/3)
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x 2))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))) 2)) (cbrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x))))) (sqrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)) 2))
(log.f64 (exp.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.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 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(exp.f64 (log.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))) 2))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(+.f64 0 (/.f64 1 (expm1.f64 x)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))))
(-.f64 (+.f64 1 (/.f64 1 (expm1.f64 x))) 1)
(*.f64 1 (/.f64 1 (expm1.f64 x)))
(*.f64 (/.f64 1 (expm1.f64 x)) 1)
(*.f64 (/.f64 1 (expm1.f64 x)) (log.f64 (E.f64)))
(*.f64 -1 (/.f64 1 (neg.f64 (expm1.f64 x))))
(*.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) -2))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) (/.f64 1 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (expm1.f64 x) -1/2) (pow.f64 (expm1.f64 x) -1/2))
(*.f64 (pow.f64 1 1/3) (/.f64 1 (expm1.f64 x)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x)))) 2) 3) (/.f64 1 (cbrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x)))) 3) (pow.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) -3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) -3)) 1/3))
(.f64 (pow.f64 (.f64 (pow.f64 (expm1.f64 x) -2) (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)) 1/3) (cbrt.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) -5/2) 1/3) (cbrt.f64 (pow.f64 (expm1.f64 x) -1/2)))
(pow.f64 (expm1.f64 x) -1)
(pow.f64 (/.f64 1 (expm1.f64 x)) 1)
(pow.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) 3)
(pow.f64 (cbrt.f64 (expm1.f64 x)) -3)
(pow.f64 (pow.f64 (expm1.f64 x) -2) 1/2)
(pow.f64 (pow.f64 (expm1.f64 x) -3) 1/3)
(pow.f64 (pow.f64 (expm1.f64 x) 2) -1/2)
(pow.f64 (pow.f64 (expm1.f64 x) 3) -1/3)
(pow.f64 (pow.f64 (expm1.f64 x) -1/2) 2)
(pow.f64 (sqrt.f64 (expm1.f64 x)) -2)
(pow.f64 (E.f64) (neg.f64 (log.f64 (expm1.f64 x))))
(pow.f64 (neg.f64 (neg.f64 (expm1.f64 x))) -1)
(pow.f64 (exp.f64 -1) (log.f64 (expm1.f64 x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log.f64 (expm1.f64 x)))) 2)) (cbrt.f64 (neg.f64 (log.f64 (expm1.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log.f64 (expm1.f64 x))))) (sqrt.f64 (neg.f64 (log.f64 (expm1.f64 x)))))
(sqrt.f64 (pow.f64 (expm1.f64 x) -2))
(log.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))
(cbrt.f64 (pow.f64 (expm1.f64 x) -3))
(expm1.f64 (log1p.f64 (/.f64 1 (expm1.f64 x))))
(exp.f64 (neg.f64 (log.f64 (expm1.f64 x))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (cbrt.f64 (expm1.f64 x)))) 3))
(exp.f64 (*.f64 (log.f64 (pow.f64 (expm1.f64 x) -3)) 1/3))
(exp.f64 (.f64 (.f64 -1/2 (log.f64 (expm1.f64 x))) 2))
(log1p.f64 (expm1.f64 (/.f64 1 (expm1.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 2 (fma.f64 1/2 (pow.f64 x 2) (fma.f64 1/6 (pow.f64 x 3) x)))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1/2)
(+.f64 (/.f64 1 x) -1/2)
(-.f64 (+.f64 (*.f64 1/12 x) (/.f64 1 x)) 1/2)
(+.f64 (fma.f64 1/12 x (/.f64 1 x)) -1/2)
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) -1/2)
(+.f64 (/.f64 1 x) (fma.f64 x 1/12 -1/2))
(-.f64 (+.f64 (.f64 -1/720 (pow.f64 x 3)) (+.f64 (.f64 1/12 x) (/.f64 1 x))) 1/2)
(+.f64 (fma.f64 -1/720 (pow.f64 x 3) (fma.f64 1/12 x (/.f64 1 x))) -1/2)
(+.f64 (fma.f64 (pow.f64 x 3) -1/720 (fma.f64 x 1/12 (/.f64 1 x))) -1/2)
(+.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 (pow.f64 x 3) -1/720 -1/2))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(/.f64 1 (-.f64 (exp.f64 x) 1))
(/.f64 1 (expm1.f64 x))
(+.f64 0 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 2 x)) (expm1.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 2 x)) (expm1.f64 x))))))
(.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 2 x)) (expm1.f64 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x))))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (.f64 2 x)) (expm1.f64 x))))))
(-.f64 (+.f64 1 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))) 1)
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (expm1.f64 x)) (/.f64 1 (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 1 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x 2))))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))
(/.f64 (expm1.f64 (*.f64 2 x)) (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 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (sqrt.f64 (expm1.f64 (.f64 x 2))) (/.f64 (expm1.f64 x) (sqrt.f64 (expm1.f64 (.f64 x 2)))))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x 2))) (neg.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (.f64 (expm1.f64 (.f64 x 2)) -1) (neg.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (.f64 -1 (expm1.f64 (.f64 x 2))) (neg.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (/.f64 (expm1.f64 (*.f64 x 2)) 1) (expm1.f64 x))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)) 1)
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (cbrt.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))) 3)
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)) 2) 1/2)
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)) 3) 1/3)
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))) 2)
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (E.f64) (log.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (/.f64 (pow.f64 (expm1.f64 (*.f64 x 2)) 3) (pow.f64 (expm1.f64 x) 3)) 1/3)
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x 2))) -1)
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))) 2)) (cbrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 2 x)) (expm1.f64 x)))) 2)) (cbrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 2 x)) (expm1.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x))))) (sqrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 2 x)) (expm1.f64 x))))) (sqrt.f64 (log.f64 (/.f64 (expm1.f64 (.f64 2 x)) (expm1.f64 x)))))
(sqrt.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)) 2))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(log.f64 (exp.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(cbrt.f64 (pow.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)) 3))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(cbrt.f64 (/.f64 (pow.f64 (expm1.f64 (*.f64 x 2)) 3) (pow.f64 (expm1.f64 x) 3)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(expm1.f64 (log1p.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(exp.f64 (log.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))) 3))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x)))) 1/3))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 x 2)) (expm1.f64 x)))) 2))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(log1p.f64 (expm1.f64 (/.f64 (expm1.f64 (*.f64 x 2)) (expm1.f64 x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(+.f64 0 (/.f64 1 (expm1.f64 x)))
(/.f64 1 (expm1.f64 x))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))))
(*.f64 3 (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))))
(*.f64 2 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))))
(-.f64 (+.f64 1 (/.f64 1 (expm1.f64 x))) 1)
(/.f64 1 (expm1.f64 x))
(*.f64 1 (/.f64 1 (expm1.f64 x)))
(/.f64 1 (expm1.f64 x))
(*.f64 (/.f64 1 (expm1.f64 x)) 1)
(/.f64 1 (expm1.f64 x))
(*.f64 (/.f64 1 (expm1.f64 x)) (log.f64 (E.f64)))
(/.f64 1 (expm1.f64 x))
(*.f64 -1 (/.f64 1 (neg.f64 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(*.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) -2))
(/.f64 1 (expm1.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) (/.f64 1 (cbrt.f64 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(*.f64 (pow.f64 (expm1.f64 x) -1/2) (pow.f64 (expm1.f64 x) -1/2))
(/.f64 1 (expm1.f64 x))
(*.f64 (pow.f64 1 1/3) (/.f64 1 (expm1.f64 x)))
(/.f64 1 (expm1.f64 x))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x)))) 2) 3) (/.f64 1 (cbrt.f64 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x)))) 3) (pow.f64 (sqrt.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x)))) 3))
(/.f64 1 (expm1.f64 x))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) -3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) -3)) 1/3))
(*.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) -3))) (cbrt.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) -3))))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) -3/2)) (cbrt.f64 (pow.f64 (expm1.f64 x) -3/2)))
(.f64 (pow.f64 (.f64 (pow.f64 (expm1.f64 x) -2) (pow.f64 (cbrt.f64 (expm1.f64 x)) -2)) 1/3) (cbrt.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x)))))
(.f64 (cbrt.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x)))) (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) -2) (pow.f64 (expm1.f64 x) -2))))
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) -5/2) 1/3) (cbrt.f64 (pow.f64 (expm1.f64 x) -1/2)))
(*.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) -5/2)) (cbrt.f64 (pow.f64 (expm1.f64 x) -1/2)))
(pow.f64 (expm1.f64 x) -1)
(/.f64 1 (expm1.f64 x))
(pow.f64 (/.f64 1 (expm1.f64 x)) 1)
(/.f64 1 (expm1.f64 x))
(pow.f64 (/.f64 1 (cbrt.f64 (expm1.f64 x))) 3)
(/.f64 1 (expm1.f64 x))
(pow.f64 (cbrt.f64 (expm1.f64 x)) -3)
(/.f64 1 (expm1.f64 x))
(pow.f64 (pow.f64 (expm1.f64 x) -2) 1/2)
(/.f64 1 (expm1.f64 x))
(pow.f64 (pow.f64 (expm1.f64 x) -3) 1/3)
(/.f64 1 (expm1.f64 x))
(pow.f64 (pow.f64 (expm1.f64 x) 2) -1/2)
(pow.f64 (pow.f64 (expm1.f64 x) 3) -1/3)
(*.f64 (pow.f64 (pow.f64 (expm1.f64 x) 3) -1/6) (pow.f64 (pow.f64 (expm1.f64 x) 3) -1/6))
(pow.f64 (pow.f64 (expm1.f64 x) -1/2) 2)
(/.f64 1 (expm1.f64 x))
(pow.f64 (sqrt.f64 (expm1.f64 x)) -2)
(pow.f64 (E.f64) (neg.f64 (log.f64 (expm1.f64 x))))
(pow.f64 (neg.f64 (neg.f64 (expm1.f64 x))) -1)
(/.f64 1 (expm1.f64 x))
(pow.f64 (exp.f64 -1) (log.f64 (expm1.f64 x)))
(/.f64 1 (expm1.f64 x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log.f64 (expm1.f64 x)))) 2)) (cbrt.f64 (neg.f64 (log.f64 (expm1.f64 x)))))
(pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log.f64 (expm1.f64 x))))) (sqrt.f64 (neg.f64 (log.f64 (expm1.f64 x)))))
(sqrt.f64 (pow.f64 (expm1.f64 x) -2))
(/.f64 1 (expm1.f64 x))
(log.f64 (exp.f64 (/.f64 1 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(cbrt.f64 (pow.f64 (expm1.f64 x) -3))
(/.f64 1 (expm1.f64 x))
(expm1.f64 (log1p.f64 (/.f64 1 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(exp.f64 (neg.f64 (log.f64 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))
(exp.f64 (*.f64 (neg.f64 (log.f64 (cbrt.f64 (expm1.f64 x)))) 3))
(/.f64 1 (expm1.f64 x))
(exp.f64 (*.f64 (log.f64 (pow.f64 (expm1.f64 x) -3)) 1/3))
(/.f64 1 (expm1.f64 x))
(exp.f64 (.f64 (.f64 -1/2 (log.f64 (expm1.f64 x))) 2))
(/.f64 1 (expm1.f64 x))
(log1p.f64 (expm1.f64 (/.f64 1 (expm1.f64 x))))
(/.f64 1 (expm1.f64 x))

eval40.0ms (1.3%)

Compiler: Compiled 1559 to 1128 computations (27.6% saved)

prune15.0ms (0.5%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	111	5	116

Accuracy

100.0%

Counts

116 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	70.0%	(sqrt.f64 (+.f64 2 (+.f64 x (*.f64 1/2 (pow.f64 x 2)))))
✓	68.2%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	99.4%	(sqrt.f64 (.f64 (/.f64 1 (expm1.f64 x)) (expm1.f64 (.f64 x 2))))
✓	74.2%	(sqrt.f64 2)

Compiler

Compiled 88 to 70 computations (20.5% saved)

regimes11.0ms (0.3%)

Counts

7 → 1

Calls

Call 1

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

5.0ms	x
2.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))
2.0ms	(sqrt.f64 (/.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 79 to 62 computations (21.5% saved)

regimes4.0ms (0.1%)

Accuracy

Total -4.1b remaining (-24.8%)

Threshold costs -4.1b (-24.8%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
74.2%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify2.0ms (0.1%)

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 (1.9%)

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%)

preprocess26.0ms (0.8%)

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

analyze127.0ms (4%)

sample2.1s (65.6%)

preprocess211.0ms (6.7%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize57.0ms (1.8%)

series2.0ms (0.1%)

rewrite122.0ms (3.9%)

simplify90.0ms (2.9%)

eval46.0ms (1.5%)

prune20.0ms (0.6%)

localize111.0ms (3.5%)

series2.0ms (0.1%)

rewrite59.0ms (1.9%)

simplify74.0ms (2.4%)

eval40.0ms (1.3%)

prune15.0ms (0.5%)

regimes11.0ms (0.3%)

regimes4.0ms (0.1%)

simplify2.0ms (0.1%)

soundness58.0ms (1.9%)

end0.0ms (0%)

preprocess26.0ms (0.8%)

Profiling