Details

analyze177.0ms (5.6%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.3s (71.5%)

Results

1.3s	2787×	body	1024	valid
541.0ms	3804×	body	256	valid
282.0ms	1363×	body	512	valid
173.0ms	302×	body	2048	valid
6.0ms	57×	body	256	infinite
0.0ms	3×	body	256	unsamplable

Bogosity

preprocess76.0ms (2.4%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify67.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 5

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Accurracy

100.0%

Counts

6 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize7.0ms (0.2%)

Local Accuracy

Found 2 expressions with local accuracy:

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

Compiler

Compiled 14 to 8 computations (42.9% saved)

series1.0ms (0%)

Counts

2 → 8

Calls

6 calls:

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

rewrite88.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1452×	`pow1`
1340×	`add-exp-log`
1340×	`log1p-expm1-u`
1340×	`expm1-log1p-u`
1312×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	157	26
2	1871	26

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

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

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

simplify85.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1378×	`times-frac`
1140×	`distribute-lft-in`
1108×	`distribute-rgt-in`
974×	`fma-def`
388×	`div-sub`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	1828
1	359	1584
2	1199	1240
3	3682	1214

Stop Event

1×	node limit

Counts

66 → 94

Calls

Call 1

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

eval30.0ms (0.9%)

Compiler: Compiled 1144 to 824 computations (28% saved)

prune11.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	4	95

Accurracy

100.0%

Counts

95 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.2%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	72.6%	(sqrt.f64 2)
▶	99.0%	(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))

Compiler

Compiled 22 to 19 computations (13.6% saved)

localize11.0ms (0.3%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
	100.0%	(+.f64 1 (exp.f64 x))
✓	100.0%	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
✓	99.0%	(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))

Compiler

Compiled 23 to 15 computations (34.8% saved)

series46.0ms (1.4%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	x	@	inf	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
20.0ms	x	@	-inf	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
0.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
0.0ms	x	@	0	(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
0.0ms	x	@	inf	(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))

rewrite65.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1742×	`pow1`
1628×	`add-exp-log`
1626×	`log1p-expm1-u`
1626×	`expm1-log1p-u`
1596×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	201	32
2	2356	32

Stop Event

1×	node limit

Counts

2 → 40

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)

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

simplify59.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

730×	`distribute-rgt-in`
726×	`distribute-lft-in`
720×	`unswap-sqr`
648×	`associate-/l*`
648×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	1652
1	318	1570
2	909	1462
3	3279	1392

Stop Event

1×	node limit

Counts

64 → 83

Calls

Call 1

Inputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 8)
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (sqrt.f64 8))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8)))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (+.f64 (sqrt.f64 8) (.f64 27/128 (.f64 (sqrt.f64 8) (pow.f64 x 3))))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(-.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 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (sqrt.f64 (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 (pow.f64 1 1/3) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) 1/3) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) 1/3))
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(pow.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 3)
(pow.f64 (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 2)
(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)))))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(exp.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(-.f64 (+.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)) 1)
(*.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(*.f64 (+.f64 1 (exp.f64 x)) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1)
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) (pow.f64 (+.f64 1 (exp.f64 x)) 3/4))
(*.f64 (pow.f64 1 3/2) (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 3/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3/2))
(*.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3/2) (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3/2))
(.f64 (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(.f64 (.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))) (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(log.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(cbrt.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(exp.f64 (*.f64 3/2 (log1p.f64 (exp.f64 x))))
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))

Outputs
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
(fma.f64 1/2 (/.f64 x (sqrt.f64 2)) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (*.f64 1/2 (/.f64 x (sqrt.f64 2)))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x))) (/.f64 x (sqrt.f64 2)))))
(fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x)))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)))))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.f64 1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (pow.f64 x 3)) (sqrt.f64 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 x 2)) (sqrt.f64 2))) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (/.f64 (+.f64 1/6 (.f64 -1/2 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (pow.f64 (sqrt.f64 2) 2)))) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (.f64 1/2 (+.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (*.f64 x x))) (/.f64 x (sqrt.f64 2))))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (+.f64 (/.f64 x (sqrt.f64 2)) (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (/.f64 (sqrt.f64 2) (.f64 x x)))) (/.f64 (.f64 7/192 (pow.f64 x 3)) (sqrt.f64 2))))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (/.f64 (-.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 2)) 2)) (sqrt.f64 2)) (*.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(fma.f64 1/2 (fma.f64 (/.f64 7/96 (sqrt.f64 2)) (pow.f64 x 3) (fma.f64 (-.f64 (/.f64 1/2 (sqrt.f64 2)) (/.f64 1/2 (.f64 4 (sqrt.f64 2)))) (.f64 x x) (/.f64 x (sqrt.f64 2)))) (sqrt.f64 2))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 8)
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (sqrt.f64 8))
(fma.f64 3/4 (*.f64 x (sqrt.f64 8)) (sqrt.f64 8))
(.f64 (+.f64 (.f64 x 3/4) 1) (sqrt.f64 8))
(fma.f64 x (*.f64 (sqrt.f64 8) 3/4) (sqrt.f64 8))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (sqrt.f64 8)))
(fma.f64 3/4 (.f64 x (sqrt.f64 8)) (fma.f64 15/32 (.f64 (*.f64 x x) (sqrt.f64 8)) (sqrt.f64 8)))
(fma.f64 3/4 (.f64 x (sqrt.f64 8)) (fma.f64 15/32 (.f64 x (*.f64 x (sqrt.f64 8))) (sqrt.f64 8)))
(+.f64 (sqrt.f64 8) (.f64 (sqrt.f64 8) (+.f64 (.f64 x 3/4) (.f64 x (.f64 x 15/32)))))
(+.f64 (sqrt.f64 8) (.f64 (.f64 x (sqrt.f64 8)) (+.f64 3/4 (*.f64 x 15/32))))
(+.f64 (.f64 3/4 (.f64 (sqrt.f64 8) x)) (+.f64 (.f64 15/32 (.f64 (sqrt.f64 8) (pow.f64 x 2))) (+.f64 (sqrt.f64 8) (.f64 27/128 (.f64 (sqrt.f64 8) (pow.f64 x 3))))))
(fma.f64 3/4 (.f64 x (sqrt.f64 8)) (+.f64 (fma.f64 15/32 (.f64 (.f64 x x) (sqrt.f64 8)) (sqrt.f64 8)) (.f64 (*.f64 27/128 (sqrt.f64 8)) (pow.f64 x 3))))
(fma.f64 3/4 (.f64 x (sqrt.f64 8)) (fma.f64 15/32 (.f64 x (.f64 x (sqrt.f64 8))) (fma.f64 27/128 (.f64 (pow.f64 x 3) (sqrt.f64 8)) (sqrt.f64 8))))
(+.f64 (fma.f64 (.f64 x x) (.f64 (sqrt.f64 8) 15/32) (sqrt.f64 8)) (.f64 (sqrt.f64 8) (+.f64 (.f64 (pow.f64 x 3) 27/128) (*.f64 x 3/4))))
(+.f64 (sqrt.f64 8) (.f64 (sqrt.f64 8) (+.f64 (.f64 (pow.f64 x 3) 27/128) (.f64 x (+.f64 3/4 (.f64 x 15/32))))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(-.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 1 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(*.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3/2)
(*.f64 (pow.f64 1 1/3) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) 1/3) (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) 1/3))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4)) (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4)))
(pow.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) 1/6) 4)
(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (*.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) 3/2)) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1/2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 1)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 3)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(pow.f64 (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) 2)
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(fabs.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(hypot.f64 1 (sqrt.f64 (exp.f64 x)))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(exp.f64 (log.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(-.f64 (+.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)) 1)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 1 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (+.f64 1 (exp.f64 x)) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 1 (exp.f64 x)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/4) (pow.f64 (+.f64 1 (exp.f64 x)) 3/4))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (pow.f64 1 3/2) (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 3/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3/2))
(*.f64 (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3/2) (pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 3/2))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(.f64 (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))) (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) 7))
(.f64 (.f64 (+.f64 1 (exp.f64 x)) (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))))) (sqrt.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x)))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(log.f64 (exp.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(cbrt.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 3))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)
(exp.f64 (*.f64 3/2 (log1p.f64 (exp.f64 x))))
(pow.f64 (exp.f64 3/2) (log1p.f64 (exp.f64 x)))
(log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(fabs.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (+.f64 1 (exp.f64 x)) 3/2)

localize2.0ms (0.1%)

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

localize16.0ms (0.5%)

Compiler: Compiled 10 to 7 computations (30% saved)

eval41.0ms (1.3%)

Compiler: Compiled 1835 to 1375 computations (25.1% saved)

prune20.0ms (0.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	134	4	138

Accurracy

100.0%

Counts

138 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.2%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	72.6%	(sqrt.f64 2)
✓	99.0%	(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))

Compiler

Compiled 22 to 19 computations (13.6% saved)

regimes10.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(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:

4.0ms	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 58 to 46 computations (20.7% saved)

regimes5.0ms (0.1%)

Accuracy

Total -4.4b remaining (-25.1%)

Threshold costs -4.4b (-25.1%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
72.6%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	13	20

Stop Event

1×	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)

soundness64.0ms (2%)

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Compiler

Compiled 85 to 56 computations (34.1% saved)

end19.0ms (0.6%)

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

Details

analyze177.0ms (5.6%)

sample2.3s (71.5%)

preprocess76.0ms (2.4%)

simplify67.0ms (2.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.2%)

series1.0ms (0%)

rewrite88.0ms (2.8%)

simplify85.0ms (2.7%)

eval30.0ms (0.9%)

prune11.0ms (0.3%)

localize11.0ms (0.3%)

series46.0ms (1.4%)

rewrite65.0ms (2.1%)

simplify59.0ms (1.9%)

localize2.0ms (0.1%)

localize16.0ms (0.5%)

eval41.0ms (1.3%)

prune20.0ms (0.6%)

regimes10.0ms (0.3%)

regimes5.0ms (0.1%)

simplify4.0ms (0.1%)

soundness64.0ms (2%)

end19.0ms (0.6%)

Profiling