Metrics for sqrtexp (problem 3.4.4)

analyze124.0ms (3.6%)

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

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.5s (72.5%)

Results

1.3s	2751×	body	1024	valid
444.0ms	3780×	body	256	valid
416.0ms	1357×	body	512	valid
212.0ms	2744×	body	256	unsamplable
161.0ms	312×	body	2048	valid
6.0ms	56×	body	256	infinite

Bogosity

preprocess39.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1352×	`associate-/l*`
1124×	`associate-r`
1066×	`associate-/r*`
890×	`associate-l`
680×	`fma-def`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	21	83
1	48	79
2	78	79
3	157	79
4	375	67
5	1504	49

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)))

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)))
(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)))
(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))))

Compiler

Compiled 13 to 11 computations (15.4% saved)

eval1.0ms (0%)

Compiler: Compiled 29 to 20 computations (31% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize24.0ms (0.7%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 15 to 9 computations (40% saved)

series1.0ms (0%)

Counts

1 → 4

Calls

3 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)))

rewrite55.0ms (1.6%)

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	15
1	157	15
2	1871	15

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(sqrt.f64 (+.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)))))

simplify60.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1274×	`fma-def`
1136×	`unswap-sqr`
782×	`cancel-sign-sub-inv`
648×	`times-frac`
640×	`associate-/l*`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	973
1	210	803
2	547	699
3	1719	611
4	5703	611

Stop Event

1×	node limit

Counts

27 → 48

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))))))
(-.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)))))

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 (sqrt.f64 2)) (+.f64 x (.f64 3/8 (*.f64 x x)))))
(+.f64 (sqrt.f64 2) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (.f64 x (*.f64 x 3/8)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (/.f64 (.f64 (-.f64 1/6 (.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))
(+.f64 (sqrt.f64 2) (fma.f64 (/.f64 3/16 (sqrt.f64 2)) (.f64 x x) (.f64 (/.f64 1/2 (sqrt.f64 2)) (+.f64 x (*.f64 7/96 (pow.f64 x 3))))))
(-.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)))
(*.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)))
(*.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)))
(*.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 (cbrt.f64 (sqrt.f64 (+.f64 1 (exp.f64 x)))) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(+.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)))
(*.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 1/2) (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)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (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 (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 (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)))
(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)))
(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)))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) 2)
(+.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)))
(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)))
(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)))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2))
(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)))
(+.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)))

eval15.0ms (0.4%)

Compiler: Compiled 655 to 512 computations (21.8% saved)

prune13.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	3	49

Accuracy

100.0%

Counts

49 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.6%	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	74.1%	(sqrt.f64 2)
▶	68.6%	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	74.1%	(sqrt.f64 2)

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize49.0ms (1.4%)

Localize:

Found 2 expressions with local error:

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

Compiler

Compiled 29 to 25 computations (13.8% saved)

series2.0ms (0.1%)

Counts

2 → 3

Calls

6 calls:

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

rewrite71.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

990×	`log-prod`
978×	`prod-diff`
588×	`pow-prod-down`
450×	`pow-exp`
448×	`pow-prod-up`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	217	34
2	2827	34

Stop Event

1×	node limit

Counts

2 → 106

Calls

Call 1

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

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

simplify63.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1430×	`fma-def`
1000×	`distribute-lft-in`
960×	`distribute-rgt-in`
698×	`unswap-sqr`
452×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3069
1	570	2891
2	1812	2839

Stop Event

1×	node limit

Counts

109 → 140

Calls

Call 1

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

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

eval50.0ms (1.4%)

Compiler: Compiled 2094 to 1823 computations (12.9% saved)

prune19.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	139	4	143

Accuracy

100.0%

Counts

143 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.6%	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
▶	2.9%	(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.1%	(sqrt.f64 2)
✓	68.6%	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
▶	2.9%	(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.1%	(sqrt.f64 2)

Compiler

Compiled 52 to 46 computations (11.5% saved)

localize33.0ms (0.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
	99.3%	(/.f64 x (sqrt.f64 2))

Compiler

Compiled 17 to 14 computations (17.6% saved)

eval13.0ms (0.4%)

Compiler: Compiled 567 to 474 computations (16.4% saved)

prune11.0ms (0.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	52	5	57

Accuracy

100.0%

Counts

57 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.6%	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓	2.9%	(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
▶	2.9%	(.f64 1/2 (.f64 (pow.f64 2 -1/2) x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.1%	(sqrt.f64 2)
✓	68.6%	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
✓	2.9%	(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
▶	2.9%	(.f64 1/2 (.f64 (pow.f64 2 -1/2) x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.1%	(sqrt.f64 2)

Compiler

Compiled 68 to 60 computations (11.8% saved)

localize37.0ms (1.1%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.3%	(*.f64 (pow.f64 2 -1/2) x)

Compiler

Compiled 21 to 18 computations (14.3% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite55.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1224×	`pow1`
1134×	`add-exp-log`
1132×	`log1p-expm1-u`
1132×	`expm1-log1p-u`
1112×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	146	11
2	1583	11

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

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

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1908×	`log-prod`
986×	`fma-neg`
812×	`*-commutative`
666×	`distribute-lft-out`
640×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	253
1	79	253
2	271	253
3	1588	253
4	4502	253
5	6870	253

Stop Event

1×	node limit

Counts

23 → 12

Calls

Call 1

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

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

eval3.0ms (0.1%)

Compiler: Compiled 102 to 89 computations (12.7% saved)

prune5.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	11	1	12
Fresh	0	0	0
Picked	1	0	1
Done	1	3	4
Total	13	4	17

Accuracy

100.0%

Counts

17 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.6%	(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))
	2.9%	(.f64 1/2 (.f64 (sqrt.f64 1/2) x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	74.1%	(sqrt.f64 2)

Compiler

Compiled 74 to 63 computations (14.9% saved)

regimes11.0ms (0.3%)

Counts

7 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(.f64 1/2 (.f64 (sqrt.f64 1/2) x))
(*.f64 1/2 (/.f64 x (sqrt.f64 2)))
(.f64 1/2 (.f64 (pow.f64 2 -1/2) x))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 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 75 to 62 computations (17.3% saved)

regimes6.0ms (0.2%)

Accuracy

Total -45.5b remaining (-274.7%)

Threshold costs -45.5b (-274.7%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 2)

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
74.1%	1	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	13	20

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

soundness68.0ms (2%)

Rules

1352×	`associate-/l*`
1124×	`associate-r`
1066×	`associate-/r*`
890×	`associate-l`
680×	`fma-def`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	21	83
1	48	79
2	78	79
3	157	79
4	375	67
5	1504	49

Stop Event

1×	node limit

Compiler

Compiled 85 to 56 computations (34.1% saved)

end0.0ms (0%)

preprocess51.0ms (1.5%)

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

analyze124.0ms (3.6%)

sample2.5s (72.5%)

preprocess39.0ms (1.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize24.0ms (0.7%)

series1.0ms (0%)

rewrite55.0ms (1.6%)

simplify60.0ms (1.7%)

eval15.0ms (0.4%)

prune13.0ms (0.4%)

localize49.0ms (1.4%)

series2.0ms (0.1%)

rewrite71.0ms (2%)

simplify63.0ms (1.8%)

eval50.0ms (1.4%)

prune19.0ms (0.5%)

localize33.0ms (0.9%)

eval13.0ms (0.4%)

prune11.0ms (0.3%)

localize37.0ms (1.1%)

series2.0ms (0.1%)

rewrite55.0ms (1.6%)

simplify65.0ms (1.9%)

eval3.0ms (0.1%)

prune5.0ms (0.1%)

regimes11.0ms (0.3%)

regimes6.0ms (0.2%)

simplify4.0ms (0.1%)

soundness68.0ms (2%)

end0.0ms (0%)

preprocess51.0ms (1.5%)

Profiling