Metrics for Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

analyze2.0ms (0.1%)

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
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.4s (60.7%)

Results

1.4s	8256×	body	256	valid
0.0ms	6×	body	256	invalid

Bogosity

preprocess164.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

1654×	`fma-def`
1194×	`sub-neg`
1138×	`distribute-lft-out`
868×	`associate-+r+`
716×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	28	34
2	46	34
3	91	34
4	134	34
5	216	34
6	342	34
7	620	34
8	1227	34
9	2094	34
10	4780	34
11	6467	34
12	7228	34
13	7526	34
14	7582	34
15	7614	34
16	7867	34

Stop Event

1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (-.f64 1 (*.f64 (neg.f64 x) (neg.f64 x))))

Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))
(sqrt.f64 (-.f64 1 (*.f64 (neg.f64 x) (neg.f64 x))))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (fma.f64 x (neg.f64 x) 1))

Symmetry

(abs x)

Compiler

Compiled 8 to 6 computations (25% saved)

simplify165.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

1468×	`fma-def`
1260×	`distribute-lft-out`
1098×	`unsub-neg`
944×	`distribute-rgt-out--`
798×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	15	17
2	22	17
3	34	17
4	51	17
5	79	17
6	126	17
7	348	17
8	734	17
9	1549	17
10	2918	17
11	4603	17
12	5570	17
13	5888	17
14	6174	17
15	6343	17
16	6420	17
17	6687	17
18	7685	17

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(sqrt.f64 (neg.f64 (fma.f64 x x -1)))

eval0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Accurracy

100.0%

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize24.0ms (1.1%)

Local Accuracy

Found 2 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(-.f64 1 (*.f64 x x))

Compiler

Compiled 18 to 9 computations (50% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite66.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1512×	`pow1`
1404×	`add-exp-log`
1402×	`log1p-expm1-u`
1402×	`expm1-log1p-u`
1374×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	164	30
2	1986	30

Stop Event

1×	node limit

Counts

2 → 55

Calls

Call 1

Inputs
(-.f64 1 (*.f64 x x))
(sqrt.f64 (-.f64 1 (*.f64 x x)))

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

simplify68.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1080×	`fma-def`
1076×	`div-sub`
880×	`fma-neg`
660×	`cancel-sign-sub-inv`
410×	`associate-/r*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	2071
1	410	1811
2	1416	1673
3	4555	1673

Stop Event

1×	node limit

Counts

79 → 117

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(*.f64 -1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(*.f64 -1 (pow.f64 x 2))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(*.f64 (sqrt.f64 -1) x)
(+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x)) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(-.f64 (.f64 -1 (.f64 (sqrt.f64 -1) x)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x)))))
(+.f64 1 (*.f64 x (neg.f64 x)))
(+.f64 1 (.f64 (.f64 x (neg.f64 x)) 1))
(+.f64 (*.f64 x (neg.f64 x)) 1)
(.f64 1 (-.f64 1 (.f64 x x)))
(.f64 (-.f64 1 (.f64 x x)) 1)
(.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (sqrt.f64 (-.f64 1 (*.f64 x x))))
(.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2))
(.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 (+.f64 1 (pow.f64 x 4)) (.f64 x x))))
(.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (.f64 x x))))
(.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (pow.f64 (-.f64 1 (.f64 x x)) 1/4)) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 (-.f64 1 (.f64 x x)))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(/.f64 1 (/.f64 (+.f64 (+.f64 1 (pow.f64 x 4)) (*.f64 x x)) (-.f64 1 (pow.f64 x 6))))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) (-.f64 1 (pow.f64 x 4))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 (+.f64 1 (pow.f64 x 4)) (*.f64 x x)))
(/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 6))) (neg.f64 (+.f64 (+.f64 1 (pow.f64 x 4)) (*.f64 x x))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 4))) (neg.f64 (+.f64 1 (*.f64 x x))))
(/.f64 (+.f64 1 (pow.f64 (.f64 x (neg.f64 x)) 3)) (+.f64 1 (-.f64 (.f64 (.f64 x (neg.f64 x)) (.f64 x (neg.f64 x))) (*.f64 x (neg.f64 x)))))
(/.f64 (-.f64 1 (.f64 (.f64 x (neg.f64 x)) (.f64 x (neg.f64 x)))) (-.f64 1 (.f64 x (neg.f64 x))))
(pow.f64 (-.f64 1 (*.f64 x x)) 1)
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 2)
(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 3)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2) 1/2)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3) 1/3)
(sqrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2))
(log.f64 (exp.f64 (-.f64 1 (*.f64 x x))))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3))
(expm1.f64 (log1p.f64 (-.f64 1 (*.f64 x x))))
(exp.f64 (log1p.f64 (*.f64 x (neg.f64 x))))
(log1p.f64 (expm1.f64 (-.f64 1 (*.f64 x x))))
(-.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))
(.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)
(.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (.f64 x x))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 (+.f64 1 (pow.f64 x 4)) (*.f64 x x))))
(pow.f64 (-.f64 1 (*.f64 x x)) 1/2)
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)
(fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))

Outputs
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (*.f64 x x))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (*.f64 x x))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (*.f64 x x))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (*.f64 x x))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (*.f64 x x))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (*.f64 x x))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (*.f64 x x))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (*.f64 x x))
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(-.f64 1 (*.f64 x x))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (.f64 (.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (.f64 -1/8 (pow.f64 x 4))))
(+.f64 (fma.f64 (.f64 x x) -1/2 1) (.f64 -1/8 (pow.f64 x 4)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 -1/8 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 x 2)) (+.f64 (.f64 -1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 -1/2 (.f64 x x) (fma.f64 -1/16 (pow.f64 x 6) (.f64 -1/8 (pow.f64 x 4)))))
(+.f64 (fma.f64 (.f64 x x) -1/2 1) (fma.f64 -1/8 (pow.f64 x 4) (.f64 -1/16 (pow.f64 x 6))))
(+.f64 1 (fma.f64 x (.f64 x -1/2) (fma.f64 -1/8 (pow.f64 x 4) (.f64 -1/16 (pow.f64 x 6)))))
(*.f64 (sqrt.f64 -1) x)
(*.f64 x (sqrt.f64 -1))
(+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (*.f64 (sqrt.f64 -1) x))
(+.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/2 (.f64 x (sqrt.f64 -1))))
(fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x)) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (-.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (fma.f64 x (sqrt.f64 -1) (/.f64 -1/8 (*.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3)))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))) (.f64 (sqrt.f64 -1) x))) (.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (-.f64 (.f64 x (sqrt.f64 -1)) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))) (+.f64 (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (/.f64 -1/8 (.f64 (neg.f64 (sqrt.f64 -1)) (pow.f64 x 3)))))
(+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))) (+.f64 (/.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 (sqrt.f64 -1) 5)) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))))
(+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (+.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3)))) (/.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 (sqrt.f64 -1) 5))))
(.f64 -1 (.f64 (sqrt.f64 -1) x))
(neg.f64 (*.f64 x (sqrt.f64 -1)))
(*.f64 x (neg.f64 (sqrt.f64 -1)))
(*.f64 (sqrt.f64 -1) (neg.f64 x))
(-.f64 (.f64 -1 (.f64 (sqrt.f64 -1) x)) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(-.f64 (neg.f64 (.f64 x (sqrt.f64 -1))) (/.f64 1/2 (.f64 x (sqrt.f64 -1))))
(neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))
(-.f64 (/.f64 -1/2 (.f64 x (sqrt.f64 -1))) (.f64 x (sqrt.f64 -1)))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x))))
(+.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (-.f64 (neg.f64 (.f64 x (sqrt.f64 -1))) (/.f64 1/2 (*.f64 x (sqrt.f64 -1)))))
(fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)))))
(-.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))
(-.f64 (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))) (.f64 -1 (.f64 (sqrt.f64 -1) x))) (+.f64 (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) x)))))
(+.f64 (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))) (-.f64 (neg.f64 (.f64 x (sqrt.f64 -1))) (+.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) (/.f64 1/16 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))
(-.f64 (fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (neg.f64 (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/2 x) (sqrt.f64 -1))))) (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))
(-.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 3))) (+.f64 (/.f64 (/.f64 1/2 x) (sqrt.f64 -1)) (fma.f64 x (sqrt.f64 -1) (/.f64 (/.f64 1/16 (pow.f64 x 5)) (pow.f64 (sqrt.f64 -1) 5)))))
(+.f64 1 (*.f64 x (neg.f64 x)))
(-.f64 1 (*.f64 x x))
(+.f64 1 (.f64 (.f64 x (neg.f64 x)) 1))
(-.f64 1 (*.f64 x x))
(+.f64 (*.f64 x (neg.f64 x)) 1)
(-.f64 1 (*.f64 x x))
(.f64 1 (-.f64 1 (.f64 x x)))
(-.f64 1 (*.f64 x x))
(.f64 (-.f64 1 (.f64 x x)) 1)
(-.f64 1 (*.f64 x x))
(.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (sqrt.f64 (-.f64 1 (*.f64 x x))))
(-.f64 1 (*.f64 x x))
(.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 2))
(-.f64 1 (*.f64 x x))
(.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(-.f64 1 (*.f64 x x))
(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(-.f64 1 (*.f64 x x))
(.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(-.f64 1 (*.f64 x x))
(.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 (+.f64 1 (pow.f64 x 4)) (.f64 x x))))
(.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (+.f64 (pow.f64 x 4) (.f64 x x)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (.f64 x x))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (pow.f64 (-.f64 1 (.f64 x x)) 1/4)) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(-.f64 1 (*.f64 x x))
(.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 (-.f64 1 (.f64 x x)))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(-.f64 1 (*.f64 x x))
(/.f64 1 (/.f64 (+.f64 (+.f64 1 (pow.f64 x 4)) (*.f64 x x)) (-.f64 1 (pow.f64 x 6))))
(.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (+.f64 (pow.f64 x 4) (.f64 x x)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) (-.f64 1 (pow.f64 x 4))))
(.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (.f64 x x))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 (+.f64 1 (pow.f64 x 4)) (*.f64 x x)))
(.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (+.f64 (pow.f64 x 4) (.f64 x x)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (+.f64 1 (*.f64 x x)))
(.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (.f64 x x))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 6))) (neg.f64 (+.f64 (+.f64 1 (pow.f64 x 4)) (*.f64 x x))))
(.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (+.f64 (pow.f64 x 4) (.f64 x x)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 x 4))) (neg.f64 (+.f64 1 (*.f64 x x))))
(.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (.f64 x x))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(/.f64 (+.f64 1 (pow.f64 (.f64 x (neg.f64 x)) 3)) (+.f64 1 (-.f64 (.f64 (.f64 x (neg.f64 x)) (.f64 x (neg.f64 x))) (*.f64 x (neg.f64 x)))))
(.f64 (-.f64 1 (pow.f64 x 6)) (/.f64 1 (+.f64 1 (+.f64 (pow.f64 x 4) (.f64 x x)))))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (fma.f64 x x 1)))
(/.f64 (-.f64 1 (pow.f64 x 6)) (+.f64 1 (fma.f64 x x (pow.f64 x 4))))
(/.f64 (-.f64 1 (.f64 (.f64 x (neg.f64 x)) (.f64 x (neg.f64 x)))) (-.f64 1 (.f64 x (neg.f64 x))))
(.f64 (-.f64 1 (pow.f64 x 4)) (/.f64 1 (+.f64 1 (.f64 x x))))
(/.f64 (-.f64 1 (pow.f64 x 4)) (fma.f64 x x 1))
(pow.f64 (-.f64 1 (*.f64 x x)) 1)
(-.f64 1 (*.f64 x x))
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 2)
(-.f64 1 (*.f64 x x))
(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 3)
(-.f64 1 (*.f64 x x))
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2) 1/2)
(-.f64 1 (*.f64 x x))
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3) 1/3)
(-.f64 1 (*.f64 x x))
(sqrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 2))
(-.f64 1 (*.f64 x x))
(log.f64 (exp.f64 (-.f64 1 (*.f64 x x))))
(-.f64 1 (*.f64 x x))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3))
(-.f64 1 (*.f64 x x))
(expm1.f64 (log1p.f64 (-.f64 1 (*.f64 x x))))
(-.f64 1 (*.f64 x x))
(exp.f64 (log1p.f64 (*.f64 x (neg.f64 x))))
(exp.f64 (log1p.f64 (neg.f64 (*.f64 x x))))
(log1p.f64 (expm1.f64 (-.f64 1 (*.f64 x x))))
(-.f64 1 (*.f64 x x))
(-.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (cbrt.f64 (-.f64 1 (*.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (pow.f64 (-.f64 1 (.f64 x x)) 1/4) (pow.f64 (-.f64 1 (*.f64 x x)) 1/4))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (-.f64 1 (.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x x))) 2) 1/2) (pow.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1/2))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (hypot.f64 1 x))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 (+.f64 1 (pow.f64 x 4)) (*.f64 x x))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (+.f64 (pow.f64 x 4) (*.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 (pow.f64 x 4) (fma.f64 x x 1))))
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 6))) (sqrt.f64 (+.f64 1 (fma.f64 x x (pow.f64 x 4)))))
(pow.f64 (-.f64 1 (*.f64 x x)) 1/2)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(pow.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(pow.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) 3)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2) 1/3)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(pow.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 2)
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(fabs.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(log.f64 (exp.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 3/2))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
(pow.f64 (exp.f64 (log1p.f64 (neg.f64 (*.f64 x x)))) 1/2)
(sqrt.f64 (exp.f64 (log1p.f64 (*.f64 x (neg.f64 x)))))
(sqrt.f64 (exp.f64 (log1p.f64 (neg.f64 (*.f64 x x)))))
(log1p.f64 (expm1.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))))
(+.f64 1 (-.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))
(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 0)
(sqrt.f64 (-.f64 1 (*.f64 x x)))

eval39.0ms (1.7%)

Compiler: Compiled 1605 to 1157 computations (27.9% saved)

prune13.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	2	118

Accurracy

100.0%

Counts

118 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(+.f64 1 (.f64 (.f64 x x) -1/2))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶	99.5%	(+.f64 1 (.f64 (.f64 x x) -1/2))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize25.0ms (1.1%)

Local Accuracy

Found 2 expressions with local accuracy:

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

Compiler

Compiled 20 to 11 computations (45% saved)

series1.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite60.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1538×	`pow1`
1432×	`add-exp-log`
1430×	`log1p-expm1-u`
1430×	`expm1-log1p-u`
1408×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	32
1	165	28
2	2003	28

Stop Event

1×	node limit

Counts

2 → 44

Calls

Call 1

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

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

simplify65.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1428×	`fma-neg`
1116×	`distribute-lft-neg-in`
970×	`fma-def`
752×	`unswap-sqr`
688×	`log-prod`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	1400
1	235	1326
2	836	1282
3	4575	1252

Stop Event

1×	node limit

Counts

68 → 56

Calls

Call 1

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

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

eval16.0ms (0.7%)

Compiler: Compiled 689 to 503 computations (27% saved)

prune7.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	55	3	58

Accurracy

100.0%

Counts

58 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(+.f64 1 (.f64 (.f64 x x) -1/2))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.9%	1
✓	99.5%	(+.f64 1 (.f64 (.f64 x x) -1/2))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.9%	1

Compiler

Compiled 34 to 26 computations (23.5% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	2	2
Total	3	3

Accurracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(+.f64 1 (.f64 (.f64 x x) -1/2))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.9%	1
✓	99.5%	(+.f64 1 (.f64 (.f64 x x) -1/2))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.9%	1

Compiler

Compiled 34 to 26 computations (23.5% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	2	2
Total	3	3

Accurracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(+.f64 1 (.f64 (.f64 x x) -1/2))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.9%	1

Compiler

Compiled 32 to 23 computations (28.1% saved)

regimes11.0ms (0.5%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (-.f64 1 (*.f64 x x)))

Calls

4 calls:

4.0ms	(-.f64 1 (*.f64 x x))
2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Results

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

Compiler

Compiled 34 to 22 computations (35.3% saved)

regimes5.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes2.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
1

Outputs
1

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
98.9%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative`
6×	`sub-neg`
6×	`*-commutative`
4×	`neg-mul-1`
4×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	20	37
2	27	37
3	31	37
4	33	37

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

soundness109.0ms (4.8%)

Rules

1080×	`fma-def`
1076×	`div-sub`
880×	`fma-neg`
660×	`cancel-sign-sub-inv`
410×	`associate-/r*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	2071
1	410	1811
2	1416	1673
3	4555	1673

Stop Event

1×	node limit

Compiler

Compiled 22 to 18 computations (18.2% saved)

end0.0ms (0%)

preprocess26.0ms (1.2%)

Remove: (abs x)
Compiler: Compiled 58 to 40 computations (31% saved)

analyze2.0ms (0.1%)

sample1.4s (60.7%)

preprocess164.0ms (7.3%)

simplify165.0ms (7.4%)

eval0.0ms (0%)

prune1.0ms (0%)

localize24.0ms (1.1%)

series2.0ms (0.1%)

rewrite66.0ms (2.9%)

simplify68.0ms (3%)

eval39.0ms (1.7%)

prune13.0ms (0.6%)

localize25.0ms (1.1%)

series1.0ms (0.1%)

rewrite60.0ms (2.7%)

simplify65.0ms (2.9%)

eval16.0ms (0.7%)

prune7.0ms (0.3%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes11.0ms (0.5%)

regimes5.0ms (0.2%)

regimes2.0ms (0.1%)

simplify5.0ms (0.2%)

soundness109.0ms (4.8%)

end0.0ms (0%)

preprocess26.0ms (1.2%)

Profiling