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)

sample718.0ms (39.1%)

Results

708.0ms	8256×	body	256	valid
0.0ms	5×	body	256	invalid

Bogosity

preprocess170.0ms (9.3%)

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)

simplify170.0ms (9.3%)

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)))

eval1.0ms (0%)

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

prune1.0ms (0.1%)

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)

localize222.0ms (12.1%)

Local Accuracy

Found 1 expressions with local accuracy:

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

Compiler

Compiled 18 to 9 computations (50% saved)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite96.0ms (5.3%)

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	17
1	164	17
2	1986	17

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs
(-.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 1 (+.f64 (*.f64 x x) (pow.f64 x 4)))))
(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)))))

simplify81.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

2014×	`fma-def`
570×	`associate-*r/`
540×	`*-commutative`
506×	`unswap-sqr`
408×	`sub-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1256
1	270	1124
2	731	1014
3	2413	962
4	7145	962

Stop Event

1×	node limit

Counts

34 → 79

Calls

Call 1

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

eval52.0ms (2.8%)

Compiler: Compiled 1157 to 891 computations (23% saved)

prune10.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	3	80

Accurracy

100.0%

Counts

80 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.2%	1
▶	99.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.2%	1

Compiler

Compiled 34 to 26 computations (23.5% saved)

localize24.0ms (1.3%)

Local Accuracy

Found 1 expressions with local accuracy:

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

Compiler

Compiled 20 to 11 computations (45% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite51.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1058×	`pow1`
1024×	`add-sqr-sqrt`
976×	`add-exp-log`
976×	`log1p-expm1-u`
976×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1384	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

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

simplify68.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

2120×	`log-prod`
1106×	`distribute-rgt-in`
1092×	`distribute-lft-in`
810×	`associate-r`
672×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	299
1	91	299
2	320	299
3	2107	299
4	6963	299

Stop Event

1×	node limit

Counts

23 → 14

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

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

eval3.0ms (0.2%)

Compiler: Compiled 125 to 91 computations (27.2% saved)

prune3.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	14	3	17

Accurracy

100.0%

Counts

17 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.2%	1
✓	99.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.2%	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
✓	99.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.2%	1
✓	99.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.2%	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
✓	99.1%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
	98.2%	1

Compiler

Compiled 32 to 23 computations (28.1% saved)

regimes10.0ms (0.5%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
2.0ms	(-.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 (0.3%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes3.0ms (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
98.2%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.3%)

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

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

soundness104.0ms (5.7%)

Rules

2014×	`fma-def`
570×	`associate-*r/`
540×	`*-commutative`
506×	`unswap-sqr`
408×	`sub-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1256
1	270	1124
2	731	1014
3	2413	962
4	7145	962

Stop Event

1×	node limit

Compiler

Compiled 15 to 12 computations (20% saved)

end0.0ms (0%)

preprocess28.0ms (1.5%)

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

analyze2.0ms (0.1%)

sample718.0ms (39.1%)

preprocess170.0ms (9.3%)

simplify170.0ms (9.3%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize222.0ms (12.1%)

series1.0ms (0.1%)

rewrite96.0ms (5.3%)

simplify81.0ms (4.4%)

eval52.0ms (2.8%)

prune10.0ms (0.6%)

localize24.0ms (1.3%)

series2.0ms (0.1%)

rewrite51.0ms (2.8%)

simplify68.0ms (3.7%)

eval3.0ms (0.2%)

prune3.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes10.0ms (0.5%)

regimes5.0ms (0.3%)

regimes3.0ms (0.1%)

simplify5.0ms (0.3%)

soundness104.0ms (5.7%)

end0.0ms (0%)

preprocess28.0ms (1.5%)

Profiling