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

analyze1.4s (17.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	199.9%	-99.9%	0%	0%	0%	1
0%	0%	399.8%	-299.8%	0%	0%	0%	2
0%	0%	799.6%	-699.6%	0%	0%	0%	3
0%	0%	1599.2%	-1499.2%	0%	0%	0%	4
0%	0%	3198.4%	-3098.4%	0%	0%	0%	5
0%	0%	6396.9%	-6296.9%	0%	0%	0%	6
0%	0%	12793.8%	-12693.8%	0%	0%	0%	7
0%	0%	25587.5%	-25487.5%	0%	0%	0%	8
0%	0%	51175%	-51075%	0%	0%	0%	9
0%	0%	102350%	-102250%	0%	0%	0%	10
0%	0%	204700%	-204600%	0%	0%	0%	11
0%	0%	409400%	-409300%	0%	0%	0%	12

Compiler

Compiled 8 to 6 computations (25% saved)

sample4.9s (58.4%)

Results

2.0s	4208×	body	2048	valid
1.5s	8281×	body	256	invalid
848.0ms	2041×	body	1024	valid
278.0ms	989×	body	512	valid
193.0ms	1017×	body	256	valid
0.0ms	1×	body	4096	valid

Bogosity

preprocess203.0ms (2.4%)

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)

simplify293.0ms (3.5%)

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)))

eval2.0ms (0%)

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

prune4.0ms (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)

localize138.0ms (1.6%)

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%)

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)))

rewrite60.0ms (0.7%)

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)))))

simplify80.0ms (1%)

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)))

eval26.0ms (0.3%)

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

prune11.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	4	80

Accurracy

100.0%

Counts

80 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶	100.0%	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
	98.8%	1
▶	99.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
▶	100.0%	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
	98.8%	1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize317.0ms (3.8%)

Local Accuracy

Found 3 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(.f64 -1/2 (.f64 x x))
✓	100.0%	(log1p.f64 (*.f64 x (neg.f64 x)))
✓	100.0%	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)

Compiler

Compiled 48 to 20 computations (58.3% saved)

series10.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)
2.0ms	x	@	inf	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)
1.0ms	x	@	0	(.f64 -1/2 (.f64 x x))
1.0ms	x	@	inf	(.f64 -1/2 (.f64 x x))
1.0ms	x	@	-inf	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)

rewrite185.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1730×	`pow1`
1590×	`add-exp-log`
1588×	`log1p-expm1-u`
1588×	`expm1-log1p-u`
1556×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	243	41
2	2805	41

Stop Event

1×	node limit

Counts

3 → 37

Calls

Call 1

Inputs
(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)
(log1p.f64 (*.f64 x (neg.f64 x)))
(.f64 -1/2 (.f64 x x))

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

simplify158.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1174×	`fma-def`
1094×	`log-prod`
1014×	`fma-neg`
896×	`unswap-sqr`
628×	`sub-neg`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	2093
1	410	1813
2	1467	1653
3	5047	1609

Stop Event

1×	node limit

Counts

73 → 144

Calls

Call 1

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

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

eval95.0ms (1.1%)

Compiler: Compiled 2346 to 1747 computations (25.5% saved)

prune35.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	1	1
Picked	0	2	2
Done	0	1	1
Total	144	4	148

Accurracy

100.0%

Counts

148 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
	98.8%	1
✓	99.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
	98.8%	1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune5.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
	98.8%	1
✓	99.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
	98.8%	1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune4.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	3	3
Total	4	4

Accurracy

100.0%

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(+.f64 1 (.f64 -1/2 (.f64 x x)))
✓	100.0%	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	100.0%	(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
	98.8%	1

Compiler

Compiled 49 to 36 computations (26.5% saved)

regimes19.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

Inputs
1
(+.f64 1 (.f64 -1/2 (.f64 x x)))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))

Outputs
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))

Calls

4 calls:

5.0ms	x
4.0ms	(*.f64 x x)
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
4.0ms	(-.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 42 to 28 computations (33.3% saved)

regimes31.0ms (0.4%)

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:

17.0ms	(*.f64 x x)
5.0ms	x
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
3.0ms	(-.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)

regimes10.0ms (0.1%)

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:

5.0ms	x
4.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
1

Outputs
1

Calls

1 calls:

12.0ms

Results

Accuracy	Segments	Branch
98.8%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	62
1	30	62
2	35	62
3	38	62
4	39	62

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
(sqrt.f64 (-.f64 1 (*.f64 x x)))
(+.f64 1 (.f64 -1/2 (.f64 x x)))
1

Outputs
(exp.f64 (.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2))
(exp.f64 (.f64 (log1p.f64 (neg.f64 (.f64 x x))) 1/2))
(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 26 to 20 computations (23.1% saved)

soundness285.0ms (3.4%)

Rules

2014×	`fma-def`
1512×	`pow1`
1404×	`add-exp-log`
1402×	`log1p-expm1-u`
1402×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	164	17
2	1986	17
0	108	1256
1	270	1124
2	731	1014
3	2413	962
4	7145	962

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 64 to 44 computations (31.3% saved)

end0.0ms (0%)

preprocess63.0ms (0.8%)

Remove: (abs x)
Compiler: Compiled 78 to 54 computations (30.8% saved)

analyze1.4s (17.1%)

sample4.9s (58.4%)

preprocess203.0ms (2.4%)

simplify293.0ms (3.5%)

eval2.0ms (0%)

prune4.0ms (0%)

localize138.0ms (1.6%)

series1.0ms (0%)

rewrite60.0ms (0.7%)

simplify80.0ms (1%)

eval26.0ms (0.3%)

prune11.0ms (0.1%)

localize317.0ms (3.8%)

series10.0ms (0.1%)

rewrite185.0ms (2.2%)

simplify158.0ms (1.9%)

eval95.0ms (1.1%)

prune35.0ms (0.4%)

localize0.0ms (0%)

eval0.0ms (0%)

prune5.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune4.0ms (0.1%)

regimes19.0ms (0.2%)

regimes31.0ms (0.4%)

regimes10.0ms (0.1%)

regimes13.0ms (0.2%)

simplify11.0ms (0.1%)

soundness285.0ms (3.4%)

end0.0ms (0%)

preprocess63.0ms (0.8%)

Profiling