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

analyze5.0ms (0.3%)

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)

sample657.0ms (33.5%)

Results

647.0ms	8256×	body	256	valid
0.0ms	2×	body	256	invalid

Bogosity

preprocess173.0ms (8.8%)

Algorithm

2×	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
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify171.0ms (8.7%)

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)

localize32.0ms (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 (0.1%)

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)))

rewrite53.0ms (2.7%)

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)))))

simplify69.0ms (3.5%)

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)))

eval182.0ms (9.3%)

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

prune11.0ms (0.5%)

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
▶	99.5%	(+.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))
	99.1%	1
▶	99.5%	(+.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))
	99.1%	1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize125.0ms (6.4%)

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)

series5.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)
1.0ms	x	@	0	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)
0.0ms	x	@	0	(.f64 -1/2 (.f64 x x))
0.0ms	x	@	inf	(.f64 -1/2 (.f64 x x))
0.0ms	x	@	-inf	(.f64 (log1p.f64 (.f64 x (neg.f64 x))) 1/2)

rewrite61.0ms (3.1%)

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))))

simplify71.0ms (3.6%)

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))

eval47.0ms (2.4%)

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

prune30.0ms (1.5%)

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
✓	99.5%	(+.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))
	99.1%	1
✓	99.5%	(+.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))
	99.1%	1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (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
✓	99.5%	(+.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))
	99.1%	1
✓	99.5%	(+.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))
	99.1%	1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune2.0ms (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
✓	99.5%	(+.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))
	99.1%	1

Compiler

Compiled 49 to 36 computations (26.5% saved)

regimes39.0ms (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:

30.0ms	(-.f64 1 (*.f64 x x))
4.0ms	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 42 to 28 computations (33.3% 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:

4.0ms	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:

3.0ms	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)

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
99.1%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.3%)

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)

soundness160.0ms (8.2%)

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)

end40.0ms (2%)

Compiler: Compiled 60 to 40 computations (33.3% saved)

analyze5.0ms (0.3%)

sample657.0ms (33.5%)

preprocess173.0ms (8.8%)

simplify171.0ms (8.7%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize32.0ms (1.6%)

series1.0ms (0.1%)

rewrite53.0ms (2.7%)

simplify69.0ms (3.5%)

eval182.0ms (9.3%)

prune11.0ms (0.5%)

localize125.0ms (6.4%)

series5.0ms (0.2%)

rewrite61.0ms (3.1%)

simplify71.0ms (3.6%)

eval47.0ms (2.4%)

prune30.0ms (1.5%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes39.0ms (2%)

regimes10.0ms (0.5%)

regimes5.0ms (0.3%)

regimes3.0ms (0.1%)

simplify6.0ms (0.3%)

soundness160.0ms (8.2%)

end40.0ms (2%)

Profiling