Metrics for Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

analyze11.0ms (0.5%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample846.0ms (39.1%)

Results

739.0ms	7245×	256	valid
97.0ms	1011×	256	infinite

Bogosity

preprocess171.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

1932×	`fma-def`
1642×	`div-sub`
1492×	`fma-neg`
662×	`distribute-rgt-in`
652×	`associate-/r*`

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
1	-	-	`(/.f64 (+.f64 x y) (+.f64 y y))`
0	-	-	`x`
0	-	-	`(+.f64 x y)`
0	-	-	`y`
0	-	-	`(+.f64 y y)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (+.f64 x y) (+.f64 y y))`	n/o	1

Confusion

1	0
0	255

Precision

1.0

Recall

1.0

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	220
1	47	196
2	103	196
3	289	184
4	1295	162
5	3738	151
6	6374	151
7	7852	151

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 (neg.f64 x) y) (+.f64 y y))
(/.f64 (+.f64 x (neg.f64 y)) (+.f64 (neg.f64 y) (neg.f64 y)))
(neg.f64 (/.f64 (+.f64 (neg.f64 x) y) (+.f64 y y)))
(neg.f64 (/.f64 (+.f64 x (neg.f64 y)) (+.f64 (neg.f64 y) (neg.f64 y))))
(/.f64 (+.f64 y x) (+.f64 x x))

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 x y) (*.f64 2 y))
(/.f64 (+.f64 x y) (*.f64 y 2))
(-.f64 (*.f64 x (/.f64 1/2 y)) -1/2)
(fma.f64 x (/.f64 1/2 y) 1/2)
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 x y) (*.f64 2 y))
(/.f64 (+.f64 x y) (*.f64 y 2))
(-.f64 (*.f64 x (/.f64 1/2 y)) -1/2)
(fma.f64 x (/.f64 1/2 y) 1/2)
(/.f64 (+.f64 (neg.f64 x) y) (+.f64 y y))
(/.f64 (+.f64 y (neg.f64 x)) (*.f64 2 y))
(/.f64 (-.f64 y x) (*.f64 y 2))
(-.f64 1/2 (/.f64 x (*.f64 y 2)))
(fma.f64 x (/.f64 -1/2 y) 1/2)
(/.f64 (+.f64 x (neg.f64 y)) (+.f64 (neg.f64 y) (neg.f64 y)))
(/.f64 (+.f64 y (neg.f64 x)) (*.f64 2 y))
(/.f64 (-.f64 y x) (*.f64 y 2))
(-.f64 1/2 (/.f64 x (*.f64 y 2)))
(fma.f64 x (/.f64 -1/2 y) 1/2)
(neg.f64 (/.f64 (+.f64 (neg.f64 x) y) (+.f64 y y)))
(/.f64 (neg.f64 (+.f64 y (neg.f64 x))) (*.f64 2 y))
(/.f64 (-.f64 x y) (*.f64 y 2))
(+.f64 (/.f64 x (*.f64 y 2)) -1/2)
(fma.f64 1/2 (/.f64 x y) -1/2)
(fma.f64 x (/.f64 1/2 y) -1/2)
(neg.f64 (/.f64 (+.f64 x (neg.f64 y)) (+.f64 (neg.f64 y) (neg.f64 y))))
(/.f64 (neg.f64 (+.f64 y (neg.f64 x))) (*.f64 2 y))
(/.f64 (-.f64 x y) (*.f64 y 2))
(+.f64 (/.f64 x (*.f64 y 2)) -1/2)
(fma.f64 1/2 (/.f64 x y) -1/2)
(fma.f64 x (/.f64 1/2 y) -1/2)
(/.f64 (+.f64 y x) (+.f64 x x))
(/.f64 (+.f64 x y) (*.f64 2 x))
(/.f64 (+.f64 x y) (*.f64 x 2))
(-.f64 1/2 (/.f64 (/.f64 y x) -2))

Compiler

Compiled 54 to 22 computations (59.3% saved)

eval1.0ms (0%)

Compiler: Compiled 29 to 18 computations (37.9% saved)

prune2.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (+.f64 x y) (+.f64 y y))
▶	99.9%	(-.f64 (*.f64 x (/.f64 1/2 y)) -1/2)

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize55.0ms (2.5%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	99.6%	(/.f64 (+.f64 x y) (+.f64 y y))
✓	99.7%	(*.f64 x (/.f64 1/2 y))

Compiler

Compiled 37 to 18 computations (51.4% saved)

series7.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

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

rewrite207.0ms (9.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1326×	`prod-diff`
806×	`log1p-expm1-u`
806×	`expm1-log1p-u`
790×	`log-prod`
478×	`fma-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	179	41
2	2910	41

Stop Event

1×	node limit

Counts

2 → 67

Calls

Call 1

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

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

simplify23.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

50×	`*-commutative`
42×	`sqr-pow`
24×	`associate-*l/`
22×	`associate-*r/`
16×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	168	2284
1	462	2284

Stop Event

1×

unsound

Counts

115 → 93

Calls

Call 1

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

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

eval20.0ms (0.9%)

Compiler: Compiled 997 to 679 computations (31.9% saved)

prune22.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	90	5	95

Accuracy

100.0%

Counts

95 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (+.f64 x y) (+.f64 y y))
▶	8.8%	(-.f64 (/.f64 x 0) -1/2)
✓	99.9%	(-.f64 (*.f64 x (/.f64 1/2 y)) -1/2)
▶	54.4%	1/2
▶	2.2%	-1

Compiler

Compiled 31 to 24 computations (22.6% saved)

localize21.0ms (1%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	3	3
Done	2	2
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(/.f64 (+.f64 x y) (+.f64 y y))
✓	8.8%	(-.f64 (/.f64 x 0) -1/2)
✓	99.9%	(-.f64 (*.f64 x (/.f64 1/2 y)) -1/2)
✓	54.4%	1/2
✓	2.2%	-1

Compiler

Compiled 54 to 40 computations (25.9% saved)

regimes15.0ms (0.7%)

Counts

5 → 1

Calls

Call 1

Inputs
-1
1/2
(-.f64 (/.f64 x 0) -1/2)
(-.f64 (*.f64 x (/.f64 1/2 y)) -1/2)
(/.f64 (+.f64 x y) (+.f64 y y))

Outputs
(-.f64 (*.f64 x (/.f64 1/2 y)) -1/2)

Calls

3 calls:

6.0ms	x
5.0ms	y
4.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 15 to 9 computations (40% saved)

regimes18.0ms (0.8%)

Counts

3 → 3

Calls

Call 1

Inputs
-1
1/2
(-.f64 (/.f64 x 0) -1/2)

Outputs
1/2
(-.f64 (/.f64 x 0) -1/2)
1/2

Calls

2 calls:

14.0ms	y
4.0ms	x

Results

Accuracy	Segments	Branch
54.4%	1	`x`
58.8%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
1/2

Outputs
1/2

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
54.4%	1	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes7.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
-1

Outputs
-1

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
2.2%	1	`x`
2.2%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch27.0ms (1.2%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	9.473687158550883e-146	3.5224599321678643e-144
14.0ms	-6.386033086887842e-305	3.337469573985255e-308

Results

15.0ms	154×	256	valid
8.0ms	86×	256	infinite

Compiler

Compiled 194 to 174 computations (10.3% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`sub-neg`
6×	`+-commutative`
4×	`*-commutative`
2×	`neg-mul-1`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	69
1	35	69
2	39	69
3	41	69
4	42	69

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(-.f64 (*.f64 x (/.f64 1/2 y)) -1/2)
(if (<=.f64 y -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) 1/2 (if (<=.f64 y 5736115088042575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (-.f64 (/.f64 x 0) -1/2) 1/2))
1/2
-1

Outputs
(-.f64 (*.f64 x (/.f64 1/2 y)) -1/2)
(if (<=.f64 y -20240225330731/50600563326827654588123836679729326762389162441035529589225339506857584891998836722990095925359281123796769466079202977847452184346448369216753349985184627480379356069141590341116726935523304085309941919618186267140501870856173174654525838912289889085202514128089692388083353653807625633046581877161501565826926935273373696) 1/2 (if (<=.f64 y 5736115088042575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (-.f64 (/.f64 x 0) -1/2) 1/2))
1/2
-1

Compiler

Compiled 32 to 27 computations (15.6% saved)

soundness650.0ms (30%)

Rules

1932×	`fma-def`
1642×	`div-sub`
1492×	`fma-neg`
1326×	`prod-diff`
1326×	`prod-diff`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	220
1	47	196
2	103	196
3	289	184
4	1295	162
5	3738	151
6	6374	151
7	7852	151
0	13	47
1	179	41
2	2910	41
0	168	2284
1	462	2284
0	13	47
1	179	41
2	2910	41
0	168	2284
1	462	2284

Stop Event

1×	unsound
1×	node limit
1×	unsound
1×	node limit
1×	node limit

Compiler

Compiled 410 to 147 computations (64.1% saved)

end0.0ms (0%)

preprocess48.0ms (2.2%)

Compiler: Compiled 88 to 66 computations (25% saved)

analyze11.0ms (0.5%)

sample846.0ms (39.1%)

preprocess171.0ms (7.9%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize55.0ms (2.5%)

series7.0ms (0.3%)

rewrite207.0ms (9.6%)

simplify23.0ms (1.1%)

eval20.0ms (0.9%)

prune22.0ms (1%)

localize21.0ms (1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes15.0ms (0.7%)

regimes18.0ms (0.8%)

regimes4.0ms (0.2%)

regimes7.0ms (0.3%)

bsearch27.0ms (1.2%)

simplify6.0ms (0.3%)

soundness650.0ms (30%)

end0.0ms (0%)

preprocess48.0ms (2.2%)

Profiling