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

analyze11.0ms (0.4%)

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)

sample1.3s (42.7%)

Results

1.1s	7231×	body	256	valid
223.0ms	1025×	body	256	infinite

Bogosity

preprocess155.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

2080×	`div-sub`
2076×	`fma-def`
1234×	`fma-neg`
972×	`sub-neg`
762×	`times-frac`

Problems

256×

No Errors

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	21	148
1	37	140
2	77	140
3	183	134
4	414	134
5	1018	120
6	2946	109
7	5156	109
8	6176	109
9	6786	109
10	7287	109
11	7608	109

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

Compiler

Compiled 27 to 11 computations (59.3% saved)

eval1.0ms (0%)

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

prune3.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (+.f64 x y) (+.f64 y y))
▶	99.8%	(-.f64 1/2 (*.f64 x (/.f64 -1/2 y)))
▶	100.0%	(/.f64 (+.f64 x y) (+.f64 y y))
▶	99.8%	(-.f64 1/2 (*.f64 x (/.f64 -1/2 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize49.0ms (1.6%)

Localize:

Found 2 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 (+.f64 x y) (+.f64 y y))
✓	99.7%	(*.f64 x (/.f64 -1/2 y))

Compiler

Compiled 37 to 18 computations (51.4% saved)

series6.0ms (0.2%)

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))
0.0ms	y	@	inf	(*.f64 x (/.f64 -1/2 y))

rewrite117.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1326×	`prod-diff`
905×	`log1p-expm1-u`
905×	`expm1-log1p-u`
484×	`fma-def`
290×	`expm1-udef`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	179	44
2	2819	44

Stop Event

1×	node limit

Counts

2 → 59

Calls

Call 1

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

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

simplify27.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

38×	`*-commutative`
36×	`sqr-pow`
16×	`associate-*l/`
16×	`cube-mult`
14×	`unpow3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	144	1897
1	373	1897

Stop Event

1×

unsound

Counts

107 → 79

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 (exp.f64 (log1p.f64 (/.f64 (*.f64 x -1/2) y))) 1)
(/.f64 x (*.f64 y -2))
(/.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 (*.f64 x -1/2) y) 1)
(pow.f64 (cbrt.f64 (/.f64 (*.f64 x -1/2) y)) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 x -1/2) y) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (*.f64 x -1/2) y)) 2)
(sqrt.f64 (pow.f64 (/.f64 (*.f64 x -1/2) y) 2))
(log.f64 (exp.f64 (/.f64 (*.f64 x -1/2) y)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 x -1/2) y))))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 x -1/2) y) 3))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1/2 y) 3)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 -1/2 y) 3) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 x -1/2) y)))
(exp.f64 (log.f64 (/.f64 (*.f64 x -1/2) y)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x -1/2) y)) 1))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 x -1/2) y)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))) 1)
(*.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 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (cbrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))))
(.f64 (cbrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))) (pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) (/.f64 0 0))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))) 2) (cbrt.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
(.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))))
(.f64 (sqrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))) (sqrt.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
(*.f64 1/2 (/.f64 (+.f64 x y) y))
(*.f64 (neg.f64 (+.f64 x y)) (/.f64 0 0))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1) (cbrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (/.f64 0 0)) (cbrt.f64 (.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) (sqrt.f64 (.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 (cbrt.f64 (*.f64 (+.f64 x y) (/.f64 0 0))) 3)
(pow.f64 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.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 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 2))
(log.f64 (exp.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
(log.f64 (+.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 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 (/.f64 x y) 1/2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 x -1/2) y))) 1)
(*.f64 -1/2 (/.f64 x y))
(/.f64 x (*.f64 y -2))
(/.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 (*.f64 x -1/2) y) 1)
(*.f64 -1/2 (/.f64 x y))
(pow.f64 (cbrt.f64 (/.f64 (*.f64 x -1/2) y)) 3)
(*.f64 -1/2 (/.f64 x y))
(pow.f64 (pow.f64 (/.f64 (*.f64 x -1/2) y) 3) 1/3)
(*.f64 -1/2 (/.f64 x y))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 x -1/2) y)) 2)
(pow.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 x y))) 2)
(sqrt.f64 (pow.f64 (/.f64 (*.f64 x -1/2) y) 2))
(sqrt.f64 (pow.f64 (*.f64 -1/2 (/.f64 x y)) 2))
(log.f64 (exp.f64 (/.f64 (*.f64 x -1/2) y)))
(*.f64 -1/2 (/.f64 x y))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 x -1/2) y))))
(*.f64 -1/2 (/.f64 x y))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 x -1/2) y) 3))
(*.f64 -1/2 (/.f64 x y))
(cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 -1/2 y) 3)))
(cbrt.f64 (*.f64 (pow.f64 x 3) (/.f64 -1/8 (pow.f64 y 3))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 -1/2 y) 3) (pow.f64 x 3)))
(cbrt.f64 (*.f64 (pow.f64 x 3) (/.f64 -1/8 (pow.f64 y 3))))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 x -1/2) y)))
(*.f64 -1/2 (/.f64 x y))
(exp.f64 (log.f64 (/.f64 (*.f64 x -1/2) y)))
(*.f64 -1/2 (/.f64 x y))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x -1/2) y)) 1))
(*.f64 -1/2 (/.f64 x y))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 x -1/2) y)))
(*.f64 -1/2 (/.f64 x y))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))) 1)
0
(*.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 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (cbrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))))
(pow.f64 (cbrt.f64 (+.f64 x y)) 2)
(.f64 (cbrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))) (pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) (/.f64 0 0))) 2))
0
(.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))) 2) (cbrt.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
0
(.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))))
(*.f64 0 (sqrt.f64 (+.f64 x y)))
(.f64 (sqrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))) (sqrt.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
0
(*.f64 1/2 (/.f64 (+.f64 x y) y))
(/.f64 (*.f64 1/2 (+.f64 x y)) y)
(*.f64 (neg.f64 (+.f64 x y)) (/.f64 0 0))
-1
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1) (cbrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))))
(pow.f64 (cbrt.f64 (+.f64 x y)) 2)
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (/.f64 0 0)) (cbrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))))
(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) (sqrt.f64 (.f64 (+.f64 x y) (/.f64 0 0))))
(*.f64 0 (sqrt.f64 (+.f64 x y)))
(*.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 (+.f64 x y) 2) (pow.f64 y 3)) (fma.f64 y y 0))
(*.f64 (/.f64 (+.f64 x y) 0) 0)
0
(pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 1)
0
(pow.f64 (cbrt.f64 (*.f64 (+.f64 x y) (/.f64 0 0))) 3)
0
(pow.f64 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 3) 1/3)
0
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) (/.f64 0 0))) 2)
0
(pow.f64 (/.f64 (/.f64 0 0) (+.f64 x y)) -1)
0
(neg.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))
-1
(sqrt.f64 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 2))
0
(log.f64 (exp.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
0
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))))
0
(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

eval17.0ms (0.6%)

Compiler: Compiled 781 to 522 computations (33.2% saved)

prune15.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	77	4	81

Accuracy

100.0%

Counts

81 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 1/2 (/.f64 (*.f64 x -1/2) y))
▶	55.6%	(*.f64 (/.f64 x y) 1/2)
	44.8%	1/2
	2.2%	-1
▶	100.0%	(-.f64 1/2 (/.f64 (*.f64 x -1/2) y))
▶	55.6%	(*.f64 (/.f64 x y) 1/2)
	44.8%	1/2
	2.2%	-1

Compiler

Compiled 44 to 36 computations (18.2% saved)

localize42.0ms (1.4%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 33 to 19 computations (42.4% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite55.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

762×	`unpow-prod-down`
514×	`cbrt-prod`
512×	`log-prod`
460×	`log1p-expm1-u`
460×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	94	19
2	1221	19

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

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

Outputs
(+.f64 0 (/.f64 x (/.f64 y 1/2)))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 (/.f64 x y)))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))))
(+.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))) (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))))
(-.f64 (+.f64 1 (/.f64 x (/.f64 y 1/2))) 1)
(/.f64 x (/.f64 y 1/2))
(/.f64 1/2 (/.f64 y x))
(/.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 1/2 (neg.f64 x)) (neg.f64 y))
(/.f64 (*.f64 (neg.f64 x) 1/2) (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 y 1/2)) 1)
(pow.f64 (cbrt.f64 (/.f64 x (/.f64 y 1/2))) 3)
(pow.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 (/.f64 y x) -3) 1/8) 1/3)
(pow.f64 (sqrt.f64 (/.f64 x (/.f64 y 1/2))) 2)
(pow.f64 (E.f64) (log.f64 (/.f64 x (/.f64 y 1/2))))
(pow.f64 (/.f64 y (*.f64 x 1/2)) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2)))) 2)) (cbrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2))))) (sqrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2)))))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))
(log.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 y x) -3) 1/8))
(expm1.f64 (log1p.f64 (/.f64 x (/.f64 y 1/2))))
(exp.f64 (log.f64 (/.f64 x (/.f64 y 1/2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 x (/.f64 y 1/2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (/.f64 y x) -3) 1/8)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 x (/.f64 y 1/2)))) 2))
(log1p.f64 (expm1.f64 (/.f64 x (/.f64 y 1/2))))

simplify66.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1776×	`log-prod`
1524×	`fma-neg`
954×	`associate-/r*`
882×	`associate-/l*`
750×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	1270
1	207	1270
2	500	1270
3	1515	1270
4	7192	1270

Stop Event

1×	node limit

Counts

56 → 41

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))
(+.f64 0 (/.f64 x (/.f64 y 1/2)))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 (/.f64 x y)))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))))
(+.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))) (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))))
(-.f64 (+.f64 1 (/.f64 x (/.f64 y 1/2))) 1)
(/.f64 x (/.f64 y 1/2))
(/.f64 1/2 (/.f64 y x))
(/.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 1/2 (neg.f64 x)) (neg.f64 y))
(/.f64 (*.f64 (neg.f64 x) 1/2) (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 y 1/2)) 1)
(pow.f64 (cbrt.f64 (/.f64 x (/.f64 y 1/2))) 3)
(pow.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) 1/2)
(pow.f64 (*.f64 (pow.f64 (/.f64 y x) -3) 1/8) 1/3)
(pow.f64 (sqrt.f64 (/.f64 x (/.f64 y 1/2))) 2)
(pow.f64 (E.f64) (log.f64 (/.f64 x (/.f64 y 1/2))))
(pow.f64 (/.f64 y (*.f64 x 1/2)) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2)))) 2)) (cbrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2))))) (sqrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2)))))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))
(log.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 y x) -3) 1/8))
(expm1.f64 (log1p.f64 (/.f64 x (/.f64 y 1/2))))
(exp.f64 (log.f64 (/.f64 x (/.f64 y 1/2))))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 x (/.f64 y 1/2)))) 3))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (/.f64 y x) -3) 1/8)) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 x (/.f64 y 1/2)))) 2))
(log1p.f64 (expm1.f64 (/.f64 x (/.f64 y 1/2))))

Outputs
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(+.f64 0 (/.f64 x (/.f64 y 1/2)))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(+.f64 (log.f64 (cbrt.f64 (exp.f64 (/.f64 x y)))) (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))))
(+.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))) (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))))
(*.f64 2 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))))
(*.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))) 2)
(-.f64 (+.f64 1 (/.f64 x (/.f64 y 1/2))) 1)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 x (/.f64 y 1/2))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 1/2 (/.f64 y x))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 1 (/.f64 y (*.f64 x 1/2)))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 (*.f64 x 1/2) y)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 (neg.f64 (*.f64 x 1/2)) (neg.f64 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 (*.f64 1/2 (neg.f64 x)) (neg.f64 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 (*.f64 (neg.f64 x) 1/2) (neg.f64 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 (/.f64 (*.f64 x 1/2) 1) y)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 (/.f64 (*.f64 x 1/2) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 (/.f64 (*.f64 x 1/2) (sqrt.f64 y)) (sqrt.f64 y))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (/.f64 x (/.f64 y 1/2)) 1)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (cbrt.f64 (/.f64 x (/.f64 y 1/2))) 3)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4) 1/2)
(sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))
(pow.f64 (*.f64 (pow.f64 (/.f64 y x) -3) 1/8) 1/3)
(cbrt.f64 (*.f64 (pow.f64 (/.f64 y x) -3) 1/8))
(cbrt.f64 (*.f64 1/8 (pow.f64 (/.f64 y x) -3)))
(pow.f64 (sqrt.f64 (/.f64 x (/.f64 y 1/2))) 2)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (E.f64) (log.f64 (/.f64 x (/.f64 y 1/2))))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (/.f64 y (*.f64 x 1/2)) -1)
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2)))) 2)) (cbrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 1/2 (/.f64 x y)))) 2)) (cbrt.f64 (log.f64 (.f64 1/2 (/.f64 x y)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (/.f64 1/2 y)))) 2)) (cbrt.f64 (log.f64 (.f64 x (/.f64 1/2 y)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2))))) (sqrt.f64 (log.f64 (/.f64 x (/.f64 y 1/2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 1/2 (/.f64 x y))))) (sqrt.f64 (log.f64 (.f64 1/2 (/.f64 x y)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (/.f64 1/2 y))))) (sqrt.f64 (log.f64 (.f64 x (/.f64 1/2 y)))))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))
(log.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 y x) -3) 1/8))
(cbrt.f64 (*.f64 1/8 (pow.f64 (/.f64 y x) -3)))
(expm1.f64 (log1p.f64 (/.f64 x (/.f64 y 1/2))))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(exp.f64 (log.f64 (/.f64 x (/.f64 y 1/2))))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 x (/.f64 y 1/2)))) 3))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (/.f64 y x) -3) 1/8)) 1/3))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 y x) -3) 1/8))
(cbrt.f64 (*.f64 1/8 (pow.f64 (/.f64 y x) -3)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 x (/.f64 y 1/2)))) 2))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(log1p.f64 (expm1.f64 (/.f64 x (/.f64 y 1/2))))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))

eval10.0ms (0.3%)

Compiler: Compiled 385 to 246 computations (36.1% saved)

prune35.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	40	1	41
Fresh	0	2	2
Picked	0	2	2
Done	0	0	0
Total	40	5	45

Accuracy

100.0%

Counts

45 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 1/2 (/.f64 (*.f64 x -1/2) y))
✓	55.6%	(*.f64 (/.f64 x y) 1/2)
▶	55.5%	(*.f64 x (/.f64 1/2 y))
	44.8%	1/2
	2.2%	-1
✓	100.0%	(-.f64 1/2 (/.f64 (*.f64 x -1/2) y))
✓	55.6%	(*.f64 (/.f64 x y) 1/2)
▶	55.5%	(*.f64 x (/.f64 1/2 y))
	44.8%	1/2
	2.2%	-1

Compiler

Compiled 58 to 46 computations (20.7% saved)

localize37.0ms (1.2%)

Localize:

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite55.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`unpow-prod-down`
468×	`log-prod`
464×	`cbrt-prod`
418×	`log1p-expm1-u`
418×	`expm1-log1p-u`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	95	19
2	1150	19

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

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

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

simplify56.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1338×	`log-div`
1146×	`associate-r`
1070×	`associate-l`
910×	`times-frac`
572×	`associate-/l*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	1306
1	240	1270
2	827	1260
3	6723	1260

Stop Event

1×	node limit

Counts

58 → 51

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

Outputs
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(+.f64 0 (/.f64 (*.f64 x 1/2) y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 x 1/2) y))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (.f64 x 1/2) y)))))
(+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (.f64 1/2 (/.f64 x y)))))) (log.f64 (cbrt.f64 (exp.f64 (*.f64 1/2 (/.f64 x y))))))
(*.f64 3 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/2) (/.f64 x y)))))
(*.f64 (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))) 3)
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (.f64 x 1/2) y)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (.f64 x 1/2) y)))))
(.f64 2 (log.f64 (sqrt.f64 (exp.f64 (.f64 1/2 (/.f64 x y))))))
(*.f64 2 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/2) (/.f64 x y)))))
(*.f64 2 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 (/.f64 x y))))))
(-.f64 (+.f64 1 (/.f64 (*.f64 x 1/2) y)) 1)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(/.f64 x (*.f64 y 2))
(*.f64 1/2 (/.f64 x y))
(*.f64 x (/.f64 1/2 y))
(/.f64 1 (/.f64 y (*.f64 x 1/2)))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(/.f64 (*.f64 x 1/2) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(/.f64 (neg.f64 (*.f64 x 1/2)) (neg.f64 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(/.f64 (*.f64 x -1/2) (neg.f64 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(/.f64 (*.f64 -1/2 x) (neg.f64 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(/.f64 (/.f64 (*.f64 x 1/2) 1) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(/.f64 (/.f64 (*.f64 x 1/2) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(/.f64 (/.f64 (*.f64 x 1/2) (sqrt.f64 y)) (sqrt.f64 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(/.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 x 1/2) y) 2) (*.f64 x 1/2))) (cbrt.f64 y))
(/.f64 (cbrt.f64 (.f64 (.f64 1/2 x) (pow.f64 (*.f64 1/2 (/.f64 x y)) 2))) (cbrt.f64 y))
(/.f64 (cbrt.f64 (.f64 1/2 (.f64 x (pow.f64 (/.f64 x (*.f64 y 2)) 2)))) (cbrt.f64 y))
(/.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 x 3) y) (/.f64 1/8 y))) (cbrt.f64 y))
(pow.f64 (/.f64 (*.f64 x 1/2) y) 1)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (cbrt.f64 (/.f64 (*.f64 x 1/2) y)) 3)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (pow.f64 (/.f64 (*.f64 x 1/2) y) 2) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (pow.f64 (/.f64 (*.f64 x 1/2) y) 3) 1/3)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (sqrt.f64 (/.f64 (*.f64 x 1/2) y)) 2)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (E.f64) (log.f64 (/.f64 (*.f64 x 1/2) y)))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (/.f64 y (*.f64 x 1/2)) -1)
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (.f64 x 1/2) y))) 2)) (cbrt.f64 (log.f64 (/.f64 (.f64 x 1/2) y))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 1/2 (/.f64 x y)))) 2)) (cbrt.f64 (log.f64 (.f64 1/2 (/.f64 x y)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 x (.f64 y 2)))) 2)) (cbrt.f64 (log.f64 (/.f64 x (.f64 y 2)))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (/.f64 1/2 y)))) 2)) (cbrt.f64 (log.f64 (.f64 x (/.f64 1/2 y)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (.f64 x 1/2) y)))) (sqrt.f64 (log.f64 (/.f64 (.f64 x 1/2) y))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 1/2 (/.f64 x y))))) (sqrt.f64 (log.f64 (.f64 1/2 (/.f64 x y)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 x (.f64 y 2))))) (sqrt.f64 (log.f64 (/.f64 x (.f64 y 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (/.f64 1/2 y))))) (sqrt.f64 (log.f64 (.f64 x (/.f64 1/2 y)))))
(sqrt.f64 (pow.f64 (/.f64 (*.f64 x 1/2) y) 2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(log.f64 (exp.f64 (/.f64 (*.f64 x 1/2) y)))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 x 1/2) y) 3))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (*.f64 y 2) 3)))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 x 1/2) 3) (pow.f64 y 3)))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 x 1/2) y)))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(exp.f64 (log.f64 (/.f64 (*.f64 x 1/2) y)))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 (.f64 x 1/2) y))) 3))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (*.f64 x 1/2) y))) 1/3))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (.f64 x 1/2) y))) 2))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 x 1/2) y)))
(*.f64 1/2 (/.f64 x y))
(/.f64 x (*.f64 y 2))
(*.f64 x (/.f64 1/2 y))

eval30.0ms (1%)

Compiler: Compiled 539 to 383 computations (28.9% saved)

prune10.0ms (0.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	51	5	56

Accuracy

100.0%

Counts

56 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 1/2 (/.f64 (*.f64 x -1/2) y))
✓	55.6%	(*.f64 (/.f64 x y) 1/2)
✓	55.5%	(*.f64 x (/.f64 1/2 y))
	44.8%	1/2
	2.2%	-1
✓	100.0%	(-.f64 1/2 (/.f64 (*.f64 x -1/2) y))
✓	55.6%	(*.f64 (/.f64 x y) 1/2)
✓	55.5%	(*.f64 x (/.f64 1/2 y))
	44.8%	1/2
	2.2%	-1

Compiler

Compiled 58 to 46 computations (20.7% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune4.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

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

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 1/2 (/.f64 (*.f64 x -1/2) y))
✓	55.6%	(*.f64 (/.f64 x y) 1/2)
✓	55.5%	(*.f64 x (/.f64 1/2 y))
	44.8%	1/2
	2.2%	-1

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes16.0ms (0.5%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	y
5.0ms	x
3.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 50 to 32 computations (36% saved)

regimes46.0ms (1.5%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

40.0ms	x
5.0ms	y

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`y`

Compiler

Compiled 27 to 19 computations (29.6% saved)

regimes40.0ms (1.3%)

Counts

4 → 5

Calls

Call 1

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

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

Calls

2 calls:

21.0ms	x
19.0ms	y

Results

Accuracy	Segments	Branch
80.3%	5	`x`
75.4%	5	`y`

Compiler

Compiled 20 to 14 computations (30% saved)

regimes21.0ms (0.7%)

Counts

3 → 5

Calls

Call 1

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

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

Calls

1 calls:

20.0ms

Results

Accuracy	Segments	Branch
80.2%	5	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes8.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
1/2

Outputs
1/2

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
44.8%	1	`y`
44.8%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes6.0ms (0.2%)

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	y
3.0ms	x

Results

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch47.0ms (1.5%)

Algorithm

4×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
8.0ms	1302375922005196.5	4012349561373694.5
14.0ms	2.1688433465605327e-49	3.477970986602358e-48
13.0ms	7.568522807991556e-129	1.3988508863686253e-124
12.0ms	-5.7051027685804634e-70	-4.4086595849602917e-72

Results

38.0ms	430×	body	256	valid
0.0ms	2×	body	256	infinite

Compiler

Compiled 338 to 279 computations (17.5% saved)

bsearch49.0ms (1.6%)

Algorithm

4×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
8.0ms	1302375922005196.5	4012349561373694.5
14.0ms	2.1688433465605327e-49	3.477970986602358e-48
13.0ms	7.568522807991556e-129	1.3988508863686253e-124
14.0ms	-5.7051027685804634e-70	-4.4086595849602917e-72

Results

40.0ms	430×	body	256	valid
0.0ms	2×	body	256	infinite

Compiler

Compiled 338 to 279 computations (17.5% saved)

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative`
16×	`sub-neg`
16×	`not-or`
16×	`+-commutative`
12×	`neg-mul-1`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	242
1	65	242
2	87	230
3	115	222
4	131	222
5	143	222
6	146	222
7	148	222

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(-.f64 1/2 (/.f64 (*.f64 x -1/2) y))
(-.f64 1/2 (*.f64 x (/.f64 -1/2 y)))
(if (<=.f64 x -2331202670670875/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 (/.f64 x y) 1/2) (if (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) 1/2 (if (<=.f64 x 3027728385471019/13164036458569648337239753460458804039861886925068638906788872192) (.f64 (/.f64 x y) 1/2) (if (<=.f64 x 1350000000000000) 1/2 (*.f64 (/.f64 x y) 1/2)))))
(if (<=.f64 x -7149021523390683/31082702275611665134711390509176302506278509424834232340028998555822468563283335970816) (.f64 x (/.f64 1/2 y)) (if (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) 1/2 (if (<=.f64 x 2501166927128233/6582018229284824168619876730229402019930943462534319453394436096) (.f64 x (/.f64 1/2 y)) (if (<=.f64 x 1600000000000000) 1/2 (*.f64 x (/.f64 1/2 y))))))
1/2
-1

Outputs
(-.f64 1/2 (/.f64 (*.f64 x -1/2) y))
(-.f64 1/2 (*.f64 x (/.f64 -1/2 y)))
(if (<=.f64 x -2331202670670875/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 (/.f64 x y) 1/2) (if (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) 1/2 (if (<=.f64 x 3027728385471019/13164036458569648337239753460458804039861886925068638906788872192) (.f64 (/.f64 x y) 1/2) (if (<=.f64 x 1350000000000000) 1/2 (*.f64 (/.f64 x y) 1/2)))))
(if (<=.f64 x -2331202670670875/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 1/2 (/.f64 x y)) (if (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) 1/2 (if (or (<=.f64 x 3027728385471019/13164036458569648337239753460458804039861886925068638906788872192) (not (<=.f64 x 1350000000000000))) (.f64 1/2 (/.f64 x y)) 1/2)))
(if (or (<=.f64 x -2331202670670875/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (not (or (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) (not (or (<=.f64 x 3027728385471019/13164036458569648337239753460458804039861886925068638906788872192) (not (<=.f64 x 1350000000000000))))))) (*.f64 1/2 (/.f64 x y)) 1/2)
(if (or (<=.f64 x -2331202670670875/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (not (or (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) (and (not (<=.f64 x 3027728385471019/13164036458569648337239753460458804039861886925068638906788872192)) (<=.f64 x 1350000000000000))))) (*.f64 1/2 (/.f64 x y)) 1/2)
(if (<=.f64 x -7149021523390683/31082702275611665134711390509176302506278509424834232340028998555822468563283335970816) (.f64 x (/.f64 1/2 y)) (if (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) 1/2 (if (<=.f64 x 2501166927128233/6582018229284824168619876730229402019930943462534319453394436096) (.f64 x (/.f64 1/2 y)) (if (<=.f64 x 1600000000000000) 1/2 (*.f64 x (/.f64 1/2 y))))))
(if (<=.f64 x -7149021523390683/31082702275611665134711390509176302506278509424834232340028998555822468563283335970816) (.f64 x (/.f64 1/2 y)) (if (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) 1/2 (if (or (<=.f64 x 2501166927128233/6582018229284824168619876730229402019930943462534319453394436096) (not (<=.f64 x 1600000000000000))) (.f64 x (/.f64 1/2 y)) 1/2)))
(if (or (<=.f64 x -7149021523390683/31082702275611665134711390509176302506278509424834232340028998555822468563283335970816) (not (or (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) (not (or (<=.f64 x 2501166927128233/6582018229284824168619876730229402019930943462534319453394436096) (not (<=.f64 x 1600000000000000))))))) (*.f64 x (/.f64 1/2 y)) 1/2)
(if (or (<=.f64 x -7149021523390683/31082702275611665134711390509176302506278509424834232340028998555822468563283335970816) (not (or (<=.f64 x 6430603855783981/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616) (and (not (<=.f64 x 2501166927128233/6582018229284824168619876730229402019930943462534319453394436096)) (<=.f64 x 1600000000000000))))) (*.f64 x (/.f64 1/2 y)) 1/2)
1/2
-1

Compiler

Compiled 76 to 60 computations (21.1% saved)

soundness621.0ms (20.5%)

Rules

2080×	`div-sub`
2076×	`fma-def`
1776×	`log-prod`
1524×	`fma-neg`
1326×	`prod-diff`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	148
1	37	140
2	77	140
3	183	134
4	414	134
5	1018	120
6	2946	109
7	5156	109
8	6176	109
9	6786	109
10	7287	109
11	7608	109
0	13	47
1	179	44
2	2819	44
0	13	47
1	179	44
2	2819	44
0	144	1897
1	373	1897
0	144	1897
1	373	1897
0	97	1270
1	207	1270
2	500	1270
3	1515	1270
4	7192	1270

Stop Event

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

Compiler

Compiled 474 to 183 computations (61.4% saved)

end0.0ms (0%)

preprocess67.0ms (2.2%)

Compiler: Compiled 168 to 124 computations (26.2% saved)

analyze11.0ms (0.4%)

sample1.3s (42.7%)

preprocess155.0ms (5.1%)

eval1.0ms (0%)

prune3.0ms (0.1%)

localize49.0ms (1.6%)

series6.0ms (0.2%)

rewrite117.0ms (3.9%)

simplify27.0ms (0.9%)

eval17.0ms (0.6%)

prune15.0ms (0.5%)

localize42.0ms (1.4%)

series1.0ms (0%)

rewrite55.0ms (1.8%)

simplify66.0ms (2.2%)

eval10.0ms (0.3%)

prune35.0ms (1.2%)

localize37.0ms (1.2%)

series1.0ms (0%)

rewrite55.0ms (1.8%)

simplify56.0ms (1.9%)

eval30.0ms (1%)

prune10.0ms (0.3%)

localize0.0ms (0%)

eval0.0ms (0%)

prune4.0ms (0.1%)

regimes16.0ms (0.5%)

regimes46.0ms (1.5%)

regimes40.0ms (1.3%)

regimes21.0ms (0.7%)

regimes8.0ms (0.2%)

regimes6.0ms (0.2%)

bsearch47.0ms (1.5%)

bsearch49.0ms (1.6%)

simplify13.0ms (0.4%)

soundness621.0ms (20.5%)

end0.0ms (0%)

preprocess67.0ms (2.2%)

Profiling