Metrics for Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 10 to 6 computations (40% saved)

sample677.0ms (42.2%)

Results

501.0ms	6231×	body	256	valid
165.0ms	2025×	body	256	infinite

Bogosity

preprocess46.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-def`
136×	`fma-neg`
110×	`sub-neg`
100×	`distribute-rgt-in`
96×	`associate-+l-`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	64
1	48	60
2	111	60
3	284	60
4	529	60
5	804	60
6	1086	60
7	1166	60
8	1180	60

Stop Event

1×

saturated

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`fma-def`
4×	`+-commutative`
2×	`associate-+r+`
2×	`*-commutative`
2×	`associate-+l+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	17	15
3	19	15
4	20	15

Stop Event

1×

saturated

Counts

1 → 3

Calls

Call 1

Inputs
(+.f64 (+.f64 (*.f64 x x) y) y)

Outputs
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 y (fma.f64 x x y))
(fma.f64 x x (+.f64 y y))

eval1.0ms (0%)

Compiler: Compiled 21 to 9 computations (57.1% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1	2	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	3	4

Accurracy

100.0%

Counts

4 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x (+.f64 y y))
▶	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
▶	100.0%	(fma.f64 x x (+.f64 y y))
▶	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)

Compiler

Compiled 34 to 18 computations (47.1% saved)

localize34.0ms (2.1%)

Local Accuracy

Found 2 expressions with local accuracy:

New	Accuracy	Program
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	100.0%	(+.f64 (*.f64 x x) y)

Compiler

Compiled 31 to 8 computations (74.2% saved)

series2.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite64.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

1914×	`pow1`
1784×	`add-exp-log`
1784×	`log1p-expm1-u`
1784×	`expm1-log1p-u`
178×	`add-sqr-sqrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	162	24
2	2428	24

Stop Event

1×	node limit

Counts

2 → 73

Calls

Call 1

Inputs
(+.f64 (*.f64 x x) y)
(+.f64 (+.f64 (*.f64 x x) y) y)

Outputs
(-.f64 (+.f64 1 (fma.f64 x x y)) 1)
(-.f64 (/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y)))
(*.f64 (fma.f64 x x y) 1)
(*.f64 1 (fma.f64 x x y))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))
(*.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))
(.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (*.f64 x x))))))
(.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (-.f64 (*.f64 x x) y)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))
(/.f64 1 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x 4) (.f64 y y))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 x 4) (.f64 x (*.f64 x y)))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(pow.f64 (fma.f64 x x y) 1)
(pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)
(pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)
(sqrt.f64 (pow.f64 (fma.f64 x x y) 2))
(log.f64 (exp.f64 (fma.f64 x x y)))
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3))
(expm1.f64 (log1p.f64 (fma.f64 x x y)))
(exp.f64 (log.f64 (fma.f64 x x y)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) 1))
(log1p.f64 (expm1.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(fma.f64 1 (*.f64 x x) y)
(fma.f64 1 y (*.f64 x x))
(fma.f64 (cbrt.f64 (.f64 y y)) (cbrt.f64 y) (.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) y)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))
(-.f64 (+.f64 1 (+.f64 y (fma.f64 x x y))) 1)
(-.f64 (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (fma.f64 x x y) y)) (/.f64 (*.f64 y y) (-.f64 (fma.f64 x x y) y)))
(*.f64 (+.f64 y (fma.f64 x x y)) 1)
(*.f64 1 (+.f64 y (fma.f64 x x y)))
(*.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2) (cbrt.f64 (+.f64 y (fma.f64 x x y))))
(*.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) (sqrt.f64 (+.f64 y (fma.f64 x x y))))
(.f64 (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))
(.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y)) (/.f64 1 (-.f64 (fma.f64 x x y) y)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))) (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3))))
(/.f64 1 (/.f64 (-.f64 (fma.f64 x x y) y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))))
(/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (fma.f64 x x y)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 y y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (*.f64 x x) (+.f64 y y)))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (.f64 x x) (+.f64 y y)))
(/.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))
(pow.f64 (+.f64 y (fma.f64 x x y)) 1)
(pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 3)
(pow.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3) 1/3)
(pow.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) 2)
(sqrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 2))
(log.f64 (exp.f64 (+.f64 y (fma.f64 x x y))))
(cbrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3))
(expm1.f64 (log1p.f64 (+.f64 y (fma.f64 x x y))))
(exp.f64 (log.f64 (+.f64 y (fma.f64 x x y))))
(exp.f64 (*.f64 (log.f64 (+.f64 y (fma.f64 x x y))) 1))
(log1p.f64 (expm1.f64 (+.f64 y (fma.f64 x x y))))
(fma.f64 x x (+.f64 y y))
(fma.f64 1 (*.f64 x x) (+.f64 y y))
(fma.f64 1 y (fma.f64 x x y))
(fma.f64 1 (fma.f64 x x y) y)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)
(fma.f64 (cbrt.f64 (*.f64 y y)) (cbrt.f64 y) (fma.f64 x x y))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (+.f64 y y))
(fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))

simplify86.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

1716×	`fma-def`
832×	`unswap-sqr`
776×	`times-frac`
694×	`log-prod`
510×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2503
1	422	2389
2	1526	2319
3	7736	2319

Stop Event

1×	node limit

Counts

121 → 93

Calls

Call 1

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

Outputs
y
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(*.f64 2 y)
(+.f64 y y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(*.f64 2 y)
(+.f64 y y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(*.f64 2 y)
(+.f64 y y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(-.f64 (+.f64 1 (fma.f64 x x y)) 1)
(fma.f64 x x y)
(-.f64 (/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(*.f64 (fma.f64 x x y) 1)
(fma.f64 x x y)
(*.f64 1 (fma.f64 x x y))
(fma.f64 x x y)
(*.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))
(fma.f64 x x y)
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(*.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))
(fma.f64 x x y)
(.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (-.f64 (*.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))
(.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(/.f64 1 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x 4) (.f64 y y))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))))
(.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 x 4) (.f64 x (*.f64 x y)))))
(.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (fma.f64 y (-.f64 y (*.f64 x x)) (pow.f64 x 4)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(pow.f64 (fma.f64 x x y) 1)
(fma.f64 x x y)
(pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)
(fma.f64 x x y)
(pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)
(fma.f64 x x y)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)
(fma.f64 x x y)
(sqrt.f64 (pow.f64 (fma.f64 x x y) 2))
(fma.f64 x x y)
(log.f64 (exp.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3))
(fma.f64 x x y)
(expm1.f64 (log1p.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(exp.f64 (log.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) 1))
(fma.f64 x x y)
(log1p.f64 (expm1.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(fma.f64 x x y)
(fma.f64 1 (*.f64 x x) y)
(fma.f64 x x y)
(fma.f64 1 y (*.f64 x x))
(fma.f64 x x y)
(fma.f64 (cbrt.f64 (.f64 y y)) (cbrt.f64 y) (.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) y)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))
(fma.f64 x x y)
(-.f64 (+.f64 1 (+.f64 y (fma.f64 x x y))) 1)
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (fma.f64 x x y) y)) (/.f64 (*.f64 y y) (-.f64 (fma.f64 x x y) y)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (fma.f64 x x 0))
(*.f64 (+.f64 y (fma.f64 x x y)) 1)
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(*.f64 1 (+.f64 y (fma.f64 x x y)))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(*.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 2) (cbrt.f64 (+.f64 y (fma.f64 x x y))))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(*.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) (sqrt.f64 (+.f64 y (fma.f64 x x y))))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(.f64 (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))
(.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) 2)))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y y (*.f64 (fma.f64 x x y) (fma.f64 x x 0))))
(.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y)) (/.f64 1 (-.f64 (fma.f64 x x y) y)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (fma.f64 x x 0))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))) (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3))))
(.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) 2)))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y y (*.f64 (fma.f64 x x y) (fma.f64 x x 0))))
(/.f64 1 (/.f64 (-.f64 (fma.f64 x x y) y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (fma.f64 x x 0))
(/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))))
(.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) 2)))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y y (*.f64 (fma.f64 x x y) (fma.f64 x x 0))))
(/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (fma.f64 x x y)))))
(.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) 2)))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y y (*.f64 (fma.f64 x x y) (fma.f64 x x 0))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (fma.f64 x x 0))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 x x y) 3) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y))))))
(.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y (-.f64 y (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) 2)))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (fma.f64 y y (*.f64 (fma.f64 x x y) (fma.f64 x x 0))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (fma.f64 x x 0))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 y y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (*.f64 x x) (+.f64 y y)))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 y y) 3)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 y y) (-.f64 (+.f64 y y) (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 x 6) (.f64 (pow.f64 y 3) 8)) (fma.f64 (+.f64 y y) (+.f64 y (-.f64 y (.f64 x x))) (pow.f64 x 4)))
(/.f64 (fma.f64 (pow.f64 y 3) 8 (pow.f64 x 6)) (fma.f64 y (.f64 2 (-.f64 y (-.f64 (.f64 x x) y))) (pow.f64 x 4)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (.f64 x x) (+.f64 y y)))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 4 (.f64 y y))) (fma.f64 x x (*.f64 y -2)))
(/.f64 (+.f64 (pow.f64 x 4) (.f64 (.f64 y y) -4)) (fma.f64 y -2 (*.f64 x x)))
(/.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (fma.f64 x x 0))
(pow.f64 (+.f64 y (fma.f64 x x y)) 1)
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(pow.f64 (cbrt.f64 (+.f64 y (fma.f64 x x y))) 3)
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(pow.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3) 1/3)
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(pow.f64 (sqrt.f64 (+.f64 y (fma.f64 x x y))) 2)
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(sqrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 2))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(log.f64 (exp.f64 (+.f64 y (fma.f64 x x y))))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(cbrt.f64 (pow.f64 (+.f64 y (fma.f64 x x y)) 3))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(expm1.f64 (log1p.f64 (+.f64 y (fma.f64 x x y))))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(exp.f64 (log.f64 (+.f64 y (fma.f64 x x y))))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (+.f64 y (fma.f64 x x y))) 1))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(log1p.f64 (expm1.f64 (+.f64 y (fma.f64 x x y))))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(fma.f64 1 (*.f64 x x) (+.f64 y y))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(fma.f64 1 y (fma.f64 x x y))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(fma.f64 1 (fma.f64 x x y) y)
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(fma.f64 (cbrt.f64 (*.f64 y y)) (cbrt.f64 y) (fma.f64 x x y))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (+.f64 y y))
(+.f64 y (fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) y))
(fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))
(fma.f64 x x (+.f64 y y))
(+.f64 y (fma.f64 x x y))
(fma.f64 y 2 (*.f64 x x))

eval18.0ms (1.1%)

Compiler: Compiled 1263 to 473 computations (62.5% saved)

prune14.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	91	4	95

Accurracy

100.0%

Counts

95 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
▶	57.2%	(+.f64 (*.f64 x x) y)
▶	51.9%	(+.f64 y y)
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
▶	57.2%	(+.f64 (*.f64 x x) y)
▶	51.9%	(+.f64 y y)

Compiler

Compiled 58 to 32 computations (44.8% saved)

localize23.0ms (1.4%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
	100.0%	(+.f64 (*.f64 x x) y)

Compiler

Compiled 17 to 6 computations (64.7% saved)

eval7.0ms (0.5%)

Compiler: Compiled 397 to 165 computations (58.4% saved)

prune8.0ms (0.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	37	2	39
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	37	6	43

Accurracy

100.0%

Counts

43 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	57.2%	(+.f64 (*.f64 x x) y)
✓	51.9%	(+.f64 y y)
▶	49.3%	(*.f64 x x)
	11.1%	y
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	57.2%	(+.f64 (*.f64 x x) y)
✓	51.9%	(+.f64 y y)
▶	49.3%	(*.f64 x x)
	11.1%	y

Compiler

Compiled 74 to 42 computations (43.2% saved)

localize15.0ms (1%)

Compiler: Compiled 7 to 4 computations (42.9% saved)

eval0.0ms (0%)

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

prune4.0ms (0.3%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	4	4
Total	6	6

Accurracy

100.0%

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	57.2%	(+.f64 (*.f64 x x) y)
✓	51.9%	(+.f64 y y)
✓	49.3%	(*.f64 x x)
	11.1%	y
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	57.2%	(+.f64 (*.f64 x x) y)
✓	51.9%	(+.f64 y y)
✓	49.3%	(*.f64 x x)
	11.1%	y

Compiler

Compiled 74 to 42 computations (43.2% saved)

localize0.0ms (0%)

eval0.0ms (0%)

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

prune3.0ms (0.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	5	5
Total	6	6

Accurracy

100.0%

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	57.2%	(+.f64 (*.f64 x x) y)
✓	51.9%	(+.f64 y y)
✓	49.3%	(*.f64 x x)
	11.1%	y

Compiler

Compiled 64 to 28 computations (56.3% saved)

regimes19.0ms (1.2%)

Counts

6 → 1

Calls

Call 1

Inputs
y
(*.f64 x x)
(+.f64 y y)
(+.f64 (*.f64 x x) y)
(+.f64 (+.f64 (*.f64 x x) y) y)
(fma.f64 x x (+.f64 y y))

Outputs
(fma.f64 x x (+.f64 y y))

Calls

4 calls:

6.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
5.0ms	y
4.0ms	x
3.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 47 to 19 computations (59.6% saved)

regimes204.0ms (12.7%)

Counts

5 → 1

Calls

Call 1

Inputs
y
(*.f64 x x)
(+.f64 y y)
(+.f64 (*.f64 x x) y)
(+.f64 (+.f64 (*.f64 x x) y) y)

Outputs
(+.f64 (+.f64 (*.f64 x x) y) y)

Calls

4 calls:

76.0ms	x
4.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
4.0ms	y
3.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 41 to 18 computations (56.1% saved)

regimes80.0ms (5%)

Counts

4 → 2

Calls

Call 1

Inputs
y
(*.f64 x x)
(+.f64 y y)
(+.f64 (*.f64 x x) y)

Outputs
(+.f64 y y)
(+.f64 (*.f64 x x) y)

Calls

3 calls:

60.0ms	y
11.0ms	x
8.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
88.1%	2	`x`
75.1%	9	`y`
88.1%	2	`(*.f64 x x)`

Compiler

Compiled 25 to 12 computations (52% saved)

regimes29.0ms (1.8%)

Counts

3 → 4

Calls

Call 1

Inputs
y
(*.f64 x x)
(+.f64 y y)

Outputs
(+.f64 y y)
(*.f64 x x)
(+.f64 y y)
(*.f64 x x)

Calls

2 calls:

16.0ms	x
12.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
88.7%	4	`x`
88.7%	4	`(*.f64 x x)`

Compiler

Compiled 17 to 9 computations (47.1% saved)

regimes15.0ms (1%)

Counts

2 → 2

Calls

Call 1

Inputs
y
(*.f64 x x)

Outputs
y
(*.f64 x x)

Calls

3 calls:

6.0ms	x
5.0ms	(*.f64 x x)
4.0ms	y

Results

Accuracy	Segments	Branch
49.3%	1	`y`
54.8%	2	`x`
54.8%	2	`(*.f64 x x)`

Compiler

Compiled 17 to 10 computations (41.2% saved)

regimes6.0ms (0.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
y

Outputs
y

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
11.1%	1	`y`
11.1%	1	`x`

Compiler

Compiled 9 to 6 computations (33.3% saved)

bsearch6.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	1.1869044799707475e-38	1.991454200657636e-38

Results

5.0ms

64×

body

256

valid

Compiler

Compiled 62 to 41 computations (33.9% saved)

bsearch35.0ms (2.2%)

Algorithm

3×	binary-search

Stop Event

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

Steps

Time	Left	Right
10.0ms	2.542579591465303e+81	3.6244830280055874e+83
9.0ms	1.3468415335282925e-6	2.589949186768147e-5
15.0ms	1.1869044799707475e-38	1.991454200657636e-38

Results

31.0ms

288×

body

256

valid

Compiler

Compiled 194 to 135 computations (30.4% saved)

bsearch8.0ms (0.5%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	5.744678652114422e-196	2.5806829244676053e-195

Results

7.0ms

96×

body

256

valid

Compiler

Compiled 62 to 45 computations (27.4% saved)

simplify9.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

4×	`not-or`
4×	`+-commutative`
4×	`if-if-or-not`
2×	`not-not`
2×	`if-not`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	166
1	35	166
2	38	166
3	41	162
4	42	162
5	43	162

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x x (+.f64 y y))
(+.f64 (+.f64 (*.f64 x x) y) y)
(if (<=.f64 (.f64 x x) 1819838454778243/95780971304118053647396689196894323976171195136475136) (+.f64 y y) (+.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) 5938420220855319/383123885216472214589586756787577295904684780545900544) (+.f64 y y) (if (<=.f64 (.f64 x x) 4486248158726163/2361183241434822606848) (.f64 x x) (if (<=.f64 (.f64 x x) 3400000000000000027232808317223784076751188561078435589060261083555929616732389376) (+.f64 y y) (*.f64 x x))))
(if (<=.f64 (.f64 x x) 8942231032632235/5260135901548373507240989882880128665550339802823173859498280903068732154297080822113666536277588451226982968856178217713019432250183803863127814770651880849955223671128444598191663757884322717271293251735781376) y (.f64 x x))
y

Outputs
(fma.f64 x x (+.f64 y y))
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 y (+.f64 y (*.f64 x x)))
(if (<=.f64 (.f64 x x) 1819838454778243/95780971304118053647396689196894323976171195136475136) (+.f64 y y) (+.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) 1819838454778243/95780971304118053647396689196894323976171195136475136) (+.f64 y y) (+.f64 y (.f64 x x)))
(if (<=.f64 (.f64 x x) 5938420220855319/383123885216472214589586756787577295904684780545900544) (+.f64 y y) (if (<=.f64 (.f64 x x) 4486248158726163/2361183241434822606848) (.f64 x x) (if (<=.f64 (.f64 x x) 3400000000000000027232808317223784076751188561078435589060261083555929616732389376) (+.f64 y y) (*.f64 x x))))
(if (or (<=.f64 (.f64 x x) 5938420220855319/383123885216472214589586756787577295904684780545900544) (and (not (<=.f64 (.f64 x x) 4486248158726163/2361183241434822606848)) (<=.f64 (.f64 x x) 3400000000000000027232808317223784076751188561078435589060261083555929616732389376))) (+.f64 y y) (.f64 x x))
(if (<=.f64 (.f64 x x) 8942231032632235/5260135901548373507240989882880128665550339802823173859498280903068732154297080822113666536277588451226982968856178217713019432250183803863127814770651880849955223671128444598191663757884322717271293251735781376) y (.f64 x x))
y

Compiler

Compiled 75 to 39 computations (48% saved)

soundness127.0ms (7.9%)

Rules

1716×	`fma-def`
832×	`unswap-sqr`
776×	`times-frac`
694×	`log-prod`
510×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	17	15
3	19	15
4	20	15
0	172	2503
1	422	2389
2	1526	2319
3	7736	2319

Stop Event

1×	node limit
1×	saturated

Compiler

Compiled 34 to 15 computations (55.9% saved)

end0.0ms (0%)

preprocess62.0ms (3.9%)

Remove: (abs x)
Compiler: Compiled 182 to 74 computations (59.3% saved)

analyze0.0ms (0%)

sample677.0ms (42.2%)

preprocess46.0ms (2.8%)

simplify3.0ms (0.2%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize34.0ms (2.1%)

series2.0ms (0.1%)

rewrite64.0ms (4%)

simplify86.0ms (5.3%)

eval18.0ms (1.1%)

prune14.0ms (0.8%)

localize23.0ms (1.4%)

eval7.0ms (0.5%)

prune8.0ms (0.5%)

localize15.0ms (1%)

eval0.0ms (0%)

prune4.0ms (0.3%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.2%)

regimes19.0ms (1.2%)

regimes204.0ms (12.7%)

regimes80.0ms (5%)

regimes29.0ms (1.8%)

regimes15.0ms (1%)

regimes6.0ms (0.3%)

bsearch6.0ms (0.3%)

bsearch35.0ms (2.2%)

bsearch8.0ms (0.5%)

simplify9.0ms (0.6%)

soundness127.0ms (7.9%)

end0.0ms (0%)

preprocess62.0ms (3.9%)

Profiling