Metrics for Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

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 7 to 6 computations (14.3% saved)

sample466.0ms (15.2%)

Memory

26.3MiB live, 771.9MiB allocated

Samples

292.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 108.0ms

ival-add: 100.0ms (92.6% of total)

ival-true: 5.0ms (4.6% of total)

ival-assert: 3.0ms (2.8% of total)

Bogosity

explain66.0ms (2.2%)

Memory

-16.0MiB live, 65.4MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`y`
-	-	`(+.f64 x y)`
-	-	`(+.f64 (+.f64 x y) x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

22.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-add: 5.0ms (96% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess23.0ms (0.7%)

Memory

1.6MiB live, 38.2MiB allocated

Algorithm

1×	egg-herbie

Rules

82×	`distribute-rgt-in`
72×	`sub-neg`
62×	`cancel-sign-sub-inv`
60×	`associate-+l-`
50×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	38	25
2	98	25
3	254	25
4	431	25
5	506	25
6	518	25
0	4	5
0	6	5
1	9	5
2	12	5
3	14	5
4	15	5
0	15	4

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

Outputs
(+.f64 (+.f64 x y) x)
(fma.f64 #s(literal 2 binary64) x y)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 x y)
cost-diff	0	(+.f64 (+.f64 x y) x)

Rules

14×	`lower-+.f32`
10×	`lower-+.f64`
4×	`associate-+l+`
4×	`lift-+.f64`
4×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	9	10
2	12	10
3	14	10
4	15	10
0	15	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(+.f64 (+.f64 x y) x)
(fma.f64 #s(literal 2 binary64) x y)
(+.f64 x y)
(+.f64 y x)
x
y

localize11.0ms (0.4%)

Memory

22.4MiB live, 22.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.00390625	(+.f64 (+.f64 x y) x)

Samples

8.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-add: 2.0ms (78.4% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory

-31.1MiB live, 6.2MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())
#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())

Outputs
#s(alt (* 2 x) (taylor 0 y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt (+.f64 (+.f64 x y) x) (patch (+.f64 (+.f64 x y) x) #<representation:binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation:binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((+ (+ x y) x) (+ x y))
0.0ms	y	@	inf	((+ (+ x y) x) (+ x y))
0.0ms	x	@	inf	((+ (+ x y) x) (+ x y))
0.0ms	y	@	-inf	((+ (+ x y) x) (+ x y))
0.0ms	x	@	0	((+ (+ x y) x) (+ x y))

simplify161.0ms (5.3%)

Memory

11.3MiB live, 171.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 404×	`lower-fma.f64`
8 404×	`lower-fma.f32`
2 172×	`lower-*.f64`
2 172×	`lower-*.f32`
1 692×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	162
1	102	162
2	231	162
3	684	162
4	1813	162
5	2759	162
6	3836	162
7	4303	162
8	4593	162
9	4688	162
10	6579	162
0	8363	144

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 39

Calls

Call 1

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

Outputs
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
y
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 #s(literal 2 binary64) x y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 #s(literal 2 binary64) x y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 #s(literal 2 binary64) x y)
y
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
y
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 #s(literal 2 binary64) x y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 #s(literal 2 binary64) x y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 #s(literal 2 binary64) x y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
y
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ y x)))
(fma.f64 #s(literal 2 binary64) x y)
(* x (+ 2 (/ y x)))
(fma.f64 #s(literal 2 binary64) x y)
(* x (+ 2 (/ y x)))
(fma.f64 #s(literal 2 binary64) x y)
x
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 #s(literal 2 binary64) x y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 #s(literal 2 binary64) x y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 #s(literal 2 binary64) x y)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)

rewrite266.0ms (8.7%)

Memory

31.0MiB live, 293.1MiB allocated

Rules

5 968×	`lower-fma.f64`
5 968×	`lower-fma.f32`
4 498×	`lower-*.f64`
4 498×	`lower-*.f32`
2 178×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	32	8
2	279	8
3	4621	8
0	8114	7

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

2 → 205

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (/.f64 (+.f64 #s(literal 0 binary64) y) (-.f64 (pow.f64 (+.f64 y x) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (hypot.f64 (+.f64 y x) x) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 0 binary64) y) (-.f64 (pow.f64 (+.f64 y x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 x x) (hypot.f64 (+.f64 y x) x) (pow.f64 (+.f64 y x) #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (neg.f64 x) y (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (-.f64 (pow.f64 (+.f64 y x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (neg.f64 x) y (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (hypot.f64 (pow.f64 (+.f64 y x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (hypot.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (.f64 (+.f64 y x) x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (+.f64 #s(literal 0 binary64) y) (fma.f64 #s(literal 2 binary64) x y)) (-.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (+.f64 y x) x (hypot.f64 (+.f64 y x) x)))
(.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 y x) #s(literal 3/2 binary64))) (-.f64 (pow.f64 (+.f64 y x) #s(literal 4 binary64)) (pow.f64 (.f64 (neg.f64 x) y) #s(literal 2 binary64)))) (-.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (*.f64 (neg.f64 x) y)))
(.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (+.f64 y x) #s(literal 3/2 binary64))) (fma.f64 #s(literal -1 binary64) (pow.f64 (.f64 y x) #s(literal 3 binary64)) (pow.f64 (+.f64 y x) #s(literal 6 binary64)))) (fma.f64 (.f64 (neg.f64 x) y) (-.f64 (.f64 (neg.f64 x) y) (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (pow.f64 (+.f64 y x) #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (+.f64 #s(literal 0 binary64) y) (fma.f64 #s(literal 2 binary64) x y)) (*.f64 (+.f64 #s(literal 0 binary64) y) (fma.f64 #s(literal 2 binary64) x y))) (fma.f64 #s(literal 2 binary64) x y))
(.f64 (.f64 (fma.f64 #s(literal 2 binary64) x y) (neg.f64 y)) (pow.f64 (neg.f64 y) #s(literal -1 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 0 binary64) y) #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 (+.f64 #s(literal 0 binary64) y) (fma.f64 #s(literal 2 binary64) x y)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 0 binary64) y) #s(literal -1 binary64)) (.f64 (+.f64 #s(literal 0 binary64) y) (fma.f64 #s(literal 2 binary64) x y)))
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(fma.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (/.f64 (+.f64 y x) (-.f64 (hypot.f64 y x) (.f64 y x))) x)
(fma.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (.f64 (+.f64 y x) (pow.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)) #s(literal -1 binary64))) x)
(fma.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)) #s(literal -1 binary64)) x)
(fma.f64 (+.f64 y x) (pow.f64 (/.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1 binary64)) x)
(fma.f64 (+.f64 y x) (pow.f64 (*.f64 (-.f64 x y) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) #s(literal 1 binary64)) x)
(fma.f64 (+.f64 y x) (/.f64 (-.f64 x y) (-.f64 x y)) x)
(fma.f64 (+.f64 y x) (/.f64 (+.f64 y x) (+.f64 #s(literal 0 binary64) y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 0 binary64) y)))))
(fma.f64 (+.f64 y x) (*.f64 (-.f64 x y) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) x)
(-.f64 (+.f64 x (.f64 x (/.f64 x (-.f64 x y)))) (.f64 y (/.f64 y (-.f64 x y))))
(-.f64 (/.f64 (*.f64 x x) (neg.f64 y)) (/.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (neg.f64 y)))
(-.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) y)) (*.f64 x (/.f64 x (+.f64 #s(literal 0 binary64) y))))
(-.f64 (.f64 x (/.f64 x (-.f64 x y))) (-.f64 (.f64 y (/.f64 y (-.f64 x y))) x))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x y) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal 2 binary64) x) y)
(+.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 0 binary64) y)))))
(+.f64 (+.f64 y x) x)
(+.f64 y (*.f64 #s(literal 2 binary64) x))
(+.f64 x (+.f64 y x))
(.f64 (exp.f64 (log.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))))) (exp.f64 (neg.f64 (log.f64 (-.f64 (hypot.f64 y x) (.f64 y x))))))
(.f64 (exp.f64 (log.f64 (.f64 (-.f64 x y) (+.f64 y x)))) (exp.f64 (neg.f64 (log.f64 (-.f64 x y)))))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) #s(literal 1 binary64)) (pow.f64 (+.f64 (hypot.f64 y x) (*.f64 y x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 y x) y) #s(literal 2 binary64)))) #s(literal 1 binary64)) (pow.f64 (-.f64 (.f64 x x) (.f64 (-.f64 y x) y)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (.f64 (-.f64 y x) y) (-.f64 (.f64 (-.f64 y x) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (*.f64 (-.f64 x y) (+.f64 y x))) #s(literal 1 binary64)) (+.f64 y x))
(.f64 (pow.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (neg.f64 (-.f64 x y)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (neg.f64 (-.f64 (hypot.f64 y x) (.f64 y x))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal 1 binary64)) (pow.f64 (/.f64 (+.f64 y x) (-.f64 (hypot.f64 y x) (*.f64 y x))) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal 1 binary64)) (pow.f64 (.f64 (+.f64 y x) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64)) #s(literal 1 binary64)) (pow.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) #s(literal 1 binary64)))
(.f64 (pow.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (hypot.f64 y x) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (+.f64 (hypot.f64 y x) (*.f64 y x)))
(.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 y x) y) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 (-.f64 y x) y)))
(.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 y x) y) (-.f64 (.f64 (-.f64 y x) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (*.f64 (-.f64 x y) (+.f64 y x))) (+.f64 y x))
(.f64 (.f64 (+.f64 y x) (-.f64 y x)) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (pow.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (.f64 (-.f64 x y) (+.f64 y x)))
(.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64)) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 y x))
(.f64 (neg.f64 (.f64 (-.f64 x y) (+.f64 y x))) (pow.f64 (neg.f64 (-.f64 x y)) #s(literal -1 binary64)))
(.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (pow.f64 (neg.f64 (-.f64 (hypot.f64 y x) (.f64 y x))) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (-.f64 x y) #s(literal -1 binary64)))
(.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (/.f64 (+.f64 y x) (-.f64 (hypot.f64 y x) (*.f64 y x))))
(.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (.f64 (+.f64 y x) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64)))
(*.f64 (+.f64 y x) (pow.f64 (/.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1 binary64)))
(.f64 (+.f64 y x) (pow.f64 (.f64 (-.f64 x y) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) #s(literal 1 binary64)))
(*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (-.f64 x y)))
(.f64 (+.f64 y x) (.f64 (-.f64 x y) (pow.f64 (-.f64 x y) #s(literal -1 binary64))))
(pow.f64 (/.f64 (-.f64 y x) (*.f64 (+.f64 y x) (-.f64 y x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (+.f64 y x) #s(literal 1 binary64))
(/.f64 (exp.f64 (log.f64 (*.f64 (+.f64 y x) (-.f64 y x)))) (exp.f64 (log.f64 (-.f64 y x))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))))) (exp.f64 (log.f64 (neg.f64 (-.f64 x y)))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))))) (exp.f64 (log.f64 (neg.f64 (-.f64 (hypot.f64 y x) (*.f64 y x))))))
(/.f64 (exp.f64 (log.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))))) (exp.f64 (log.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)))))
(/.f64 (exp.f64 (log.f64 (*.f64 (-.f64 x y) (+.f64 y x)))) (exp.f64 (log.f64 (-.f64 x y))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (hypot.f64 y x))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (fma.f64 (.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))
(/.f64 (.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) #s(literal -1 binary64))) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x y))) #s(literal 2 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 x y))) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 x y) #s(literal -3 binary64))) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (-.f64 x y) #s(literal -3 binary64)))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x y))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 x y))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 x y))) (*.f64 y (/.f64 y (-.f64 x y)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x)))) (neg.f64 (neg.f64 (-.f64 x y))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)))))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) #s(literal 1 binary64)) (-.f64 (hypot.f64 y x) (.f64 y x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (*.f64 y x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (*.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))) (-.f64 x y)))
(/.f64 (.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (-.f64 (hypot.f64 y x) (.f64 y x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (hypot.f64 y x) (-.f64 x y)))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x y)) (.f64 (-.f64 x y) (.f64 y y))) (pow.f64 (-.f64 x y) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (*.f64 (-.f64 x y) (hypot.f64 y x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (-.f64 x y) (fma.f64 (.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (-.f64 y x))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (+.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (*.f64 (+.f64 y x) (-.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (-.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (-.f64 (hypot.f64 y x) (*.f64 y x))))
(/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 x y))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (-.f64 (hypot.f64 y x) (*.f64 y x)))
(neg.f64 (neg.f64 (+.f64 y x)))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (+.f64 (hypot.f64 y x) (.f64 y x)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (+.f64 y x) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 (.f64 x x) (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(-.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x y))) (.f64 y (/.f64 y (-.f64 x y))))
(exp.f64 (*.f64 (log.f64 (+.f64 y x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 y x))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (+.f64 y x)))
(+.f64 (.f64 x (/.f64 x (-.f64 x y))) (neg.f64 (.f64 y (/.f64 y (-.f64 x y)))))
(+.f64 y x)
(+.f64 x y)

eval29.0ms (0.9%)

Memory: 9.6MiB live, 85.2MiB allocated
Compiler: Compiled 4 436 to 619 computations (86% saved)

prune9.0ms (0.3%)

Memory

-23.0MiB live, 24.7MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	243	2	245

Accuracy

100.0%

Counts

245 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 #s(literal 2 binary64) x y)
▶	51.9%	#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))

Compiler

Compiled 8 to 9 computations (-12.5% saved)

simplify4.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 #s(literal 2 binary64) x y)
cost-diff	0	(*.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))

Rules

14×	`lower-+.f64`
14×	`lower-+.f32`
6×	`+-commutative`
4×	`associate-+l+`
4×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	21
0	10	21
1	15	21
2	18	20
3	18	20
0	18	20

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
x
y

Outputs
#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
x
y

localize18.0ms (0.6%)

Memory

-4.3MiB live, 34.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	30.75771053524746	#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))

Samples

12.0ms

256×

valid

Compiler

Compiled 20 to 9 computations (55% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-add: 4.0ms (75% of total)

ival-mult: 1.0ms (18.7% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs

#s(alt #s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())

#s(alt (*.f64 #s(literal 2 binary64) x) (patch (*.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())

#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())

Outputs
#s(alt (* 2 x) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ (+ x y) x) (.f64 #s(literal 2 binary64) x)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation:binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((+ (+ x y) x) (* 2 x) (+ (* 2 x) y))
0.0ms	x	@	inf	((+ (+ x y) x) (* 2 x) (+ (* 2 x) y))
0.0ms	x	@	0	((+ (+ x y) x) (* 2 x) (+ (* 2 x) y))
0.0ms	y	@	inf	((+ (+ x y) x) (* 2 x) (+ (* 2 x) y))
0.0ms	y	@	-inf	((+ (+ x y) x) (* 2 x) (+ (* 2 x) y))

simplify200.0ms (6.5%)

Memory

-15.5MiB live, 131.4MiB allocated

Algorithm

1×	egg-herbie

Rules

4 188×	`lower-/.f32`
4 188×	`lower-/.f64`
3 666×	`associate-/r*`
2 352×	`lower-fma.f64`
2 352×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	240
1	64	240
2	141	240
3	398	240
4	1108	240
5	2539	240
6	3437	240
7	4311	240
8	4789	240
9	4964	240
10	5054	240
11	5752	240
12	6068	240
13	6070	240
14	6070	240
15	6070	240
0	8131	204

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 54

Calls

Call 1

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

Outputs
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
y
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 x #s(literal 2 binary64) y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 x #s(literal 2 binary64) y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 x #s(literal 2 binary64) y)
y
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 x #s(literal 2 binary64) y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 x #s(literal 2 binary64) y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 x #s(literal 2 binary64) y)
y
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 x #s(literal 2 binary64) y)
y
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 x #s(literal 2 binary64) y)
y
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
y
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ y x)))
(fma.f64 x #s(literal 2 binary64) y)
(* x (+ 2 (/ y x)))
(fma.f64 x #s(literal 2 binary64) y)
(* x (+ 2 (/ y x)))
(fma.f64 x #s(literal 2 binary64) y)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ y x)))
(fma.f64 x #s(literal 2 binary64) y)
(* x (+ 2 (/ y x)))
(fma.f64 x #s(literal 2 binary64) y)
(* x (+ 2 (/ y x)))
(fma.f64 x #s(literal 2 binary64) y)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 x #s(literal 2 binary64) y)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 x #s(literal 2 binary64) y)

rewrite194.0ms (6.3%)

Memory

6.5MiB live, 266.2MiB allocated

Rules

4 950×	`lower-fma.f32`
4 948×	`lower-fma.f64`
4 332×	`lower-*.f32`
4 330×	`lower-*.f64`
2 798×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	16
0	10	16
1	48	16
2	404	15
3	6029	15
0	8033	15

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

3 → 149

Calls

Call 1

Inputs
#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(fma.f64 #s(literal 2 binary64) x y)

Outputs
#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) #s(literal 0 binary64))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))))
(+.f64 x x)
(.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 y) y)) (-.f64 (.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 y (fma.f64 #s(literal 2 binary64) x y))))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (.f64 #s(literal 2 binary64) x)) (fma.f64 y y (.f64 #s(literal -4 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 y) (*.f64 (fma.f64 #s(literal 2 binary64) x y) (neg.f64 y))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x y) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 #s(literal 2 binary64) x y) #s(literal -1 binary64)))
(/.f64 (fma.f64 #s(literal 512 binary64) (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) y) (.f64 (.f64 y x) #s(literal 2 binary64))) (-.f64 (fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 3 binary64)))))
(/.f64 (hypot.f64 (pow.f64 (+.f64 y x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64))) (.f64 (fma.f64 (neg.f64 x) y (pow.f64 (+.f64 y x) #s(literal 2 binary64))) (-.f64 (hypot.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (.f64 (+.f64 y x) x) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 y) y))) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y)))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) y) (.f64 (*.f64 y x) #s(literal 2 binary64)))))
(/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x y) (fma.f64 #s(literal -1 binary64) y #s(literal 0 binary64))) (fma.f64 #s(literal -1 binary64) y #s(literal 0 binary64)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 (+.f64 y x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 (neg.f64 x) y (pow.f64 (+.f64 y x) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 y) y)) (-.f64 (*.f64 #s(literal 2 binary64) x) y))
(/.f64 (*.f64 (+.f64 #s(literal 0 binary64) y) (fma.f64 #s(literal 2 binary64) x y)) (+.f64 #s(literal 0 binary64) y))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) y) (.f64 (*.f64 y x) #s(literal 2 binary64))))
(/.f64 (hypot.f64 (pow.f64 (+.f64 y x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (fma.f64 (neg.f64 x) y (pow.f64 (+.f64 y x) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 y) y))) (-.f64 (*.f64 #s(literal 2 binary64) x) y)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) y) (.f64 (*.f64 y x) #s(literal 2 binary64)))))
(neg.f64 (/.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x y) (fma.f64 #s(literal -1 binary64) y #s(literal 0 binary64))) (+.f64 #s(literal 0 binary64) y)))
(neg.f64 (/.f64 (neg.f64 (hypot.f64 (pow.f64 (+.f64 y x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (fma.f64 (neg.f64 x) y (pow.f64 (+.f64 y x) #s(literal 2 binary64)))))
(neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 y) y)) (neg.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) y))))
(neg.f64 (/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (neg.f64 (-.f64 (hypot.f64 (.f64 #s(literal 2 binary64) x) y) (.f64 (*.f64 y x) #s(literal 2 binary64))))))
(neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 0 binary64) y) (fma.f64 #s(literal 2 binary64) x y)) (fma.f64 #s(literal -1 binary64) y #s(literal 0 binary64))))
(neg.f64 (/.f64 (hypot.f64 (pow.f64 (+.f64 y x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (fma.f64 (neg.f64 x) y (pow.f64 (+.f64 y x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64))) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 y (fma.f64 #s(literal 2 binary64) x y))) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (fma.f64 (.f64 #s(literal 4 binary64) x) x (.f64 (neg.f64 y) y))) (fma.f64 #s(literal 2 binary64) x y) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (-.f64 (pow.f64 (+.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (+.f64 y x) x (hypot.f64 (+.f64 y x) x)) (neg.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 0 binary64) y)))))
(fma.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal 0 binary64) y) (fma.f64 #s(literal 2 binary64) x y))) (fma.f64 #s(literal 2 binary64) x y) (neg.f64 (.f64 x (/.f64 x (+.f64 #s(literal 0 binary64) y)))))
(fma.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (+.f64 (hypot.f64 y x) (.f64 y x)) x)
(fma.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 y x) y) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (*.f64 (-.f64 y x) y)) x)
(fma.f64 (/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 y x) y) (-.f64 (.f64 (-.f64 y x) y) (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) x)
(fma.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (.f64 (-.f64 x y) (+.f64 y x))) (+.f64 y x) x)
(fma.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (/.f64 #s(literal 2 binary64) (-.f64 (.f64 #s(literal 2 binary64) x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 (.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (.f64 #s(literal 2 binary64) x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 #s(literal 4 binary64) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal 2 binary64) x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 (fma.f64 y y (*.f64 (neg.f64 x) x)) (pow.f64 (-.f64 y x) #s(literal -1 binary64)) x)
(fma.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (*.f64 (-.f64 x y) (+.f64 y x)) x)
(fma.f64 (pow.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)) #s(literal -1 binary64)) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) x)
(fma.f64 #s(literal 1 binary64) (+.f64 y x) x)
(fma.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x))) (pow.f64 (neg.f64 (-.f64 x y)) #s(literal -1 binary64)) x)
(fma.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (pow.f64 (neg.f64 (-.f64 (hypot.f64 y x) (*.f64 y x))) #s(literal -1 binary64)) x)
(fma.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (-.f64 x y) #s(literal -1 binary64)) x)
(fma.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (pow.f64 (-.f64 (.f64 #s(literal 2 binary64) x) y) #s(literal -1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (/.f64 (+.f64 y x) (-.f64 (hypot.f64 y x) (.f64 y x))) x)
(fma.f64 (-.f64 (hypot.f64 y x) (.f64 y x)) (.f64 (+.f64 y x) (pow.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)) #s(literal -1 binary64))) x)
(fma.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (-.f64 (hypot.f64 y x) (*.f64 y x)) #s(literal -1 binary64)) x)
(fma.f64 (.f64 x x) (/.f64 #s(literal 4 binary64) (-.f64 (.f64 #s(literal 2 binary64) x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 0 binary64) y) #s(literal -1 binary64)) (neg.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 0 binary64) y)))))
(fma.f64 (.f64 #s(literal 2 binary64) x) (/.f64 (.f64 #s(literal 2 binary64) x) (-.f64 (.f64 #s(literal 2 binary64) x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 #s(literal 2 binary64) (/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal 2 binary64) x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 #s(literal 2 binary64) x y)
(fma.f64 (+.f64 y x) (/.f64 (+.f64 y x) (+.f64 #s(literal 0 binary64) y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 0 binary64) y)))))
(fma.f64 (+.f64 y x) (/.f64 (-.f64 x y) (-.f64 x y)) x)
(fma.f64 (+.f64 y x) (*.f64 (-.f64 x y) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) x)
(fma.f64 x (/.f64 (.f64 #s(literal 4 binary64) x) (-.f64 (.f64 #s(literal 2 binary64) x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 #s(literal 2 binary64) x) y)))))
(fma.f64 x #s(literal 2 binary64) y)
(-.f64 (+.f64 x (.f64 x (/.f64 x (-.f64 x y)))) (.f64 y (/.f64 y (-.f64 x y))))
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 #s(literal 2 binary64) x))) (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 y (*.f64 #s(literal 2 binary64) x))))
(-.f64 (/.f64 (*.f64 x x) (neg.f64 y)) (/.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (neg.f64 y)))
(-.f64 (.f64 (.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (.f64 #s(literal 2 binary64) x) y))) (.f64 y (/.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y))))
(-.f64 (.f64 x (/.f64 x (-.f64 x y))) (-.f64 (.f64 y (/.f64 y (-.f64 x y))) x))
(-.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) y)) (*.f64 x (/.f64 x (+.f64 #s(literal 0 binary64) y))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 #s(literal 2 binary64) x y) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 #s(literal 4 binary64) x) (/.f64 x (-.f64 (.f64 #s(literal 2 binary64) x) y))) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 #s(literal 2 binary64) x) y)))))
(+.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) y)) (neg.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 0 binary64) y)))))
(+.f64 (*.f64 #s(literal 2 binary64) x) y)
(+.f64 (+.f64 y x) x)
(+.f64 y (*.f64 #s(literal 2 binary64) x))
(+.f64 x (+.f64 y x))

eval24.0ms (0.8%)

Memory: 2.6MiB live, 53.4MiB allocated
Compiler: Compiled 3 436 to 449 computations (86.9% saved)

prune9.0ms (0.3%)

Memory

-12.2MiB live, 25.5MiB allocated

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	203	2	205

Accuracy

100.0%

Counts

205 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 #s(literal 2 binary64) x y)
▶	51.9%	#s(approx (+ (+ x y) x) (+.f64 x x))

Compiler

Compiled 8 to 8 computations (0% saved)

simplify4.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	-128	(+.f64 x x)
cost-diff	0	#s(approx (+ (+ x y) x) (+.f64 x x))

Rules

14×	`lower-+.f32`
12×	`lower-+.f64`
4×	`associate-+l+`
4×	`lower-*.f64`
4×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
0	7	13
1	12	13
2	15	13
0	15	12

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (+ x y) x) (+.f64 x x))
(+.f64 x x)
x

Outputs
#s(approx (+ (+ x y) x) (+.f64 x x))
#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))
(+.f64 x x)
(*.f64 #s(literal 2 binary64) x)
x

localize27.0ms (0.9%)

Memory

-18.7MiB live, 19.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x x)
accuracy	30.75771053524746	#s(approx (+ (+ x y) x) (+.f64 x x))

Samples

23.0ms

256×

valid

Compiler

Compiled 11 to 7 computations (36.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-add: 18.0ms (98.6% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory

2.1MiB live, 2.1MiB allocated

Counts

2 → 36

Calls

Call 1

Inputs
#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())
#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())

Outputs
#s(alt (* 2 x) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* x (+ 2 (/ y x))) (taylor inf x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) x) (+.f64 x x)) (patch #s(approx (+ (+ x y) x) (+.f64 x x)) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (+.f64 x x) (patch (+.f64 x x) #<representation:binary64>) () ())) ())

Calls

6 calls:

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

simplify418.0ms (13.6%)

Memory

25.2MiB live, 140.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4 188×	`lower-/.f32`
4 188×	`lower-/.f64`
3 666×	`associate-/r*`
2 352×	`lower-fma.f64`
2 352×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	138
1	64	138
2	141	138
3	398	138
4	1108	138
5	2539	138
6	3437	138
7	4311	138
8	4789	138
9	4964	138
10	5054	138
11	5752	138
12	6068	138
13	6070	138
14	6070	138
15	6070	138
0	8131	120

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 33

Calls

Call 1

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

Outputs
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
y
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 x #s(literal 2 binary64) y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 x #s(literal 2 binary64) y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 x #s(literal 2 binary64) y)
y
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* y (- (* -2 (/ x y)) 1)))
(fma.f64 x #s(literal 2 binary64) y)
y
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(+ y (* 2 x))
(fma.f64 x #s(literal 2 binary64) y)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ y x)))
(fma.f64 x #s(literal 2 binary64) y)
(* x (+ 2 (/ y x)))
(fma.f64 x #s(literal 2 binary64) y)
(* x (+ 2 (/ y x)))
(fma.f64 x #s(literal 2 binary64) y)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 x #s(literal 2 binary64) y)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(fma.f64 x #s(literal 2 binary64) y)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))

rewrite38.0ms (1.2%)

Memory

11.7MiB live, 47.5MiB allocated

Rules

148×	`lower-*.f64`
148×	`lower-*.f32`
146×	`lower-/.f64`
146×	`lower-/.f32`
136×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
0	7	12
1	41	12
0	346	11

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

2 → 12

Calls

Call 1

Inputs
#s(approx (+ (+ x y) x) (+.f64 x x))
(+.f64 x x)

Outputs
#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(*.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(+.f64 x x)

eval27.0ms (0.9%)

Memory: -25.8MiB live, 12.1MiB allocated
Compiler: Compiled 256 to 42 computations (83.6% saved)

prune3.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	45	2	47

Accuracy

100.0%

Counts

47 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 #s(literal 2 binary64) x y)
✓	51.9%	#s(approx (+ (+ x y) x) (+.f64 x x))

Compiler

Compiled 25 to 18 computations (28% saved)

regimes65.0ms (2.1%)

Memory

-32.6MiB live, 60.8MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ x y) x) (+.f64 x x))
#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))
(+.f64 (+.f64 x y) x)
(fma.f64 #s(literal 2 binary64) x y)

Outputs
(fma.f64 #s(literal 2 binary64) x y)

Calls

3 calls:

2.0ms	(+.f64 (+.f64 x y) x)
2.0ms	y
2.0ms	x

Results

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

Compiler

Compiled 7 to 8 computations (-14.3% saved)

regimes6.0ms (0.2%)

Memory

19.0MiB live, 19.0MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ x y) x) (+.f64 x x))
#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))
(+.f64 (+.f64 x y) x)

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

Calls

3 calls:

2.0ms	(+.f64 (+.f64 x y) x)
2.0ms	x
2.0ms	y

Results

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

Compiler

Compiled 7 to 8 computations (-14.3% saved)

regimes5.0ms (0.2%)

Memory

15.9MiB live, 15.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ x y) x) (+.f64 x x))
#s(approx (+ (+ x y) x) (*.f64 #s(literal 2 binary64) x))

Outputs
#s(approx (+ (+ x y) x) (+.f64 x x))

Calls

3 calls:

2.0ms	x
2.0ms	(+.f64 (+.f64 x y) x)
1.0ms	y

Results

Accuracy	Segments	Branch
51.9%	1	`x`
51.9%	1	`y`
51.9%	1	`(+.f64 (+.f64 x y) x)`

Compiler

Compiled 7 to 8 computations (-14.3% saved)

simplify28.0ms (0.9%)

Memory

6.1MiB live, 81.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	12	18

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 #s(literal 2 binary64) x y)
(+.f64 (+.f64 x y) x)
#s(approx (+ (+ x y) x) (+.f64 x x))

Outputs
(fma.f64 #s(literal 2 binary64) x y)
(+.f64 (+.f64 x y) x)
(+.f64 (+.f64 y x) x)
#s(approx (+ (+ x y) x) (+.f64 x x))

soundness889.0ms (29.1%)

Memory

-115.0MiB live, 373.0MiB allocated

Rules

8 404×	`lower-fma.f64`
8 404×	`lower-fma.f32`
5 968×	`lower-fma.f64`
5 968×	`lower-fma.f32`
4 950×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	162
1	102	162
2	231	162
3	684	162
4	1813	162
5	2759	162
6	3836	162
7	4303	162
8	4593	162
9	4688	162
10	6579	162
0	8363	144
0	4	8
0	6	8
1	32	8
2	279	8
3	4621	8
0	8114	7
0	8	16
0	10	16
1	48	16
2	404	15
3	6029	15
0	8033	15

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit

Compiler

Compiled 29 to 23 computations (20.7% saved)

preprocess58.0ms (1.9%)

Memory: 15.7MiB live, 136.3MiB allocated
Compiler: Compiled 46 to 34 computations (26.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	27
1	38	25
2	98	25
3	254	25
4	431	25
5	506	25
6	518	25
0	4	5
0	6	5
1	9	5
2	12	5
3	14	5
4	15	5
0	15	4

Iter	Nodes	Cost
0	12	27
1	38	25
2	98	25
3	254	25
4	431	25
5	506	25
6	518	25
0	4	5
0	6	5
1	9	5
2	12	5
3	14	5
4	15	5
0	15	4

start0.0ms (0%)

analyze0.0ms (0%)

sample466.0ms (15.2%)

explain66.0ms (2.2%)

preprocess23.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize11.0ms (0.4%)

series5.0ms (0.2%)

simplify161.0ms (5.3%)

rewrite266.0ms (8.7%)

eval29.0ms (0.9%)

prune9.0ms (0.3%)

simplify4.0ms (0.1%)

localize18.0ms (0.6%)

series3.0ms (0.1%)

simplify200.0ms (6.5%)

rewrite194.0ms (6.3%)

eval24.0ms (0.8%)

prune9.0ms (0.3%)

simplify4.0ms (0.1%)

localize27.0ms (0.9%)

series2.0ms (0.1%)

simplify418.0ms (13.6%)

rewrite38.0ms (1.2%)

eval27.0ms (0.9%)

prune3.0ms (0.1%)

regimes65.0ms (2.1%)

regimes6.0ms (0.2%)

regimes5.0ms (0.2%)

simplify28.0ms (0.9%)

soundness889.0ms (29.1%)

preprocess58.0ms (1.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	27
1	38	25
2	98	25
3	254	25
4	431	25
5	506	25
6	518	25
0	4	5
0	6	5
1	9	5
2	12	5
3	14	5
4	15	5
0	15	4