Metrics for Examples.Basics.ProofTests:f4 from sbv-4.4

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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 15 to 11 computations (26.7% saved)

sample801.0ms (18.5%)

Memory

20.2MiB live, 1 032.8MiB allocated

Samples

550.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 334.0ms

ival-mult: 226.0ms (67.7% of total)

ival-add: 94.0ms (28.2% of total)

ival-true: 6.0ms (1.8% of total)

exact: 5.0ms (1.5% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain163.0ms (3.8%)

Memory

-20.2MiB live, 219.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
11	-	-	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`
8	-	-	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
0	-	-	`(*.f64 x #s(literal 2 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`(.f64 (.f64 x #s(literal 2 binary64)) y)`
0	-	-	`y`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(*.f64 y y)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f64`	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	nan-rescue	11	0
↳	`(*.f64 x x)`	overflow	61
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	35
`+.f64`	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`	nan-rescue	8	0
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	overflow	76
↳	`(*.f64 x x)`	overflow	61
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	35
↳	`(*.f64 y y)`	overflow	59

Confusion

	Predicted +	Predicted -
+	16	0
-	0	240

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	16	0	0
-	0	0	240

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	240
1	13
2	3

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms

512×

valid

Compiler

Compiled 173 to 59 computations (65.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 12.0ms (69% of total)

ival-add: 4.0ms (23% of total)

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

exact: 0.0ms (0% of total)

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

preprocess47.0ms (1.1%)

Memory

-0.7MiB live, 40.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	71
1	77	57
2	250	55
3	638	55
4	1214	55
5	1509	55
6	1539	55
0	9	13
0	15	13
1	23	11
2	43	11
3	51	11
0	51	9

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort x y)

Compiler

Compiled 13 to 9 computations (30.8% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	93.7%	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify4.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
cost-diff	448	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	15	39
1	23	35
2	43	35
3	51	35
0	51	32

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize90.0ms (2.1%)

Memory

18.9MiB live, 55.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	1.0078125000000002	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
accuracy	2.945306307490618	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Samples

84.0ms

256×

valid

Compiler

Compiled 80 to 20 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 6.0ms (64.1% of total)

ival-add: 3.0ms (32% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

-17.3MiB live, 21.2MiB allocated

Counts

5 → 17

Calls

Call 1

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

Outputs
(* 2 (* x y))
(* x (+ x (* 2 y)))
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(pow x 2)
(* 2 x)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	x	@	0	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	y	@	0	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	x	@	-inf	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	y	@	inf	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))

simplify121.0ms (2.8%)

Memory

4.0MiB live, 102.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	129
1	166	129
2	468	129
3	1326	129
4	3270	129
5	6410	129
0	8142	110

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 17

Calls

Call 1

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

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

rewrite230.0ms (5.3%)

Memory

2.7MiB live, 228.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
0	15	33
1	50	29
2	420	29
3	6357	29
0	8219	26

Stop Event

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

Counts

5 → 210

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (.f64 #s(literal 2 binary64) x)))))
(.f64 (/.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (.f64 #s(literal 2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (.f64 #s(literal 2 binary64) x))) (-.f64 (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (*.f64 #s(literal 2 binary64) x))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(.f64 (/.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) x) (/.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) (-.f64 x (*.f64 y #s(literal 2 binary64)))))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(.f64 (-.f64 (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))))
(.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))))
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (pow.f64 (.f64 (neg.f64 x) (-.f64 x (*.f64 y #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (pow.f64 (.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))))
(.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64))))
(.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (/.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x)))
(.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) (pow.f64 (.f64 (-.f64 x (*.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64))))
(*.f64 x (fma.f64 y #s(literal 2 binary64) x))
(pow.f64 (/.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (-.f64 (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 4 binary64))) (pow.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64))) (fma.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 6 binary64))) (pow.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64))) (+.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 4 binary64) (.f64 y y)) (pow.f64 (.f64 y (*.f64 #s(literal 2 binary64) x)) #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) y) #s(literal 2 binary64)) #s(literal 3 binary64))))
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(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 (neg.f64 y) y (.f64 (fma.f64 y #s(literal 2 binary64) x) x))))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 3 binary64)))) (fma.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) (pow.f64 y #s(literal 4 binary64)))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (fma.f64 (neg.f64 y) y (.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(neg.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 3 binary64))) (neg.f64 (fma.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) (pow.f64 y #s(literal 4 binary64))))))
(fma.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 y #s(literal 2 binary64) x) (pow.f64 x #s(literal 4 binary64))) (.f64 y y))
(fma.f64 (/.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (.f64 #s(literal 2 binary64) x)))) (.f64 y y))
(fma.f64 (/.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (.f64 #s(literal 2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (.f64 #s(literal 2 binary64) x))) (-.f64 (.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (.f64 y (.f64 #s(literal 2 binary64) x))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (*.f64 y y))
(fma.f64 (/.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 y y) (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (.f64 x x)) (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(fma.f64 (/.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (.f64 x x)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(fma.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (.f64 y y))
(fma.f64 (/.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) x) (/.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) (-.f64 x (.f64 y #s(literal 2 binary64)))) (*.f64 y y))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(fma.f64 (.f64 y x) #s(literal 2 binary64) (fma.f64 y y (.f64 x x)))
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
(fma.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (neg.f64 (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (.f64 y (-.f64 (.f64 #s(literal 2 binary64) x) y)) #s(literal -1 binary64)) (.f64 x x))
(fma.f64 (-.f64 (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (pow.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (*.f64 y y))
(fma.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 y y))
(fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (.f64 y y))
(fma.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (.f64 #s(literal 2 binary64) x) (pow.f64 y #s(literal 3 binary64))))) #s(literal -1 binary64)) (*.f64 x x))
(fma.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (pow.f64 (.f64 (neg.f64 x) (-.f64 x (.f64 y #s(literal 2 binary64)))) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (.f64 y #s(literal 2 binary64)) x (fma.f64 y y (.f64 x x)))
(fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (pow.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))) (.f64 y y))
(fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) (.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64))) (*.f64 y y))
(fma.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))) (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (*.f64 y y))
(fma.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (pow.f64 (fma.f64 (neg.f64 y) y (.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(fma.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (/.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x)) (.f64 y y))
(fma.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (/.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (fma.f64 (neg.f64 y) y (.f64 (fma.f64 y #s(literal 2 binary64) x) x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(fma.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) (pow.f64 (.f64 (-.f64 x (.f64 y #s(literal 2 binary64))) x) #s(literal -1 binary64))) (*.f64 y y))
(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x))
(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(fma.f64 y (.f64 #s(literal 2 binary64) x) (fma.f64 y y (.f64 x x)))
(fma.f64 (.f64 #s(literal 2 binary64) x) y (fma.f64 y y (.f64 x x)))
(fma.f64 #s(literal 2 binary64) (.f64 y x) (fma.f64 y y (.f64 x x)))
(fma.f64 x (fma.f64 y #s(literal 2 binary64) x) (*.f64 y y))
(fma.f64 x (.f64 y #s(literal 2 binary64)) (fma.f64 y y (.f64 x x)))
(fma.f64 x x (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(-.f64 (fma.f64 y y (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) x) (-.f64 x (.f64 y #s(literal 2 binary64))))) (/.f64 (/.f64 (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) x) (-.f64 x (.f64 y #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (.f64 y y) (.f64 (fma.f64 y #s(literal 2 binary64) x) x))) (/.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (-.f64 (.f64 y y) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 2 binary64) x y) y))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #s(literal 2 binary64)) (-.f64 (.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) x) (-.f64 x (.f64 y #s(literal 2 binary64)))) (-.f64 (/.f64 (/.f64 (pow.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)) x) (-.f64 x (.f64 y #s(literal 2 binary64)))) (*.f64 y y)))
(-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) y (.f64 (fma.f64 y #s(literal 2 binary64) x) x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (fma.f64 y y (.f64 x x)) (.f64 y (*.f64 #s(literal 2 binary64) x)))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (fma.f64 (neg.f64 y) y (.f64 (fma.f64 y #s(literal 2 binary64) x) x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))))
(+.f64 (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (.f64 x x))
(+.f64 (.f64 y y) (.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(+.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) (.f64 y y))
(+.f64 (.f64 y (.f64 #s(literal 2 binary64) x)) (fma.f64 y y (*.f64 x x)))
(+.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 2 binary64) x y) y))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(.f64 (.f64 y x) #s(literal 2 binary64))
(.f64 (.f64 y #s(literal 2 binary64)) x)
(.f64 y (.f64 #s(literal 2 binary64) x))
(.f64 (.f64 #s(literal 2 binary64) x) y)
(.f64 #s(literal 2 binary64) (.f64 y x))
(.f64 x (.f64 y #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))

eval24.0ms (0.6%)

Memory: 7.4MiB live, 43.6MiB allocated
Compiler: Compiled 6 527 to 649 computations (90.1% saved)

prune10.0ms (0.2%)

Memory

-34.1MiB live, 14.1MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	213	4	217
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	214	4	218

Accuracy

100.0%

Counts

218 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
▶	100.0%	(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
▶	57.1%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
▶	57.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 55 to 36 computations (34.5% saved)

simplify4.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	92
0	28	92
1	43	84
2	56	84
3	59	84
0	59	84

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize74.0ms (1.7%)

Memory

29.1MiB live, 64.7MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y #s(literal 2 binary64) x)
accuracy	0	(*.f64 y y)
accuracy	0.015625	(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0.015625	(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
accuracy	27.471987252609114	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
accuracy	0	(*.f64 y y)
accuracy	26.943025605146588	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Samples

63.0ms

256×

valid

Compiler

Compiled 183 to 38 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-add: 40.0ms (76.1% of total)

ival-mult: 12.0ms (22.8% of total)

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

exact: 0.0ms (0% of total)

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

series30.0ms (0.7%)

Memory

-23.8MiB live, 15.1MiB allocated

Counts

9 → 30

Calls

Call 1

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

Outputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
y
(+ y (* 2 x))
(pow x 2)
(* 2 y)
(+ x (* 2 y))
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* 2 (* x y))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* 2 x)
(* x (+ 2 (/ y x)))
x
(* x (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(* -1 (* x (- (* -2 (/ y x)) 1)))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* y (+ y (* 2 x)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 2 (/ x y))))
(* y (+ 2 (/ x y)))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (- (* -2 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 2)))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ (* 2 x) y) y) (* x x)) (* x x) (+ (* (+ (* y 2) x) x) (* y y)) (+ (* y 2) x))
1.0ms	x	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ (* 2 x) y) y) (* x x)) (* x x) (+ (* (+ (* y 2) x) x) (* y y)) (+ (* y 2) x))
1.0ms	x	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ (* 2 x) y) y) (* x x)) (* x x) (+ (* (+ (* y 2) x) x) (* y y)) (+ (* y 2) x))
1.0ms	y	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ (* 2 x) y) y) (* x x)) (* x x) (+ (* (+ (* y 2) x) x) (* y y)) (+ (* y 2) x))
1.0ms	x	@	0	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ (* 2 x) y) y) (* x x)) (* x x) (+ (* (+ (* y 2) x) x) (* y y)) (+ (* y 2) x))

simplify116.0ms (2.7%)

Memory

27.5MiB live, 142.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	192
1	248	192
2	662	192
3	2006	184
4	4583	184
5	7406	184
0	8165	155

Stop Event

1×	iter limit
1×	node limit

Counts

30 → 28

Calls

Call 1

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

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

rewrite333.0ms (7.7%)

Memory

-39.6MiB live, 268.9MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	75
0	28	75
1	112	67
2	968	67
0	8569	67

Stop Event

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

Counts

9 → 415

Calls

Call 1

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

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

eval89.0ms (2.1%)

Memory: 8.4MiB live, 82.0MiB allocated
Compiler: Compiled 9 608 to 910 computations (90.5% saved)

prune6.0ms (0.1%)

Memory

13.8MiB live, 13.8MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	339	3	342
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	339	7	346

Accuracy

100.0%

Counts

346 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
✓	100.0%	(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
▶	58.6%	(fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 y y))
▶	59.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	57.1%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
▶	17.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 #s(approx (+ ( 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
✓	57.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 114 to 75 computations (34.2% saved)

simplify19.0ms (0.4%)

Memory

-34.6MiB live, 4.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	114
0	32	114
1	47	108
2	64	108
3	68	108
0	68	103

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize53.0ms (1.2%)

Memory

0.3MiB live, 45.8MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 y #s(literal 2 binary64))
accuracy	0.015625	(fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 y y))
accuracy	31.464985088132163	#s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64)))
accuracy	0	(fma.f64 y #s(literal 2 binary64) x)
accuracy	0.00390625	(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
accuracy	26.087580323943005	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.015625	(.f64 #s(approx (+ ( 2 x) y) (*.f64 #s(literal 2 binary64) x)) y)
accuracy	27.471987252609114	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 #s(approx (+ ( 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
accuracy	31.763305897614764	#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))

Samples

27.0ms

256×

valid

Compiler

Compiled 202 to 43 computations (78.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 12.0ms (69.6% of total)

ival-add: 5.0ms (29% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

11 → 33

Calls

Call 1

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

Outputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
y
(+ y (* 2 x))
(* 2 x)
(* 2 (* x y))
(* x (+ x (* 2 y)))
(* 2 y)
(+ x (* 2 y))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* x (+ 2 (/ y x)))
x
(* x (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(* -1 (* x (- (* -2 (/ y x)) 1)))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* y (+ y (* 2 x)))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* 2 (/ x y))))
(* y (+ (* 2 x) (/ (pow x 2) y)))
(* y (+ 2 (/ x y)))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))
(* -1 (* y (- (* -2 (/ x y)) 1)))
(* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))
(* -1 (* y (- (* -1 (/ x y)) 2)))

Calls

6 calls:

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

simplify170.0ms (3.9%)

Memory

0.5MiB live, 157.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	205
1	269	205
2	745	205
3	2205	205
4	4641	205
5	7612	205
0	8080	173

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 31

Calls

Call 1

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

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

rewrite287.0ms (6.6%)

Memory

-3.2MiB live, 268.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	105
0	32	105
1	106	99
2	804	99
0	8688	94

Stop Event

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

Counts

11 → 173

Calls

Call 1

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

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 #s(approx (+ ( 2 x) y) (*.f64 #s(literal 2 binary64) x)) y))
(.f64 #s(approx (+ ( 2 x) y) (*.f64 #s(literal 2 binary64) x)) y)
(.f64 y #s(approx (+ ( 2 x) y) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(.f64 (/.f64 (.f64 (fma.f64 y #s(literal 2 binary64) x) x) x) (/.f64 (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64)))) (-.f64 x (*.f64 y #s(literal 2 binary64)))))
(.f64 (.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 (neg.f64 x) x)) x) (pow.f64 (-.f64 (*.f64 y #s(literal 2 binary64)) x) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x) (pow.f64 (fma.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))) (.f64 #s(literal 4 binary64) (*.f64 y y))) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 (neg.f64 x) x))) (pow.f64 (-.f64 (*.f64 y #s(literal 2 binary64)) x) #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))) (.f64 #s(literal 4 binary64) (*.f64 y y))) #s(literal -1 binary64)))
(.f64 (-.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x))))
(.f64 #s(literal 1 binary64) (.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) (-.f64 x (*.f64 y #s(literal 2 binary64))))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (pow.f64 x #s(literal 4 binary64))))))
(.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64))) (pow.f64 (.f64 x (-.f64 x (*.f64 y #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (*.f64 y #s(literal 2 binary64)))))))
(.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(*.f64 x (fma.f64 y #s(literal 2 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64)))))) (.f64 (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) (fma.f64 (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (*.f64 y #s(literal 2 binary64)))))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 (neg.f64 x) x)) x)) (neg.f64 (-.f64 (.f64 y #s(literal 2 binary64)) x)))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x)) (neg.f64 (fma.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))) (.f64 #s(literal 4 binary64) (.f64 y y)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 (neg.f64 x) x)))) (neg.f64 (-.f64 (.f64 y #s(literal 2 binary64)) x)))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (fma.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))) (.f64 #s(literal 4 binary64) (.f64 y y)))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64))))) (neg.f64 (.f64 (neg.f64 x) (-.f64 x (.f64 y #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64))) (fma.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (pow.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 #s(literal 4 binary64) (.f64 y y))))) (.f64 x (-.f64 x (*.f64 y #s(literal 2 binary64))))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 6 binary64))) (.f64 (pow.f64 x #s(literal 9 binary64)) (.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64))))) (fma.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64))) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))))) (.f64 (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64)))) (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)))) (pow.f64 (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64)))) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 (neg.f64 x) x)) x) (-.f64 (.f64 y #s(literal 2 binary64)) x))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))) (.f64 #s(literal 4 binary64) (.f64 y y))))
(/.f64 (.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 (neg.f64 x) x))) (-.f64 (.f64 y #s(literal 2 binary64)) x))
(/.f64 (.f64 x (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))) (.f64 #s(literal 4 binary64) (.f64 y y))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 y #s(literal 2 binary64)) x) (.f64 (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 (neg.f64 x) x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))) (.f64 #s(literal 4 binary64) (.f64 y y))) (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 y #s(literal 2 binary64)) x) (.f64 x (fma.f64 (.f64 #s(literal 4 binary64) y) y (.f64 (neg.f64 x) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x (.f64 y #s(literal 2 binary64))) (.f64 #s(literal 4 binary64) (.f64 y y))) (.f64 x (fma.f64 #s(literal 8 binary64) (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 (.f64 y #s(literal 2 binary64)) x)) (-.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))))) (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)))) (.f64 (neg.f64 x) (-.f64 x (.f64 y #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64))) (.f64 x (-.f64 x (.f64 y #s(literal 2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64))))))
(/.f64 (fma.f64 (pow.f64 (.f64 y x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (.f64 (.f64 y x) #s(literal 2 binary64)) (.f64 x (-.f64 (*.f64 y #s(literal 2 binary64)) x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y #s(literal 2 binary64) x)))
(neg.f64 (*.f64 (neg.f64 x) (fma.f64 y #s(literal 2 binary64) x)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) x) (/.f64 x (-.f64 x (.f64 y #s(literal 2 binary64)))) (neg.f64 (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (*.f64 y #s(literal 2 binary64)))))))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 (.f64 x x) (-.f64 x (.f64 y #s(literal 2 binary64)))) (neg.f64 (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (*.f64 y #s(literal 2 binary64)))))))
(fma.f64 (/.f64 x x) (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x (.f64 y #s(literal 2 binary64)))) (neg.f64 (/.f64 (.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) #s(literal 4 binary64)) (.f64 x (-.f64 x (*.f64 y #s(literal 2 binary64)))))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (.f64 (.f64 y x) #s(literal 2 binary64)))
(fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 x x))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 y y)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64))) (fma.f64 y y (.f64 (neg.f64 x) #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y (.f64 (neg.f64 x) #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))))) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 y y))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x) (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y)))) (+.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (*.f64 y #s(literal 2 binary64))) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 y y))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (fma.f64 (.f64 y y) (fma.f64 y y (.f64 (neg.f64 x) #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))))) (pow.f64 (.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 (neg.f64 x) #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))))) (pow.f64 (.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y))))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 (neg.f64 x) #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))))) (pow.f64 (.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
(neg.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y)))))
(neg.f64 (/.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64))) (neg.f64 (fma.f64 (.f64 y y) (fma.f64 y y (.f64 (neg.f64 x) #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))))) (pow.f64 (.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64))))))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (.f64 #s(approx (+ ( y 2) x) (*.f64 y #s(literal 2 binary64))) x))
(fma.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y)) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y)))))
(fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 y y))
(fma.f64 y y (.f64 #s(approx (+ ( y 2) x) (*.f64 y #s(literal 2 binary64))) x))
(fma.f64 x #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) (.f64 y y))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 (neg.f64 x) #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64)))))) (/.f64 (pow.f64 (.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)) (fma.f64 y y (.f64 (neg.f64 x) #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64)))))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)) (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) #s(literal 2 binary64)) (fma.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 (neg.f64 y) y)))))
(+.f64 (.f64 #s(approx (+ ( y 2) x) (.f64 y #s(literal 2 binary64))) x) (.f64 y y))
(+.f64 (.f64 y y) (.f64 #s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64))) x))
#s(approx (+ (* y 2) x) (*.f64 y #s(literal 2 binary64)))
(*.f64 y #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) y)
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval28.0ms (0.6%)

Memory: 0.3MiB live, 45.1MiB allocated
Compiler: Compiled 6 785 to 668 computations (90.2% saved)

prune5.0ms (0.1%)

Memory

23.5MiB live, 23.5MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	0	0
Picked	1	2	3
Done	0	4	4
Total	183	7	190

Accuracy

100.0%

Counts

190 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
✓	100.0%	(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
✓	58.6%	(fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 y y))
✓	59.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	57.1%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
✓	57.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
▶	56.4%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 106 to 70 computations (34% saved)

simplify4.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
0	12	21
1	20	19
2	40	19
3	48	19
0	48	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize26.0ms (0.6%)

Memory

-6.7MiB live, 65.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(*.f64 x x)
accuracy	27.921733345287635	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Samples

21.0ms

256×

valid

Compiler

Compiled 40 to 22 computations (45% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 6.0ms (67.1% of total)

ival-add: 2.0ms (22.4% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

2 → 12

Calls

Call 1

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

Outputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(+ (* 2 (* x y)) (pow x 2))
(+ (* y (+ y (* 2 x))) (pow x 2))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))

Calls

6 calls:

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

simplify120.0ms (2.8%)

Memory

2.5MiB live, 126.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	108
1	144	108
2	385	108
3	1133	108
4	2655	100
5	4932	100
0	8448	84

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 12

Calls

Call 1

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

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

rewrite204.0ms (4.7%)

Memory

-5.0MiB live, 214.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
0	12	20
1	47	18
2	417	18
3	6330	18
0	8192	16

Stop Event

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

Counts

2 → 9

Calls

Call 1

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

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval1.0ms (0%)

Memory: 6.0MiB live, 6.0MiB allocated
Compiler: Compiled 272 to 45 computations (83.5% saved)

prune4.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	14	7	21

Accuracy

100.0%

Counts

21 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
✓	100.0%	(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
✓	58.6%	(fma.f64 #s(approx (+ (* y 2) x) (.f64 y #s(literal 2 binary64))) x (.f64 y y))
✓	59.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	57.1%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
✓	57.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
✓	56.4%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 250 to 107 computations (57.2% saved)

regimes101.0ms (2.3%)

Memory

-25.0MiB live, 49.8MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

50.0ms	y
47.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
3.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes100.0ms (2.3%)

Memory

-19.7MiB live, 15.3MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

3 calls:

94.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
91.7%	2	`x`
87.7%	2	`y`
64.4%	3	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes2.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
91.7%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes4.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

1.0ms	x
1.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
1.0ms	y

Results

Accuracy	Segments	Branch
56.4%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
56.4%	1	`y`
56.4%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch23.0ms (0.5%)

Memory

-1.8MiB live, 33.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
21.0ms	-3.4353986199433645e-68	-9.213032205676622e-76

Samples

16.0ms

144×

valid

Compiler

Compiled 349 to 248 computations (28.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 12.0ms (92.5% of total)

ival-add: 1.0ms (7.7% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-3.4353986199433645e-68	-9.213032205676622e-76

Compiler

Compiled 322 to 230 computations (28.6% saved)

simplify29.0ms (0.7%)

Memory

-26.7MiB live, 59.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	105
1	22	105

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(if (<=.f64 x #s(literal -8256342791959349/242833611528216133864932738352939863330300854881517440156476551217363035650651062272 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 x #s(literal -8256342791959349/242833611528216133864932738352939863330300854881517440156476551217363035650651062272 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Outputs
(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))
(if (<=.f64 x #s(literal -8256342791959349/242833611528216133864932738352939863330300854881517440156476551217363035650651062272 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 x #s(literal -8256342791959349/242833611528216133864932738352939863330300854881517440156476551217363035650651062272 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

soundness918.0ms (21.2%)

Memory

17.5MiB live, 445.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	205
1	269	205
2	745	205
3	2205	205
4	4641	205
5	7612	205
0	8080	173
0	9	33
0	15	33
1	50	29
2	420	29
3	6357	29
0	8219	26
0	56	129
1	166	129
2	468	129
3	1326	129
4	3270	129
5	6410	129
0	8142	110
0	78	192
1	248	192
2	662	192
3	2006	184
4	4583	184
5	7406	184
0	8165	155

Stop Event

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

Compiler

Compiled 139 to 59 computations (57.6% saved)

preprocess77.0ms (1.8%)

Memory: 12.1MiB live, 100.1MiB allocated
Compiler: Compiled 280 to 92 computations (67.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample801.0ms (18.5%)

explain163.0ms (3.8%)

preprocess47.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize90.0ms (2.1%)

series9.0ms (0.2%)

simplify121.0ms (2.8%)

rewrite230.0ms (5.3%)

eval24.0ms (0.6%)

prune10.0ms (0.2%)

simplify4.0ms (0.1%)

localize74.0ms (1.7%)

series30.0ms (0.7%)

simplify116.0ms (2.7%)

rewrite333.0ms (7.7%)

eval89.0ms (2.1%)

prune6.0ms (0.1%)

simplify19.0ms (0.4%)

localize53.0ms (1.2%)

series6.0ms (0.1%)

simplify170.0ms (3.9%)

rewrite287.0ms (6.6%)

eval28.0ms (0.6%)

prune5.0ms (0.1%)

simplify4.0ms (0.1%)

localize26.0ms (0.6%)

series2.0ms (0%)

simplify120.0ms (2.8%)

rewrite204.0ms (4.7%)

eval1.0ms (0%)

prune4.0ms (0.1%)

regimes101.0ms (2.3%)

regimes100.0ms (2.3%)

regimes2.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch23.0ms (0.5%)

bsearch1.0ms (0%)

simplify29.0ms (0.7%)

soundness918.0ms (21.2%)

preprocess77.0ms (1.8%)

end0.0ms (0%)

Profiling