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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

1.2MiB live, 1.2MiB 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)

sample1.3s (29.7%)

Memory

60.2MiB live, 1 657.5MiB allocated

Samples

977.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 630.0ms

ival-mult: 459.0ms (72.8% of total)

ival-add: 156.0ms (24.8% of total)

ival-true: 7.0ms (1.1% of total)

exact: 5.0ms (0.8% of total)

ival-assert: 4.0ms (0.6% of total)

Bogosity

explain130.0ms (2.9%)

Memory

5.1MiB live, 295.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
10	-	-	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`
7	-	-	`(+.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	10	0
↳	`(*.f64 x x)`	overflow	60
↳	`(.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	7	0
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	overflow	70
↳	`(*.f64 x x)`	overflow	60
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	35
↳	`(*.f64 y y)`	overflow	63

Confusion

	Predicted +	Predicted -
+	13	0
-	0	243

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	13	0	0
-	0	0	243

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	243
1	9
2	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms

512×

valid

Compiler

Compiled 95 to 31 computations (67.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 13.0ms (69.8% of total)

ival-add: 4.0ms (21.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess186.0ms (4.2%)

Memory

-28.3MiB live, 167.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	71
1	95	57
2	314	57
3	611	55
4	1031	55
5	1555	35
6	2248	35
7	3008	35
8	3674	35
9	3996	35
10	4004	35
11	4004	35
12	4046	35
13	4088	35
14	4102	35
0	9	13
0	15	13
1	38	11
2	127	11
3	330	11
4	634	11
5	971	7
6	1297	7
7	1855	7
8	2503	7
9	2794	7
10	3048	7
11	3066	7
0	3066	7

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

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
▶	94.9%	(+.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)

simplify61.0ms (1.4%)

Memory

29.6MiB live, 76.2MiB 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	3	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
cost-diff	3	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	15	39
1	38	35
2	127	35
3	330	35
4	634	35
5	971	31
6	1297	31
7	1855	31
8	2503	31
9	2794	31
10	3048	31
11	3066	31
0	3066	30

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

localize44.0ms (1%)

Memory

3.3MiB live, 48.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	1.4062500000000002	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
accuracy	2.707018864981235	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Samples

37.0ms

256×

valid

Compiler

Compiled 41 to 11 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 25.0ms (90.5% of total)

ival-add: 2.0ms (7.2% of total)

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

exact: 0.0ms (0% of total)

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

series60.0ms (1.3%)

Memory

-31.7MiB live, 23.4MiB allocated

Counts

5 → 17

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

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

Calls

6 calls:

Time	Variable		Point	Expression
48.0ms	y	@	0	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))
6.0ms	y	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))
2.0ms	x	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	x	@	0	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	x	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))

simplify187.0ms (4.2%)

Memory

2.6MiB live, 233.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	177
1	194	169
2	746	157
3	3571	149
0	8118	140

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 17

Calls

Call 1

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

rewrite241.0ms (5.4%)

Memory

38.7MiB live, 270.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
0	15	33
1	65	29
2	568	29
0	9286	26

Stop Event

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

Counts

5 → 255

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

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

eval96.0ms (2.2%)

Memory: -43.3MiB live, 60.5MiB allocated
Compiler: Compiled 8 056 to 793 computations (90.2% saved)

prune4.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	264	4	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	4	269

Accuracy

100.0%

Counts

269 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.8%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
▶	59.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
▶	100.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
▶	56.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 78 to 49 computations (37.2% saved)

simplify65.0ms (1.5%)

Memory

22.1MiB live, 67.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	120
0	29	120
1	70	108
2	197	96
3	539	96
4	936	96
5	1235	96
6	1736	96
7	2386	96
8	2734	96
9	2986	96
10	3072	96
0	3072	96

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

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

localize85.0ms (1.9%)

Memory

-5.1MiB live, 79.2MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 #s(literal 2 binary64) y x)
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
accuracy	27.000931378430753	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
accuracy	0.0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0.015625	(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
accuracy	26.257878302300007	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
accuracy	0.0	(+.f64 y x)
accuracy	0.0	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
accuracy	0.0078125	(*.f64 (+.f64 y x) (+.f64 y x))
accuracy	0.0	(*.f64 y y)
accuracy	27.688688427350236	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Samples

70.0ms

256×

valid

Compiler

Compiled 100 to 19 computations (81% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 13.0ms (58.8% of total)

ival-add: 8.0ms (36.2% 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

18.5MiB live, 18.5MiB allocated

Counts

11 → 38

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

Outputs
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* x (+ x (* 2 y))) (pow y 2))
y
(+ x y)
(+ y (* 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
(* x (+ 1 (/ y x)))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* 2 x)
(* x (+ 2 (/ y x)))
(* x (+ 1 (* 2 (/ y x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -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 (/ x y)))
(* 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 (- (* -1 (/ x y)) 1)))
(* -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
2.0ms	y	@	0	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))
1.0ms	y	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))
1.0ms	x	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))
1.0ms	y	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))
1.0ms	x	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))

simplify277.0ms (6.2%)

Memory

-27.8MiB live, 237.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	326
1	317	318
2	1075	302
3	4184	302
0	8302	282

Stop Event

1×	iter limit
1×	node limit

Counts

38 → 36

Calls

Call 1

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

rewrite272.0ms (6.1%)

Memory

-3.9MiB live, 372.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	111
0	29	107
1	128	95
2	1095	95
0	8678	91

Stop Event

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

Counts

11 → 573

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

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

eval183.0ms (4.1%)

Memory: -5.8MiB live, 242.1MiB allocated
Compiler: Compiled 26 155 to 2 342 computations (91% saved)

prune24.0ms (0.5%)

Memory

4.0MiB live, 48.7MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	683	1	684
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	683	5	688

Accuracy

100.0%

Counts

688 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.8%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
✓	59.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
✓	100.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
✓	56.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
▶	57.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 95 to 60 computations (36.8% saved)

simplify68.0ms (1.5%)

Memory

-16.2MiB live, 83.8MiB 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: 5 (0.0ms)

Iter	Nodes	Cost
0	11	21
0	12	21
1	35	19
2	124	19
3	327	19
4	628	19
5	962	15
6	1286	15
7	1844	15
8	2492	15
9	2783	15
10	3037	15
11	3055	15
0	3055	15

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

localize23.0ms (0.5%)

Memory

11.2MiB live, 55.9MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x x)
accuracy	27.41225195252607	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Samples

18.0ms

256×

valid

Compiler

Compiled 19 to 11 computations (42.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 7.0ms (59.6% of total)

ival-add: 4.0ms (34.1% 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

6.7MiB live, 6.7MiB 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	@	0	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x))

simplify200.0ms (4.5%)

Memory

16.8MiB live, 244.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	142
1	172	132
2	641	124
3	3245	116
0	8105	108

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

rewrite133.0ms (3%)

Memory

-19.9MiB live, 219.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
0	12	20
1	62	18
2	565	18
0	9262	16

Stop Event

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

Counts

2 → 15

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 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval3.0ms (0.1%)

Memory: 9.1MiB live, 9.1MiB allocated
Compiler: Compiled 488 to 84 computations (82.8% saved)

prune3.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	24	5	29

Accuracy

100.0%

Counts

29 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.8%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
✓	59.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
✓	100.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
✓	56.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
✓	57.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 203 to 87 computations (57.1% saved)

regimes61.0ms (1.4%)

Memory

-39.2MiB live, 72.1MiB allocated

Counts

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

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

Calls

3 calls:

56.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
2.0ms	x
2.0ms	y

Results

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

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes4.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated

Counts

2 → 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))

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

3 calls:

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

Results

Accuracy	Segments	Branch
60.2%	2	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
90.4%	2	`x`
87.0%	2	`y`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes4.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB 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	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
57.2%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
57.2%	1	`y`
57.2%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch14.0ms (0.3%)

Memory

-11.1MiB live, 34.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-7.275959239544354e-92	-6.556025671364147e-94

Samples

9.0ms

112×

valid

Compiler

Compiled 254 to 182 computations (28.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 3.0ms (69.7% of total)

ival-add: 1.0ms (23.2% of total)

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

exact: 0.0ms (0% of total)

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

simplify54.0ms (1.2%)

Memory

0.8MiB live, 45.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	19	76
1	42	68
2	130	68
3	338	68
4	661	68
5	1019	52
6	1497	52
7	3848	52
8	6120	52

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

(if (<=.f64 x #s(literal -160544903119305/2293498615990071511610820895302086940796564989168281123737588839386922876088484808070018553110125686554624 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

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

(if (<=.f64 x #s(literal -160544903119305/2293498615990071511610820895302086940796564989168281123737588839386922876088484808070018553110125686554624 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))

soundness533.0ms (12%)

Memory

-3.0MiB live, 367.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	326
1	317	318
2	1075	302
3	4184	302
0	8302	282
0	56	177
1	194	169
2	746	157
3	3571	149
0	8118	140

Stop Event

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

Compiler

Compiled 98 to 38 computations (61.2% saved)

preprocess108.0ms (2.4%)

Memory: 47.8MiB live, 139.1MiB allocated
Remove: (sort x y)
Compiler: Compiled 246 to 98 computations (60.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.3s (29.7%)

explain130.0ms (2.9%)

preprocess186.0ms (4.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify61.0ms (1.4%)

localize44.0ms (1%)

series60.0ms (1.3%)

simplify187.0ms (4.2%)

rewrite241.0ms (5.4%)

eval96.0ms (2.2%)

prune4.0ms (0.1%)

simplify65.0ms (1.5%)

localize85.0ms (1.9%)

series9.0ms (0.2%)

simplify277.0ms (6.2%)

rewrite272.0ms (6.1%)

eval183.0ms (4.1%)

prune24.0ms (0.5%)

simplify68.0ms (1.5%)

localize23.0ms (0.5%)

series2.0ms (0%)

simplify200.0ms (4.5%)

rewrite133.0ms (3%)

eval3.0ms (0.1%)

prune3.0ms (0.1%)

regimes61.0ms (1.4%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch14.0ms (0.3%)

simplify54.0ms (1.2%)

soundness533.0ms (12%)

preprocess108.0ms (2.4%)

end0.0ms (0%)

Profiling