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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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)

sample1.1s (16.2%)

Memory

-10.1MiB live, 1 052.8MiB allocated

Samples

841.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 551.0ms

ival-mult: 414.0ms (75.1% of total)

ival-add: 123.0ms (22.3% of total)

ival-true: 6.0ms (1.1% of total)

exact: 5.0ms (0.9% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain140.0ms (2.1%)

Memory

-6.8MiB live, 205.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
12	-	-	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`
10	-	-	`(+.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	12	0
↳	`(*.f64 x x)`	overflow	60
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	26
`+.f64`	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`	nan-rescue	10	0
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	overflow	65
↳	`(*.f64 x x)`	overflow	60
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	26
↳	`(*.f64 y y)`	overflow	66

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	10
2	6

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

40.0ms

512×

valid

Compiler

Compiled 134 to 40 computations (70.1% saved)

Precisions

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

ival-mult: 13.0ms (71.1% of total)

ival-add: 4.0ms (21.9% of total)

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

exact: 0.0ms (0% of total)

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

preprocess379.0ms (5.6%)

Memory

6.8MiB live, 234.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	71
1	109	57
2	371	55
3	1231	55
4	2630	55
5	3603	35
6	3930	35
7	5808	35
8	6416	35
9	6870	35
0	9	13
0	15	13
1	40	11
2	141	11
3	460	11
4	1553	11
5	2724	7
6	3291	7
7	5174	7
8	5768	7
9	6220	7
10	6766	7
0	8448	7

Stop Event

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

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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.5MiB live, 1.4MiB 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)

simplify304.0ms (4.5%)

Memory

19.8MiB live, 179.6MiB 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	448	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
cost-diff	512	(+.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	40	35
2	141	35
3	460	35
4	1553	35
5	2724	31
6	3291	31
7	5174	31
8	5768	31
9	6220	31
10	6766	31
0	8448	30

Stop Event

1×	iter limit
1×	node limit
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)

localize33.0ms (0.5%)

Memory

-5.7MiB live, 32.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	1.5976562500000002	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
accuracy	2.6132729933208236	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Samples

26.0ms

256×

valid

Compiler

Compiled 80 to 20 computations (75% saved)

Precisions

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

ival-mult: 7.0ms (76% of total)

ival-add: 2.0ms (21.7% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

13.9MiB live, 13.9MiB 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
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	y	@	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))
1.0ms	y	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))

simplify206.0ms (3%)

Memory

6.9MiB live, 163.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	169
1	194	161
2	736	153
3	3310	141
0	8231	130

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

rewrite289.0ms (4.2%)

Memory

-21.7MiB live, 194.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
0	15	33
1	67	29
2	609	29
0	9606	26

Stop Event

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

Counts

5 → 515

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

eval171.0ms (2.5%)

Memory: 16.8MiB live, 122.7MiB allocated
Compiler: Compiled 11 007 to 1 180 computations (89.3% saved)

prune58.0ms (0.8%)

Memory

-25.2MiB live, 24.9MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	522	5	527
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	523	5	528

Accuracy

100.0%

Counts

528 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x))
▶	59.8%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
▶	53.4%	#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)))
▶	54.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 174 to 110 computations (36.8% saved)

simplify226.0ms (3.3%)

Memory

8.5MiB live, 168.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	-6208	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 #s(literal 2 binary64) x y)
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 y)
cost-diff	0	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
cost-diff	-6592	(*.f64 (+.f64 y x) (+.f64 y x))
cost-diff	0	(+.f64 y x)
cost-diff	0	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	139
0	34	121
1	84	121
2	238	113
3	796	113
4	3077	106
5	4880	106
6	7042	106
0	8077	106

Stop Event

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

Calls

Call 1

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

Outputs
#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)) (sqrt.f64 (pow.f64 (+.f64 y x) #s(literal 4 binary64))))
(*.f64 (+.f64 y x) (+.f64 y x))
(sqrt.f64 (pow.f64 (+.f64 y x) #s(literal 4 binary64)))
(+.f64 y x)
y
x
#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
#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
(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x))
(sqrt.f64 (pow.f64 (+.f64 y x) #s(literal 4 binary64)))
y
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
x
(*.f64 x x)

localize124.0ms (1.8%)

Memory

-8.9MiB live, 66.5MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x))
accuracy	0	(fma.f64 #s(literal 2 binary64) y x)
accuracy	0.00390625	(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
accuracy	25.755090463211555	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
accuracy	29.797868046047412	#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	29.297514030473476	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
accuracy	0	(+.f64 y x)
accuracy	0	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
accuracy	0.01171875	(*.f64 (+.f64 y x) (+.f64 y x))

Samples

113.0ms

256×

valid

Compiler

Compiled 261 to 44 computations (83.1% saved)

Precisions

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

ival-mult: 15.0ms (68.8% of total)

ival-add: 6.0ms (27.5% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

13 → 38

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(+.f64 y x)
(*.f64 (+.f64 y x) (+.f64 y x))
#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)
#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)
(*.f64 x x)
(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x 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 x) (* (+ y x) (+ y x)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* 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) (* x x) (+ (* y (+ (* 2 x) y)) (* x x)))
2.0ms	x	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ y x) (* (+ y x) (+ y x)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* 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) (* x x) (+ (* y (+ (* 2 x) y)) (* x x)))
1.0ms	y	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ y x) (* (+ y x) (+ y x)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* 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) (* x x) (+ (* y (+ (* 2 x) y)) (* x x)))
1.0ms	x	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ y x) (* (+ y x) (+ y x)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* 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) (* x x) (+ (* y (+ (* 2 x) y)) (* x x)))
1.0ms	y	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ y x) (* (+ y x) (+ y x)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* 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) (* x x) (+ (* y (+ (* 2 x) y)) (* x x)))

simplify196.0ms (2.9%)

Memory

3.7MiB live, 206.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	220
1	324	220
2	1105	220
3	4315	196
0	8801	176

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

rewrite327.0ms (4.8%)

Memory

-27.5MiB live, 252.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	123
0	34	103
1	152	103
2	1345	103
0	9131	103

Stop Event

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

Counts

13 → 1 116

Calls

Call 1

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

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (+.f64 y x)))
(.f64 (pow.f64 (.f64 (-.f64 y x) (+.f64 y x)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 (pow.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 x x (.f64 (neg.f64 y) y)) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(*.f64 #s(literal -1 binary64) (+.f64 y x))
(.f64 (neg.f64 (.f64 (-.f64 y x) (+.f64 y x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 y x))))
(.f64 (neg.f64 (.f64 (-.f64 y x) (+.f64 y x))) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))
(.f64 (neg.f64 (-.f64 (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 y) (.f64 y y)))))
(.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) #s(literal -1 binary64)))
(.f64 (fabs.f64 (fma.f64 x x (.f64 (neg.f64 y) y))) (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 x y))))
(.f64 (fabs.f64 (fma.f64 x x (.f64 (neg.f64 y) y))) (fabs.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64))))
(.f64 (fabs.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fabs.f64 (fma.f64 x (-.f64 x y) (.f64 y y)))))
(.f64 (fabs.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fabs.f64 (pow.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) #s(literal -1 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 y x))
(.f64 (.f64 (-.f64 y x) (+.f64 y x)) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 y x))))
(.f64 (.f64 (-.f64 y x) (+.f64 y x)) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))
(.f64 (-.f64 (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 y) (*.f64 y x)))))
(.f64 (-.f64 (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 y) (.f64 y y)))))
(.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (+.f64 y x) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 y y) (-.f64 y x))) (.f64 (/.f64 (.f64 x x) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)))) (+.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y)))) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))))) (-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 y x) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (+.f64 y x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 y y) (-.f64 y x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 y x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 y y) (-.f64 y x)) (fma.f64 (/.f64 (.f64 x x) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)) (.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (*.f64 x x) (-.f64 y x))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y)))) (.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y)))))))
(/.f64 (neg.f64 (fma.f64 x x (*.f64 (neg.f64 y) y))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (fabs.f64 (fma.f64 x x (*.f64 (neg.f64 y) y)))) (neg.f64 (fabs.f64 (-.f64 x y))))
(/.f64 (neg.f64 (fabs.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (fabs.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x)))) (neg.f64 (neg.f64 (-.f64 y x))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x)))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(/.f64 (neg.f64 (neg.f64 (-.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 (-.f64 (.f64 (.f64 y y) (-.f64 y x)) (.f64 (-.f64 y x) (.f64 x x))) (pow.f64 (-.f64 y x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y)) (.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 y x) (+.f64 y x)) (+.f64 y x))) (sqrt.f64 (-.f64 y x)))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 y x))) (sqrt.f64 (fma.f64 x (-.f64 x y) (.f64 y y))))
(/.f64 (sqrt.f64 (.f64 (+.f64 y x) (.f64 (-.f64 y x) (+.f64 y x)))) (sqrt.f64 (-.f64 y x)))
(/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 x (-.f64 x y) (.f64 y y))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 (+.f64 y x) y) #s(literal 2 binary64)) (pow.f64 (.f64 (+.f64 y x) x) #s(literal 2 binary64)))) (+.f64 y x))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (.f64 (+.f64 y x) y) #s(literal 3 binary64)) (pow.f64 (.f64 (+.f64 y x) x) #s(literal 3 binary64)))) (sqrt.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 (sqrt.f64 (.f64 (.f64 (-.f64 y x) (+.f64 y x)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (.f64 (-.f64 y x) (fma.f64 x (-.f64 x y) (.f64 y y)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (-.f64 y x) (+.f64 y x)))) (sqrt.f64 (.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) (-.f64 y x))))
(/.f64 (fma.f64 x x (*.f64 (neg.f64 y) y)) (-.f64 (neg.f64 x) (neg.f64 y)))
(/.f64 (fma.f64 x x (*.f64 (neg.f64 y) y)) (-.f64 x y))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x)))
(/.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))) (neg.f64 (neg.f64 (-.f64 y x))))
(/.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x))) (-.f64 y x))
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (.f64 y y) (.f64 y x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)))))
(/.f64 (neg.f64 (-.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 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x y) (*.f64 y y)))
(/.f64 (fabs.f64 (fma.f64 x x (*.f64 (neg.f64 y) y))) (fabs.f64 (-.f64 x y)))
(/.f64 (fabs.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fabs.f64 (fma.f64 x x (-.f64 (.f64 y y) (.f64 y x)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fabs.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (fma.f64 x x (*.f64 (neg.f64 y) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 (.f64 y y) (.f64 y x))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (-.f64 x y)) (fabs.f64 (fma.f64 x x (*.f64 (neg.f64 y) y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fabs.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))) (fabs.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (neg.f64 (*.f64 (-.f64 y x) (+.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (-.f64 x y) (*.f64 y y)) (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (-.f64 y x)) (*.f64 (-.f64 y x) (+.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (fma.f64 x (-.f64 x y) (*.f64 y y))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x)))
(/.f64 (*.f64 (-.f64 y x) (+.f64 y x)) (neg.f64 (-.f64 y x)))
(/.f64 (*.f64 (-.f64 y x) (+.f64 y x)) (-.f64 y x))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y y (fma.f64 x x (*.f64 y (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 y y (-.f64 (.f64 x x) (.f64 (neg.f64 y) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 y y) (.f64 (neg.f64 x) (neg.f64 y)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 y y) (.f64 y x))))
(/.f64 (-.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 (-.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 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (+.f64 y x))
(neg.f64 (+.f64 y x))
(fma.f64 (sqrt.f64 (neg.f64 y)) (sqrt.f64 (neg.f64 y)) x)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) x)
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) y)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) y)
(fma.f64 #s(literal -1 binary64) (neg.f64 y) x)
(fma.f64 #s(literal -1 binary64) (neg.f64 x) y)
(fma.f64 #s(literal -1 binary64) y (neg.f64 x))
(fma.f64 #s(literal -1 binary64) x (neg.f64 y))
(fma.f64 #s(literal 1 binary64) y x)
(fma.f64 #s(literal 1 binary64) x y)
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x (-.f64 x y) (.f64 y y)) #s(literal -1 binary64)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x (-.f64 x y) (.f64 y y))))
(fma.f64 (.f64 y y) (pow.f64 (-.f64 y x) #s(literal -1 binary64)) (neg.f64 (/.f64 (.f64 x x) (-.f64 y x))))
(fma.f64 (.f64 y y) (pow.f64 (-.f64 y x) #s(literal -1 binary64)) (/.f64 (.f64 (neg.f64 x) x) (-.f64 y x)))
(sqrt.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))
(-.f64 (/.f64 (.f64 y y) (neg.f64 (-.f64 y x))) (/.f64 (.f64 x x) (neg.f64 (-.f64 y x))))
(-.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)))
(-.f64 #s(literal 0 binary64) (+.f64 y x))
(-.f64 (neg.f64 y) x)
(-.f64 (neg.f64 x) y)
(-.f64 y (neg.f64 x))
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(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 3 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) y) y)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 2 binary64)) (.f64 (.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x x) x) y) y)))))
(+.f64 (fma.f64 y y (.f64 x x)) (.f64 (*.f64 y x) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 x x) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (.f64 (neg.f64 y) y)) (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x y) y) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x y) y) #s(literal 3 binary64)) (fma.f64 (.f64 x x) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (.f64 (neg.f64 y) y)) (pow.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x y) y) #s(literal 2 binary64)))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x y) y) #s(literal 3 binary64)) (fma.f64 (.f64 x x) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (.f64 (neg.f64 y) y)) (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x y) y) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 x x) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (.f64 (neg.f64 y) y)) (pow.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x y) y) #s(literal 2 binary64)))))
(+.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (neg.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x))) (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 3 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (neg.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x))) (pow.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 2 binary64)))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 3 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (neg.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x))) (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 2 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (neg.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x))) (pow.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 2 binary64)))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x y) y) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -2 binary64) x y) y (.f64 (neg.f64 x) x))) (neg.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal -2 binary64) x y) y (*.f64 (neg.f64 x) x)))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x y) y) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -2 binary64) x y) y (.f64 (neg.f64 x) x))) (/.f64 (.f64 (.f64 (neg.f64 x) x) (.f64 x x)) (fma.f64 (fma.f64 #s(literal -2 binary64) x y) y (.f64 (neg.f64 x) x))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x y) y) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -2 binary64) x y) y (.f64 (neg.f64 x) x))) (/.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))) (fma.f64 (fma.f64 #s(literal -2 binary64) x y) y (*.f64 (neg.f64 x) x))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (.f64 (neg.f64 y) y))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (*.f64 (neg.f64 y) y)))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (.f64 (neg.f64 y) y))) (/.f64 (.f64 (.f64 (neg.f64 y) y) (.f64 y y)) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (.f64 (neg.f64 y) y))))
(+.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (.f64 (neg.f64 y) y))) (/.f64 (neg.f64 (pow.f64 y #s(literal 4 binary64))) (fma.f64 (fma.f64 #s(literal -2 binary64) x x) x (*.f64 (neg.f64 y) y))))
(+.f64 (.f64 (fma.f64 #s(literal -2 binary64) x x) x) (.f64 y y))
(+.f64 (.f64 (fma.f64 #s(literal -2 binary64) x y) y) (.f64 x x))
(+.f64 (.f64 x x) (neg.f64 (.f64 (neg.f64 (fma.f64 #s(literal -2 binary64) x y)) y)))
(+.f64 (.f64 x x) (neg.f64 (.f64 (neg.f64 y) (fma.f64 #s(literal -2 binary64) x y))))
(+.f64 (.f64 x x) (neg.f64 (fma.f64 (.f64 y x) #s(literal 2 binary64) (*.f64 (neg.f64 y) y))))
(+.f64 (.f64 x x) (.f64 (fma.f64 #s(literal -2 binary64) x y) y))
(+.f64 (.f64 y y) (.f64 (fma.f64 #s(literal -2 binary64) x x) x))
(+.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)))

eval407.0ms (6%)

Memory: 13.5MiB live, 366.8MiB allocated
Compiler: Compiled 44 526 to 3 820 computations (91.4% saved)

prune93.0ms (1.4%)

Memory

10.6MiB live, 92.8MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1 392	2	1 394
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	1 393	6	1 399

Accuracy

100.0%

Counts

1 399 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.3%	(fma.f64 y #s(approx (+ (* 2 x) y) (.f64 #s(literal 2 binary64) x)) (.f64 x x))
✓	59.8%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
✓	53.4%	#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)))
▶	13.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 #s(approx (+ ( 2 y) x) (*.f64 y #s(literal 2 binary64))) x))
✓	54.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 117 to 75 computations (35.9% saved)

simplify241.0ms (3.5%)

Memory

-3.2MiB live, 118.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	83
0	27	83
1	62	81
2	183	81
3	593	81
4	1799	77
5	2907	77
6	3441	77
7	5333	77
8	5957	77
9	6422	77
10	6929	77
11	7347	77
12	7852	77
0	8013	72

Stop Event

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

Calls

Call 1

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

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

localize74.0ms (1.1%)

Memory

1.6MiB live, 78.7MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.01171875	(fma.f64 y #s(approx (+ (* 2 x) y) (.f64 #s(literal 2 binary64) x)) (.f64 x x))
accuracy	29.262971838516954	#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))
accuracy	0	(*.f64 y #s(literal 2 binary64))
accuracy	0.00390625	(.f64 #s(approx (+ ( 2 y) x) (*.f64 y #s(literal 2 binary64))) x)
accuracy	25.755090463211555	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 #s(approx (+ ( 2 y) x) (*.f64 y #s(literal 2 binary64))) x))
accuracy	33.977292046455844	#s(approx (+ (* 2 y) x) (*.f64 y #s(literal 2 binary64)))

Samples

65.0ms

256×

valid

Compiler

Compiled 141 to 41 computations (70.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-add: 42.0ms (75.3% of total)

ival-mult: 13.0ms (23.3% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

8 → 30

Calls

Call 1

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

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

Calls

6 calls:

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

simplify163.0ms (2.4%)

Memory

-23.4MiB live, 171.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	184
1	274	184
2	940	184
3	3927	160
0	8639	143

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

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

rewrite208.0ms (3.1%)

Memory

-3.5MiB live, 251.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	77
0	27	77
1	121	75
2	1085	75
0	9506	68

Stop Event

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

Counts

8 → 411

Calls

Call 1

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

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

eval36.0ms (0.5%)

Memory: 2.0MiB live, 75.4MiB allocated
Compiler: Compiled 9 592 to 1 004 computations (89.5% saved)

prune6.0ms (0.1%)

Memory

25.3MiB live, 25.4MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	278	6	284

Accuracy

100.0%

Counts

284 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.3%	(fma.f64 y #s(approx (+ (* 2 x) y) (.f64 #s(literal 2 binary64) x)) (.f64 x x))
✓	59.8%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
✓	53.4%	#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)))
▶	39.5%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 #s(approx (+ ( 2 y) x) (+.f64 x x)) x))
✓	54.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 117 to 74 computations (36.8% saved)

simplify184.0ms (2.7%)

Memory

4.9MiB live, 124.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	49
0	17	49
1	46	47
2	152	47
3	538	47
4	1665	43
5	2739	43
6	3290	43
7	5178	43
8	5802	43
9	6293	43
10	6800	43
11	7218	43
12	7723	43
13	7960	43
0	8310	40

Stop Event

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

Calls

Call 1

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

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

localize89.0ms (1.3%)

Memory

-31.6MiB live, 88.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x x)
accuracy	0.00390625	(.f64 #s(approx (+ ( 2 y) x) (+.f64 x x)) x)
accuracy	25.755090463211555	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 #s(approx (+ ( 2 y) x) (+.f64 x x)) x))
accuracy	56.52854739120381	#s(approx (+ (* 2 y) x) (+.f64 x x))

Samples

83.0ms

256×

valid

Compiler

Compiled 80 to 30 computations (62.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 76.0ms

ival-mult: 71.0ms (93.4% of total)

ival-add: 4.0ms (5.3% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

4 → 24

Calls

Call 1

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

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

Calls

6 calls:

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

simplify210.0ms (3.1%)

Memory

12.7MiB live, 203.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	174
1	235	170
2	843	166
3	3625	166
0	8626	144

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 23

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

rewrite94.0ms (1.4%)

Memory

5.9MiB live, 40.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
0	17	48
1	90	46
0	918	41

Stop Event

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

Counts

4 → 27

Calls

Call 1

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

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

eval4.0ms (0.1%)

Memory: 8.0MiB live, 8.0MiB allocated
Compiler: Compiled 1 022 to 158 computations (84.5% saved)

prune4.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	38	6	44

Accuracy

100.0%

Counts

44 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.3%	(fma.f64 y #s(approx (+ (* 2 x) y) (.f64 #s(literal 2 binary64) x)) (.f64 x x))
✓	59.8%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
✓	53.4%	#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)))
✓	54.2%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
	60.4%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 290 to 113 computations (61% saved)

regimes19.0ms (0.3%)

Memory

-32.8MiB live, 19.6MiB allocated

Counts

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

11.0ms	y
3.0ms	x
3.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

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)

regimes6.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated

Counts

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

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:

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

Results

Accuracy	Segments	Branch
88.6%	2	`x`
89.6%	2	`y`
67.7%	5	`(+.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)

regimes4.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB 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	y
1.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Results

Accuracy	Segments	Branch
60.4%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
60.4%	1	`x`
60.4%	1	`y`

Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch15.0ms (0.2%)

Memory

-23.5MiB live, 13.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	1.083487540848211e-9	1.1294999512157693e-8

Samples

10.0ms

96×

valid

Compiler

Compiled 220 to 158 computations (28.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 7.0ms (84.8% of total)

ival-add: 1.0ms (12.1% of total)

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

exact: 0.0ms (0% of total)

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

simplify30.0ms (0.4%)

Memory

13.3MiB live, 49.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	76
1	20	76

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 y #s(literal 7253554917687775/2417851639229258349412352 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 y #s(literal 7253554917687775/2417851639229258349412352 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))

soundness1.3s (19.3%)

Memory

-10.3MiB live, 594.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	174
1	235	170
2	843	166
3	3625	166
0	8626	144
0	21	77
0	27	77
1	121	75
2	1085	75
0	9506	68
0	56	169
1	194	161
2	736	153
3	3310	141
0	8231	130
0	93	220
1	324	220
2	1105	220
3	4315	196
0	8801	176

Stop Event

1×	fuel
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 154 to 78 computations (49.4% saved)

preprocess32.0ms (0.5%)

Memory: 8.6MiB live, 86.7MiB 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%)

sample1.1s (16.2%)

explain140.0ms (2.1%)

preprocess379.0ms (5.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify304.0ms (4.5%)

localize33.0ms (0.5%)

series7.0ms (0.1%)

simplify206.0ms (3%)

rewrite289.0ms (4.2%)

eval171.0ms (2.5%)

prune58.0ms (0.8%)

simplify226.0ms (3.3%)

localize124.0ms (1.8%)

series9.0ms (0.1%)

simplify196.0ms (2.9%)

rewrite327.0ms (4.8%)

eval407.0ms (6%)

prune93.0ms (1.4%)

simplify241.0ms (3.5%)

localize74.0ms (1.1%)

series5.0ms (0.1%)

simplify163.0ms (2.4%)

rewrite208.0ms (3.1%)

eval36.0ms (0.5%)

prune6.0ms (0.1%)

simplify184.0ms (2.7%)

localize89.0ms (1.3%)

series3.0ms (0%)

simplify210.0ms (3.1%)

rewrite94.0ms (1.4%)

eval4.0ms (0.1%)

prune4.0ms (0.1%)

regimes19.0ms (0.3%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch15.0ms (0.2%)

simplify30.0ms (0.4%)

soundness1.3s (19.3%)

preprocess32.0ms (0.5%)

end0.0ms (0%)

Profiling