Metrics for Examples.Basics.BasicTests:f3 from sbv-4.4

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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 9 to 6 computations (33.3% saved)

sample675.0ms (20.9%)

Memory

40.2MiB live, 772.8MiB allocated

Samples

473.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 185.0ms

ival-add: 120.0ms (64.9% of total)

ival-mult: 56.0ms (30.3% of total)

ival-true: 5.0ms (2.7% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

explain51.0ms (1.6%)

Memory

-23.5MiB live, 101.1MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

17.0ms

512×

valid

Compiler

Compiled 35 to 16 computations (54.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-add: 3.0ms (46% of total)

ival-mult: 3.0ms (46% of total)

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

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

preprocess85.0ms (2.6%)

Memory

20.8MiB live, 56.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	50	35
2	210	35
3	533	35
4	1075	35
5	1970	35
6	2756	35
7	2900	35
8	2900	35
9	2900	35
10	2942	35
11	2958	35
0	4	7
0	6	7
1	13	7
2	29	7
3	57	7
4	80	7
5	96	7
6	105	7
7	111	7
0	111	7

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort x y)

Compiler

Compiled 7 to 4 computations (42.9% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify9.0ms (0.3%)

Memory

-28.6MiB live, 17.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	12
0	6	12
1	13	12
2	29	12
3	57	12
4	80	12
5	96	12
6	105	12
7	111	12
0	111	12

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize19.0ms (0.6%)

Memory

9.5MiB live, 48.9MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.0234375	(*.f64 (+.f64 x y) (+.f64 x y))

Samples

11.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 4.0ms (67.8% of total)

ival-mult: 2.0ms (33.9% of total)

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

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

series3.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

2 → 48

Calls

Call 1

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

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

Calls

6 calls:

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

simplify117.0ms (3.6%)

Memory

7.2MiB live, 83.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	270
1	193	264
2	488	264
3	1576	252
4	3881	252
5	6929	252
0	8083	222

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 42

Calls

Call 1

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

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

rewrite254.0ms (7.9%)

Memory

-28.5MiB live, 185.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	8
1	28	8
2	220	8
3	2817	8
0	9151	8

Stop Event

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

Counts

2 → 989

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval155.0ms (4.8%)

Memory: 18.7MiB live, 317.9MiB allocated
Compiler: Compiled 43 687 to 2 966 computations (93.2% saved)

prune21.0ms (0.6%)

Memory

18.1MiB live, 93.7MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1 137	4	1 141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1 137	5	1 142

Accuracy

100.0%

Counts

1 142 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) x))
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
▶	63.9%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
▶	57.6%	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
▶	62.7%	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify6.0ms (0.2%)

Memory

14.0MiB live, 14.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (+.f64 y x) x)
cost-diff	0	(+.f64 y x)
cost-diff	384	(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) x))
cost-diff	0	(fma.f64 y #s(literal 2 binary64) x)
cost-diff	0	(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
cost-diff	0	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	77
0	24	74
1	39	74
2	55	74
3	90	74
4	115	74
5	130	74
6	141	74
0	141	74

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize43.0ms (1.3%)

Memory

-13.6MiB live, 97.4MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y x)
accuracy	0.00390625	(*.f64 (+.f64 y x) x)
accuracy	1.003895240422241	(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) x))
accuracy	0	(fma.f64 y #s(literal 2 binary64) x)
accuracy	0.0078125	(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
accuracy	23.126996961235864	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
accuracy	0	(*.f64 y y)
accuracy	27.13732082781709	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
accuracy	0	(*.f64 x x)
accuracy	23.901437085898596	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Samples

31.0ms

256×

valid

Compiler

Compiled 67 to 16 computations (76.1% saved)

Precisions

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

ival-mult: 12.0ms (54.9% of total)

ival-add: 10.0ms (45.7% of total)

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

exact: 0.0ms (0% of total)

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

series15.0ms (0.5%)

Memory

12.5MiB live, 51.4MiB allocated

Counts

10 → 216

Calls

Call 1

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

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

Calls

6 calls:

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

simplify191.0ms (5.9%)

Memory

-39.4MiB live, 126.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	1368
1	280	1308
2	738	1308
3	2147	1260
4	4795	1260
0	8103	1104

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 207

Calls

Call 1

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

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

rewrite214.0ms (6.7%)

Memory

5.6MiB live, 160.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	70
0	24	59
1	82	59
2	664	59
0	8266	59

Stop Event

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

Counts

10 → 700

Calls

Call 1

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

Outputs
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eval166.0ms (5.2%)

Memory: -1.1MiB live, 273.0MiB allocated
Compiler: Compiled 24 689 to 2 152 computations (91.3% saved)

prune23.0ms (0.7%)

Memory

17.6MiB live, 92.2MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	1 028	1	1 029
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	1 028	6	1 034

Accuracy

100.0%

Counts

1 034 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) x))
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
▶	56.8%	#s(approx (* (+ x y) (+ x y)) (fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 x x)))
✓	63.9%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	57.6%	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
✓	62.7%	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Compiler

Compiled 41 to 30 computations (26.8% saved)

simplify8.0ms (0.2%)

Memory

-26.9MiB live, 11.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(*.f64 y x)
cost-diff	0	#s(approx (* (+ x y) (+ x y)) (fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 x x)))
cost-diff	320	(fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
0	13	33
1	25	33
2	39	31
3	65	31
4	89	31
5	104	31
6	114	31
0	114	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize48.0ms (1.5%)

Memory

-17.6MiB live, 39.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y x)
accuracy	0	(*.f64 x x)
accuracy	4.0898396216604125	(fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 x x))
accuracy	23.126996961235864	#s(approx (* (+ x y) (+ x y)) (fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 x x)))

Samples

37.0ms

256×

valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 27.0ms (89.8% of total)

ival-add: 2.0ms (6.7% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

11.5MiB live, 11.5MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

6 calls:

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

simplify137.0ms (4.3%)

Memory

10.7MiB live, 168.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	504
1	166	462
2	470	462
3	1334	450
4	3275	450
5	6426	450
0	8157	402

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

rewrite225.0ms (7%)

Memory

8.4MiB live, 200.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
0	13	28
1	51	28
2	394	26
3	4673	26
0	8212	24

Stop Event

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

Counts

4 → 94

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval33.0ms (1%)

Memory: -14.5MiB live, 23.6MiB allocated
Compiler: Compiled 3 139 to 379 computations (87.9% saved)

prune6.0ms (0.2%)

Memory

12.4MiB live, 12.4MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	178	6	184

Accuracy

100.0%

Counts

184 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) x))
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
✓	56.8%	#s(approx (* (+ x y) (+ x y)) (fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 x x)))
✓	63.9%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	57.6%	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
✓	62.7%	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Compiler

Compiled 82 to 48 computations (41.5% saved)

regimes11.0ms (0.3%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	(+.f64 x y)
3.0ms	x
3.0ms	y
2.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

Results

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

Compiler

Compiled 12 to 11 computations (8.3% saved)

regimes82.0ms (2.5%)

Memory

-28.0MiB live, 11.7MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

76.0ms	x
2.0ms	(+.f64 x y)
2.0ms	y
2.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

Results

Accuracy	Segments	Branch
90.4%	2	`x`
87.4%	2	`y`
63.9%	1	`(*.f64 (+.f64 x y) (+.f64 x y))`
98.8%	2	`(+.f64 x y)`

Compiler

Compiled 12 to 11 computations (8.3% saved)

regimes2.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

(+.f64 x y)

Results

Accuracy	Segments	Branch
97.9%	2	`(+.f64 x y)`

Compiler

Compiled 3 to 3 computations (0% saved)

regimes5.0ms (0.2%)

Memory

8.5MiB live, 8.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
62.7%	1	`(*.f64 (+.f64 x y) (+.f64 x y))`
62.7%	1	`y`
62.7%	1	`x`
62.7%	1	`(+.f64 x y)`

Compiler

Compiled 12 to 11 computations (8.3% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5292246800625092e-153	-6.083381031626443e-165

Compiler

Compiled 8 to 9 computations (-12.5% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5292246800625092e-153	-6.083381031626443e-165

Compiler

Compiled 8 to 9 computations (-12.5% saved)

simplify38.0ms (1.2%)

Memory

-16.4MiB live, 31.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	77
1	20	77

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (+.f64 x y) (+.f64 x y))
(if (<=.f64 (+.f64 x y) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) #s(approx (* (+ x y) (+ x y)) (.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(approx ( (+ x y) (+ x y)) (*.f64 y y)))
(if (<=.f64 (+.f64 x y) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) #s(approx (* (+ x y) (+ x y)) (.f64 x x)) #s(approx ( (+ x y) (+ x y)) (*.f64 y y)))
#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Outputs
(*.f64 (+.f64 x y) (+.f64 x y))
(*.f64 (+.f64 y x) (+.f64 y x))
(if (<=.f64 (+.f64 x y) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) #s(approx (* (+ x y) (+ x y)) (.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(approx ( (+ x y) (+ x y)) (*.f64 y y)))
(if (<=.f64 (+.f64 y x) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) #s(approx (* (+ x y) (+ x y)) (.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(approx ( (+ x y) (+ x y)) (*.f64 y y)))
(if (<=.f64 (+.f64 x y) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) #s(approx (* (+ x y) (+ x y)) (.f64 x x)) #s(approx ( (+ x y) (+ x y)) (*.f64 y y)))
(if (<=.f64 (+.f64 y x) #s(literal -7547924849643083/7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653952 binary64)) #s(approx (* (+ x y) (+ x y)) (.f64 x x)) #s(approx ( (+ x y) (+ x y)) (*.f64 y y)))
#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

soundness428.0ms (13.3%)

Memory

-0.8MiB live, 117.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	270
1	193	264
2	488	264
3	1576	252
4	3881	252
5	6929	252
0	8083	222

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 54 to 30 computations (44.4% saved)

preprocess145.0ms (4.5%)

Memory: 0.1MiB live, 122.1MiB allocated
Remove: (sort x y)
Compiler: Compiled 152 to 74 computations (51.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample675.0ms (20.9%)

explain51.0ms (1.6%)

preprocess85.0ms (2.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.3%)

localize19.0ms (0.6%)

series3.0ms (0.1%)

simplify117.0ms (3.6%)

rewrite254.0ms (7.9%)

eval155.0ms (4.8%)

prune21.0ms (0.6%)

simplify6.0ms (0.2%)

localize43.0ms (1.3%)

series15.0ms (0.5%)

simplify191.0ms (5.9%)

rewrite214.0ms (6.7%)

eval166.0ms (5.2%)

prune23.0ms (0.7%)

simplify8.0ms (0.2%)

localize48.0ms (1.5%)

series7.0ms (0.2%)

simplify137.0ms (4.3%)

rewrite225.0ms (7%)

eval33.0ms (1%)

prune6.0ms (0.2%)

regimes11.0ms (0.3%)

regimes82.0ms (2.5%)

regimes2.0ms (0.1%)

regimes5.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify38.0ms (1.2%)

soundness428.0ms (13.3%)

preprocess145.0ms (4.5%)

end0.0ms (0%)

Profiling