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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample686.0ms (21.8%)

Memory

27.8MiB live, 939.8MiB allocated

Samples

394.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 170.0ms

ival-add: 96.0ms (56.3% of total)

ival-mult: 64.0ms (37.6% of total)

ival-true: 7.0ms (4.1% of total)

ival-assert: 4.0ms (2.3% of total)

Bogosity

explain94.0ms (3%)

Memory

-20.8MiB live, 57.8MiB 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

18.0ms

512×

valid

Compiler

Compiled 47 to 20 computations (57.4% saved)

Precisions

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

ival-add: 3.0ms (42% of total)

ival-mult: 3.0ms (42% of total)

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

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

preprocess92.0ms (2.9%)

Memory

5.7MiB live, 45.7MiB 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

simplify5.0ms (0.1%)

Memory

4.1MiB live, 4.1MiB 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

localize12.0ms (0.4%)

Memory

17.9MiB live, 17.9MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.0078125	(*.f64 (+.f64 x y) (+.f64 x y))

Samples

9.0ms

256×

valid

Compiler

Compiled 26 to 10 computations (61.5% saved)

Precisions

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

ival-mult: 2.0ms (58.9% of total)

ival-add: 1.0ms (29.4% of total)

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

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

series3.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB 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
0.0ms	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))

simplify164.0ms (5.2%)

Memory

-20.9MiB live, 89.7MiB 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)

rewrite210.0ms (6.7%)

Memory

20.9MiB live, 302.5MiB 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>
#<batchref>
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eval152.0ms (4.8%)

Memory: 17.9MiB live, 401.2MiB allocated
Compiler: Compiled 43 687 to 2 966 computations (93.2% saved)

prune22.0ms (0.7%)

Memory

3.6MiB live, 81.6MiB 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
▶	95.3%	(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) x))
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
▶	56.2%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
▶	57.4%	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
▶	59.5%	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify8.0ms (0.3%)

Memory

-27.1MiB live, 11.8MiB 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 #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 y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
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 #s(literal 2 binary64) x y) y))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
x
y
(fma.f64 (+.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 #s(literal 2 binary64) x y) y))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(fma.f64 #s(literal 2 binary64) x y)
#s(literal 2 binary64)
x
y
(fma.f64 (+.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)

localize59.0ms (1.9%)

Memory

-28.7MiB live, 125.0MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y x)
accuracy	0.00390625	(*.f64 (+.f64 y x) x)
accuracy	3.0038732212667223	(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) x))
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0	(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
accuracy	28.06360807934103	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
accuracy	0	(*.f64 y y)
accuracy	27.29243639216226	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
accuracy	0	(*.f64 x x)
accuracy	25.933527419797496	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Samples

49.0ms

256×

valid

Compiler

Compiled 123 to 29 computations (76.4% saved)

Precisions

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

ival-add: 17.0ms (61.3% of total)

ival-mult: 10.0ms (36.1% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.4%)

Memory

27.2MiB live, 27.2MiB 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 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<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 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* x y)) (pow x 2)) (taylor 0 y) (#s(alt #s(approx (* (+ x y) (+ x y)) (.f64 (fma.f64 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (fma.f64 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (fma.f64 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* x y)) (taylor 0 y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ y (* 2 x))) (taylor 0 y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ y (* 2 x))) (taylor 0 y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* y (+ y (* 2 x))) (taylor 0 y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (+ y (* 2 x)) (taylor 0 y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (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 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (fma.f64 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (fma.f64 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (fma.f64 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* 2 (/ x y)))) (taylor inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (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 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (fma.f64 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (fma.f64 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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 (fma.f64 #s(literal 2 binary64) x y) y)) (patch #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x y)))) (taylor -inf y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x y)))) (taylor -inf y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (* 2 (/ x y)))) (taylor -inf y) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -2 (/ x y)) 1))) (taylor -inf y) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 #s(literal 2 binary64) x y) y) (patch (.f64 (fma.f64 #s(literal 2 binary64) x y) y) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 2))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 2 binary64) x y) (patch (fma.f64 #s(literal 2 binary64) x y) #<representation binary64>) () ())) ())
#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
1.0ms	y	@	inf	((* (+ x y) (+ x y)) (* x x) (* (+ x y) (+ x y)) (* y y) (* (+ x y) (+ x y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ 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)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ 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)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ 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)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ 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)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (* (+ y x) y) (* (+ y x) x)) (+ y x) (* (+ y x) x))

simplify419.0ms (13.3%)

Memory

-14.1MiB live, 181.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	1284
1	283	1260
2	768	1260
3	2244	1260
4	4776	1260
5	7926	1260
0	8343	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))
(* 2 (* x y))
(* y (+ y (* 2 x)))
(* y (+ y (* 2 x)))
(* y (+ y (* 2 x)))
(* 2 x)
(+ y (* 2 x))
(+ y (* 2 x))
(+ y (* 2 x))
(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)))))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
y
(* y (+ 1 (* 2 (/ x y))))
(* y (+ 1 (* 2 (/ x y))))
(* y (+ 1 (* 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))))
(pow y 2)
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
(* (pow y 2) (+ 1 (* 2 (/ x y))))
y
(* -1 (* y (- (* -2 (/ x y)) 1)))
(* -1 (* y (- (* -2 (/ x y)) 1)))
(* -1 (* y (- (* -2 (/ x y)) 1)))
(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))
(pow y 2)
(+ (* 2 (* x y)) (pow y 2))
(+ (* 2 (* x y)) (pow y 2))
(+ (* 2 (* x y)) (pow y 2))
y
(+ y (* 2 x))
(+ y (* 2 x))
(+ y (* 2 x))
(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)))))
(* 2 (* x y))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* x (+ (* 2 y) (/ (pow y 2) x)))
(* 2 x)
(* x (+ 2 (/ y x)))
(* x (+ 2 (/ y x)))
(* x (+ 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))))
(* 2 (* x y))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))
(* 2 x)
(* -1 (* x (- (* -1 (/ y x)) 2)))
(* -1 (* x (- (* -1 (/ y x)) 2)))
(* -1 (* x (- (* -1 (/ y 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))))
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))
(* 2 (* x y))
(.f64 (.f64 y x) #s(literal 2 binary64))
(* y (+ y (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* y (+ y (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* y (+ y (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(+ y (* 2 x))
(fma.f64 #s(literal 2 binary64) x y)
(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))
(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))))
(*.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)
y
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 #s(literal 2 binary64) x y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 #s(literal 2 binary64) x y)
(* y (+ 1 (* 2 (/ x y))))
(fma.f64 #s(literal 2 binary64) x y)
(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))
(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))))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(* (pow y 2) (+ 1 (* 2 (/ x y))))
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(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
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(+ (* x (+ x (* 2 y))) (pow y 2))
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(*.f64 (+.f64 y x) x)
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(* (pow x 2) (+ 1 (/ y x)))
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rewrite391.0ms (12.4%)

Memory

1.6MiB live, 234.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	70
0	24	59
1	82	59
2	664	59
0	8270	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 #s(literal 2 binary64) x y) y))
(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
(fma.f64 #s(literal 2 binary64) x y)
(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) x))
(+.f64 y x)
(*.f64 (+.f64 y x) x)

Outputs
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eval138.0ms (4.4%)

Memory: 0.0MiB live, 195.3MiB allocated
Compiler: Compiled 24 689 to 2 154 computations (91.3% saved)

prune46.0ms (1.5%)

Memory

12.4MiB live, 51.3MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	1 029	0	1 029
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	1 029	5	1 034

Accuracy

100.0%

Counts

1 034 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	95.3%	(fma.f64 (+.f64 y x) y (*.f64 (+.f64 y x) x))
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
✓	56.2%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
✓	57.4%	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
✓	59.5%	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Compiler

Compiled 64 to 38 computations (40.6% saved)

regimes10.0ms (0.3%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

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

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

Calls

4 calls:

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

regimes8.0ms (0.2%)

Memory

8.5MiB live, 8.5MiB 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 #s(literal 2 binary64) x y) y))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
90.3%	2	`x`
90.4%	2	`y`
64.2%	3	`(*.f64 (+.f64 x y) (+.f64 x y))`
99.4%	2	`(+.f64 x y)`

Compiler

Compiled 12 to 11 computations (8.3% saved)

regimes2.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB 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
99.2%	2	`(+.f64 x y)`

Compiler

Compiled 3 to 3 computations (0% saved)

regimes28.0ms (0.9%)

Memory

-40.1MiB live, 10.9MiB 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:

24.0ms	(+.f64 x y)
1.0ms	y
1.0ms	x
1.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

Results

Accuracy	Segments	Branch
59.5%	1	`(*.f64 (+.f64 x y) (+.f64 x y))`
59.5%	1	`x`
59.5%	1	`y`
59.5%	1	`(+.f64 x y)`

Compiler

Compiled 12 to 11 computations (8.3% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.2479300994778304e-161	-4.4830448973621245e-190

Compiler

Compiled 8 to 9 computations (-12.5% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-5.2479300994778304e-161	-4.4830448973621245e-190

Compiler

Compiled 8 to 9 computations (-12.5% saved)

simplify30.0ms (0.9%)

Memory

5.7MiB live, 42.7MiB 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 -1582914569427869/31658291388557380359744322690514840324496812684955115509000071179890844813636078997800499335839109758668501942530065835436974724391264154875845907853042325493325666835033489408 binary64)) #s(approx (* (+ x y) (+ x y)) (.f64 x x)) #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 (+.f64 x y) #s(literal -1582914569427869/31658291388557380359744322690514840324496812684955115509000071179890844813636078997800499335839109758668501942530065835436974724391264154875845907853042325493325666835033489408 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 -1582914569427869/31658291388557380359744322690514840324496812684955115509000071179890844813636078997800499335839109758668501942530065835436974724391264154875845907853042325493325666835033489408 binary64)) #s(approx (* (+ x y) (+ x y)) (.f64 x x)) #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 (+.f64 y x) #s(literal -1582914569427869/31658291388557380359744322690514840324496812684955115509000071179890844813636078997800499335839109758668501942530065835436974724391264154875845907853042325493325666835033489408 binary64)) #s(approx (* (+ x y) (+ x y)) (.f64 x x)) #s(approx ( (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 (+.f64 x y) #s(literal -1582914569427869/31658291388557380359744322690514840324496812684955115509000071179890844813636078997800499335839109758668501942530065835436974724391264154875845907853042325493325666835033489408 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 -1582914569427869/31658291388557380359744322690514840324496812684955115509000071179890844813636078997800499335839109758668501942530065835436974724391264154875845907853042325493325666835033489408 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))

soundness421.0ms (13.4%)

Memory

-7.8MiB live, 190.8MiB 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 60 to 33 computations (45% saved)

preprocess137.0ms (4.3%)

Memory: 1.2MiB live, 82.7MiB 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%)

sample686.0ms (21.8%)

explain94.0ms (3%)

preprocess92.0ms (2.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize12.0ms (0.4%)

series3.0ms (0.1%)

simplify164.0ms (5.2%)

rewrite210.0ms (6.7%)

eval152.0ms (4.8%)

prune22.0ms (0.7%)

simplify8.0ms (0.3%)

localize59.0ms (1.9%)

series11.0ms (0.4%)

simplify419.0ms (13.3%)

rewrite391.0ms (12.4%)

eval138.0ms (4.4%)

prune46.0ms (1.5%)

regimes10.0ms (0.3%)

regimes8.0ms (0.2%)

regimes2.0ms (0.1%)

regimes28.0ms (0.9%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify30.0ms (0.9%)

soundness421.0ms (13.4%)

preprocess137.0ms (4.3%)

end0.0ms (0%)

Profiling