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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample607.0ms (15.4%)

Memory

-16.1MiB live, 796.4MiB allocated

Samples

394.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-mult: 74.0ms (54.6% of total)

ival-add: 51.0ms (37.6% of total)

ival-true: 7.0ms (5.2% of total)

ival-assert: 4.0ms (3% of total)

Bogosity

explain104.0ms (2.6%)

Memory

-17.5MiB live, 72.1MiB 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

40.0ms

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 (44.8% of total)

ival-mult: 3.0ms (44.8% of total)

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

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

preprocess85.0ms (2.2%)

Memory

22.1MiB live, 57.9MiB allocated

Algorithm

1×	egg-herbie

Rules

570×	`distribute-rgt-in`
518×	`unsub-neg`
446×	`distribute-lft-in`
286×	`distribute-lft-out`
280×	`associate-+l-`

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

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB 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

11.7MiB live, 11.7MiB 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))

Rules

124×	`lower-fma.f64`
124×	`lower-fma.f32`
86×	`lower-+.f32`
84×	`lower-+.f64`
50×	`associate-+r+`

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

localize16.0ms (0.4%)

Memory

3.9MiB live, 39.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.01953125	(*.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: 5.0ms

ival-add: 4.0ms (74.1% of total)

ival-mult: 1.0ms (18.5% of total)

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

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

series12.0ms (0.3%)

Memory

-25.7MiB live, 19.0MiB 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
6.0ms	y	@	inf	((* (+ x y) (+ x y)) (+ x y))
4.0ms	x	@	0	((* (+ x y) (+ x y)) (+ x y))
1.0ms	x	@	-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))

simplify219.0ms (5.5%)

Memory

-21.9MiB live, 148.8MiB allocated

Algorithm

1×	egg-herbie

Rules

7 026×	`lower-fma.f64`
7 026×	`lower-fma.f32`
2 898×	`lower-*.f64`
2 898×	`lower-*.f32`
1 650×	`unsub-neg`

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)

rewrite238.0ms (6%)

Memory

29.3MiB live, 294.8MiB allocated

Rules

5 646×	`lower-*.f32`
5 644×	`lower-*.f64`
4 194×	`lower-fma.f64`
4 194×	`lower-fma.f32`
3 878×	`lower-/.f64`

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>
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eval248.0ms (6.3%)

Memory: 5.2MiB live, 301.8MiB allocated
Compiler: Compiled 43 687 to 2 966 computations (93.2% saved)

prune72.0ms (1.8%)

Memory

7.8MiB live, 73.2MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1 134	7	1 141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1 134	8	1 142

Accuracy

100.0%

Counts

1 142 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.1%	(fma.f64 (+.f64 y x) x (*.f64 (+.f64 y x) y))
	96.9%	(fma.f64 y y (fma.f64 y x (*.f64 (+.f64 y x) x)))
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
▶	100.0%	#s(approx (* (+ x y) (+ x y)) (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x)))
▶	49.9%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
▶	60.5%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
▶	60.5%	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
▶	50.9%	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Compiler

Compiled 113 to 80 computations (29.2% saved)

simplify8.0ms (0.2%)

Memory

6.4MiB live, 6.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Rules

124×	`lower-fma.f32`
118×	`lower-fma.f64`
86×	`lower-+.f64`
86×	`lower-+.f32`
60×	`associate-+r+`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	120
0	26	120
1	40	120
2	64	120
3	112	120
4	135	116
5	147	116
6	154	116
0	154	116

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize86.0ms (2.2%)

Memory

-30.2MiB live, 81.1MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y #s(literal 2 binary64) x)
accuracy	0.015625	(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
accuracy	32.05081906577756	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0.015625	(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
accuracy	25.291534736718916	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
accuracy	0	(*.f64 y y)
accuracy	25.270011791512644	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
accuracy	0	(*.f64 x x)
accuracy	31.454346187690906	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0	(*.f64 x x)
accuracy	0	#s(approx (* (+ x y) (+ x y)) (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x)))
accuracy	0.0078125	(fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x))

Samples

69.0ms

256×

valid

Compiler

Compiled 97 to 16 computations (83.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 11.0ms (69.3% of total)

ival-add: 5.0ms (31.5% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.4%)

Memory

34.5MiB live, 34.5MiB allocated

Counts

12 → 264

Calls

Call 1

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

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

Calls

6 calls:

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

simplify198.0ms (5%)

Memory

-10.4MiB live, 222.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8 438×	`lower-fma.f64`
8 438×	`lower-fma.f32`
2 840×	`lower-*.f64`
2 840×	`lower-*.f32`
1 688×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	1800
1	269	1728
2	745	1728
3	2221	1728
4	4573	1728
5	7536	1728
0	8002	1476

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 258

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

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

rewrite240.0ms (6.1%)

Memory

0.2MiB live, 294.2MiB allocated

Rules

9 402×	`lower-fma.f32`
9 396×	`lower-fma.f64`
5 518×	`lower-*.f32`
5 510×	`lower-*.f64`
3 566×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	102
0	26	92
1	86	92
2	663	92
3	7926	92
0	8485	92

Stop Event

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

Counts

12 → 338

Calls

Call 1

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

Outputs
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eval85.0ms (2.2%)

Memory: -13.7MiB live, 176.9MiB allocated
Compiler: Compiled 13 158 to 1 425 computations (89.2% saved)

prune20.0ms (0.5%)

Memory

23.2MiB live, 61.2MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	701	2	703
Fresh	2	0	2
Picked	1	4	5
Done	0	1	1
Total	704	7	711

Accuracy

100.0%

Counts

711 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
▶	100.0%	#s(approx (* (+ x y) (+ x y)) (fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y)))
▶	57.7%	#s(approx (* (+ x y) (+ x y)) (fma.f64 y y (.f64 (.f64 x #s(literal 2 binary64)) y)))
✓	49.9%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	60.5%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
✓	60.5%	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
✓	50.9%	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Compiler

Compiled 48 to 38 computations (20.8% saved)

simplify27.0ms (0.7%)

Memory

-22.0MiB live, 15.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(fma.f64 y #s(literal 2 binary64) x)
cost-diff	0	#s(approx (* (+ x y) (+ x y)) (fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y)))
cost-diff	384	(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
cost-diff	0	#s(approx (* (+ x y) (+ x y)) (fma.f64 y y (.f64 (.f64 x #s(literal 2 binary64)) y)))
cost-diff	320	(fma.f64 y y (.f64 (.f64 x #s(literal 2 binary64)) y))

Rules

124×	`lower-fma.f32`
118×	`lower-fma.f64`
86×	`lower-+.f64`
86×	`lower-+.f32`
56×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	71
0	21	69
1	39	69
2	63	69
3	98	69
4	121	65
5	133	65
6	140	65
0	140	63

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize57.0ms (1.4%)

Memory

-9.8MiB live, 76.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y #s(literal 2 binary64) x)
accuracy	0	(*.f64 y y)
accuracy	0	#s(approx (* (+ x y) (+ x y)) (fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y)))
accuracy	0.0078125	(fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y))
accuracy	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	1.7538869832389217	(fma.f64 y y (.f64 (.f64 x #s(literal 2 binary64)) y))
accuracy	25.291534736718916	#s(approx (* (+ x y) (+ x y)) (fma.f64 y y (.f64 (.f64 x #s(literal 2 binary64)) y)))

Samples

46.0ms

256×

valid

Compiler

Compiled 58 to 15 computations (74.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-add: 28.0ms (75.8% of total)

ival-mult: 9.0ms (24.4% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.3%)

Memory

25.8MiB live, 25.8MiB allocated

Counts

8 → 168

Calls

Call 1

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

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

Calls

6 calls:

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

simplify128.0ms (3.2%)

Memory

6.4MiB live, 126.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 410×	`lower-fma.f64`
9 410×	`lower-fma.f32`
3 506×	`lower-*.f64`
3 506×	`lower-*.f32`
1 122×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	1038
1	208	1020
2	567	1020
3	1703	1020
4	3755	1020
5	6201	1020
0	8049	894

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 165

Calls

Call 1

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

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

rewrite310.0ms (7.8%)

Memory

-13.2MiB live, 229.6MiB allocated

Rules

10 006×	`lower-fma.f32`
10 000×	`lower-fma.f64`
6 498×	`lower-*.f32`
6 492×	`lower-*.f64`
4 266×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	65
0	21	59
1	85	59
2	683	59
0	8289	57

Stop Event

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

Counts

8 → 302

Calls

Call 1

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

Outputs
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eval252.0ms (6.4%)

Memory: -2.1MiB live, 82.5MiB allocated
Compiler: Compiled 10 793 to 1 161 computations (89.2% saved)

prune77.0ms (1.9%)

Memory

-8.2MiB live, 30.2MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	467	0	467
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	467	7	474

Accuracy

100.0%

Counts

474 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
✓	100.0%	#s(approx (* (+ x y) (+ x y)) (fma.f64 (fma.f64 y #s(literal 2 binary64) x) x (*.f64 y y)))
✓	57.7%	#s(approx (* (+ x y) (+ x y)) (fma.f64 y y (.f64 (.f64 x #s(literal 2 binary64)) y)))
✓	49.9%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	60.5%	#s(approx (* (+ x y) (+ x y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
✓	60.5%	#s(approx (* (+ x y) (+ x y)) (*.f64 y y))
✓	50.9%	#s(approx (* (+ x y) (+ x y)) (*.f64 x x))

Compiler

Compiled 127 to 67 computations (47.2% saved)

regimes15.0ms (0.4%)

Memory

23.2MiB live, 23.2MiB allocated

Counts

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

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

Calls

4 calls:

4.0ms	(+.f64 x y)
4.0ms	y
4.0ms	x
4.0ms	(*.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)

regimes26.0ms (0.7%)

Memory

-22.4MiB live, 17.0MiB 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 #s(literal 2 binary64) x 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 y y (.f64 (.f64 x #s(literal 2 binary64)) y)))

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

Calls

4 calls:

18.0ms	(+.f64 x y)
3.0ms	x
3.0ms	y
3.0ms	(*.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)

regimes9.0ms (0.2%)

Memory

16.4MiB live, 16.4MiB allocated

Counts

4 → 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))
#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:

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

Results

Accuracy	Segments	Branch
89.2%	2	`x`
89.5%	2	`y`
65.2%	3	`(*.f64 (+.f64 x y) (+.f64 x y))`
99.2%	2	`(+.f64 x y)`

Compiler

Compiled 12 to 11 computations (8.3% saved)

regimes2.0ms (0.1%)

Memory

3.8MiB live, 3.8MiB 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 y y))

Calls

1 calls:

2.0ms

(+.f64 x y)

Results

Accuracy	Segments	Branch
99.0%	2	`(+.f64 x y)`

Compiler

Compiled 3 to 3 computations (0% saved)

regimes20.0ms (0.5%)

Memory

-26.9MiB live, 12.6MiB 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:

16.0ms	y
1.0ms	x
1.0ms	(+.f64 x y)
1.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

Results

Accuracy	Segments	Branch
50.9%	1	`(*.f64 (+.f64 x y) (+.f64 x y))`
50.9%	1	`x`
50.9%	1	`y`
50.9%	1	`(+.f64 x y)`

Compiler

Compiled 12 to 11 computations (8.3% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.644518333233204e-162	-1.0664029575170545e-167

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	-7.644518333233204e-162	-1.0664029575170545e-167

Compiler

Compiled 8 to 9 computations (-12.5% saved)

simplify42.0ms (1.1%)

Memory

-2.5MiB live, 42.2MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`-commutative-binary64-.f64`
2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	94
1	23	94

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (* (+ x y) (+ x y)) (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x)))
(*.f64 (+.f64 x y) (+.f64 x y))
(if (<=.f64 (+.f64 x y) #s(literal -5065326622169181/1013065324433836171511818326096474890383898005918563696288002277756507034036354527929615978746851512277392062160962106733983191180520452956027069051297354415786421338721071661056 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 -5065326622169181/1013065324433836171511818326096474890383898005918563696288002277756507034036354527929615978746851512277392062160962106733983191180520452956027069051297354415786421338721071661056 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
#s(approx (* (+ x y) (+ x y)) (fma.f64 (fma.f64 #s(literal 2 binary64) x y) y (*.f64 x x)))
(*.f64 (+.f64 x y) (+.f64 x y))
(*.f64 (+.f64 y x) (+.f64 y x))
(if (<=.f64 (+.f64 x y) #s(literal -5065326622169181/1013065324433836171511818326096474890383898005918563696288002277756507034036354527929615978746851512277392062160962106733983191180520452956027069051297354415786421338721071661056 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 -5065326622169181/1013065324433836171511818326096474890383898005918563696288002277756507034036354527929615978746851512277392062160962106733983191180520452956027069051297354415786421338721071661056 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 -5065326622169181/1013065324433836171511818326096474890383898005918563696288002277756507034036354527929615978746851512277392062160962106733983191180520452956027069051297354415786421338721071661056 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 -5065326622169181/1013065324433836171511818326096474890383898005918563696288002277756507034036354527929615978746851512277392062160962106733983191180520452956027069051297354415786421338721071661056 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))

soundness601.0ms (15.2%)

Memory

-4.5MiB live, 232.6MiB allocated

Rules

7 026×	`lower-fma.f64`
7 026×	`lower-fma.f32`
2 898×	`lower-*.f64`
2 898×	`lower-*.f32`
1 650×	`unsub-neg`

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 64 to 33 computations (48.4% saved)

preprocess112.0ms (2.8%)

Memory: 9.7MiB live, 93.2MiB allocated
Remove: (sort x y)
Compiler: Compiled 184 to 92 computations (50% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample607.0ms (15.4%)

explain104.0ms (2.6%)

preprocess85.0ms (2.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize16.0ms (0.4%)

series12.0ms (0.3%)

simplify219.0ms (5.5%)

rewrite238.0ms (6%)

eval248.0ms (6.3%)

prune72.0ms (1.8%)

simplify8.0ms (0.2%)

localize86.0ms (2.2%)

series14.0ms (0.4%)

simplify198.0ms (5%)

rewrite240.0ms (6.1%)

eval85.0ms (2.2%)

prune20.0ms (0.5%)

simplify27.0ms (0.7%)

localize57.0ms (1.4%)

series11.0ms (0.3%)

simplify128.0ms (3.2%)

rewrite310.0ms (7.8%)

eval252.0ms (6.4%)

prune77.0ms (1.9%)

regimes15.0ms (0.4%)

regimes26.0ms (0.7%)

regimes9.0ms (0.2%)

regimes2.0ms (0.1%)

regimes20.0ms (0.5%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify42.0ms (1.1%)

soundness601.0ms (15.2%)

preprocess112.0ms (2.8%)

end0.0ms (0%)

Profiling