Metrics for Examples.Basics.BasicTests:f1 from sbv-4.4

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB 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 7 computations (22.2% saved)

sample778.0ms (12.3%)

Memory

11.4MiB live, 632.8MiB allocated

Samples

563.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 270.0ms

ival-add: 133.0ms (49.3% of total)

ival-mult: 87.0ms (32.3% of total)

ival-sub: 42.0ms (15.6% of total)

ival-true: 6.0ms (2.2% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain62.0ms (1%)

Memory

3.8MiB live, 98.0MiB allocated

FPErrors

Click to see full error table

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

24.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

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

ival-sub: 3.0ms (33.3% of total)

ival-add: 3.0ms (33.3% of total)

ival-mult: 3.0ms (33.3% of total)

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

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

preprocess798.0ms (12.6%)

Memory

0.8MiB live, 279.3MiB allocated

Algorithm

1×	egg-herbie

Rules

37 776×	`lower-fma.f64`
37 776×	`lower-fma.f32`
8 740×	`lower-+.f32`
8 738×	`lower-+.f64`
3 244×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	44	37
2	151	35
3	524	35
4	1147	35
5	1954	35
6	2477	35
7	3171	35
8	4140	35
9	4740	35
10	4944	35
11	5010	35
12	5074	35
13	5106	35
14	6378	35
15	7802	35
0	5	7
0	8	7
1	12	7
2	31	7
3	69	7
4	180	7
5	344	7
6	682	7
7	1276	7
8	2204	7
9	2825	7
10	2993	7
11	3035	7
12	3073	7
13	3073	7
14	3073	7
15	3075	7
0	9343	7

Stop Event

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

Calls

Call 1

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

Outputs
(*.f64 (+.f64 x y) (-.f64 x y))
(fma.f64 (neg.f64 y) y (*.f64 x x))

Symmetry

(abs y)

(abs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify835.0ms (13.2%)

Memory

-184.9MiB live, 386.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

37 776×	`lower-fma.f64`
37 776×	`lower-fma.f32`
8 740×	`lower-+.f32`
8 738×	`lower-+.f64`
3 244×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	12	15
2	31	15
3	69	15
4	180	15
5	344	15
6	682	15
7	1276	15
8	2204	15
9	2825	15
10	2993	15
11	3035	15
12	3073	15
13	3073	15
14	3073	15
15	3075	15
0	9343	15

Stop Event

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

Calls

Call 1

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

Outputs
(*.f64 (+.f64 x y) (-.f64 x y))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+.f64 x y)
(+.f64 y x)
x
y
(-.f64 x y)

localize16.0ms (0.2%)

Memory

-1.9MiB live, 36.0MiB allocated

Localize:

Found 3 expressions of interest:

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

Samples

12.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-sub: 1.0ms (24.1% of total)

ival-add: 1.0ms (24.1% of total)

ival-mult: 1.0ms (24.1% of total)

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

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

series4.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

3 → 72

Calls

Call 1

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

Inputs

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

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

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

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

Calls

6 calls:

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

simplify311.0ms (4.9%)

Memory

-34.6MiB live, 208.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 152×	`lower-fma.f64`
14 152×	`lower-fma.f32`
2 614×	`lower--.f64`
2 614×	`lower--.f32`
2 222×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	86	309
1	265	249
2	786	249
3	3277	249
0	8535	249

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 63

Calls

Call 1

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

Outputs
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(pow x 2)
(*.f64 x x)
(+ (* y (+ x (* -1 x))) (pow x 2))
(*.f64 x x)
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(fma.f64 (neg.f64 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)
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(fma.f64 (neg.f64 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)
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(*.f64 (neg.f64 y) y)
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(fma.f64 (neg.f64 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)
x
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(fma.f64 (neg.f64 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)
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(fma.f64 (neg.f64 y) y (*.f64 x x))

rewrite374.0ms (5.9%)

Memory

-2.5MiB live, 375.9MiB allocated

Rules

5 088×	`lower-fma.f64`
5 088×	`lower-fma.f32`
4 974×	`lower-*.f32`
4 972×	`lower-*.f64`
3 706×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	29	13
2	250	13
3	3945	13
0	9475	13

Stop Event

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

Counts

3 → 1 091

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (-.f64 x y)) #s(literal -1 binary64)) (pow.f64 (/.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (+.f64 y x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (+.f64 y x)) #s(literal -1 binary64)) (pow.f64 (/.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (-.f64 x y)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (+.f64 y x) (-.f64 y x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (fma.f64 (-.f64 x y) x (.f64 y y))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (-.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (neg.f64 (-.f64 x y)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (+.f64 y x) y (*.f64 x x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 x y))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (-.f64 x y))) #s(literal -1 binary64)) (pow.f64 (+.f64 y x) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal 2 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (fma.f64 (-.f64 x y) x (.f64 y y))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 x y)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) #s(literal -1 binary64)) (+.f64 y x)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) #s(literal -1 binary64)) (-.f64 x y)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 x y) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 (fma.f64 (+.f64 y x) y (*.f64 x x))))
(.f64 (/.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (neg.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))) (neg.f64 (+.f64 y x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 y x) y) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (.f64 (-.f64 y x) y)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 (-.f64 y x) y) (-.f64 (.f64 (-.f64 y x) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (fma.f64 (neg.f64 y) y (*.f64 x x))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal 1 binary64)) (pow.f64 (-.f64 x y) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64))) (fma.f64 (+.f64 y x) y (*.f64 x x)))
(.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) #s(literal -1 binary64)) (fma.f64 (neg.f64 y) y (*.f64 x x))) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (fma.f64 (neg.f64 y) y (*.f64 x x))) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 y x) (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64))) (/.f64 (-.f64 x y) (fma.f64 (-.f64 x y) x (.f64 y y))))
(.f64 (/.f64 (+.f64 y x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 (-.f64 x y) (pow.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) #s(literal -1 binary64))))
(.f64 (/.f64 (-.f64 x y) (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64))) (/.f64 (+.f64 y x) (fma.f64 (-.f64 x y) x (.f64 y y))))
(*.f64 (/.f64 (-.f64 x y) #s(literal 1 binary64)) (/.f64 (+.f64 y x) (-.f64 x y)))
(.f64 (/.f64 (-.f64 x y) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (/.f64 (+.f64 y x) (pow.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 y x) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)) (fma.f64 (+.f64 y x) y (.f64 x x)))
(.f64 (.f64 (+.f64 y x) (-.f64 y x)) (pow.f64 (-.f64 y x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (+.f64 y x)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (/.f64 (+.f64 y x) (pow.f64 (+.f64 y x) #s(literal -1 binary64))))
(.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) (-.f64 x y)) #s(literal -1 binary64)))
(.f64 (pow.f64 (-.f64 x y) #s(literal -1 binary64)) (fma.f64 (neg.f64 y) y (.f64 x x)))
(.f64 (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 y x))
(.f64 (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (pow.f64 (neg.f64 (-.f64 x y)) #s(literal -1 binary64)))
(.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (pow.f64 (neg.f64 (fma.f64 (-.f64 x y) x (.f64 y y))) #s(literal -1 binary64)))
(.f64 (fma.f64 (neg.f64 y) y (.f64 x x)) (pow.f64 (-.f64 x y) #s(literal -1 binary64)))
(.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64)))
(.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (.f64 (+.f64 y x) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64))))
(.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) (/.f64 (+.f64 y x) (fma.f64 (-.f64 x y) x (*.f64 y y))))
(*.f64 (-.f64 x y) (pow.f64 (/.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)))
(.f64 (-.f64 x y) (.f64 (+.f64 y x) (pow.f64 (-.f64 x y) #s(literal -1 binary64))))
(*.f64 (-.f64 x y) (/.f64 (+.f64 y x) (-.f64 x y)))
(*.f64 (+.f64 y x) #s(literal 1 binary64))
(pow.f64 (/.f64 (-.f64 y x) (*.f64 (+.f64 y x) (-.f64 y x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (+.f64 y x) #s(literal 1 binary64))
(/.f64 (-.f64 (/.f64 (.f64 x x) (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64))) (/.f64 (.f64 y y) (.f64 (/.f64 (+.f64 y x) (fma.f64 (+.f64 y x) y (.f64 x x))) #s(literal 1 binary64)))) (fma.f64 (-.f64 x y) x (*.f64 y y)))
(/.f64 (-.f64 (/.f64 (.f64 x x) #s(literal 1 binary64)) (/.f64 (.f64 y y) #s(literal 1 binary64))) (-.f64 x y))
(/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 y y) #s(literal 1 binary64))) (-.f64 x y))
(/.f64 (-.f64 (neg.f64 (.f64 x x)) (.f64 (neg.f64 y) y)) (neg.f64 (-.f64 x y)))
(/.f64 (-.f64 (/.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 y y)) (-.f64 x y))
(/.f64 (/.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)) #s(literal 1 binary64)) (-.f64 x y))
(/.f64 (.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x)) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (fma.f64 (+.f64 y x) y (*.f64 x x)))
(/.f64 (.f64 (.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) (-.f64 x y)) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (+.f64 y x))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (fma.f64 y y (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (-.f64 x y) #s(literal -1 binary64))) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (fma.f64 (-.f64 x y) x (.f64 y y))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64))) (+.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (*.f64 y x) #s(literal 3 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (+.f64 y x) (-.f64 y x))) (-.f64 y x))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (neg.f64 y) y (.f64 x x)))) (neg.f64 (-.f64 x y)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 (fma.f64 (-.f64 x y) x (.f64 y y))))
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eval187.0ms (2.9%)

Memory: 2.2MiB live, 384.6MiB allocated
Compiler: Compiled 37 757 to 2 885 computations (92.4% saved)

prune163.0ms (2.6%)

Memory

21.8MiB live, 425.6MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1 152	2	1 154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1 152	3	1 155

Accuracy

100.0%

Counts

1 155 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 x y) (-.f64 x y))
▶	57.0%	#s(approx (* (+ x y) (- x y)) (*.f64 (neg.f64 y) y))
▶	52.7%	#s(approx (* (+ x y) (- x y)) (*.f64 x x))

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify1.0s (15.9%)

Memory

20.2MiB live, 492.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Rules

74 416×	`lower-fma.f64`
74 416×	`lower-fma.f32`
6 048×	`lower-*.f32`
6 044×	`lower-*.f64`
4 262×	`distribute-rgt-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
0	13	34
1	23	34
2	45	34
3	99	34
4	265	34
5	500	34
6	964	34
7	1631	34
8	3019	34
9	3888	34
10	4127	34
11	4252	34
12	4341	34
13	4343	34
14	4830	34
15	5312	34
16	5712	34
17	5892	34
18	5952	34
19	5976	34
20	6000	34
21	6000	34
22	6096	34
23	6096	34
24	6585	34
25	6985	34
26	7145	34
27	7305	34
28	7385	34
29	7385	34
30	7385	34
0	9937	34

Stop Event

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

Calls

Call 1

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

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

localize22.0ms (0.3%)

Memory

4.8MiB live, 41.8MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 (neg.f64 y) y)
accuracy	0	(neg.f64 y)
accuracy	27.52093490258527	#s(approx (* (+ x y) (- x y)) (*.f64 (neg.f64 y) y))
accuracy	0	(*.f64 x x)
accuracy	30.28610843689	#s(approx (* (+ x y) (- x y)) (*.f64 x x))

Samples

17.0ms

256×

valid

Compiler

Compiled 27 to 10 computations (63% saved)

Precisions

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

ival-mult: 4.0ms (48% of total)

ival-sub: 1.0ms (12% of total)

ival-add: 1.0ms (12% of total)

ival-neg: 1.0ms (12% of total)

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

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

series27.0ms (0.4%)

Memory

-35.7MiB live, 8.5MiB allocated

Counts

5 → 84

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
23.0ms	y	@	inf	((* (+ x y) (- x y)) (* x x) (* (+ x y) (- x y)) (* (neg y) y) (neg y))
1.0ms	y	@	-inf	((* (+ x y) (- x y)) (* x x) (* (+ x y) (- x y)) (* (neg y) y) (neg y))
1.0ms	y	@	0	((* (+ x y) (- x y)) (* x x) (* (+ x y) (- x y)) (* (neg y) y) (neg y))
0.0ms	x	@	-inf	((* (+ x y) (- x y)) (* x x) (* (+ x y) (- x y)) (* (neg y) y) (neg y))
0.0ms	x	@	inf	((* (+ x y) (- x y)) (* x x) (* (+ x y) (- x y)) (* (neg y) y) (neg y))

simplify157.0ms (2.5%)

Memory

18.4MiB live, 204.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 420×	`lower-fma.f64`
14 420×	`lower-fma.f32`
2 986×	`lower-*.f64`
2 986×	`lower-*.f32`
2 168×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	624
1	194	480
2	604	456
3	2453	456
4	7125	424
0	8327	416

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

rewrite93.0ms (1.5%)

Memory

20.3MiB live, 144.2MiB allocated

Rules

2 452×	`lower-fma.f64`
2 452×	`lower-fma.f32`
2 294×	`lower-/.f64`
2 294×	`lower-/.f32`
1 924×	`lower-*.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	32
0	13	32
1	40	32
2	275	32
3	4253	25
0	10067	25

Stop Event

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

Counts

5 → 70

Calls

Call 1

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

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

eval34.0ms (0.5%)

Memory: -17.3MiB live, 20.6MiB allocated
Compiler: Compiled 1 153 to 228 computations (80.2% saved)

prune10.0ms (0.2%)

Memory

17.2MiB live, 17.2MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	153	4	157

Accuracy

100.0%

Counts

157 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 x y) (-.f64 x y))
✓	57.0%	#s(approx (* (+ x y) (- x y)) (*.f64 (neg.f64 y) y))
▶	13.7%	#s(approx (* (+ x y) (- x y)) (*.f64 y y))
✓	52.7%	#s(approx (* (+ x y) (- x y)) (*.f64 x x))

Compiler

Compiled 20 to 18 computations (10% saved)

simplify570.0ms (9%)

Memory

-18.1MiB live, 313.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

37 776×	`lower-fma.f64`
37 776×	`lower-fma.f32`
8 740×	`lower-+.f64`
8 740×	`lower-+.f32`
3 216×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
0	8	15
1	12	15
2	31	15
3	73	15
4	184	15
5	348	15
6	689	15
7	1309	15
8	2239	15
9	2858	15
10	3026	15
11	3068	15
12	3106	15
13	3106	15
14	3106	15
15	3108	15
0	9313	15

Stop Event

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

Calls

Call 1

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

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

localize17.0ms (0.3%)

Memory

-4.9MiB live, 33.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(*.f64 y y)
accuracy	55.21656665418183	#s(approx (* (+ x y) (- x y)) (*.f64 y y))

Samples

13.0ms

256×

valid

Compiler

Compiled 13 to 8 computations (38.5% saved)

Precisions

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

ival-mult: 3.0ms (52.6% of total)

ival-sub: 1.0ms (17.5% of total)

ival-add: 1.0ms (17.5% of total)

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

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

series2.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

2 → 36

Calls

Call 1

Inputs

#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>) () ())

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

Calls

6 calls:

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

simplify135.0ms (2.1%)

Memory

16.5MiB live, 213.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 420×	`lower-fma.f64`
14 420×	`lower-fma.f32`
2 986×	`lower-*.f64`
2 986×	`lower-*.f32`
2 168×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	294
1	194	222
2	604	210
3	2453	210
4	7125	194
0	8327	190

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

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

rewrite216.0ms (3.4%)

Memory

-20.6MiB live, 234.1MiB allocated

Rules

5 258×	`lower-fma.f64`
5 258×	`lower-fma.f32`
5 008×	`lower-*.f32`
5 006×	`lower-*.f64`
3 706×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
0	8	14
1	30	14
2	255	14
3	3956	14
0	9598	14

Stop Event

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

Counts

2 → 18

Calls

Call 1

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

Outputs
#s(approx (* (+ x y) (- x y)) (*.f64 y y))
(.f64 (pow.f64 (.f64 (neg.f64 y) #s(literal -1 binary64)) #s(literal 1 binary64)) y)
(*.f64 (pow.f64 (neg.f64 y) #s(literal 1 binary64)) (pow.f64 (neg.f64 y) #s(literal 1 binary64)))
(.f64 (.f64 (neg.f64 y) #s(literal -1 binary64)) y)
(.f64 #s(literal -1 binary64) (pow.f64 (.f64 (neg.f64 y) y) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 y) y))
(.f64 #s(literal 1 binary64) (.f64 y y))
(*.f64 (neg.f64 y) (neg.f64 y))
(.f64 (.f64 y y) #s(literal 1 binary64))
(*.f64 y y)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 y))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 y) y))
(exp.f64 (*.f64 (log.f64 (neg.f64 y)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval8.0ms (0.1%)

Memory: -25.4MiB live, 12.8MiB allocated
Compiler: Compiled 354 to 67 computations (81.1% saved)

prune5.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	54	4	58

Accuracy

100.0%

Counts

58 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 x y) (-.f64 x y))
✓	57.0%	#s(approx (* (+ x y) (- x y)) (*.f64 (neg.f64 y) y))
✓	13.7%	#s(approx (* (+ x y) (- x y)) (*.f64 y y))
✓	52.7%	#s(approx (* (+ x y) (- x y)) (*.f64 x x))

Compiler

Compiled 40 to 30 computations (25% saved)

regimes7.0ms (0.1%)

Memory

15.5MiB live, 15.5MiB allocated

Counts

4 → 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 (neg.f64 y) y))
(*.f64 (+.f64 x y) (-.f64 x y))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 9 computations (0% saved)

regimes8.0ms (0.1%)

Memory

-28.0MiB live, 10.8MiB 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 (neg.f64 y) y))

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

Calls

3 calls:

4.0ms	y
2.0ms	x
2.0ms	(*.f64 (+.f64 x y) (-.f64 x y))

Results

Accuracy	Segments	Branch
81.3%	2	`x`
77.4%	2	`y`
99.5%	2	`(*.f64 (+.f64 x y) (-.f64 x y))`

Compiler

Compiled 9 to 9 computations (0% saved)

regimes5.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Accuracy

Total -24.9b remaining (-82.3%)

Threshold costs -24.9b (-82.3%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
52.7%	1	`y`
52.7%	1	`x`
52.7%	1	`(*.f64 (+.f64 x y) (-.f64 x y))`

Compiler

Compiled 9 to 9 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-6.027560963e-314	-0.0

Compiler

Compiled 10 to 10 computations (0% saved)

simplify56.0ms (0.9%)

Memory

-11.1MiB live, 33.5MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`-commutative-binary64-.f64`
8×	`+-commutative-binary64-+.f64`
6×	`sub-neg-binary64-neg.f64-+.f64--.f64`
4×	`neg-sub0-binary64--.f64-neg.f64`
4×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	51
1	26	51
2	31	51
3	34	51
4	35	51

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (*.f64 (+.f64 x y) (-.f64 x y)) #s(literal -10120112665/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx (* (+ x y) (- x y)) (*.f64 (neg.f64 y) y)) #s(approx (* (+ x y) (- x y)) (*.f64 x x)))

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

Outputs
(*.f64 (+.f64 x y) (-.f64 x y))
(*.f64 (-.f64 x y) (+.f64 y x))
(if (<=.f64 (.f64 (+.f64 x y) (-.f64 x y)) #s(literal -10120112665/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx ( (+ x y) (- x y)) (.f64 (neg.f64 y) y)) #s(approx ( (+ x y) (- x y)) (*.f64 x x)))
(if (<=.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -10120112665/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) #s(approx ( (+ x y) (- x y)) (.f64 (neg.f64 y) y)) #s(approx ( (+ x y) (- x y)) (*.f64 x x)))
#s(approx (* (+ x y) (- x y)) (*.f64 x x))

soundness391.0ms (6.2%)

Memory

-0.2MiB live, 115.7MiB allocated

Rules

14 152×	`lower-fma.f64`
14 152×	`lower-fma.f32`
2 614×	`lower--.f64`
2 614×	`lower--.f32`
2 222×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	86	309
1	265	249
2	786	249
3	3277	249
0	8535	249

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 40 to 23 computations (42.5% saved)

preprocess46.0ms (0.7%)

Memory

18.0MiB live, 59.9MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 130 to 76 computations (41.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample778.0ms (12.3%)

explain62.0ms (1%)

preprocess798.0ms (12.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify835.0ms (13.2%)

localize16.0ms (0.2%)

series4.0ms (0.1%)

simplify311.0ms (4.9%)

rewrite374.0ms (5.9%)

eval187.0ms (2.9%)

prune163.0ms (2.6%)

simplify1.0s (15.9%)

localize22.0ms (0.3%)

series27.0ms (0.4%)

simplify157.0ms (2.5%)

rewrite93.0ms (1.5%)

eval34.0ms (0.5%)

prune10.0ms (0.2%)

simplify570.0ms (9%)

localize17.0ms (0.3%)

series2.0ms (0%)

simplify135.0ms (2.1%)

rewrite216.0ms (3.4%)

eval8.0ms (0.1%)

prune5.0ms (0.1%)

regimes7.0ms (0.1%)

regimes8.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

simplify56.0ms (0.9%)

soundness391.0ms (6.2%)

preprocess46.0ms (0.7%)

end0.0ms (0%)

Profiling