Metrics for Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, G

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 9 computations (0% saved)

sample577.0ms (26.2%)

Memory

17.5MiB live, 1 403.8MiB allocated

Samples

347.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 188.0ms

ival-div: 67.0ms (35.6% of total)

ival-mult: 59.0ms (31.3% of total)

ival-add: 45.0ms (23.9% of total)

ival-true: 7.0ms (3.7% of total)

exact: 7.0ms (3.7% of total)

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

Bogosity

explain57.0ms (2.6%)

Memory

-6.6MiB live, 155.2MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
-	-	`(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`y`
-	-	`#s(literal 1 binary64)`
-	-	`(+.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

26.0ms

512×

valid

Compiler

Compiled 45 to 25 computations (44.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 5.0ms (40.2% of total)

ival-div: 3.0ms (24.1% of total)

ival-add: 3.0ms (24.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess22.0ms (1%)

Memory

11.2MiB live, 52.4MiB allocated

Algorithm

1×	egg-herbie

Rules

56×	`sub-neg`
54×	`distribute-lft-neg-in`
50×	`associate--r+`
46×	`distribute-lft-in`
42×	`distribute-rgt-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	56	25
2	170	25
3	283	25
4	388	25
5	445	25
6	456	25
0	7	5
0	11	5
1	21	5
2	23	5
0	23	5

Stop Event

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

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

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

Symmetry

(sort x y)

Compiler

Compiled 7 to 7 computations (0% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

Compiler

Compiled 7 to 7 computations (0% saved)

simplify4.0ms (0.2%)

Memory

10.2MiB live, 10.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x y)
cost-diff	0	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))

Rules

12×	`lower-*.f32`
10×	`lower-*.f64`
8×	`lower-fma.f64`
8×	`lower-fma.f32`
8×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
0	11	13
1	21	13
2	23	13
0	23	13

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
(+.f64 x y)
x
y

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

localize19.0ms (0.9%)

Memory

-25.4MiB live, 53.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
accuracy	0	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
accuracy	0	(+.f64 x y)
accuracy	0	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

Samples

12.0ms

256×

valid

Compiler

Compiled 19 to 9 computations (52.6% saved)

Precisions

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

ival-mult: 3.0ms (49.9% of total)

ival-div: 2.0ms (33.3% of total)

ival-add: 1.0ms (16.6% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.2%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

3 → 48

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y)) (patch (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y)) #<representation binary64>) () ())
#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())

Inputs

#s(alt (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (patch (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) #<representation binary64>) () ())

#s(alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y)) (patch (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y)) #<representation binary64>) () ())

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((/ 1 2) (* (/ 1 2) (+ x y)) (+ x y))
0.0ms	y	@	-inf	((/ 1 2) (* (/ 1 2) (+ x y)) (+ x y))
0.0ms	y	@	inf	((/ 1 2) (* (/ 1 2) (+ x y)) (+ x y))
0.0ms	x	@	inf	((/ 1 2) (* (/ 1 2) (+ x y)) (+ x y))
0.0ms	y	@	0	((/ 1 2) (* (/ 1 2) (+ x y)) (+ x y))

simplify147.0ms (6.7%)

Memory

4.3MiB live, 200.0MiB allocated

Algorithm

1×	egg-herbie

Rules

11 640×	`lower-fma.f64`
11 640×	`lower-fma.f32`
2 608×	`lower-*.f64`
2 608×	`lower-*.f32`
2 172×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	168
1	115	168
2	264	168
3	783	168
4	1814	168
5	2648	168
6	3320	168
7	3621	168
8	3783	168
9	3819	168
10	6057	168
0	8007	168

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 42

Calls

Call 1

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

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

rewrite183.0ms (8.3%)

Memory

-4.3MiB live, 359.5MiB allocated

Rules

8 694×	`lower-fma.f64`
8 694×	`lower-fma.f32`
4 456×	`lower-/.f64`
4 456×	`lower-/.f32`
3 962×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
0	11	9
1	34	9
2	182	9
3	1529	9
0	8403	9

Stop Event

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

Counts

3 → 254

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
(+.f64 x y)

Outputs
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eval35.0ms (1.6%)

Memory: -6.4MiB live, 108.3MiB allocated
Compiler: Compiled 6 704 to 798 computations (88.1% saved)

prune5.0ms (0.2%)

Memory

22.4MiB live, 22.4MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	293	3	296
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	294	3	297

Accuracy

100.0%

Counts

297 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
▶	48.9%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
▶	52.4%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify4.0ms (0.2%)

Memory

8.1MiB live, 8.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 y x)
cost-diff	0	(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 y #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))

Rules

12×	`lower-*.f32`
8×	`lower-fma.f64`
8×	`lower-fma.f32`
8×	`lower-+.f32`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
0	18	39
1	25	39
2	26	39
0	26	39

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
(*.f64 y #s(literal 1/2 binary64))
y
#s(literal 1/2 binary64)
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+.f64 y x)
y
x
#s(literal 1/2 binary64)

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

localize29.0ms (1.3%)

Memory

-8.0MiB live, 75.2MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 y x)
accuracy	0	(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
accuracy	0	(*.f64 y #s(literal 1/2 binary64))
accuracy	32.69556463404888	#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	30.479729688933507	#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))

Samples

22.0ms

256×

valid

Compiler

Compiled 37 to 14 computations (62.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 6.0ms (54.1% of total)

ival-div: 2.0ms (18% of total)

ival-add: 2.0ms (18% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.3%)

Memory

-22.4MiB live, 16.9MiB allocated

Counts

6 → 120

Calls

Call 1

Inputs
#s(alt #s(approx (* (/ 1 2) (+ x y)) (.f64 x #s(literal 1/2 binary64))) (patch #s(approx ( (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/2 binary64)) (patch (.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ 1 2) (+ x y)) (.f64 y #s(literal 1/2 binary64))) (patch #s(approx ( (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 y #s(literal 1/2 binary64)) (patch (.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 y x) #s(literal 1/2 binary64)) (patch (.f64 (+.f64 y x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 y x) (patch (+.f64 y x) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	((* (/ 1 2) (+ x y)) (* x 1/2) (* (/ 1 2) (+ x y)) (* y 1/2) (* (+ y x) 1/2) (+ y x))
1.0ms	y	@	-inf	((* (/ 1 2) (+ x y)) (* x 1/2) (* (/ 1 2) (+ x y)) (* y 1/2) (* (+ y x) 1/2) (+ y x))
0.0ms	y	@	0	((* (/ 1 2) (+ x y)) (* x 1/2) (* (/ 1 2) (+ x y)) (* y 1/2) (* (+ y x) 1/2) (+ y x))
0.0ms	x	@	inf	((* (/ 1 2) (+ x y)) (* x 1/2) (* (/ 1 2) (+ x y)) (* y 1/2) (* (+ y x) 1/2) (+ y x))
0.0ms	x	@	-inf	((* (/ 1 2) (+ x y)) (* x 1/2) (* (/ 1 2) (+ x y)) (* y 1/2) (* (+ y x) 1/2) (+ y x))

simplify183.0ms (8.3%)

Memory

31.3MiB live, 273.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 640×	`lower-fma.f64`
11 640×	`lower-fma.f32`
2 608×	`lower-*.f64`
2 608×	`lower-*.f32`
2 172×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	456
1	115	456
2	264	456
3	783	456
4	1814	456
5	2648	456
6	3320	456
7	3621	456
8	3783	456
9	3819	456
10	6057	456
0	8007	456

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 114

Calls

Call 1

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

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

rewrite147.0ms (6.7%)

Memory

8.3MiB live, 278.0MiB allocated

Rules

4 506×	`lower-fma.f64`
4 506×	`lower-fma.f32`
4 364×	`lower-/.f64`
4 364×	`lower-/.f32`
3 548×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
0	18	32
1	46	32
2	257	32
3	2658	32
0	8360	32

Stop Event

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

Counts

6 → 262

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
(*.f64 y #s(literal 1/2 binary64))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(+.f64 y x)

Outputs
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eval44.0ms (2%)

Memory: -4.2MiB live, 120.7MiB allocated
Compiler: Compiled 7 044 to 936 computations (86.7% saved)

prune12.0ms (0.5%)

Memory

-4.1MiB live, 33.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	376	0	376
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	376	3	379

Accuracy

100.0%

Counts

379 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
✓	48.9%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
✓	52.4%	#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))

Compiler

Compiled 33 to 29 computations (12.1% saved)

regimes34.0ms (1.6%)

Memory

-39.5MiB live, 53.0MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

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

Calls

4 calls:

25.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
4.0ms	x
2.0ms	(+.f64 x y)
2.0ms	y

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
100.0%	1	`(+.f64 x y)`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

regimes7.0ms (0.3%)

Memory

19.2MiB live, 19.2MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64)))

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

Calls

4 calls:

2.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
2.0ms	(+.f64 x y)
2.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
82.8%	2	`x`
87.9%	2	`y`
97.9%	2	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
97.9%	2	`(+.f64 x y)`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

regimes7.0ms (0.3%)

Memory

-23.1MiB live, 16.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))

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

Calls

4 calls:

1.0ms	y
1.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))
1.0ms	(+.f64 x y)
1.0ms	x

Results

Accuracy	Segments	Branch
52.4%	1	`x`
52.4%	1	`y`
52.4%	1	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))`
52.4%	1	`(+.f64 x y)`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0967124523631728e-250	1.554513895208913e-275

Compiler

Compiled 10 to 12 computations (-20% saved)

simplify26.0ms (1.2%)

Memory

27.2MiB live, 66.4MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`
2×	`+-commutative-binary64-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	25	38

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (+.f64 x y) #s(literal -1612226962694291/16122269626942909129404900662735492142298807557254685123533957184651913530173488143140175045399694454793530120643833272670970079330526292030350920973600450955456136596649325078391464772840162385651374295294530896122681527488756156580761624107880751845994219387748352 binary64)) #s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64))) #s(approx (* (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64))))

#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))

Outputs
(*.f64 (+.f64 y x) #s(literal 1/2 binary64))
(*.f64 (+.f64 x y) #s(literal 1/2 binary64))
(if (<=.f64 (+.f64 x y) #s(literal -1612226962694291/16122269626942909129404900662735492142298807557254685123533957184651913530173488143140175045399694454793530120643833272670970079330526292030350920973600450955456136596649325078391464772840162385651374295294530896122681527488756156580761624107880751845994219387748352 binary64)) #s(approx (* (/ 1 2) (+ x y)) (.f64 x #s(literal 1/2 binary64))) #s(approx ( (/ 1 2) (+ x y)) (*.f64 y #s(literal 1/2 binary64))))
(if (<=.f64 (+.f64 x y) #s(literal -1612226962694291/16122269626942909129404900662735492142298807557254685123533957184651913530173488143140175045399694454793530120643833272670970079330526292030350920973600450955456136596649325078391464772840162385651374295294530896122681527488756156580761624107880751845994219387748352 binary64)) #s(approx (* (/ 1 2) (+ x y)) (.f64 #s(literal 1/2 binary64) x)) #s(approx ( (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) y)))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 x #s(literal 1/2 binary64)))
#s(approx (* (/ 1 2) (+ x y)) (*.f64 #s(literal 1/2 binary64) x))

soundness596.0ms (27.1%)

Memory

-18.0MiB live, 300.8MiB allocated

Rules

11 640×	`lower-fma.f64`
11 640×	`lower-fma.f32`
8 694×	`lower-fma.f64`
8 694×	`lower-fma.f32`
4 456×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
0	11	9
1	34	9
2	182	9
3	1529	9
0	8403	9
0	38	168
1	115	168
2	264	168
3	783	168
4	1814	168
5	2648	168
6	3320	168
7	3621	168
8	3783	168
9	3819	168
10	6057	168
0	8007	168

Stop Event

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

Compiler

Compiled 58 to 36 computations (37.9% saved)

preprocess52.0ms (2.4%)

Memory: -2.2MiB live, 155.8MiB allocated
Remove: (sort x y)
Compiler: Compiled 100 to 78 computations (22% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample577.0ms (26.2%)

explain57.0ms (2.6%)

preprocess22.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize19.0ms (0.9%)

series3.0ms (0.2%)

simplify147.0ms (6.7%)

rewrite183.0ms (8.3%)

eval35.0ms (1.6%)

prune5.0ms (0.2%)

simplify4.0ms (0.2%)

localize29.0ms (1.3%)

series6.0ms (0.3%)

simplify183.0ms (8.3%)

rewrite147.0ms (6.7%)

eval44.0ms (2%)

prune12.0ms (0.5%)

regimes34.0ms (1.6%)

regimes7.0ms (0.3%)

regimes7.0ms (0.3%)

bsearch0.0ms (0%)

simplify26.0ms (1.2%)

soundness596.0ms (27.1%)

preprocess52.0ms (2.4%)

end0.0ms (0%)

Profiling