Metrics for Numeric.Integration.TanhSinh:everywhere from integration-0.2.1

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 8 computations (11.1% saved)

sample727.0ms (10.3%)

Memory

-19.9MiB live, 909.0MiB allocated

Samples

504.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 251.0ms

ival-mult: 194.0ms (77.3% of total)

ival-add: 43.0ms (17.1% of total)

ival-true: 6.0ms (2.4% of total)

exact: 5.0ms (2% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

preprocess127.0ms (1.8%)

Memory

-7.4MiB live, 31.8MiB allocated

Algorithm

1×	egg-herbie

Rules

158×	`associate-r`
124×	`distribute-lft-in`
112×	`unsub-neg`
92×	`associate-l`
82×	`distribute-lft-neg-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs y)

(negabs x)

explain82.0ms (1.2%)

Memory

-8.0MiB live, 112.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
15	-	-	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
0	-	-	`y`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 y y)`
0	-	-	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`	*no**	15	0

Confusion

	Predicted +	Predicted -
+	15	0
-	0	241

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	15	0	0
-	0	0	241

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	241
1	15

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms

512×

valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

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

ival-mult: 8.0ms (73.8% of total)

ival-add: 2.0ms (18.4% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	94.4%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify6.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Rules

46×	`lower-*.f32`
42×	`lower-*.f64`
22×	`lower-fma.f64`
22×	`lower-fma.f32`
14×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	19	18
2	27	18
3	49	18
4	49	18
0	49	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (0.2%)

Memory

26.4MiB live, 26.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 y y))
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	94.4%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Samples

11.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 3.0ms (62% of total)

ival-add: 1.0ms (20.7% of total)

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

exact: 0.0ms (0% of total)

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

series19.0ms (0.3%)

Memory

-32.4MiB live, 6.5MiB allocated

Counts

3 → 48

Calls

Call 1

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

Inputs

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

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

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

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

Calls

12 calls:

Time	Variable		Point	Expression
16.0ms	x	@	inf	(* x (+ 1 (* y y)))
1.0ms	x	@	0	(* x (+ 1 (* y y)))
1.0ms	x	@	-inf	(* x (+ 1 (* y y)))
0.0ms	y	@	inf	(+ 1 (* y y))
0.0ms	y	@	0	(+ 1 (* y y))

simplify343.0ms (4.9%)

Memory

4.5MiB live, 564.4MiB allocated

Algorithm

1×	egg-herbie

Rules

9 064×	`lower-fma.f64`
9 064×	`lower-fma.f32`
6 574×	`lower-*.f64`
6 574×	`lower-*.f32`
2 468×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	246
1	42	246
2	74	246
3	212	246
4	695	246
5	1887	246
6	2663	246
7	3730	246
8	5074	246
9	5970	246
10	6935	246
11	7278	246
12	7397	246
13	7474	246
14	7543	246
15	7690	246
0	8226	216

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

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

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

rewrite384.0ms (5.5%)

Memory

28.9MiB live, 584.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 176×	`lower-fma.f64`
5 176×	`lower-fma.f32`
4 882×	`lower-/.f64`
4 882×	`lower-/.f32`
4 246×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	34	15
2	209	15
3	1404	15
0	8269	13

Stop Event

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

Counts

3 → 368

Calls

Call 1

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

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

eval48.0ms (0.7%)

Memory: 0.7MiB live, 118.3MiB allocated
Compiler: Compiled 15 373 to 1 102 computations (92.8% saved)

prune198.0ms (2.8%)

Memory

-8.0MiB live, 109.0MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	409	6	415
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	410	6	416

Accuracy

100.0%

Counts

416 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	94.4%	(fma.f64 (*.f64 y y) x x)
▶	99.9%	(fma.f64 (*.f64 y x) y x)
	70.5%	(/.f64 (.f64 (fma.f64 y (.f64 y (*.f64 y y)) #s(literal -1 binary64)) x) (fma.f64 y y #s(literal -1 binary64)))
▶	94.4%	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))))
▶	45.5%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
▶	52.8%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 114 to 62 computations (45.6% saved)

simplify8.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 y y #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))
✓	cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))))
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(fma.f64 (*.f64 y y) x x)
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	#s(approx (+ 1 (* y y)) (*.f64 y y))
✓	cost-diff	0	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	cost-diff	0	#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
✓	cost-diff	0	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
✓	cost-diff	0	(*.f64 y x)
✓	cost-diff	0	(fma.f64 (*.f64 y x) y x)

Rules

74×	`lower-*.f32`
66×	`lower-*.f64`
30×	`lower-/.f32`
26×	`lower-/.f64`
22×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	86
0	27	80
1	42	80
2	50	80
3	61	80
4	104	80
5	104	80
6	105	80
0	105	80

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize137.0ms (1.9%)

Memory

-11.0MiB live, 46.6MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 y y #s(literal 1 binary64))
✓	accuracy	98.8%	(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))
✓	accuracy	95.5%	(/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))))
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	94.4%	(fma.f64 (*.f64 y y) x x)
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	94.4%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	accuracy	50.8%	#s(approx (+ 1 (* y y)) (*.f64 y y))
✓	accuracy	94.4%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
✓	accuracy	52.5%	#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 y x)
✓	accuracy	99.9%	(fma.f64 (*.f64 y x) y x)

Samples

27.0ms

256×

valid

Compiler

Compiled 81 to 16 computations (80.2% saved)

Precisions

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

ival-mult: 8.0ms (51.5% of total)

ival-add: 4.0ms (25.7% of total)

ival-div: 3.0ms (19.3% of total)

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

exact: 0.0ms (0% of total)

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

series213.0ms (3%)

Memory

-30.0MiB live, 8.1MiB allocated

Counts

11 → 204

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor inf y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor -inf y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) 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 (* x y) (taylor 0 y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf y) (#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 (* x y) (taylor 0 x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor inf y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor -inf y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (pow y 2) 1))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2)) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2)) (taylor inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2)) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2)) (taylor -inf y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor -inf y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor -inf y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor -inf y) (#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())) ())

Calls

51 calls:

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

simplify245.0ms (3.5%)

Memory

34.8MiB live, 467.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 220×	`lower-fma.f64`
10 220×	`lower-fma.f32`
2 984×	`lower-*.f64`
2 984×	`lower-*.f32`
1 546×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	1202
1	110	1200
2	259	1196
3	775	1192
4	2593	1192
5	6407	1192
0	8196	1058

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 199

Calls

Call 1

Inputs
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))

Outputs
x
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(fma.f64 x (*.f64 y y) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(fma.f64 x (*.f64 y y) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(fma.f64 x (*.f64 y y) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(fma.f64 x (*.f64 y y) x)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
x
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
x
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
x
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(fma.f64 x (*.f64 y y) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(fma.f64 x (*.f64 y y) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(fma.f64 x (*.f64 y y) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (+ 1 (pow y 2)))
(fma.f64 x (*.f64 y y) x)
x
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(+ x (* x (pow y 2)))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(fma.f64 x (*.f64 y y) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(fma.f64 (*.f64 y y) (fma.f64 y y #s(literal -1 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 y y)) (fma.f64 y (.f64 y (.f64 y y)) #s(literal 1 binary64)))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 y y))) (.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 y y))) (.f64 y y))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 y y))) (.f64 y y))) (.f64 y y))) (.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 y y))) (.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 y y))) (.f64 y y))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 y y))) (.f64 y y))) (.f64 y y))) (.f64 y y))
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))

rewrite318.0ms (4.5%)

Memory

-3.5MiB live, 473.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 494×	`lower-fma.f32`
4 488×	`lower-fma.f64`
3 754×	`lower-*.f32`
3 746×	`lower-*.f64`
2 380×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	72
0	27	66
1	105	66
2	562	66
3	5687	66
0	8063	66

Stop Event

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

Counts

11 → 873

Calls

Call 1

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

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

eval187.0ms (2.7%)

Memory: 31.5MiB live, 253.1MiB allocated
Compiler: Compiled 25 687 to 1 387 computations (94.6% saved)

prune106.0ms (1.5%)

Memory

-13.3MiB live, 243.2MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1 093	2	1 095
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	1 095	6	1 101

Accuracy

100.0%

Counts

1 101 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (/.f64 y (/.f64 #s(literal 1 binary64) x)) y x)
✓	94.4%	(fma.f64 (*.f64 y y) x x)
✓	99.9%	(fma.f64 (*.f64 y x) y x)
▶	45.5%	(/.f64 #s(approx (+ 1 (* y y)) (*.f64 y y)) (/.f64 #s(literal 1 binary64) x))
✓	45.5%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	52.8%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 50 to 28 computations (44% saved)

simplify9.0ms (0.1%)

Memory

-24.0MiB live, 15.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(fma.f64 (/.f64 y (/.f64 #s(literal 1 binary64) x)) y x)
✓	cost-diff	1088	(/.f64 y (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	#s(approx (+ 1 (* y y)) (*.f64 y y))
✓	cost-diff	1088	(/.f64 #s(approx (+ 1 (* y y)) (*.f64 y y)) (/.f64 #s(literal 1 binary64) x))

Rules

62×	`lower-*.f32`
60×	`lower-*.f64`
32×	`lower-/.f32`
26×	`lower-/.f64`
22×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	50
0	17	50
1	27	44
2	40	44
3	53	44
4	54	44
5	61	44
6	63	44
7	89	44
8	89	44
9	96	44
10	96	44
11	97	44
0	97	42

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize64.0ms (0.9%)

Memory

24.9MiB live, 64.0MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.9%	(fma.f64 (/.f64 y (/.f64 #s(literal 1 binary64) x)) y x)
✓	accuracy	99.7%	(/.f64 y (/.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	94.2%	(/.f64 #s(approx (+ 1 (* y y)) (*.f64 y y)) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	50.8%	#s(approx (+ 1 (* y y)) (*.f64 y y))

Samples

51.0ms

256×

valid

Compiler

Compiled 45 to 12 computations (73.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-div: 37.0ms (86.1% of total)

ival-mult: 3.0ms (7% of total)

ival-add: 2.0ms (4.7% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

-31.5MiB live, 7.5MiB allocated

Counts

6 → 108

Calls

Call 1

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

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

Calls

27 calls:

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

simplify173.0ms (2.5%)

Memory

33.9MiB live, 151.1MiB allocated

Algorithm

1×	egg-herbie

Rules

3 120×	`lower-fma.f64`
3 120×	`lower-fma.f32`
2 272×	`lower-*.f64`
2 272×	`lower-*.f32`
2 122×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	512
1	59	512
2	122	512
3	347	512
4	1501	512
5	4675	512
6	7808	512
0	8047	461

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 106

Calls

Call 1

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

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

rewrite294.0ms (4.2%)

Memory

-33.9MiB live, 406.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 912×	`lower-fma.f32`
4 910×	`lower-fma.f64`
3 234×	`lower-*.f32`
3 232×	`lower-*.f64`
2 136×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
0	17	41
1	74	35
2	457	35
3	5154	35
0	8308	33

Stop Event

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

Counts

6 → 253

Calls

Call 1

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

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

eval42.0ms (0.6%)

Memory: 17.4MiB live, 92.8MiB allocated
Compiler: Compiled 6 240 to 651 computations (89.6% saved)

prune50.0ms (0.7%)

Memory

25.6MiB live, 103.8MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	394	3	397
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	395	8	403

Accuracy

100.0%

Counts

403 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (/.f64 x (/.f64 #s(literal 1 binary64) y)) y x)
▶	99.8%	(fma.f64 (*.f64 (/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) y x)
✓	94.4%	(fma.f64 (*.f64 y y) x x)
✓	99.9%	(fma.f64 (*.f64 y x) y x)
▶	86.5%	(/.f64 (fma.f64 x (/.f64 #s(literal 1 binary64) (.f64 y x)) y) (/.f64 #s(literal 1 binary64) (.f64 y x)))
✓	45.5%	(/.f64 #s(approx (+ 1 (* y y)) (*.f64 y y)) (/.f64 #s(literal 1 binary64) x))
✓	45.5%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	52.8%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 80 to 44 computations (45% saved)

simplify867.0ms (12.3%)

Memory

-35.9MiB live, 939.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) y)
✓	cost-diff	0	(fma.f64 (/.f64 x (/.f64 #s(literal 1 binary64) y)) y x)
✓	cost-diff	1088	(/.f64 x (/.f64 #s(literal 1 binary64) y))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(*.f64 (/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
✓	cost-diff	0	(fma.f64 (*.f64 (/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) y x)
✓	cost-diff	0	(*.f64 y x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 y x))
✓	cost-diff	512	(fma.f64 x (/.f64 #s(literal 1 binary64) (*.f64 y x)) y)
✓	cost-diff	1920	(/.f64 (fma.f64 x (/.f64 #s(literal 1 binary64) (.f64 y x)) y) (/.f64 #s(literal 1 binary64) (.f64 y x)))

Rules

30 780×	`lower-fma.f32`
30 774×	`lower-fma.f64`
8 314×	`lower-*.f32`
8 310×	`lower-*.f64`
2 848×	`lower-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	91
0	32	95
1	55	88
2	102	82
3	204	82
4	516	76
5	1992	76
6	2400	76
7	2676	76
8	3595	76
9	4361	76
10	4687	76
11	4847	76
12	5069	76
13	5197	76
14	6119	76
0	8680	76

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (fma.f64 x (/.f64 #s(literal 1 binary64) (.f64 y x)) y) (/.f64 #s(literal 1 binary64) (.f64 y x)))
(fma.f64 x (/.f64 #s(literal 1 binary64) (*.f64 y x)) y)
x
(/.f64 #s(literal 1 binary64) (*.f64 y x))
#s(literal 1 binary64)
(*.f64 y x)
y
(fma.f64 (*.f64 (/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) y x)
(*.f64 (/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
y
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 x)
(fma.f64 (/.f64 x (/.f64 #s(literal 1 binary64) y)) y x)
(/.f64 x (/.f64 #s(literal 1 binary64) y))
x
(/.f64 #s(literal 1 binary64) y)
#s(literal 1 binary64)
y

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

localize59.0ms (0.8%)

Memory

24.2MiB live, 143.6MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) y)
✓	accuracy	99.9%	(fma.f64 (/.f64 x (/.f64 #s(literal 1 binary64) y)) y x)
✓	accuracy	99.6%	(/.f64 x (/.f64 #s(literal 1 binary64) y))
✓	accuracy	99.9%	(fma.f64 (*.f64 (/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) y x)
✓	accuracy	99.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(*.f64 (/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(*.f64 y x)
✓	accuracy	98.8%	(/.f64 #s(literal 1 binary64) (*.f64 y x))
✓	accuracy	87.4%	(fma.f64 x (/.f64 #s(literal 1 binary64) (*.f64 y x)) y)
✓	accuracy	87.3%	(/.f64 (fma.f64 x (/.f64 #s(literal 1 binary64) (.f64 y x)) y) (/.f64 #s(literal 1 binary64) (.f64 y x)))

Samples

38.0ms

256×

valid

Compiler

Compiled 97 to 21 computations (78.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-div: 12.0ms (44.6% of total)

ival-mult: 8.0ms (29.7% of total)

ival-add: 3.0ms (11.1% of total)

ival-sqrt: 3.0ms (11.1% of total)

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

exact: 0.0ms (0% of total)

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

series16.0ms (0.2%)

Memory

-5.0MiB live, 33.5MiB allocated

Counts

11 → 240

Calls

Call 1

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

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

Calls

60 calls:

Time	Variable		Point	Expression
2.0ms	y	@	0	(/ (+ (* x (/ 1 (* y x))) y) (/ 1 (* y x)))
1.0ms	x	@	0	(/ (+ (* x (/ 1 (* y x))) y) (/ 1 (* y x)))
1.0ms	x	@	-inf	(/ y (sqrt (/ 1 x)))
1.0ms	y	@	-inf	(/ (+ (* x (/ 1 (* y x))) y) (/ 1 (* y x)))
0.0ms	y	@	0	(/ y (sqrt (/ 1 x)))

simplify279.0ms (4%)

Memory

14.4MiB live, 365.2MiB allocated

Algorithm

1×	egg-herbie

Rules

7 846×	`lower-fma.f64`
7 846×	`lower-fma.f32`
3 040×	`lower-*.f64`
3 040×	`lower-*.f32`
1 472×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	1250
1	100	1120
2	214	1116
3	492	1112
4	1749	1112
5	5397	1112
0	8153	1053

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 235

Calls

Call 1

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

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

rewrite388.0ms (5.5%)

Memory

-10.5MiB live, 619.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 302×	`lower-fma.f32`
7 298×	`lower-fma.f64`
4 232×	`lower-*.f32`
4 228×	`lower-*.f64`
3 174×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	77
0	32	73
1	134	64
2	887	47
0	9057	47

Stop Event

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

Counts

11 → 1 354

Calls

Call 1

Inputs
(/.f64 (fma.f64 x (/.f64 #s(literal 1 binary64) (.f64 y x)) y) (/.f64 #s(literal 1 binary64) (.f64 y x)))
(fma.f64 x (/.f64 #s(literal 1 binary64) (*.f64 y x)) y)
(/.f64 #s(literal 1 binary64) (*.f64 y x))
(*.f64 y x)
(fma.f64 (*.f64 (/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) y x)
(*.f64 (/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(/.f64 y (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 x (/.f64 #s(literal 1 binary64) y))
(fma.f64 (/.f64 x (/.f64 #s(literal 1 binary64) y)) y x)
(/.f64 #s(literal 1 binary64) y)

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

eval278.0ms (3.9%)

Memory: 18.0MiB live, 374.7MiB allocated
Compiler: Compiled 31 354 to 1 949 computations (93.8% saved)

prune175.0ms (2.5%)

Memory

6.6MiB live, 320.3MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	1 740	2	1 742
Fresh	0	0	0
Picked	2	1	3
Done	0	5	5
Total	1 742	8	1 750

Accuracy

100.0%

Counts

1 750 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (/.f64 x (/.f64 #s(literal 1 binary64) y)) y x)
	99.7%	(fma.f64 (.f64 (.f64 (sqrt.f64 x) y) (sqrt.f64 x)) y x)
✓	94.4%	(fma.f64 (*.f64 y y) x x)
✓	99.9%	(fma.f64 (*.f64 y x) y x)
	87.2%	(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) y) y) (/.f64 #s(literal -1 binary64) (*.f64 x y)))
✓	45.5%	(/.f64 #s(approx (+ 1 (* y y)) (*.f64 y y)) (/.f64 #s(literal 1 binary64) x))
✓	45.5%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	52.8%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 200 to 85 computations (57.5% saved)

regimes27.0ms (0.4%)

Memory

-31.9MiB live, 30.8MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

5 calls:

9.0ms	(*.f64 y y)
5.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
4.0ms	x
4.0ms	y
4.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
99.9%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
99.9%	1	`(*.f64 y y)`

Compiler

Compiled 27 to 18 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

-11.8MiB live, 26.1MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	y
2.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
2.0ms	x
1.0ms	(*.f64 y y)
1.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Results

Accuracy	Segments	Branch
56.7%	3	`x`
93.3%	2	`y`
75.9%	2	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
93.3%	2	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
93.3%	2	`(*.f64 y y)`

Compiler

Compiled 27 to 18 computations (33.3% saved)

regimes6.0ms (0.1%)

Memory

22.1MiB live, 22.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
52.8%	1	`x`
52.8%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
52.8%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
52.8%	1	`(*.f64 y y)`
52.8%	1	`y`

Compiler

Compiled 27 to 18 computations (33.3% saved)

bsearch13.0ms (0.2%)

Memory

-0.3MiB live, 38.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.05399766715047813	11898.007917427805

Samples

7.0ms

144×

valid

Compiler

Compiled 156 to 101 computations (35.3% saved)

Precisions

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

ival-mult: 2.0ms (71.1% of total)

ival-add: 1.0ms (35.5% of total)

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

exact: 0.0ms (0% of total)

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

simplify8.0ms (0.1%)

Memory

-19.8MiB live, 17.3MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	20	39

Stop Event

1×

saturated

Calls

Call 1

Inputs

(fma.f64 (*.f64 y x) y x)

(if (<=.f64 y #s(literal 1 binary64)) (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))))

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

Outputs

(fma.f64 (*.f64 y x) y x)

(if (<=.f64 y #s(literal 1 binary64)) (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))))

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

soundness898.0ms (12.7%)

Memory

0.3MiB live, 239.2MiB allocated

Rules

9 064×	`lower-fma.f64`
9 064×	`lower-fma.f32`
6 574×	`lower-*.f64`
6 574×	`lower-*.f32`
5 176×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	246
1	42	246
2	74	246
3	212	246
4	695	246
5	1887	246
6	2663	246
7	3730	246
8	5074	246
9	5970	246
10	6935	246
11	7278	246
12	7397	246
13	7474	246
14	7543	246
15	7690	246
0	8226	216
0	6	15
0	9	15
1	34	15
2	209	15
3	1404	15
0	8269	13

Stop Event

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

Compiler

Compiled 58 to 30 computations (48.3% saved)

preprocess220.0ms (3.1%)

Memory

1.1MiB live, 78.4MiB allocated

Remove

(negabs x)

(abs y)

Compiler

Compiled 120 to 58 computations (51.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Iter	Nodes	Cost
0	11	50
0	17	50
1	27	44
2	40	44
3	53	44
4	54	44
5	61	44
6	63	44
7	89	44
8	89	44
9	96	44
10	96	44
11	97	44
0	97	42

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Iter	Nodes	Cost
0	11	50
0	17	50
1	27	44
2	40	44
3	53	44
4	54	44
5	61	44
6	63	44
7	89	44
8	89	44
9	96	44
10	96	44
11	97	44
0	97	42

analyze0.0ms (0%)

sample727.0ms (10.3%)

preprocess127.0ms (1.8%)

explain82.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize18.0ms (0.2%)

series19.0ms (0.3%)

simplify343.0ms (4.9%)

rewrite384.0ms (5.5%)

eval48.0ms (0.7%)

prune198.0ms (2.8%)

simplify8.0ms (0.1%)

localize137.0ms (1.9%)

series213.0ms (3%)

simplify245.0ms (3.5%)

rewrite318.0ms (4.5%)

eval187.0ms (2.7%)

prune106.0ms (1.5%)

simplify9.0ms (0.1%)

localize64.0ms (0.9%)

series4.0ms (0.1%)

simplify173.0ms (2.5%)

rewrite294.0ms (4.2%)

eval42.0ms (0.6%)

prune50.0ms (0.7%)

simplify867.0ms (12.3%)

localize59.0ms (0.8%)

series16.0ms (0.2%)

simplify279.0ms (4%)

rewrite388.0ms (5.5%)

eval278.0ms (3.9%)

prune175.0ms (2.5%)

regimes27.0ms (0.4%)

regimes9.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch13.0ms (0.2%)

simplify8.0ms (0.1%)

soundness898.0ms (12.7%)

preprocess220.0ms (3.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Iter	Nodes	Cost
0	11	50
0	17	50
1	27	44
2	40	44
3	53	44
4	54	44
5	61	44
6	63	44
7	89	44
8	89	44
9	96	44
10	96	44
11	97	44
0	97	42