Metrics for Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample592.0ms (27.4%)

Memory

4.1MiB live, 363.0MiB allocated

Samples

378.0ms

8 256×

valid

Precisions

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

ival-add: 66.0ms (48.6% of total)

ival-mult: 62.0ms (45.6% of total)

ival-true: 5.0ms (3.7% of total)

ival-assert: 3.0ms (2.2% of total)

Bogosity

explain52.0ms (2.4%)

Memory

30.5MiB live, 30.5MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

20.0ms

512×

valid

Compiler

Compiled 66 to 24 computations (63.6% saved)

Precisions

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

ival-add: 4.0ms (47.1% of total)

ival-mult: 4.0ms (47.1% of total)

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

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

preprocess32.0ms (1.5%)

Memory

-24.5MiB live, 15.3MiB allocated

Algorithm

1×	egg-herbie

Rules

118×	`sub-neg`
108×	`unsub-neg`
72×	`associate-+l-`
64×	`distribute-rgt-in`
58×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 9 to 5 computations (44.4% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify4.0ms (0.2%)

Memory

5.9MiB live, 5.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	12	17
2	15	17
3	16	17
0	16	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize13.0ms (0.6%)

Memory

19.4MiB live, 19.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (*.f64 x x) y)
accuracy	0.015625	(+.f64 (+.f64 (*.f64 x x) y) y)

Samples

9.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

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

ival-add: 2.0ms (50.7% of total)

ival-mult: 2.0ms (50.7% of total)

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

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

series18.0ms (0.8%)

Memory

-30.2MiB live, 8.8MiB allocated

Counts

3 → 60

Calls

Call 1

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

Inputs

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

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

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

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

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	y	@	0	((+ (* x x) y) (+ (+ (* x x) y) y) (* x x))
1.0ms	y	@	inf	((+ (* x x) y) (+ (+ (* x x) y) y) (* x x))
1.0ms	x	@	-inf	((+ (* x x) y) (+ (+ (* x x) y) y) (* x x))
1.0ms	x	@	inf	((+ (* x x) y) (+ (+ (* x x) y) y) (* x x))
0.0ms	x	@	0	((+ (* x x) y) (+ (+ (* x x) y) y) (* x x))

simplify106.0ms (4.9%)

Memory

25.3MiB live, 68.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4 690×	`lower-fma.f64`
4 690×	`lower-fma.f32`
3 340×	`lower-*.f64`
3 340×	`lower-*.f32`
1 326×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	282
1	80	282
2	193	282
3	649	282
4	1930	282
5	3616	282
6	6722	282
0	8178	246

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 57

Calls

Call 1

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

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

rewrite236.0ms (10.9%)

Memory

3.4MiB live, 162.6MiB allocated

Rules

7 306×	`lower-fma.f64`
7 306×	`lower-fma.f32`
4 782×	`lower-*.f32`
4 780×	`lower-*.f64`
2 300×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	37	15
2	316	15
3	4987	15
0	8103	13

Stop Event

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

Counts

3 → 251

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) y) (.f64 (fma.f64 (.f64 (.f64 x x) x) x (.f64 y y)) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) x (*.f64 y y))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) y) (.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (.f64 (neg.f64 y) y) y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 x x) x)) x (.f64 (.f64 y y) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y y))))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (.f64 (neg.f64 y) y) y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (*.f64 (neg.f64 y) y) y))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)) (.f64 (.f64 y y) y)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))))))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (.f64 (neg.f64 y) y) y))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (.f64 (.f64 x x) x) x (.f64 (fma.f64 x x y) y)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y) (.f64 y (.f64 x x))))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y) (.f64 y (*.f64 x x))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) x)) (.f64 x x) (.f64 (.f64 (.f64 (-.f64 y (.f64 x x)) y) (.f64 (-.f64 y (.f64 x x)) y)) (.f64 (-.f64 y (.f64 x x)) y)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (-.f64 y (.f64 x x)) y) (-.f64 (.f64 (-.f64 y (.f64 x x)) y) (.f64 (.f64 (*.f64 x x) x) x)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) (.f64 (-.f64 (*.f64 x x) y) (fma.f64 x x y))) #s(literal 1 binary64)) (fma.f64 x x y))
(.f64 (pow.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 y (.f64 x x))) #s(literal 1 binary64)))
(.f64 (pow.f64 (neg.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 x x) y))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (neg.f64 (fma.f64 x x y))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) #s(literal 1 binary64)) (pow.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1 binary64)) (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) #s(literal 1 binary64)) (pow.f64 (.f64 (fma.f64 x x y) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #s(literal 1 binary64)) (pow.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (.f64 (neg.f64 y) y) y))) (fma.f64 (.f64 (.f64 x x) x) x (.f64 (fma.f64 x x y) y)))
(.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y) (.f64 y (.f64 x x))))) (fma.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y) (.f64 y (*.f64 x x))))
(.f64 (/.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) x)) (.f64 x x) (.f64 (.f64 (.f64 (-.f64 y (.f64 x x)) y) (.f64 (-.f64 y (.f64 x x)) y)) (.f64 (-.f64 y (.f64 x x)) y)))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 x x) x)) x (.f64 (.f64 (-.f64 y (.f64 x x)) y) (-.f64 (.f64 (-.f64 y (.f64 x x)) y) (.f64 (.f64 (*.f64 x x) x) x)))))
(.f64 (/.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) (.f64 (-.f64 (*.f64 x x) y) (fma.f64 x x y))) (fma.f64 x x y))
(.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 y (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)))
(*.f64 #s(literal 1 binary64) (fma.f64 x x y))
(.f64 (neg.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 x x) y))))
(.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (neg.f64 (fma.f64 x x y))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))))
(.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)))
(.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (.f64 (fma.f64 x x y) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))))
(.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))
(.f64 (fma.f64 x x y) (pow.f64 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (*.f64 x x) y)) #s(literal 1 binary64)))
(.f64 (fma.f64 x x y) (pow.f64 (.f64 (-.f64 (.f64 x x) y) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))) #s(literal 1 binary64)))
(.f64 (fma.f64 x x y) (/.f64 (-.f64 (.f64 x x) y) (-.f64 (*.f64 x x) y)))
(.f64 (fma.f64 x x y) (.f64 (-.f64 (.f64 x x) y) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))))
(pow.f64 (/.f64 (-.f64 y (.f64 x x)) (.f64 (fma.f64 x x y) (-.f64 y (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)) #s(literal -1 binary64))
(pow.f64 (fma.f64 x x y) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x (.f64 y y)) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))) (fma.f64 (.f64 (.f64 x x) x) x (*.f64 y y)))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (.f64 (neg.f64 y) y) y))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y))) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 x x) x)) x (.f64 (.f64 y y) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y y)))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (.f64 (neg.f64 y) y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (*.f64 (neg.f64 y) y) y)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)) (.f64 (.f64 y y) y))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))) (fma.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y))) (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y)))) (.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))) (fma.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y))) #s(literal 3 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y))) (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y))) (fma.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) (.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y))) (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x)))) (neg.f64 (-.f64 y (*.f64 x x))))
(/.f64 (neg.f64 (neg.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)))) (neg.f64 (neg.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (neg.f64 (fma.f64 x x y)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x (.f64 y y)) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) x) x (.f64 y y)) (-.f64 (.f64 x x) y)))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (.f64 (neg.f64 y) y) y))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 x x) x)) x (.f64 (.f64 y y) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y y)))) (-.f64 (*.f64 x x) y)))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (.f64 (neg.f64 y) y) y))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) (.f64 (.f64 (neg.f64 y) y) y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 (.f64 y y) y) (.f64 (.f64 y y) y)) (.f64 (.f64 y y) y))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) #s(literal 1 binary64)) (-.f64 (.f64 x x) y))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 y y))) (.f64 (-.f64 (.f64 x x) y) (-.f64 (*.f64 x x) y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) x (.f64 y y)) (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 (.f64 (.f64 x x) x) x (*.f64 y y))))
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(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (*.f64 x x) y) (fma.f64 x x y))) #s(literal -1 binary64)) y)
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (*.f64 x x) y) (fma.f64 x x y)) y)
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)) (fma.f64 x x y))) #s(literal -1 binary64)) y)
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)) (fma.f64 x x y)) y)
(fma.f64 #s(literal 1 binary64) (fma.f64 x x y) y)
(fma.f64 (.f64 (.f64 y y) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))) (*.f64 x x))
(fma.f64 (neg.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (*.f64 x x) y))) y)
(fma.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (neg.f64 (fma.f64 x x y))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))) y)
(fma.f64 #s(literal 4 binary64) (pow.f64 (.f64 y (+.f64 y y)) #s(literal 2 binary64)) (.f64 x x))
(fma.f64 #s(literal 4 binary64) (.f64 y y) (.f64 x x))
(fma.f64 (+.f64 y y) (+.f64 y y) (*.f64 x x))
(fma.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 x x y)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) y)) y)
(fma.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (/.f64 (fma.f64 x x y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) y)
(fma.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (.f64 (fma.f64 x x y) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))) y)
(fma.f64 (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y)) (fma.f64 x x y)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))) y)
(fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))
(fma.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))) (neg.f64 (.f64 y (/.f64 y (fma.f64 x x #s(literal 0 binary64))))))
(fma.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64) (*.f64 x x))
(fma.f64 #s(literal 2 binary64) (.f64 y (+.f64 y y)) (.f64 x x))
(fma.f64 #s(literal 2 binary64) y (*.f64 x x))
(fma.f64 (fma.f64 x x y) (pow.f64 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (.f64 x x) y)) #s(literal 1 binary64)) y)
(fma.f64 (fma.f64 x x y) (pow.f64 (.f64 (-.f64 (.f64 x x) y) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) y))) #s(literal 1 binary64)) y)
(fma.f64 (fma.f64 x x y) (/.f64 (-.f64 (.f64 x x) y) (-.f64 (.f64 x x) y)) y)
(fma.f64 (fma.f64 x x y) (/.f64 (fma.f64 x x y) (fma.f64 x x #s(literal 0 binary64))) (neg.f64 (*.f64 y (/.f64 y (fma.f64 x x #s(literal 0 binary64))))))
(fma.f64 (fma.f64 x x y) (.f64 (-.f64 (.f64 x x) y) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) y))) y)
(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
(fma.f64 x x (+.f64 y y))
(-.f64 (+.f64 y (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y)))) (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))
(-.f64 (/.f64 (.f64 y y) (.f64 (neg.f64 x) x)) (/.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (.f64 (neg.f64 x) x)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (-.f64 (.f64 x x) y) y)) (/.f64 (+.f64 y y) (-.f64 (-.f64 (*.f64 x x) y) y)))
(-.f64 (.f64 (.f64 (.f64 x x) x) (/.f64 x (-.f64 (.f64 x x) y))) (-.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) y))
(-.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x #s(literal 0 binary64))) (.f64 y (/.f64 y (fma.f64 x x #s(literal 0 binary64)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 x x y) y))) #s(literal -1 binary64)))
(+.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x #s(literal 0 binary64))) (neg.f64 (.f64 y (/.f64 y (fma.f64 x x #s(literal 0 binary64))))))
(+.f64 (+.f64 y y) (*.f64 x x))
(+.f64 (fma.f64 x x y) y)
(+.f64 y (fma.f64 x x y))
(+.f64 (*.f64 x x) (+.f64 y y))
(*.f64 (pow.f64 (exp.f64 (log.f64 x)) #s(literal 1 binary64)) (pow.f64 (exp.f64 (log.f64 x)) #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval75.0ms (3.5%)

Memory: -7.6MiB live, 69.3MiB allocated
Compiler: Compiled 8 891 to 696 computations (92.2% saved)

prune55.0ms (2.6%)

Memory

-21.0MiB live, 105.0MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	304	4	308
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	305	4	309

Accuracy

100.0%

Counts

309 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x (+.f64 y y))
▶	55.8%	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
▶	54.0%	#s(approx (+ (+ (* x x) y) y) (*.f64 y #s(literal 2 binary64)))
▶	47.8%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 28 to 15 computations (46.4% saved)

simplify5.0ms (0.2%)

Memory

19.0MiB live, 19.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 y y)
cost-diff	0	(fma.f64 x x (+.f64 y y))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x x) y) (*.f64 x x))
cost-diff	0	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
cost-diff	0	#s(approx (+ (+ (* x x) y) y) (*.f64 y #s(literal 2 binary64)))
cost-diff	128	(*.f64 y #s(literal 2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Rules

18×	`lower-+.f32`
14×	`lower-+.f64`
8×	`lower-fma.f32`
8×	`+-commutative`
6×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	67
0	19	65
1	25	65
0	25	63

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize26.0ms (1.2%)

Memory

5.8MiB live, 83.3MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x (+.f64 y y))
accuracy	0	(+.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.015625	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
accuracy	33.35205086907922	#s(approx (+ (* x x) y) (*.f64 x x))
accuracy	0	(*.f64 y #s(literal 2 binary64))
accuracy	29.444502648868404	#s(approx (+ (+ (* x x) y) y) (*.f64 y #s(literal 2 binary64)))
accuracy	0	(*.f64 x x)
accuracy	33.39188958194772	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Samples

19.0ms

256×

valid

Compiler

Compiled 54 to 11 computations (79.6% saved)

Precisions

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

ival-add: 5.0ms (55.9% of total)

ival-mult: 3.0ms (33.5% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.4%)

Memory

-23.4MiB live, 17.3MiB allocated

Counts

8 → 156

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	((+ (+ (* x x) y) y) (* x x) (* y 2) (+ (+ (* x x) y) y) (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))
1.0ms	y	@	inf	((+ (+ (* x x) y) y) (* x x) (* y 2) (+ (+ (* x x) y) y) (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))
0.0ms	x	@	inf	((+ (+ (* x x) y) y) (* x x) (* y 2) (+ (+ (* x x) y) y) (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))
0.0ms	x	@	-inf	((+ (+ (* x x) y) y) (* x x) (* y 2) (+ (+ (* x x) y) y) (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))
0.0ms	y	@	0	((+ (+ (* x x) y) y) (* x x) (* y 2) (+ (+ (* x x) y) y) (+ (+ (* x x) y) y) (+ (* x x) y) (+ (* x x) (+ y y)) (+ y y))

simplify107.0ms (5%)

Memory

30.4MiB live, 185.4MiB allocated

Algorithm

1×	egg-herbie

Rules

4 690×	`lower-fma.f64`
4 690×	`lower-fma.f32`
3 340×	`lower-*.f64`
3 340×	`lower-*.f32`
1 326×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	786
1	80	786
2	193	786
3	651	786
4	1923	786
5	3631	786
6	6729	786
0	8179	696

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 153

Calls

Call 1

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

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

rewrite50.0ms (2.3%)

Memory

-18.6MiB live, 97.7MiB allocated

Rules

504×	`lower-fma.f32`
502×	`lower-fma.f64`
304×	`lower-*.f32`
300×	`lower-*.f64`
260×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	57
0	19	55
1	75	55
0	667	53

Stop Event

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

Counts

8 → 134

Calls

Call 1

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

Outputs
#s(approx (+ (+ (* x x) y) y) (*.f64 x x))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) y)
(.f64 (.f64 (+.f64 y y) y) #s(literal 2 binary64))
(*.f64 (pow.f64 (+.f64 y y) #s(literal 3/2 binary64)) (pow.f64 (+.f64 y y) #s(literal 3/2 binary64)))
(.f64 #s(literal 4 binary64) (.f64 y y))
(.f64 #s(literal 8 binary64) (.f64 (*.f64 y y) y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(.f64 (.f64 y y) #s(literal 4 binary64))
(.f64 (.f64 (*.f64 y y) y) #s(literal 8 binary64))
(*.f64 (+.f64 y y) (+.f64 y y))
(.f64 #s(literal 2 binary64) (.f64 y (+.f64 y y)))
(*.f64 #s(literal 2 binary64) y)
(.f64 y (.f64 #s(literal 2 binary64) (+.f64 y y)))
(*.f64 y #s(literal 2 binary64))
(pow.f64 (+.f64 y y) #s(literal 3 binary64))
(pow.f64 (+.f64 y y) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) (+.f64 y y)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 (+.f64 y y) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (.f64 #s(literal 0 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (*.f64 #s(literal 0 binary64) (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (pow.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) #s(literal 3 binary64)) (pow.f64 (fma.f64 y y #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(fma.f64 (+.f64 y y) y (*.f64 (+.f64 y y) y))
(fma.f64 y (+.f64 y y) (*.f64 y (+.f64 y y)))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 y y)) #s(literal 3 binary64)))
(+.f64 (.f64 y (+.f64 y y)) (.f64 y (+.f64 y y)))
(+.f64 (.f64 (+.f64 y y) y) (.f64 (+.f64 y y) y))
(+.f64 y y)
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
(.f64 (.f64 (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (-.f64 #s(approx (+ ( x x) y) (.f64 x x)) y)) (/.f64 #s(literal 1 binary64) (-.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y)))
(.f64 (fma.f64 (.f64 #s(approx (+ (* x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x))) #s(approx (+ ( x x) y) (.f64 x x)) (.f64 (.f64 y y) y)) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 y #s(approx (+ ( x x) y) (.f64 x x))) (.f64 #s(approx (+ (* x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (*.f64 x x))))))
(/.f64 (-.f64 (.f64 y y) (.f64 #s(approx (+ (* x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x)))) (-.f64 y #s(approx (+ ( x x) y) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (.f64 (+.f64 #s(approx (+ (* x x) y) (.f64 x x)) y) (-.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (-.f64 y #s(approx (+ (* x x) y) (.f64 x x))) (.f64 #s(approx (+ (* x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x)))) (fma.f64 (.f64 #s(approx (+ (* x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x))) #s(approx (+ ( x x) y) (.f64 x x)) (.f64 (*.f64 y y) y))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(approx (+ ( x x) y) (.f64 x x)) y) (-.f64 #s(approx (+ ( x x) y) (.f64 x x)) y))) (neg.f64 (-.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y)))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(approx (+ ( x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x))) #s(approx (+ ( x x) y) (.f64 x x)) (.f64 (.f64 y y) y))) (neg.f64 (fma.f64 y (-.f64 y #s(approx (+ ( x x) y) (.f64 x x))) (.f64 #s(approx (+ (* x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (*.f64 x x))))))
(/.f64 (.f64 (+.f64 #s(approx (+ ( x x) y) (.f64 x x)) y) (-.f64 #s(approx (+ ( x x) y) (.f64 x x)) y)) (-.f64 #s(approx (+ ( x x) y) (*.f64 x x)) y))
(/.f64 (fma.f64 (.f64 #s(approx (+ ( x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x))) #s(approx (+ ( x x) y) (.f64 x x)) (.f64 (.f64 y y) y)) (fma.f64 y y (-.f64 (.f64 #s(approx (+ (* x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x))) (.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y))))
(/.f64 (fma.f64 (.f64 #s(approx (+ ( x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x))) #s(approx (+ ( x x) y) (.f64 x x)) (.f64 (.f64 y y) y)) (fma.f64 y (-.f64 y #s(approx (+ ( x x) y) (.f64 x x))) (.f64 #s(approx (+ (* x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (*.f64 x x)))))
(-.f64 (/.f64 (.f64 #s(approx (+ ( x x) y) (.f64 x x)) #s(approx (+ ( x x) y) (.f64 x x))) (-.f64 #s(approx (+ ( x x) y) (.f64 x x)) y)) (/.f64 (.f64 y y) (-.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)))
(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
(+.f64 y #s(approx (+ (* x x) y) (*.f64 x x)))
#s(approx (+ (* x x) y) (*.f64 x x))
(.f64 (.f64 (+.f64 (fma.f64 x x y) y) (fma.f64 x x #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 0 binary64))))
(.f64 (-.f64 (.f64 (.f64 (.f64 x x) x) x) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 (*.f64 x x) y) y)))
(.f64 (fma.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x y) (.f64 (.f64 y y) y)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (*.f64 y (-.f64 y (fma.f64 x x y))))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) x (-.f64 (+.f64 y y) (.f64 (+.f64 y y) (*.f64 x x))))))
(/.f64 (-.f64 (+.f64 y y) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 (+.f64 y y) (.f64 x x)))
(/.f64 (-.f64 (.f64 y y) (.f64 (fma.f64 x x y) (fma.f64 x x y))) (-.f64 y (fma.f64 x x y)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 (+.f64 (fma.f64 x x y) y) (fma.f64 x x #s(literal 0 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 (.f64 x x) y) y) (-.f64 (.f64 (.f64 (.f64 x x) x) x) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y)))) (fma.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x y) (.f64 (.f64 y y) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 x x) x) x (-.f64 (+.f64 y y) (.f64 (+.f64 y y) (.f64 x x)))) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (+.f64 y y))))
(/.f64 (neg.f64 (*.f64 (+.f64 (fma.f64 x x y) y) (fma.f64 x x #s(literal 0 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x x) x) x) (+.f64 y y))) (neg.f64 (-.f64 (-.f64 (.f64 x x) y) y)))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x y) (.f64 (.f64 y y) y))) (neg.f64 (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (+.f64 y y))) (neg.f64 (fma.f64 (.f64 (.f64 x x) x) x (-.f64 (+.f64 y y) (.f64 (+.f64 y y) (.f64 x x))))))
(/.f64 (*.f64 (+.f64 (fma.f64 x x y) y) (fma.f64 x x #s(literal 0 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) x) x) (+.f64 y y)) (-.f64 (-.f64 (.f64 x x) y) y))
(/.f64 (fma.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x y) (.f64 (.f64 y y) y)) (fma.f64 y y (-.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (*.f64 (fma.f64 x x y) y))))
(/.f64 (fma.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x y) (.f64 (.f64 y y) y)) (fma.f64 (fma.f64 x x y) (fma.f64 x x y) (.f64 y (-.f64 y (fma.f64 x x y)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (+.f64 y y)) (+.f64 (+.f64 y y) (-.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (+.f64 y y) (*.f64 x x)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (+.f64 y y)) (fma.f64 (.f64 (.f64 x x) x) x (-.f64 (+.f64 y y) (.f64 (+.f64 y y) (.f64 x x)))))
(fma.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) y (.f64 x x))
(fma.f64 (.f64 (+.f64 y y) y) #s(literal 2 binary64) (.f64 x x))
(fma.f64 (pow.f64 (+.f64 y y) #s(literal 3/2 binary64)) (pow.f64 (+.f64 y y) #s(literal 3/2 binary64)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (+.f64 y y))
(fma.f64 #s(literal 4 binary64) (.f64 y y) (.f64 x x))
(fma.f64 #s(literal 8 binary64) (.f64 (.f64 y y) y) (*.f64 x x))
(fma.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) y)) y)
(fma.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) (*.f64 x x))
(fma.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))) (.f64 x x))
(fma.f64 (.f64 y y) #s(literal 4 binary64) (.f64 x x))
(fma.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) (.f64 (.f64 y y) y)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) x (.f64 y (-.f64 y (.f64 x x))))) y)
(fma.f64 (.f64 (.f64 y y) y) #s(literal 8 binary64) (*.f64 x x))
(fma.f64 (+.f64 y y) (+.f64 y y) (*.f64 x x))
(fma.f64 #s(literal 2 binary64) (.f64 y (+.f64 y y)) (.f64 x x))
(fma.f64 #s(literal 2 binary64) y (*.f64 x x))
(fma.f64 y (.f64 #s(literal 2 binary64) (+.f64 y y)) (.f64 x x))
(fma.f64 y #s(literal 2 binary64) (*.f64 x x))
(fma.f64 x x (+.f64 y y))
(-.f64 (/.f64 (.f64 (fma.f64 x x y) (fma.f64 x x y)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (.f64 y y) (fma.f64 x x #s(literal 0 binary64))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) x) (-.f64 (-.f64 (.f64 x x) y) y)) (/.f64 (+.f64 y y) (-.f64 (-.f64 (*.f64 x x) y) y)))
(+.f64 (+.f64 y y) (*.f64 x x))
(+.f64 (*.f64 x x) (+.f64 y y))
(+.f64 (fma.f64 x x y) y)
(+.f64 y (fma.f64 x x y))
(.f64 (.f64 (+.f64 y y) #s(literal 2 binary64)) y)
(.f64 (.f64 (+.f64 y y) y) #s(literal 2 binary64))
(*.f64 (pow.f64 (+.f64 y y) #s(literal 3/2 binary64)) (pow.f64 (+.f64 y y) #s(literal 3/2 binary64)))
(.f64 #s(literal 4 binary64) (.f64 y y))
(.f64 #s(literal 8 binary64) (.f64 (*.f64 y y) y))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(.f64 (.f64 y y) #s(literal 4 binary64))
(.f64 (.f64 (*.f64 y y) y) #s(literal 8 binary64))
(*.f64 (+.f64 y y) (+.f64 y y))
(.f64 #s(literal 2 binary64) (.f64 y (+.f64 y y)))
(*.f64 #s(literal 2 binary64) y)
(.f64 y (.f64 #s(literal 2 binary64) (+.f64 y y)))
(*.f64 y #s(literal 2 binary64))
(pow.f64 (+.f64 y y) #s(literal 3 binary64))
(pow.f64 (+.f64 y y) #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) (+.f64 y y)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (.f64 (+.f64 y y) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (.f64 #s(literal 0 binary64) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (*.f64 #s(literal 0 binary64) (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64))))
(/.f64 (pow.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) #s(literal 3 binary64)) (pow.f64 (fma.f64 y y #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(fma.f64 (+.f64 y y) y (*.f64 (+.f64 y y) y))
(fma.f64 y (+.f64 y y) (*.f64 y (+.f64 y y)))
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 y y)) #s(literal 3 binary64)))
(+.f64 (.f64 y (+.f64 y y)) (.f64 y (+.f64 y y)))
(+.f64 (.f64 (+.f64 y y) y) (.f64 (+.f64 y y) y))
(+.f64 y y)

eval35.0ms (1.6%)

Memory: 18.5MiB live, 98.9MiB allocated
Compiler: Compiled 3 095 to 242 computations (92.2% saved)

prune24.0ms (1.1%)

Memory

-18.8MiB live, 60.3MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	302	1	303
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	303	4	307

Accuracy

100.0%

Counts

307 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	55.8%	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
▶	54.0%	#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
✓	47.8%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 28 to 14 computations (50% saved)

simplify5.0ms (0.2%)

Memory

9.0MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
0	8	15
1	13	15
2	15	15
0	15	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize23.0ms (1.1%)

Memory

-18.5MiB live, 32.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 y y)
accuracy	29.444502648868404	#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

Samples

19.0ms

256×

valid

Compiler

Compiled 13 to 8 computations (38.5% saved)

Precisions

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

ival-add: 3.0ms (61.9% of total)

ival-mult: 2.0ms (41.2% of total)

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

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

series2.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

2 → 36

Calls

Call 1

Inputs

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

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

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

Calls

6 calls:

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

simplify84.0ms (3.9%)

Memory

-1.1MiB live, 116.0MiB allocated

Algorithm

1×	egg-herbie

Rules

3 234×	`lower-fma.f64`
3 234×	`lower-fma.f32`
3 064×	`lower-*.f64`
3 064×	`lower-*.f32`
1 974×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	180
1	53	180
2	130	180
3	426	180
4	1329	180
5	3258	180
6	6178	180
0	8055	162

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

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

rewrite51.0ms (2.4%)

Memory

13.0MiB live, 94.1MiB allocated

Rules

188×	`lower-fma.f64`
188×	`lower-fma.f32`
170×	`lower-*.f64`
170×	`lower-*.f32`
150×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
0	8	14
1	43	14
0	376	13

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

2 → 12

Calls

Call 1

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

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

eval6.0ms (0.3%)

Memory: -26.6MiB live, 12.9MiB allocated
Compiler: Compiled 318 to 27 computations (91.5% saved)

prune4.0ms (0.2%)

Memory

11.8MiB live, 11.8MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	48	4	52

Accuracy

100.0%

Counts

52 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	55.8%	(+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y)
✓	54.0%	#s(approx (+ (+ (* x x) y) y) (+.f64 y y))
✓	47.8%	#s(approx (+ (+ (* x x) y) y) (*.f64 x x))

Compiler

Compiled 61 to 23 computations (62.3% saved)

regimes11.0ms (0.5%)

Memory

-10.3MiB live, 29.2MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	x
3.0ms	y
3.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
2.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 20 to 12 computations (40% saved)

regimes9.0ms (0.4%)

Memory

28.7MiB live, 28.7MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
85.6%	2	`x`
71.8%	3	`y`
77.6%	2	`(+.f64 (+.f64 (*.f64 x x) y) y)`
85.6%	2	`(*.f64 x x)`

Compiler

Compiled 20 to 12 computations (40% saved)

regimes6.0ms (0.3%)

Memory

-25.7MiB live, 15.3MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
84.8%	2	`x`
84.8%	2	`(*.f64 x x)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes5.0ms (0.2%)

Memory

19.9MiB live, 19.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
54.0%	1	`y`
54.0%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
54.0%	1	`x`
54.0%	1	`(*.f64 x x)`

Compiler

Compiled 20 to 12 computations (40% saved)

bsearch9.0ms (0.4%)

Memory

-19.7MiB live, 20.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	1.5524827678764619e-44	1.335662622594495e-41

Samples

4.0ms

128×

valid

Compiler

Compiled 124 to 74 computations (40.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-add: 1.0ms (78.5% of total)

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

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

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	1.5524827678764619e-44	1.335662622594495e-41

Compiler

Compiled 108 to 66 computations (38.9% saved)

simplify6.0ms (0.3%)

Memory

13.6MiB live, 13.6MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	73
1	17	73

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x x (+.f64 y y))
(if (<=.f64 (.f64 x x) #s(literal 8474087342772019/1569275433846670190958947355801916604025588861116008628224 binary64)) #s(approx (+ (+ ( x x) y) y) (+.f64 y y)) (+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y))
(if (<=.f64 (.f64 x x) #s(literal 8474087342772019/1569275433846670190958947355801916604025588861116008628224 binary64)) #s(approx (+ (+ ( x x) y) y) (+.f64 y y)) #s(approx (+ (+ (* x x) y) y) (*.f64 x x)))
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

Outputs
(fma.f64 x x (+.f64 y y))
(if (<=.f64 (.f64 x x) #s(literal 8474087342772019/1569275433846670190958947355801916604025588861116008628224 binary64)) #s(approx (+ (+ ( x x) y) y) (+.f64 y y)) (+.f64 #s(approx (+ (* x x) y) (*.f64 x x)) y))
(if (<=.f64 (.f64 x x) #s(literal 8474087342772019/1569275433846670190958947355801916604025588861116008628224 binary64)) #s(approx (+ (+ ( x x) y) y) (+.f64 y y)) #s(approx (+ (+ (* x x) y) y) (*.f64 x x)))
#s(approx (+ (+ (* x x) y) y) (+.f64 y y))

soundness447.0ms (20.7%)

Memory

-9.8MiB live, 306.5MiB allocated

Rules

7 306×	`lower-fma.f64`
7 306×	`lower-fma.f32`
4 782×	`lower-*.f32`
4 780×	`lower-*.f64`
4 690×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	282
1	80	282
2	193	282
3	649	282
4	1930	282
5	3616	282
6	6722	282
0	8178	246
0	14	57
0	19	55
1	75	55
0	667	53
0	5	15
0	8	15
1	37	15
2	316	15
3	4987	15
0	8103	13

Stop Event

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

Compiler

Compiled 102 to 48 computations (52.9% saved)

preprocess54.0ms (2.5%)

Memory: 13.8MiB live, 133.8MiB allocated
Remove: (abs x)
Compiler: Compiled 136 to 48 computations (64.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6

start0.0ms (0%)

analyze0.0ms (0%)

sample592.0ms (27.4%)

explain52.0ms (2.4%)

preprocess32.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize13.0ms (0.6%)

series18.0ms (0.8%)

simplify106.0ms (4.9%)

rewrite236.0ms (10.9%)

eval75.0ms (3.5%)

prune55.0ms (2.6%)

simplify5.0ms (0.2%)

localize26.0ms (1.2%)

series8.0ms (0.4%)

simplify107.0ms (5%)

rewrite50.0ms (2.3%)

eval35.0ms (1.6%)

prune24.0ms (1.1%)

simplify5.0ms (0.2%)

localize23.0ms (1.1%)

series2.0ms (0.1%)

simplify84.0ms (3.9%)

rewrite51.0ms (2.4%)

eval6.0ms (0.3%)

prune4.0ms (0.2%)

regimes11.0ms (0.5%)

regimes9.0ms (0.4%)

regimes6.0ms (0.3%)

regimes5.0ms (0.2%)

bsearch9.0ms (0.4%)

bsearch1.0ms (0%)

simplify6.0ms (0.3%)

soundness447.0ms (20.7%)

preprocess54.0ms (2.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6