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

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample530.0ms (7.2%)

Memory

-18.0MiB live, 816.7MiB allocated

Samples

362.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 143.0ms

ival-mult: 82.0ms (57.5% of total)

ival-add: 52.0ms (36.5% of total)

ival-true: 5.0ms (3.5% of total)

ival-assert: 3.0ms (2.1% of total)

Bogosity

preprocess83.0ms (1.1%)

Memory

25.8MiB live, 64.2MiB allocated

Algorithm

2×	egg-herbie

Rules

570×	`distribute-rgt-in`
516×	`unsub-neg`
444×	`distribute-lft-in`
290×	`associate-+l-`
284×	`distribute-lft-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	52
1	61	42
2	216	42
3	542	42
4	1086	42
5	1973	42
6	2789	42
7	2935	42
8	2935	42
9	2935	42
10	2977	42
11	2993	42
0	4	7
1	11	7
2	25	7
3	53	7
4	76	7
5	92	7
6	101	7
7	107	7
0	107	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (+ x y) (+ x y))

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

Call 2

Inputs
(* (+ x y) (+ x y))
(* (+ (neg x) y) (+ (neg x) y))
(* (+ x (neg y)) (+ x (neg y)))
(neg (* (+ (neg x) y) (+ (neg x) y)))
(neg (* (+ x (neg y)) (+ x (neg y))))
(* (+ y x) (+ y x))

Outputs
(* (+ x y) (+ x y))
(* (+ (neg x) y) (+ (neg x) y))
(* (- y x) (- y x))
(* (+ x (neg y)) (+ x (neg y)))
(* (- y x) (- y x))
(neg (* (+ (neg x) y) (+ (neg x) y)))
(* (- y x) (- x y))
(neg (* (+ x (neg y)) (+ x (neg y))))
(* (- y x) (- x y))
(* (+ y x) (+ y x))
(* (+ x y) (+ x y))

Symmetry

(sort x y)

explain51.0ms (0.7%)

Memory

-27.2MiB live, 131.4MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

21.0ms

512×

valid

Compiler

Compiled 46 to 20 computations (56.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-add: 3.0ms (45% of total)

ival-mult: 3.0ms (45% of total)

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 4 computations (55.6% saved)

simplify7.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

124×	`accelerator-lowering-fma.f32`
124×	`accelerator-lowering-fma.f64`
86×	`+-lowering-+.f64`
86×	`+-lowering-+.f32`
48×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	12
1	11	12
2	25	12
3	53	12
4	76	12
5	92	12
6	101	12
7	107	12
0	107	12

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (+ x y) (+ x y))
(+ x y)
x
y

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

localize16.0ms (0.2%)

Memory

-1.1MiB live, 35.9MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))

Samples

12.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

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

ival-mult: 2.0ms (61.2% of total)

ival-add: 1.0ms (30.6% of total)

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

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

series2.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (* (+ x y) (+ x y))>
#<alt (+ x y)>

Outputs
#<alt (pow y 2)>
#<alt (+ (* 2 (* x y)) (pow y 2))>
#<alt (+ (* x (+ x (* 2 y))) (pow y 2))>
#<alt (+ (* x (+ x (* 2 y))) (pow y 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))>
#<alt (pow x 2)>
#<alt (+ (* 2 (* x y)) (pow x 2))>
#<alt (+ (* y (+ y (* 2 x))) (pow x 2))>
#<alt (+ (* y (+ y (* 2 x))) (pow x 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>

Calls

12 calls:

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

rewrite600.0ms (8.2%)

Memory

-7.6MiB live, 882.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 646×	`-lowering-.f32`
5 646×	`-lowering-.f64`
4 194×	`accelerator-lowering-fma.f32`
4 194×	`accelerator-lowering-fma.f64`
3 878×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	26	8
2	218	8
3	2800	8
0	9133	8

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 989

Calls

Call 1

Inputs
(* (+ x y) (+ x y))
(+ x y)

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

simplify252.0ms (3.4%)

Memory

5.8MiB live, 406.2MiB allocated

Algorithm

1×	egg-herbie

Rules

7 026×	`accelerator-lowering-fma.f32`
7 026×	`accelerator-lowering-fma.f64`
2 898×	`-lowering-.f32`
2 898×	`-lowering-.f64`
1 650×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	264
1	193	264
2	490	264
3	1595	252
4	3905	252
5	6954	252
0	8103	222

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval149.0ms (2%)

Memory: -7.4MiB live, 359.6MiB allocated
Compiler: Compiled 53 466 to 2 965 computations (94.5% saved)

prune230.0ms (3.1%)

Memory

10.9MiB live, 420.0MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1 146	7	1 153
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1 146	8	1 154

Accuracy

100.0%

Counts

1 154 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(fma.f64 (+.f64 x y) x (*.f64 y (+.f64 x y)))
	57.7%	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) #s(literal 0 binary64))
	96.5%	(fma.f64 y y (fma.f64 x (fma.f64 y #s(literal 2 binary64) x) #s(literal 0 binary64)))
▶	55.8%	(fma.f64 y y #s(literal 0 binary64))
▶	60.4%	(fma.f64 x x #s(literal 0 binary64))
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
▶	57.2%	(*.f64 (+.f64 x y) y)
▶	59.5%	(*.f64 (+.f64 x y) x)

Compiler

Compiled 127 to 72 computations (43.3% saved)

simplify9.0ms (0.1%)

Memory

21.9MiB live, 21.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	-64	(*.f64 (+.f64 x y) y)
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	-64	(*.f64 (+.f64 x y) x)
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	(fma.f64 y y #s(literal 0 binary64))
✓	cost-diff	0	(fma.f64 x x #s(literal 0 binary64))
✓	cost-diff	-64	(*.f64 y (+.f64 x y))
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	384	(fma.f64 (+.f64 x y) x (*.f64 y (+.f64 x y)))

Rules

162×	`accelerator-lowering-fma.f32`
162×	`accelerator-lowering-fma.f64`
130×	`+-lowering-+.f64`
130×	`+-lowering-+.f32`
66×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	21	47
2	41	47
3	71	47
4	109	47
5	127	47
6	133	47
0	133	47

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* (+ x y) x) (* y (+ x y)))
(+ x y)
x
y
(* y (+ x y))
(+ (* x x) 0)
x
0
(+ (* y y) 0)
y
0
(* (+ x y) x)
(+ x y)
x
y
(* (+ x y) y)
(+ x y)
x
y

Outputs
(+ (* (+ x y) x) (* y (+ x y)))
(fma.f64 (+.f64 x y) (+.f64 x y) #s(literal 0 binary64))
(+ x y)
(+.f64 x y)
x
y
(* y (+ x y))
(fma.f64 y (+.f64 x y) #s(literal 0 binary64))
(+ (* x x) 0)
(fma.f64 x x #s(literal 0 binary64))
x
0
#s(literal 0 binary64)
(+ (* y y) 0)
(fma.f64 y y #s(literal 0 binary64))
y
0
#s(literal 0 binary64)
(* (+ x y) x)
(fma.f64 x (+.f64 x y) #s(literal 0 binary64))
(+ x y)
(+.f64 x y)
x
y
(* (+ x y) y)
(fma.f64 y (+.f64 x y) #s(literal 0 binary64))
(+ x y)
(+.f64 x y)
x
y

localize47.0ms (0.6%)

Memory

-21.7MiB live, 94.3MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 (+.f64 x y) y)
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 (+.f64 x y) x)
✓	accuracy	100.0%	(fma.f64 y y #s(literal 0 binary64))
✓	accuracy	100.0%	(fma.f64 x x #s(literal 0 binary64))
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 y (+.f64 x y))
✓	accuracy	98.4%	(fma.f64 (+.f64 x y) x (*.f64 y (+.f64 x y)))

Samples

25.0ms

256×

valid

Compiler

Compiled 54 to 14 computations (74.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-add: 8.0ms (52.2% of total)

ival-mult: 7.0ms (45.7% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated

Counts

7 → 144

Calls

Call 1

Inputs
#<alt (+ (* (+ x y) x) (* y (+ x y)))>
#<alt (+ x y)>
#<alt (* y (+ x y))>
#<alt (+ (* x x) 0)>
#<alt (+ (* y y) 0)>
#<alt (* (+ x y) x)>
#<alt (* (+ x y) y)>

Outputs
#<alt (pow y 2)>
#<alt (+ (* 2 (* x y)) (pow y 2))>
#<alt (+ (* x (+ x (* 2 y))) (pow y 2))>
#<alt (+ (* x (+ x (* 2 y))) (pow y 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))>
#<alt (pow x 2)>
#<alt (+ (* 2 (* x y)) (pow x 2))>
#<alt (+ (* y (+ y (* 2 x))) (pow x 2))>
#<alt (+ (* y (+ y (* 2 x))) (pow x 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* x y)>
#<alt (* y (+ x y))>
#<alt (* y (+ x y))>
#<alt (* y (+ x y))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (pow y 2)>
#<alt (+ (* x y) (pow y 2))>
#<alt (+ (* x y) (pow y 2))>
#<alt (+ (* x y) (pow y 2))>
#<alt (* x y)>
#<alt (* x (+ y (/ (pow y 2) x)))>
#<alt (* x (+ y (/ (pow y 2) x)))>
#<alt (* x (+ y (/ (pow y 2) x)))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ (pow y 2) x)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (* x y)>
#<alt (* x (+ x y))>
#<alt (* x (+ x y))>
#<alt (* x (+ x y))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y x)))>
#<alt (* (pow x 2) (+ 1 (/ y x)))>
#<alt (* (pow x 2) (+ 1 (/ y x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y x)))>
#<alt (* (pow x 2) (+ 1 (/ y x)))>
#<alt (* (pow x 2) (+ 1 (/ y x)))>
#<alt (pow x 2)>
#<alt (+ (* x y) (pow x 2))>
#<alt (+ (* x y) (pow x 2))>
#<alt (+ (* x y) (pow x 2))>
#<alt (* x y)>
#<alt (* y (+ x (/ (pow x 2) y)))>
#<alt (* y (+ x (/ (pow x 2) y)))>
#<alt (* y (+ x (/ (pow x 2) y)))>
#<alt (* x y)>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ (* -1 x) (* -1 (/ (pow x 2) y)))))>
#<alt (pow y 2)>
#<alt (+ (* x y) (pow y 2))>
#<alt (+ (* x y) (pow y 2))>
#<alt (+ (* x y) (pow y 2))>
#<alt (* x y)>
#<alt (* x (+ y (/ (pow y 2) x)))>
#<alt (* x (+ y (/ (pow y 2) x)))>
#<alt (* x (+ y (/ (pow y 2) x)))>
#<alt (* x y)>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -1 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* x y)>
#<alt (* y (+ x y))>
#<alt (* y (+ x y))>
#<alt (* y (+ x y))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>
#<alt (* (pow y 2) (+ 1 (/ x y)))>

Calls

36 calls:

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

rewrite596.0ms (8.1%)

Memory

-14.7MiB live, 970.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

14 046×	`accelerator-lowering-fma.f32`
14 046×	`accelerator-lowering-fma.f64`
4 954×	`-lowering-.f32`
4 954×	`-lowering-.f64`
3 656×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	68	31
2	773	29
0	8683	29

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 821

Calls

Call 1

Inputs
(+ (* (+ x y) x) (* y (+ x y)))
(+ x y)
(* y (+ x y))
(+ (* x x) 0)
(+ (* y y) 0)
(* (+ x y) x)
(* (+ x y) y)

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

simplify413.0ms (5.6%)

Memory

-1.2MiB live, 560.7MiB allocated

Algorithm

1×	egg-herbie

Rules

9 800×	`accelerator-lowering-fma.f32`
9 800×	`accelerator-lowering-fma.f64`
3 098×	`-lowering-.f32`
3 098×	`-lowering-.f64`
2 036×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	660
1	267	660
2	705	660
3	2094	648
4	4752	648
5	7846	648
0	8427	618

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

eval136.0ms (1.8%)

Memory: 25.8MiB live, 366.2MiB allocated
Compiler: Compiled 29 806 to 1 625 computations (94.5% saved)

prune247.0ms (3.4%)

Memory

-44.1MiB live, 247.6MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	1 190	3	1 193
Fresh	1	1	2
Picked	2	3	5
Done	0	1	1
Total	1 193	8	1 201

Accuracy

100.0%

Counts

1 201 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(fma.f64 (+.f64 x y) x (*.f64 y (+.f64 x y)))
▶	57.7%	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) #s(literal 0 binary64))
▶	96.5%	(fma.f64 y y (*.f64 x (+.f64 (+.f64 x y) y)))
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
✓	57.2%	(*.f64 (+.f64 x y) y)
✓	59.5%	(*.f64 (+.f64 x y) x)
▶	55.8%	(*.f64 y y)
▶	60.4%	(*.f64 x x)

Compiler

Compiled 66 to 35 computations (47% saved)

simplify10.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 #s(literal 2 binary64) x y)
✓	cost-diff	0	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) #s(literal 0 binary64))
✓	cost-diff	-64	(*.f64 x (+.f64 (+.f64 x y) y))
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	(+.f64 (+.f64 x y) y)
✓	cost-diff	384	(fma.f64 y y (*.f64 x (+.f64 (+.f64 x y) y)))
✓	cost-diff	-64	(*.f64 y y)
✓	cost-diff	-64	(*.f64 x x)

Rules

162×	`accelerator-lowering-fma.f32`
162×	`accelerator-lowering-fma.f64`
130×	`+-lowering-+.f64`
130×	`+-lowering-+.f32`
64×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	52
1	34	52
2	74	52
3	104	48
4	150	48
5	157	48
6	159	48
0	159	44

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x x)
x
(* y y)
y
(+ (* y y) (* x (+ (+ x y) y)))
y
(* x (+ (+ x y) y))
x
(+ (+ x y) y)
(+ x y)
(+ (* y (+ (* 2 x) y)) 0)
y
(+ (* 2 x) y)
2
x
0

Outputs
(* x x)
(fma.f64 x x #s(literal 0 binary64))
x
(* y y)
(fma.f64 y y #s(literal 0 binary64))
y
(+ (* y y) (* x (+ (+ x y) y)))
(fma.f64 (+.f64 x y) (+.f64 x y) #s(literal 0 binary64))
y
(* x (+ (+ x y) y))
(fma.f64 x (fma.f64 y #s(literal 2 binary64) x) #s(literal 0 binary64))
x
(+ (+ x y) y)
(fma.f64 y #s(literal 2 binary64) x)
(+ x y)
(+.f64 x y)
(+ (* y (+ (* 2 x) y)) 0)
(fma.f64 y (fma.f64 x #s(literal 2 binary64) y) #s(literal 0 binary64))
y
(+ (* 2 x) y)
(fma.f64 x #s(literal 2 binary64) y)
2
#s(literal 2 binary64)
x
0
#s(literal 0 binary64)

localize44.0ms (0.6%)

Memory

24.0MiB live, 59.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 #s(literal 2 binary64) x y)
✓	accuracy	100.0%	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) #s(literal 0 binary64))
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 x (+.f64 (+.f64 x y) y))
✓	accuracy	99.9%	(+.f64 (+.f64 x y) y)
✓	accuracy	96.5%	(fma.f64 y y (*.f64 x (+.f64 (+.f64 x y) y)))
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	100.0%	(*.f64 x x)

Samples

31.0ms

256×

valid

Compiler

Compiled 52 to 16 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-add: 13.0ms (61.8% of total)

ival-mult: 8.0ms (38% of total)

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

exact: 0.0ms (0% of total)

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

series18.0ms (0.2%)

Memory

-22.9MiB live, 14.6MiB allocated

Counts

8 → 168

Calls

Call 1

Inputs
#<alt (* x x)>
#<alt (* y y)>
#<alt (+ (* y y) (* x (+ (+ x y) y)))>
#<alt (+ (+ x y) y)>
#<alt (+ x y)>
#<alt (* x (+ (+ x y) y))>
#<alt (+ (* y (+ (* 2 x) y)) 0)>
#<alt (+ (* 2 x) y)>

Outputs
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow x 2)>
#<alt (+ (* 2 (* x y)) (pow x 2))>
#<alt (+ (* y (+ y (* 2 x))) (pow x 2))>
#<alt (+ (* y (+ y (* 2 x))) (pow x 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (* 2 (/ x y)) (/ (pow x 2) (pow y 2)))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) y))) y))))>
#<alt (pow y 2)>
#<alt (+ (* 2 (* x y)) (pow y 2))>
#<alt (+ (* x (+ x (* 2 y))) (pow y 2))>
#<alt (+ (* x (+ x (* 2 y))) (pow y 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ y x)) (/ (pow y 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 y) (* -1 (/ (pow y 2) x))) x))))>
#<alt (* 2 y)>
#<alt (+ x (* 2 y))>
#<alt (+ x (* 2 y))>
#<alt (+ x (* 2 y))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ y x))))>
#<alt (* x (+ 1 (* 2 (/ y x))))>
#<alt (* x (+ 1 (* 2 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (* -2 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -2 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -2 (/ y x)) 1)))>
#<alt x>
#<alt (+ x (* 2 y))>
#<alt (+ x (* 2 y))>
#<alt (+ x (* 2 y))>
#<alt (* 2 y)>
#<alt (* y (+ 2 (/ x y)))>
#<alt (* y (+ 2 (/ x y)))>
#<alt (* y (+ 2 (/ x y)))>
#<alt (* 2 y)>
#<alt (* -1 (* y (- (* -1 (/ x y)) 2)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 2)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 2)))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* 2 (* x y))>
#<alt (* x (+ x (* 2 y)))>
#<alt (* x (+ x (* 2 y)))>
#<alt (* x (+ x (* 2 y)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y x))))>
#<alt (pow x 2)>
#<alt (+ (* 2 (* x y)) (pow x 2))>
#<alt (+ (* 2 (* x y)) (pow x 2))>
#<alt (+ (* 2 (* x y)) (pow x 2))>
#<alt (* 2 (* x y))>
#<alt (* y (+ (* 2 x) (/ (pow x 2) y)))>
#<alt (* y (+ (* 2 x) (/ (pow x 2) y)))>
#<alt (* y (+ (* 2 x) (/ (pow x 2) y)))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ (* -2 x) (* -1 (/ (pow x 2) y)))))>
#<alt (* 2 (* x y))>
#<alt (* y (+ y (* 2 x)))>
#<alt (* y (+ y (* 2 x)))>
#<alt (* y (+ y (* 2 x)))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (pow y 2)>
#<alt (+ (* 2 (* x y)) (pow y 2))>
#<alt (+ (* 2 (* x y)) (pow y 2))>
#<alt (+ (* 2 (* x y)) (pow y 2))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 y) (/ (pow y 2) x)))>
#<alt (* x (+ (* 2 y) (/ (pow y 2) x)))>
#<alt (* x (+ (* 2 y) (/ (pow y 2) x)))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))>
#<alt y>
#<alt (+ y (* 2 x))>
#<alt (+ y (* 2 x))>
#<alt (+ y (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ y x)))>
#<alt (* x (+ 2 (/ y x)))>
#<alt (* x (+ 2 (/ y x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ y x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 2)))>
#<alt (* 2 x)>
#<alt (+ y (* 2 x))>
#<alt (+ y (* 2 x))>
#<alt (+ y (* 2 x))>
#<alt y>
#<alt (* y (+ 1 (* 2 (/ x y))))>
#<alt (* y (+ 1 (* 2 (/ x y))))>
#<alt (* y (+ 1 (* 2 (/ x y))))>
#<alt y>
#<alt (* -1 (* y (- (* -2 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -2 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -2 (/ x y)) 1)))>

Calls

42 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	(+ (* y (+ (* 2 x) y)) 0)
1.0ms	y	@	0	(+ (* y (+ (* 2 x) y)) 0)
0.0ms	y	@	-inf	(+ (* y (+ (* 2 x) y)) 0)
0.0ms	x	@	-inf	(+ (* y (+ (* 2 x) y)) 0)
0.0ms	x	@	-inf	(+ (* y y) (* x (+ (+ x y) y)))

rewrite850.0ms (11.5%)

Memory

-115.3MiB live, 958.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

13 224×	`accelerator-lowering-fma.f32`
13 224×	`accelerator-lowering-fma.f64`
5 626×	`-lowering-.f32`
5 626×	`-lowering-.f64`
3 632×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	44
1	89	44
2	918	34
0	9528	32

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 726

Calls

Call 1

Inputs
(* x x)
(* y y)
(+ (* y y) (* x (+ (+ x y) y)))
(+ (+ x y) y)
(+ x y)
(* x (+ (+ x y) y))
(+ (* y (+ (* 2 x) y)) 0)
(+ (* 2 x) y)

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

simplify726.0ms (9.9%)

Memory

2.6MiB live, 413.9MiB allocated

Algorithm

1×	egg-herbie

Rules

8 658×	`accelerator-lowering-fma.f32`
8 658×	`accelerator-lowering-fma.f64`
2 920×	`-lowering-.f32`
2 920×	`-lowering-.f64`
1 722×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	93	954
1	299	912
2	817	912
3	2404	828
4	4903	828
5	7858	828
0	8329	726

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

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

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

eval244.0ms (3.3%)

Memory: 9.3MiB live, 199.9MiB allocated
Compiler: Compiled 20 296 to 1 841 computations (90.9% saved)

prune148.0ms (2%)

Memory

6.8MiB live, 141.7MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	893	1	894
Fresh	0	0	0
Picked	1	3	4
Done	0	4	4
Total	894	8	902

Accuracy

100.0%

Counts

902 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(fma.f64 (+.f64 x y) x (*.f64 y (+.f64 x y)))
✓	96.5%	(fma.f64 y y (*.f64 x (+.f64 (+.f64 x y) y)))
▶	57.7%	(*.f64 (fma.f64 x #s(literal 2 binary64) y) y)
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
✓	57.2%	(*.f64 (+.f64 x y) y)
✓	59.5%	(*.f64 (+.f64 x y) x)
✓	55.8%	(*.f64 y y)
✓	60.4%	(*.f64 x x)

Compiler

Compiled 65 to 34 computations (47.7% saved)

simplify7.0ms (0.1%)

Memory

-32.7MiB live, 6.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
18×	`accelerator-lowering-fma.f32`
18×	`accelerator-lowering-fma.f64`
14×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	9	15
2	16	15
3	24	15
4	26	15
0	26	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (+ (* x 2) y) y)
(+ (* x 2) y)
x
2
y

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

localize17.0ms (0.2%)

Memory

23.2MiB live, 23.2MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x #s(literal 2 binary64) y)
✓	accuracy	100.0%	(*.f64 (fma.f64 x #s(literal 2 binary64) y) y)

Samples

11.0ms

256×

valid

Compiler

Compiled 15 to 8 computations (46.7% saved)

Precisions

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

ival-mult: 3.0ms (62.3% of total)

ival-add: 1.0ms (20.8% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (* (+ (* x 2) y) y)>
#<alt (+ (* x 2) y)>

Outputs
#<alt (pow y 2)>
#<alt (+ (* 2 (* x y)) (pow y 2))>
#<alt (+ (* 2 (* x y)) (pow y 2))>
#<alt (+ (* 2 (* x y)) (pow y 2))>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 y) (/ (pow y 2) x)))>
#<alt (* x (+ (* 2 y) (/ (pow y 2) x)))>
#<alt (* x (+ (* 2 y) (/ (pow y 2) x)))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* -1 (* x (+ (* -2 y) (* -1 (/ (pow y 2) x)))))>
#<alt (* 2 (* x y))>
#<alt (* y (+ y (* 2 x)))>
#<alt (* y (+ y (* 2 x)))>
#<alt (* y (+ y (* 2 x)))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt (* (pow y 2) (+ 1 (* 2 (/ x y))))>
#<alt y>
#<alt (+ y (* 2 x))>
#<alt (+ y (* 2 x))>
#<alt (+ y (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ y x)))>
#<alt (* x (+ 2 (/ y x)))>
#<alt (* x (+ 2 (/ y x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ y x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 2)))>
#<alt (* 2 x)>
#<alt (+ y (* 2 x))>
#<alt (+ y (* 2 x))>
#<alt (+ y (* 2 x))>
#<alt y>
#<alt (* y (+ 1 (* 2 (/ x y))))>
#<alt (* y (+ 1 (* 2 (/ x y))))>
#<alt (* y (+ 1 (* 2 (/ x y))))>
#<alt y>
#<alt (* -1 (* y (- (* -2 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -2 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -2 (/ x y)) 1)))>

Calls

12 calls:

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

rewrite762.0ms (10.4%)

Memory

10.8MiB live, 875.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

11 780×	`accelerator-lowering-fma.f32`
11 780×	`accelerator-lowering-fma.f64`
4 328×	`/-lowering-/.f32`
4 328×	`/-lowering-/.f64`
4 166×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	22	12
2	164	12
3	1628	12
0	8210	10

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 243

Calls

Call 1

Inputs
(* (+ (* x 2) y) y)
(+ (* x 2) y)

Outputs
(+.f64 (.f64 y y) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(+.f64 (.f64 y y) (neg.f64 (.f64 y (*.f64 x #s(literal -2 binary64)))))
(+.f64 (.f64 (.f64 x #s(literal 2 binary64)) y) (*.f64 y y))
(-.f64 (.f64 y y) (.f64 y (*.f64 x #s(literal -2 binary64))))
(-.f64 (/.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 y y)) (.f64 y (-.f64 y (*.f64 x #s(literal 2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 y y)) (fma.f64 x (.f64 #s(literal 2 binary64) y) (-.f64 #s(literal 0 binary64) (.f64 y y)))) (/.f64 (.f64 y (.f64 y (.f64 y y))) (fma.f64 x (.f64 #s(literal 2 binary64) y) (-.f64 #s(literal 0 binary64) (*.f64 y y)))))
(fma.f64 x (.f64 #s(literal 2 binary64) y) (.f64 y y))
(fma.f64 #s(literal 2 binary64) (.f64 x y) (.f64 y y))
(fma.f64 (.f64 x #s(literal 2 binary64)) y (.f64 y y))
(fma.f64 y (.f64 x #s(literal 2 binary64)) (.f64 y y))
(fma.f64 y y (.f64 (.f64 x #s(literal 2 binary64)) y))
(fma.f64 y y (neg.f64 (.f64 y (.f64 x #s(literal -2 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 y y) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(fma.f64 #s(literal 1 binary64) (.f64 y y) (neg.f64 (.f64 y (*.f64 x #s(literal -2 binary64)))))
(fma.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) y) (.f64 (.f64 x #s(literal 2 binary64)) y))
(fma.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) y) (neg.f64 (.f64 y (.f64 x #s(literal -2 binary64)))))
(fma.f64 (.f64 #s(literal 2 binary64) y) x (.f64 y y))
(fma.f64 (.f64 x y) #s(literal 2 binary64) (.f64 y y))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 y y)) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 y y)) (neg.f64 (.f64 y (*.f64 x #s(literal -2 binary64)))))
(/.f64 y (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) y)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y (fma.f64 x #s(literal 2 binary64) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) y)) y))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (fma.f64 x #s(literal 2 binary64) y))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))) (.f64 (.f64 y (fma.f64 x #s(literal 2 binary64) y)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (.f64 y (.f64 y y)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 x #s(literal 2 binary64))))) (fma.f64 y (.f64 (.f64 y (.f64 y y)) (.f64 y y)) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 y (.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 (.f64 x #s(literal 4 binary64)) (.f64 y y)) (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 y (.f64 y y)) (.f64 x #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 #s(literal 2 binary64) y) (-.f64 #s(literal 0 binary64) (.f64 y y))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 y y)) (.f64 y (.f64 y (*.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))) (.f64 y (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 y (.f64 y y)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal -2 binary64) y) (.f64 y (.f64 (fma.f64 x #s(literal 2 binary64) y) (fma.f64 x #s(literal -2 binary64) y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (.f64 x #s(literal 2 binary64))) (.f64 y (fma.f64 y y (.f64 #s(literal -4 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))) (.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 y (.f64 y y)))) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal -2 binary64) y) (.f64 (.f64 (fma.f64 x #s(literal 2 binary64) y) (fma.f64 x #s(literal -2 binary64) y)) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (.f64 x #s(literal 2 binary64))) (.f64 (fma.f64 y y (.f64 #s(literal -4 binary64) (.f64 x x))) y)))
(/.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) y))))
(/.f64 (.f64 (.f64 y (fma.f64 x #s(literal 2 binary64) y)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64))))) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 y (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 y (.f64 y y)))) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 y (fma.f64 x (.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (.f64 y y)))) (-.f64 (.f64 x #s(literal 2 binary64)) y))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 y (fma.f64 x #s(literal 2 binary64) y)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 y (fma.f64 x #s(literal 2 binary64) y)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 y (.f64 y y))))) (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (fma.f64 x (.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 y y))))) (fma.f64 x #s(literal -2 binary64) y))
(/.f64 (fma.f64 y (.f64 (.f64 y (.f64 y y)) (.f64 y y)) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 y (.f64 y y)))) (fma.f64 y (.f64 y (.f64 y y)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 x #s(literal 2 binary64))))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (fma.f64 x (.f64 (.f64 x #s(literal 4 binary64)) (.f64 y y)) (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 y (.f64 y y)) (.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 y y)) (.f64 y (.f64 y (.f64 y y)))) (fma.f64 x (.f64 #s(literal 2 binary64) y) (-.f64 #s(literal 0 binary64) (*.f64 y y))))
(/.f64 (.f64 y (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 y (.f64 y y))))) (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))))
(/.f64 (.f64 y (.f64 (fma.f64 x #s(literal 2 binary64) y) (fma.f64 x #s(literal -2 binary64) y))) (fma.f64 x #s(literal -2 binary64) y))
(/.f64 (.f64 y (fma.f64 y y (.f64 #s(literal -4 binary64) (.f64 x x)))) (-.f64 y (.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 y (.f64 y y)))) y) (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))))
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(/.f64 (.f64 (fma.f64 y y (.f64 #s(literal -4 binary64) (.f64 x x))) y) (-.f64 y (.f64 x #s(literal 2 binary64))))
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(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal -4 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 y (.f64 x #s(literal 2 binary64))))))
(.f64 (-.f64 (.f64 (.f64 (.f64 x x) (/.f64 #s(literal -4 binary64) (fma.f64 x #s(literal -2 binary64) y))) (.f64 (.f64 (.f64 x x) (/.f64 #s(literal -4 binary64) (fma.f64 x #s(literal -2 binary64) y))) (.f64 (.f64 x x) (/.f64 #s(literal -4 binary64) (fma.f64 x #s(literal -2 binary64) y))))) (.f64 (/.f64 (.f64 y y) (-.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 (.f64 y y) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) (fma.f64 x #s(literal -2 binary64) y)) (/.f64 (-.f64 #s(literal 0 binary64) y) (fma.f64 x #s(literal -2 binary64) y)))))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 16 binary64) (.f64 (/.f64 (.f64 x x) (-.f64 (.f64 x #s(literal 2 binary64)) y)) (/.f64 (.f64 x x) (-.f64 (.f64 x #s(literal 2 binary64)) y))) (fma.f64 (.f64 y y) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) (fma.f64 x #s(literal -2 binary64) y)) (/.f64 (-.f64 #s(literal 0 binary64) y) (fma.f64 x #s(literal -2 binary64) y))) (.f64 (.f64 (.f64 x x) (/.f64 #s(literal -4 binary64) (fma.f64 x #s(literal -2 binary64) y))) (/.f64 (.f64 y y) (-.f64 (*.f64 x #s(literal 2 binary64)) y)))))))
(.f64 (-.f64 (.f64 (.f64 (.f64 x x) (/.f64 #s(literal -4 binary64) (fma.f64 x #s(literal -2 binary64) y))) (.f64 (.f64 x x) (/.f64 #s(literal -4 binary64) (fma.f64 x #s(literal -2 binary64) y)))) (.f64 (.f64 y y) (.f64 (/.f64 (-.f64 #s(literal 0 binary64) y) (fma.f64 x #s(literal -2 binary64) y)) (/.f64 (-.f64 #s(literal 0 binary64) y) (fma.f64 x #s(literal -2 binary64) y))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (/.f64 #s(literal -4 binary64) (fma.f64 x #s(literal -2 binary64) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x #s(literal 2 binary64)) y)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 512 binary64) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 64 binary64))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (-.f64 #s(literal 0 binary64) (.f64 y (*.f64 y y))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (-.f64 (.f64 x #s(literal 2 binary64)) y)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y y) (fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 y y)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (.f64 y (.f64 y (.f64 y y)))) (-.f64 (.f64 x #s(literal 2 binary64)) y)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 4 binary64) (*.f64 y y))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 y (.f64 y y))) (fma.f64 (.f64 y (.f64 y y)) (.f64 (-.f64 y (.f64 x #s(literal 2 binary64))) (.f64 (-.f64 y (.f64 x #s(literal 2 binary64))) (-.f64 y (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))))) (fma.f64 (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))) (-.f64 (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))) (.f64 x (.f64 x #s(literal 4 binary64)))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (.f64 y (.f64 y y))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (.f64 y (.f64 (-.f64 y (.f64 x #s(literal 2 binary64))) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64)))))))) (-.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64))))))
(.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (.f64 y y))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))))) (fma.f64 x (.f64 x #s(literal 4 binary64)) (*.f64 y (fma.f64 x #s(literal 2 binary64) y))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y y) (fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 y y)) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x #s(literal 2 binary64)) y) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (.f64 y (.f64 y (.f64 y y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 4 binary64) (*.f64 y y))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 512 binary64) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y (.f64 y y)) (-.f64 (.f64 y (.f64 y y)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 64 binary64))))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 4 binary64)) (.f64 y (-.f64 y (.f64 x #s(literal 2 binary64))))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64) (-.f64 #s(literal 0 binary64) (.f64 y (*.f64 y y))))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) y)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 2 binary64) y)) #s(literal -1/2 binary64)))

simplify194.0ms (2.6%)

Memory

-12.0MiB live, 299.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4 690×	`-lowering-.f32`
4 690×	`-lowering-.f64`
2 808×	`accelerator-lowering-fma.f32`
2 808×	`accelerator-lowering-fma.f64`
1 176×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	252
1	120	252
2	287	252
3	745	252
4	1882	252
5	3582	252
6	5334	252
7	6392	252
8	6975	252
0	8130	216

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval36.0ms (0.5%)

Memory: -6.5MiB live, 83.6MiB allocated
Compiler: Compiled 9 239 to 770 computations (91.7% saved)

prune36.0ms (0.5%)

Memory

14.6MiB live, 92.7MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	291	0	291
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	291	8	299

Accuracy

100.0%

Counts

299 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(fma.f64 (+.f64 x y) x (*.f64 y (+.f64 x y)))
✓	96.5%	(fma.f64 y y (*.f64 x (+.f64 (+.f64 x y) y)))
✓	57.7%	(*.f64 (fma.f64 x #s(literal 2 binary64) y) y)
✓	100.0%	(*.f64 (+.f64 x y) (+.f64 x y))
✓	57.2%	(*.f64 (+.f64 x y) y)
✓	59.5%	(*.f64 (+.f64 x y) x)
✓	55.8%	(*.f64 y y)
✓	60.4%	(*.f64 x x)

Compiler

Compiled 141 to 58 computations (58.9% saved)

regimes19.0ms (0.3%)

Memory

-9.8MiB live, 33.7MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
(*.f64 x x)
(*.f64 y y)
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 y y #s(literal 0 binary64))
(*.f64 (+.f64 x y) x)
(*.f64 (+.f64 x y) y)
(*.f64 (+.f64 x y) (+.f64 x y))
(*.f64 (fma.f64 x #s(literal 2 binary64) y) y)
(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) #s(literal 0 binary64))
(fma.f64 y y (*.f64 x (+.f64 (+.f64 x y) y)))
(fma.f64 (+.f64 x y) x (*.f64 y (+.f64 x y)))
(fma.f64 y y (fma.f64 x (fma.f64 y #s(literal 2 binary64) x) #s(literal 0 binary64)))

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

Calls

4 calls:

7.0ms	y
4.0ms	(+.f64 x y)
4.0ms	x
4.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

Results

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

Compiler

Compiled 20 to 11 computations (45% saved)

regimes10.0ms (0.1%)

Memory

20.7MiB live, 20.7MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
(*.f64 x x)
(*.f64 y y)
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 y y #s(literal 0 binary64))
(*.f64 (+.f64 x y) x)
(*.f64 (+.f64 x y) y)

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
88.7%	2	`x`
88.8%	2	`y`
63.9%	3	`(*.f64 (+.f64 x y) (+.f64 x y))`
97.7%	2	`(+.f64 x y)`

Compiler

Compiled 20 to 11 computations (45% saved)

regimes3.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
(*.f64 x x)
(*.f64 y y)
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 y y #s(literal 0 binary64))
(*.f64 (+.f64 x y) x)

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

Calls

1 calls:

2.0ms

(+.f64 x y)

Results

Accuracy	Segments	Branch
97.6%	2	`(+.f64 x y)`

Compiler

Compiled 5 to 3 computations (40% saved)

regimes5.0ms (0.1%)

Memory

-32.8MiB live, 5.0MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
(*.f64 x x)
(*.f64 y y)
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 y y #s(literal 0 binary64))

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

Calls

1 calls:

4.0ms

(+.f64 x y)

Results

Accuracy	Segments	Branch
97.6%	2	`(+.f64 x y)`

Compiler

Compiled 5 to 3 computations (40% saved)

regimes5.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
60.4%	1	`(*.f64 (+.f64 x y) (+.f64 x y))`
60.4%	1	`x`
60.4%	1	`y`
60.4%	1	`(+.f64 x y)`

Compiler

Compiled 20 to 11 computations (45% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.614230205951488e-159	-4.173633312772319e-174

Compiler

Compiled 10 to 9 computations (10% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.614230205951488e-159	-4.173633312772319e-174

Compiler

Compiled 10 to 9 computations (10% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.614230205951488e-159	-4.173633312772319e-174

Compiler

Compiled 10 to 9 computations (10% saved)

simplify8.0ms (0.1%)

Memory

13.8MiB live, 13.8MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	16	52

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (+.f64 x y) (+.f64 x y))
(if (<=.f64 (+.f64 x y) #s(literal -7914572847139345/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088 binary64)) (.f64 (+.f64 x y) x) (.f64 (+.f64 x y) y))
(if (<=.f64 (+.f64 x y) #s(literal -7914572847139345/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088 binary64)) (.f64 (+.f64 x y) x) (.f64 y y))
(if (<=.f64 (+.f64 x y) #s(literal -7914572847139345/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088 binary64)) (.f64 x x) (.f64 y y))
(*.f64 x x)

Outputs
(*.f64 (+.f64 x y) (+.f64 x y))
(if (<=.f64 (+.f64 x y) #s(literal -7914572847139345/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088 binary64)) (.f64 (+.f64 x y) x) (.f64 (+.f64 x y) y))
(if (<=.f64 (+.f64 x y) #s(literal -7914572847139345/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088 binary64)) (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))
(if (<=.f64 (+.f64 x y) #s(literal -7914572847139345/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088 binary64)) (.f64 (+.f64 x y) x) (.f64 y y))
(if (<=.f64 (+.f64 x y) #s(literal -7914572847139345/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088 binary64)) (.f64 x (+.f64 x y)) (.f64 y y))
(if (<=.f64 (+.f64 x y) #s(literal -7914572847139345/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088 binary64)) (.f64 x x) (.f64 y y))
(*.f64 x x)

soundness779.0ms (10.6%)

Memory

-17.1MiB live, 339.5MiB allocated

Rules

14 046×	`accelerator-lowering-fma.f32`
14 046×	`accelerator-lowering-fma.f64`
7 026×	`accelerator-lowering-fma.f32`
7 026×	`accelerator-lowering-fma.f64`
4 954×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	68	31
2	773	29
0	8683	29
0	65	264
1	193	264
2	490	264
3	1595	252
4	3905	252
5	6954	252
0	8103	222

Stop Event

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

Compiler

Compiled 119 to 53 computations (55.5% saved)

preprocess65.0ms (0.9%)

Memory: 21.3MiB live, 60.3MiB allocated
Remove: (sort x y)
Compiler: Compiled 192 to 68 computations (64.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample530.0ms (7.2%)

preprocess83.0ms (1.1%)

explain51.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize16.0ms (0.2%)

series2.0ms (0%)

rewrite600.0ms (8.2%)

simplify252.0ms (3.4%)

eval149.0ms (2%)

prune230.0ms (3.1%)

simplify9.0ms (0.1%)

localize47.0ms (0.6%)

series5.0ms (0.1%)

rewrite596.0ms (8.1%)

simplify413.0ms (5.6%)

eval136.0ms (1.8%)

prune247.0ms (3.4%)

simplify10.0ms (0.1%)

localize44.0ms (0.6%)

series18.0ms (0.2%)

rewrite850.0ms (11.5%)

simplify726.0ms (9.9%)

eval244.0ms (3.3%)

prune148.0ms (2%)

simplify7.0ms (0.1%)

localize17.0ms (0.2%)

series1.0ms (0%)

rewrite762.0ms (10.4%)

simplify194.0ms (2.6%)

eval36.0ms (0.5%)

prune36.0ms (0.5%)

regimes19.0ms (0.3%)

regimes10.0ms (0.1%)

regimes3.0ms (0%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness779.0ms (10.6%)

preprocess65.0ms (0.9%)

end0.0ms (0%)

Profiling