Metrics for System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2

analyze1.0ms (0%)

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 10 to 7 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample686.0ms (14.5%)

Results

473.0ms	8255×	0	valid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 196.0ms

ival-mult: 134.0ms (68.2% of total)

ival-sub: 48.0ms (24.4% of total)

const: 12.0ms (6.1% of total)

backward-pass: 3.0ms (1.5% of total)

Bogosity

preprocess88.0ms (1.9%)

Algorithm

2×	egg-herbie

Rules

894×	`fnmadd-define`
828×	`fmsub-define`
798×	`fnmsub-define`
576×	`fnmadd-define`
576×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	59	36
2	156	36
3	491	36
4	1275	36
5	2972	36
6	3376	36
7	3472	36
0	6	6
1	12	6
2	23	6
3	49	6
4	87	6
5	139	6
6	272	6
7	512	6
8	932	6
9	1496	6
10	1824	6
11	1884	6
0	1884	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(* 1/2 (- (* x x) y))
(* 1/2 (- (square x) y))
(* 1/2 (- (* (neg x) (neg x)) y))
(* 1/2 (- (square x) y))
(* 1/2 (- (* x x) (neg y)))
(* 1/2 (+ (square x) y))
(neg (* 1/2 (- (* (neg x) (neg x)) y)))
(* 1/2 (- y (square x)))
(neg (* 1/2 (- (* x x) (neg y))))
(* 1/2 (fnmsub x x y))
(* 1/2 (- (* y y) x))
(* 1/2 (- (square y) x))

Symmetry

(abs x)

explain83.0ms (1.8%)

FPErrors

Click to see full error table

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

Results

60.0ms

512×

valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 9.0ms (71% of total)

ival-sub: 3.0ms (23.7% of total)

const: 1.0ms (7.9% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify111.0ms (2.4%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

576×	`fnmadd-define`
464×	`fma-define`
374×	`fmsub-define`
370×	`fnmsub-define`
360×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	12	15
2	23	15
3	49	15
4	87	15
5	139	15
6	272	15
7	512	15
8	932	15
9	1496	15
10	1824	15
11	1884	15
0	1884	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize30.0ms (0.6%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 (*.f64 x x) y)
✓	accuracy	99.7%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))

Results

23.0ms

256×

valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

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

ival-mult: 6.0ms (77.9% of total)

ival-sub: 1.0ms (13% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (* 1/2 (- (* x x) y))>
#<alt (- (* x x) y)>
#<alt (* x x)>

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

Calls

15 calls:

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

rewrite313.0ms (6.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2718×	`-lowering-.f32`
2718×	`-lowering-.f64`
2700×	`/-lowering-/.f32`
2700×	`/-lowering-/.f64`
1632×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	27	12
2	188	12
3	1894	12
0	8655	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 210

Calls

Call 1

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

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

simplify182.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

2266×	`-lowering-.f32`
2266×	`-lowering-.f64`
1868×	`sum4-define`
1066×	`fma-lowering-fma.f32`
1066×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	309
1	106	255
2	331	255
3	1152	237
4	3299	237
5	7882	237
0	8752	237

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval30.0ms (0.6%)

Compiler: Compiled 12056 to 775 computations (93.6% saved)

prune29.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	267	4	271

Accuracy

100.0%

Counts

271 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
✓	99.7%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
▶	54.0%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
▶	47.8%	(*.f64 #s(literal -1/2 binary64) y)

Compiler

Compiled 31 to 22 computations (29% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) y)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	6272	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) y)

Rules

18×	`-lowering-.f32`
18×	`-lowering-.f64`
12×	`fma-lowering-fma.f32`
12×	`fma-define`
12×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	17	30
2	22	30
0	22	30

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize51.0ms (1.1%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) y)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) y)

Results

39.0ms

256×

valid

Compiler

Compiled 36 to 10 computations (72.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 9.0ms (62.3% of total)

compiled-spec: 4.0ms (27.7% of total)

ival-add: 1.0ms (6.9% of total)

const: 1.0ms (6.9% of total)

backward-pass: 0.0ms (0% of total)

series4.0ms (0.1%)

Counts

5 → 72

Calls

Call 1

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

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

Calls

18 calls:

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

rewrite241.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3368×	`-lowering-.f32`
3368×	`-lowering-.f64`
2018×	`fma-lowering-fma.f32`
2018×	`fma-lowering-fma.f64`
1930×	`fmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	32	19
2	255	19
3	3442	19
0	8310	19

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 106

Calls

Call 1

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

Outputs
(*.f64 #s(literal -1/2 binary64) y)
(*.f64 y #s(literal -1/2 binary64))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x))) #s(literal 1 binary64)))
(pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 x (.f64 #s(literal 1/2 binary64) x))
(.f64 x (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) x) x)
(.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.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 (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (exp.f64 (log.f64 x)) #s(literal 1 binary64)) (pow.f64 (exp.f64 (log.f64 x)) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (*.f64 #s(literal -1/2 binary64) y))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x))))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))
(-.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(fma.f64 #s(literal -1/2 binary64) y (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(fma.f64 y #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(fma.f64 x (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 x (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) y))
(fma.f64 (.f64 x x) (/.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
(fma.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (/.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(fma.f64 (.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/4 binary64))) (/.f64 x (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x x))) (/.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 y (+.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))))) (neg.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(neg.f64 (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))))
(neg.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))))) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y))))
(/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y)))) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))) (.f64 #s(literal 1/512 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))))) (.f64 #s(literal -1/512 binary64) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))))) (.f64 (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) (-.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)))) (.f64 (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 y y)))))))
(/.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y)))) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)) (.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))))
(/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal -1/2 binary64) (.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)) (.f64 y (.f64 y #s(literal 1/4 binary64))))) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))) (.f64 #s(literal 1/512 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))))) (.f64 #s(literal -1/512 binary64) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) (-.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y))))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64))) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y)))) #s(literal 1 binary64)) (.f64 (.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))))) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(/.f64 (neg.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (+.f64 (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (.f64 (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (/.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(/.f64 (.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y)))) #s(literal 1 binary64)) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(/.f64 (.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))) #s(literal 1 binary64)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))) (.f64 #s(literal 1/512 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))))) (.f64 #s(literal -1/512 binary64) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))) (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) (-.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 y y))))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y)))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (*.f64 x x)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))
(.f64 (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))
(.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y))))))
(.f64 (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (.f64 (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))))
(.f64 (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x))) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))))
(.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (*.f64 x x) y)))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (*.f64 y y)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (*.f64 y y))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))) (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))) (+.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y)))) (+.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))) (.f64 (.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))) (.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))))))) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))) (-.f64 (.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64)))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y)))) (.f64 (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))))))) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 y (-.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/4 binary64))))))
(.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y))) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) #s(literal 1/8 binary64)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 y (+.f64 (.f64 y #s(literal 1/4 binary64)) (.f64 (*.f64 x x) #s(literal -1/4 binary64))))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)) (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 y y)))))))
(.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)) (-.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (.f64 y y))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y y)))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (+.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))) (.f64 #s(literal 1/512 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x x))))) (.f64 #s(literal -1/512 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) (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) (-.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 y (.f64 y #s(literal 1/4 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (.f64 #s(literal 1/2 binary64) (+.f64 (.f64 x x) y)))) (-.f64 (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) #s(literal 1/64 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (*.f64 y y)) #s(literal 1/8 binary64)))))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))

simplify124.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1952×	`-lowering-.f32`
1952×	`-lowering-.f64`
1786×	`fmsub-define`
1714×	`fnmsub-define`
1578×	`fmm-def`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	336
1	60	291
2	176	291
3	438	291
4	1261	273
5	4681	273
0	8091	273

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

eval19.0ms (0.4%)

Compiler: Compiled 4404 to 311 computations (92.9% saved)

prune16.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	192	4	196

Accuracy

100.0%

Counts

196 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
▶	54.3%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	99.7%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
✓	47.8%	(*.f64 #s(literal -1/2 binary64) y)

Compiler

Compiled 31 to 22 computations (29% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
2×	`associate-r`
2×	`square-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	8	9
2	10	9
0	10	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (* 1/2 x) x)
(* 1/2 x)
1/2
x

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

localize24.0ms (0.5%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)

Results

18.0ms

256×

valid

Compiler

Compiled 13 to 6 computations (53.8% saved)

Precisions

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

ival-mult: 4.0ms (99.3% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (* (* 1/2 x) x)>
#<alt (* 1/2 x)>

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

Calls

6 calls:

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

rewrite154.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2200×	`pow-lowering-pow.f64`
2200×	`pow-lowering-pow.f32`
1432×	`prod-exp`
1304×	`-lowering-.f32`
1304×	`-lowering-.f64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	4	10
1	8	8
2	12	8
3	19	8
4	35	8
5	93	8
6	292	2
7	1854	2
8	1886	2
9	2020	2
10	3307	2
0	8651	2

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 2

Calls

Call 1

Inputs
(* (* 1/2 x) x)
(* 1/2 x)

Outputs
#s(literal 1/2 binary64)
#s(literal 1/2 binary64)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`-lowering-.f32`
14×	`-lowering-.f64`
4×	`*-commutative`
2×	`pow-lowering-pow.f64`
2×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	96
1	9	84
2	12	84
0	12	84

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

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

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

eval2.0ms (0%)

Compiler: Compiled 126 to 6 computations (95.2% saved)

prune4.0ms (0.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	24	6	30

Accuracy

100.0%

Counts

30 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
✓	54.3%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	99.7%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
▶	5.5%	(*.f64 #s(literal 1/2 binary64) x)
✓	47.8%	(*.f64 #s(literal -1/2 binary64) y)
▶	4.0%	#s(literal 1/2 binary64)

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

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

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	4	6
0	4	6

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
1/2
(* 1/2 x)
1/2
x

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

localize20.0ms (0.4%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)

Results

15.0ms

256×

valid

Compiler

Compiled 9 to 5 computations (44.4% saved)

Precisions

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

ival-mult: 3.0ms (88.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* 1/2 x)>

Outputs
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>

Calls

3 calls:

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

rewrite9.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	4	3
0	4	3

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* 1/2 x)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	36
0	4	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)

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

eval1.0ms (0%)

Compiler: Compiled 44 to 5 computations (88.6% saved)

prune3.0ms (0.1%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	14	6	20

Accuracy

100.0%

Counts

20 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
✓	54.3%	(.f64 (.f64 #s(literal 1/2 binary64) x) x)
✓	99.7%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
✓	5.5%	(*.f64 #s(literal 1/2 binary64) x)
✓	47.8%	(*.f64 #s(literal -1/2 binary64) y)
✓	4.0%	#s(literal 1/2 binary64)

Compiler

Compiled 73 to 41 computations (43.8% saved)

regimes17.0ms (0.4%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	y
3.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
3.0ms	(-.f64 (*.f64 x x) y)
3.0ms	x
3.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 27 to 17 computations (37% saved)

regimes13.0ms (0.3%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	y
3.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
3.0ms	x
3.0ms	(-.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`y`
99.7%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
99.7%	1	`(-.f64 (*.f64 x x) y)`
99.7%	1	`(*.f64 x x)`

Compiler

Compiled 27 to 17 computations (37% saved)

regimes8.0ms (0.2%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
89.8%	2	`x`
65.8%	3	`y`
89.8%	2	`(*.f64 x x)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes4.0ms (0.1%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
89.4%	2	`x`
89.4%	2	`(*.f64 x x)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes5.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
47.8%	1	`y`
47.8%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/2 binary64)

Outputs
#s(literal 1/2 binary64)

Calls

2 calls:

1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
4.0%	1	`x`
4.0%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	9.808096044635707e+37	7.190844719870129e+39

Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	9.808096044635707e+37	7.190844719870129e+39

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	23	47
2	28	47
3	30	47
4	31	47

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) #s(literal 99999999999999997748809823456034029568 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(if (<=.f64 (.f64 x x) #s(literal 99999999999999997748809823456034029568 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(*.f64 #s(literal -1/2 binary64) y)
#s(literal 1/2 binary64)

Outputs
(fma.f64 (.f64 #s(literal 1/2 binary64) x) x (.f64 #s(literal -1/2 binary64) y))
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) #s(literal 99999999999999997748809823456034029568 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 (.f64 #s(literal 1/2 binary64) x) x))
(if (<=.f64 (.f64 x x) #s(literal 99999999999999997748809823456034029568 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 x (.f64 #s(literal 1/2 binary64) x)))
(if (<=.f64 (.f64 x x) #s(literal 99999999999999997748809823456034029568 binary64)) (.f64 #s(literal -1/2 binary64) y) (.f64 #s(literal 1/2 binary64) (.f64 x x)))
(*.f64 #s(literal -1/2 binary64) y)
#s(literal 1/2 binary64)

soundness2.4s (50.4%)

Rules

3368×	`-lowering-.f32`
3368×	`-lowering-.f64`
2718×	`-lowering-.f32`
2718×	`-lowering-.f64`
2700×	`/-lowering-/.f32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	32	19
2	255	19
3	3442	19
0	8310	19
0	35	309
1	106	255
2	331	255
3	1152	237
4	3299	237
5	7882	237
0	8752	237
0	4	10
1	8	8
2	12	8
3	19	8
4	35	8
5	93	8
6	292	2
7	1854	2
8	1886	2
9	2020	2
10	3307	2
0	8651	2
0	6	12
1	27	12
2	188	12
3	1894	12
0	8655	12

Stop Event

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

Compiler

Compiled 109 to 60 computations (45% saved)

preprocess41.0ms (0.9%)

Remove: (abs x)
Compiler: Compiled 156 to 72 computations (53.8% saved)

analyze1.0ms (0%)

sample686.0ms (14.5%)

preprocess88.0ms (1.9%)

explain83.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify111.0ms (2.4%)

localize30.0ms (0.6%)

series3.0ms (0.1%)

rewrite313.0ms (6.6%)

simplify182.0ms (3.8%)

eval30.0ms (0.6%)

prune29.0ms (0.6%)

simplify5.0ms (0.1%)

localize51.0ms (1.1%)

series4.0ms (0.1%)

rewrite241.0ms (5.1%)

simplify124.0ms (2.6%)

eval19.0ms (0.4%)

prune16.0ms (0.3%)

simplify4.0ms (0.1%)

localize24.0ms (0.5%)

series0.0ms (0%)

rewrite154.0ms (3.3%)

simplify5.0ms (0.1%)

eval2.0ms (0%)

prune4.0ms (0.1%)

simplify3.0ms (0.1%)

localize20.0ms (0.4%)

series0.0ms (0%)

rewrite9.0ms (0.2%)

simplify5.0ms (0.1%)

eval1.0ms (0%)

prune3.0ms (0.1%)

regimes17.0ms (0.4%)

regimes13.0ms (0.3%)

regimes8.0ms (0.2%)

regimes4.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.2%)

soundness2.4s (50.4%)

preprocess41.0ms (0.9%)

end0.0ms (0%)

Profiling