Metrics for Linear.Matrix:fromQuaternion from linear-1.19.1.3, B

analyze0.0ms (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 12 to 8 computations (33.3% saved)

Precisions

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

ival-add: 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)

sample796.0ms (18.4%)

Results

583.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 305.0ms

ival-mult: 249.0ms (81.5% of total)

ival-add: 44.0ms (14.4% of total)

const: 10.0ms (3.3% of total)

backward-pass: 3.0ms (1% of total)

Bogosity

preprocess122.0ms (2.8%)

Algorithm

2×	egg-herbie

Rules

2388×	`fnmadd-define`
1666×	`fma-define`
1582×	`fmsub-define`
1548×	`fnmsub-define`
1344×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	46
1	88	42
2	275	42
3	851	42
4	2126	42
5	5715	42
6	6979	42
7	7426	42
8	7523	42
9	7557	42
10	7561	42
0	7	7
1	19	7
2	42	7
3	74	7
4	78	7
0	78	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(* 2 (+ (* x x) (* x y)))
(* x (* 2 (+ x y)))
(* 2 (+ (* (neg x) (neg x)) (* (neg x) y)))
(* x (* 2 (- x y)))
(* 2 (+ (* x x) (* x (neg y))))
(* x (* 2 (- x y)))
(neg (* 2 (+ (* (neg x) (neg x)) (* (neg x) y))))
(* x (* 2 (- y x)))
(neg (* 2 (+ (* x x) (* x (neg y)))))
(* x (* 2 (- y x)))
(* 2 (+ (* y y) (* y x)))
(* 2 (* y (+ x y)))

explain64.0ms (1.5%)

FPErrors

Click to see full error table

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

Results

37.0ms

512×

valid

Compiler

Compiled 67 to 23 computations (65.7% saved)

Precisions

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

ival-mult: 12.0ms (79.6% of total)

ival-add: 2.0ms (13.3% of total)

const: 1.0ms (6.6% 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
▶	100.0%	(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

54×	`-lowering-.f32`
54×	`-lowering-.f64`
44×	`fma-define`
34×	`fma-lowering-fma.f32`
34×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	16	18
2	45	18
3	75	18
4	87	18
0	87	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize25.0ms (0.6%)

Localize:

Found 3 expressions of interest:

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

Results

18.0ms

256×

valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

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

ival-mult: 7.0ms (80.7% of total)

ival-add: 2.0ms (23.1% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Counts

3 → 72

Calls

Call 1

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

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

18 calls:

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

rewrite420.0ms (9.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2954×	`/-lowering-/.f32`
2954×	`/-lowering-/.f64`
2618×	`-lowering-.f32`
2618×	`-lowering-.f64`
2376×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	27	15
2	209	15
3	1940	15
0	9348	15

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 276

Calls

Call 1

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

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

simplify239.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

2584×	`-lowering-.f32`
2584×	`-lowering-.f64`
1400×	`fnmadd-define`
1310×	`fma-lowering-fma.f32`
1310×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	324
1	188	324
2	506	324
3	1455	324
4	3638	324
5	7015	324
0	8120	324

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

eval52.0ms (1.2%)

Compiler: Compiled 9289 to 1034 computations (88.9% saved)

prune46.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	345	3	348
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	345	4	349

Accuracy

100.0%

Counts

349 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
✓	100.0%	(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))
▶	57.9%	(.f64 #s(literal 2 binary64) (.f64 x y))
▶	60.9%	(.f64 #s(literal 2 binary64) (.f64 x x))

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x y))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	128	(/.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 x y))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 x x))

Rules

58×	`-lowering-.f32`
58×	`-lowering-.f64`
40×	`fma-define`
34×	`fma-lowering-fma.f32`
34×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	26	42
2	47	42
3	94	42
4	109	42
5	111	42
0	111	42

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize62.0ms (1.4%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 x y))
✓	accuracy	99.7%	(/.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 x y))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

46.0ms

256×

valid

Compiler

Compiled 48 to 13 computations (72.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 14.0ms (71.2% of total)

ival-div: 4.0ms (20.4% of total)

ival-add: 1.0ms (5.1% of total)

const: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Counts

8 → 156

Calls

Call 1

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

Outputs
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 2 (pow x 2))>
#<alt (* 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 (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* 2 (* x y))>
#<alt (* x (+ (* 2 x) (* 2 y)))>
#<alt (* x (+ (* 2 x) (* 2 y)))>
#<alt (* x (+ (* 2 x) (* 2 y)))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 2 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 2 (* 2 (/ y x))))>
#<alt (* 2 (pow x 2))>
#<alt (* (pow x 2) (+ 2 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 2 (* 2 (/ y x))))>
#<alt (* (pow x 2) (+ 2 (* 2 (/ y x))))>
#<alt (* 2 (pow x 2))>
#<alt (+ (* 2 (* x y)) (* 2 (pow x 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow x 2)))>
#<alt (+ (* 2 (* x y)) (* 2 (pow x 2)))>
#<alt (* 2 (* x y))>
#<alt (* y (+ (* 2 x) (* 2 (/ (pow x 2) y))))>
#<alt (* y (+ (* 2 x) (* 2 (/ (pow x 2) y))))>
#<alt (* y (+ (* 2 x) (* 2 (/ (pow x 2) y))))>
#<alt (* 2 (* x y))>
#<alt (* -1 (* y (+ (* -2 x) (* -2 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ (* -2 x) (* -2 (/ (pow x 2) y)))))>
#<alt (* -1 (* y (+ (* -2 x) (* -2 (/ (pow x 2) y)))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (/ 1 y)>
#<alt (+ (* -1 (/ x (pow y 2))) (/ 1 y))>
#<alt (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1 (/ y x))) x)>
#<alt (/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)>
#<alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ y x) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))>
#<alt (/ 1 x)>
#<alt (+ (* -1 (/ y (pow x 2))) (/ 1 x))>
#<alt (+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (/ 1 y)>
#<alt (/ (+ 1 (* -1 (/ x y))) y)>
#<alt (/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)>
#<alt (/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)>
#<alt (/ 1 y)>
#<alt (* -1 (/ (- (/ x y) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) 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

39 calls:

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

rewrite431.0ms (10%)

Algorithm

1×	batch-egg-rewrite

Rules

3438×	`-lowering-.f32`
3438×	`-lowering-.f64`
2480×	`fma-lowering-fma.f32`
2480×	`fma-lowering-fma.f64`
1738×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	53	33
2	322	33
3	3136	33
0	8926	33

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 495

Calls

Call 1

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

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

simplify303.0ms (7%)

Algorithm

1×	egg-herbie

Rules

2494×	`-lowering-.f32`
2494×	`-lowering-.f64`
2314×	`fma-lowering-fma.f32`
2314×	`fma-lowering-fma.f64`
1954×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	928
1	473	900
2	1250	856
3	4374	850
0	8260	850

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 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)
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* 2 (* x y))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* 2 (* x y))
(* x (+ (* 2 x) (* 2 y)))
(* x (+ (* 2 x) (* 2 y)))
(* x (+ (* 2 x) (* 2 y)))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(* 2 (pow x 2))
(+ (* 2 (* x y)) (* 2 (pow x 2)))
(+ (* 2 (* x y)) (* 2 (pow x 2)))
(+ (* 2 (* x y)) (* 2 (pow x 2)))
(* 2 (* x y))
(* y (+ (* 2 x) (* 2 (/ (pow x 2) y))))
(* y (+ (* 2 x) (* 2 (/ (pow x 2) y))))
(* y (+ (* 2 x) (* 2 (/ (pow x 2) y))))
(* 2 (* x y))
(* -1 (* y (+ (* -2 x) (* -2 (/ (pow x 2) y)))))
(* -1 (* y (+ (* -2 x) (* -2 (/ (pow x 2) y)))))
(* -1 (* y (+ (* -2 x) (* -2 (/ (pow x 2) y)))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(/ 1 y)
(+ (* -1 (/ x (pow y 2))) (/ 1 y))
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
(/ 1 x)
(/ (+ 1 (* -1 (/ y x))) x)
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)
(/ 1 x)
(* -1 (/ (- (/ y x) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))
(/ 1 x)
(+ (* -1 (/ y (pow x 2))) (/ 1 x))
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(/ 1 y)
(/ (+ 1 (* -1 (/ x y))) y)
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)
(/ 1 y)
(* -1 (/ (- (/ x y) 1) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) 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
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.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)
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* x (+ (* 2 x) (* 2 y)))
(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))
(* x (+ (* 2 x) (* 2 y)))
(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))
(* x (+ (* 2 x) (* 2 y)))
(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(.f64 x (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) y) x))))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(.f64 x (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) y) x))))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(.f64 x (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) y) x))))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(.f64 x (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) y) x))))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(.f64 x (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) y) x))))
(* (pow x 2) (+ 2 (* 2 (/ y x))))
(.f64 x (.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 #s(literal 2 binary64) y) x))))
(* 2 (pow x 2))
(.f64 #s(literal 2 binary64) (.f64 x x))
(+ (* 2 (* x y)) (* 2 (pow x 2)))
(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))
(+ (* 2 (* x y)) (* 2 (pow x 2)))
(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))
(+ (* 2 (* x y)) (* 2 (pow x 2)))
(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* y (+ (* 2 x) (* 2 (/ (pow x 2) y))))
(.f64 (.f64 #s(literal 2 binary64) y) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* y (+ (* 2 x) (* 2 (/ (pow x 2) y))))
(.f64 (.f64 #s(literal 2 binary64) y) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* y (+ (* 2 x) (* 2 (/ (pow x 2) y))))
(.f64 (.f64 #s(literal 2 binary64) y) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* 2 (* x y))
(.f64 #s(literal 2 binary64) (.f64 x y))
(* -1 (* y (+ (* -2 x) (* -2 (/ (pow x 2) y)))))
(.f64 (.f64 #s(literal 2 binary64) y) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* -1 (* y (+ (* -2 x) (* -2 (/ (pow x 2) y)))))
(.f64 (.f64 #s(literal 2 binary64) y) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* -1 (* y (+ (* -2 x) (* -2 (/ (pow x 2) y)))))
(.f64 (.f64 #s(literal 2 binary64) y) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(+ (* -1 (/ x (pow y 2))) (/ 1 y))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 x y) (+.f64 #s(literal -1 binary64) (/.f64 x y)))) y)
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
(+.f64 (.f64 x (.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))) (/.f64 x (pow.f64 y #s(literal 4 binary64)))))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1 (/ y x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (+.f64 (/.f64 y x) #s(literal -1 binary64))) x)) x)
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y (/.f64 (.f64 y (.f64 y (+.f64 (/.f64 y x) #s(literal -1 binary64)))) x)) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ y x) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (+.f64 (/.f64 y x) #s(literal -1 binary64))) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y (/.f64 (.f64 y (.f64 y (+.f64 (/.f64 y x) #s(literal -1 binary64)))) x)) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ y (pow x 2))) (/ 1 x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 y (+.f64 (/.f64 y x) #s(literal -1 binary64))) x)) x)
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(+.f64 (.f64 (.f64 y y) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 y (pow.f64 x #s(literal 4 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (* -1 (/ x y))) y)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 x y) (+.f64 #s(literal -1 binary64) (/.f64 x y)))) y)
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 x y))) y)) y)) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(* -1 (/ (- (/ x y) 1) y))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 x y) (+.f64 #s(literal -1 binary64) (/.f64 x y)))) y)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 x y))) y)) y)) y)
y
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
x
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 (/.f64 y x) #s(literal 1 binary64)))
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
y
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))

eval74.0ms (1.7%)

Compiler: Compiled 13062 to 1529 computations (88.3% saved)

prune95.0ms (2.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	650	1	651
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	650	5	655

Accuracy

100.0%

Counts

655 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
▶	57.8%	(/.f64 y (/.f64 #s(literal 1/2 binary64) x))
✓	100.0%	(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))
✓	57.9%	(.f64 #s(literal 2 binary64) (.f64 x y))
✓	60.9%	(.f64 #s(literal 2 binary64) (.f64 x x))

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify53.0ms (1.2%)

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

Rules

12×	`-lowering-.f32`
12×	`-lowering-.f64`
10×	`/-lowering-/.f32`
10×	`/-lowering-/.f64`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	7	11
2	10	11
3	14	11
4	15	11
0	15	11

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize21.0ms (0.5%)

Localize:

Found 2 expressions of interest:

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

Results

13.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

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

ival-div: 4.0ms (90.3% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

2 → 36

Calls

Call 1

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

Outputs
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x y))>
#<alt (* 2 (* x 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

9 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)
0.0ms	y	@	0	(/ y (/ 1/2 x))
0.0ms	x	@	inf	(/ y (/ 1/2 x))

rewrite242.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2136×	`/-lowering-/.f32`
2136×	`/-lowering-/.f64`
2052×	`-lowering-.f32`
2052×	`-lowering-.f64`
1090×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	23	8
2	120	8
3	578	8
4	3204	8
0	9469	8

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 378

Calls

Call 1

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

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

simplify17.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

24×	`-lowering-.f32`
24×	`-lowering-.f64`
10×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	156
1	11	156
2	18	156
3	20	156
0	20	156

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

eval45.0ms (1%)

Compiler: Compiled 5688 to 948 computations (83.3% saved)

prune294.0ms (6.8%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	414	0	414
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	414	5	419

Accuracy

100.0%

Counts

419 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 (*.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
✓	57.8%	(/.f64 y (/.f64 #s(literal 1/2 binary64) x))
✓	100.0%	(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x y)))
✓	57.9%	(.f64 #s(literal 2 binary64) (.f64 x y))
✓	60.9%	(.f64 #s(literal 2 binary64) (.f64 x x))

Compiler

Compiled 83 to 48 computations (42.2% saved)

regimes22.0ms (0.5%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

9.0ms	x
7.0ms	y
3.0ms	(.f64 #s(literal 2 binary64) (+.f64 (.f64 x x) (*.f64 x y)))
2.0ms	(+.f64 (.f64 x x) (.f64 x y))

Results

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

Compiler

Compiled 26 to 16 computations (38.5% saved)

regimes4.0ms (0.1%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
83.8%	3	`x`
89.0%	3	`y`

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
(.f64 #s(literal 2 binary64) (.f64 x x))

Outputs
(.f64 #s(literal 2 binary64) (.f64 x x))

Calls

2 calls:

1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
60.9%	1	`x`
60.9%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch28.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
15.0ms	4.049151065325701e+19	6.432668955882851e+32
11.0ms	-8.415594566341755e+42	-3.057278267960629e+41

Results

16.0ms

272×

valid

Compiler

Compiled 288 to 215 computations (25.3% saved)

Precisions

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

ival-mult: 6.0ms (67.6% of total)

ival-add: 2.0ms (22.5% of total)

const: 0.0ms (0% of total)

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

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`if-if-or-not_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	25	31

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 y #s(literal -579999999999999976516111781868820739653632 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x y)) (if (<=.f64 y #s(literal 299999999999999997114318848 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x x)) (*.f64 #s(literal 2 binary64) (*.f64 x y))))

(*.f64 #s(literal 2 binary64) (*.f64 x x))

Outputs

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

(if (<=.f64 y #s(literal -579999999999999976516111781868820739653632 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x y)) (if (<=.f64 y #s(literal 299999999999999997114318848 binary64)) (*.f64 #s(literal 2 binary64) (*.f64 x x)) (*.f64 #s(literal 2 binary64) (*.f64 x y))))

(*.f64 #s(literal 2 binary64) (*.f64 x x))

soundness759.0ms (17.6%)

Rules

2584×	`-lowering-.f32`
2584×	`-lowering-.f64`
1400×	`fnmadd-define`
1310×	`fma-lowering-fma.f32`
1310×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	324
1	188	324
2	506	324
3	1455	324
4	3638	324
5	7015	324
0	8120	324
0	7	7
1	19	7
2	42	7
3	74	7
4	78	7
0	78	7

Stop Event

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

Compiler

Compiled 94 to 55 computations (41.5% saved)

preprocess59.0ms (1.4%)

Compiler: Compiled 114 to 58 computations (49.1% saved)

Linear.Matrix:fromQuaternion from linear-1.19.1.3, B

analyze0.0ms (0%)

sample796.0ms (18.4%)

preprocess122.0ms (2.8%)

explain64.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify16.0ms (0.4%)

localize25.0ms (0.6%)

series4.0ms (0.1%)

rewrite420.0ms (9.7%)

simplify239.0ms (5.5%)

eval52.0ms (1.2%)

prune46.0ms (1.1%)

simplify8.0ms (0.2%)

localize62.0ms (1.4%)

series9.0ms (0.2%)

rewrite431.0ms (10%)

simplify303.0ms (7%)

eval74.0ms (1.7%)

prune95.0ms (2.2%)

simplify53.0ms (1.2%)

localize21.0ms (0.5%)

series1.0ms (0%)

rewrite242.0ms (5.6%)

simplify17.0ms (0.4%)

eval45.0ms (1%)

prune294.0ms (6.8%)

regimes22.0ms (0.5%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch28.0ms (0.6%)

simplify8.0ms (0.2%)

soundness759.0ms (17.6%)

preprocess59.0ms (1.4%)

end0.0ms (0%)

Profiling