Metrics for Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, G

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 10 to 8 computations (20% saved)

Precisions

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

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

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)

sample646.0ms (28.7%)

Results

459.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 207.0ms

ival-mult: 66.0ms (31.8% of total)

ival-add: 64.0ms (30.8% of total)

ival-div: 62.0ms (29.9% of total)

const: 13.0ms (6.3% of total)

backward-pass: 3.0ms (1.4% of total)

Bogosity

preprocess36.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

450×	`fnmsub-define`
450×	`fmsub-define`
402×	`fnmadd-define`
296×	`fmm-def`
212×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	32
1	59	30
2	180	30
3	360	30
4	732	30
5	1414	30
6	1537	30
7	1559	30
0	8	5
1	18	5
2	23	5
3	25	5
0	25	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

Symmetry

(sort x y)

explain66.0ms (2.9%)

FPErrors

Click to see full error table

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

Results

41.0ms

512×

valid

Compiler

Compiled 49 to 23 computations (53.1% saved)

Precisions

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

ival-div: 4.0ms (35.1% of total)

ival-mult: 4.0ms (35.1% of total)

ival-add: 3.0ms (26.4% of total)

const: 1.0ms (8.8% of total)

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

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

12×	`-lowering-.f32`
12×	`-lowering-.f64`
8×	`fma-lowering-fma.f32`
8×	`fma-define`
8×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	13	11
2	18	11
3	20	11
0	20	11

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize18.0ms (0.8%)

Localize:

Found 2 expressions of interest:

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

Results

12.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

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

ival-add: 2.0ms (50.5% of total)

ival-mult: 2.0ms (50.5% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Counts

2 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite389.0ms (17.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2740×	`/-lowering-/.f32`
2740×	`/-lowering-/.f64`
2606×	`-lowering-.f32`
2606×	`-lowering-.f64`
2462×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	26	8
2	195	8
3	1775	8
0	9297	8

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 193

Calls

Call 1

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

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

simplify126.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1864×	`fnmadd-define`
1816×	`fma-lowering-fma.f32`
1816×	`fma-lowering-fma.f64`
1812×	`sum5-define`
1630×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	168
1	124	168
2	302	168
3	871	168
4	2404	168
5	4335	168
0	8030	168

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval47.0ms (2.1%)

Compiler: Compiled 6607 to 680 computations (89.7% saved)

prune29.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	239	3	242

Accuracy

100.0%

Counts

242 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 #s(literal 1/2 binary64) (+.f64 x y))
▶	52.4%	(*.f64 #s(literal 1/2 binary64) y)
▶	48.4%	(*.f64 #s(literal 1/2 binary64) x)

Compiler

Compiled 17 to 13 computations (23.5% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	7	10
0	7	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize54.0ms (2.4%)

Localize:

Found 2 expressions of interest:

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

Results

48.0ms

256×

valid

Compiler

Compiled 13 to 6 computations (53.8% saved)

Precisions

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

ival-mult: 4.0ms (97.8% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0.1%)

Counts

2 → 24

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite20.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6
0	7	6

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 4

Calls

Call 1

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

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

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	7	72
0	7	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

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

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

eval3.0ms (0.1%)

Compiler: Compiled 86 to 7 computations (91.9% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	28	3	31

Accuracy

100.0%

Counts

31 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 #s(literal 1/2 binary64) (+.f64 x y))
✓	52.4%	(*.f64 #s(literal 1/2 binary64) y)
✓	48.4%	(*.f64 #s(literal 1/2 binary64) x)

Compiler

Compiled 37 to 24 computations (35.1% saved)

regimes9.0ms (0.4%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 20 to 14 computations (30% saved)

regimes3.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
83.8%	2	`x`
85.7%	2	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.6%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

12.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
48.4%	1	`x`
48.4%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch9.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	1.0898326776857246e-126	1.684703014952655e-125

Results

5.0ms

96×

valid

Compiler

Compiled 86 to 71 computations (17.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (47.4% of total)

ival-add: 1.0ms (47.4% of total)

ival-mult: 1.0ms (47.4% of total)

const: 0.0ms (0% of total)

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

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	14	18

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 y #s(literal 3143850773938835/190536410541747572716161940294993060653600960856016305594430966774009505543198585212421026798308836130360530463953040948208494609331560382464 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))

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

Outputs

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

(if (<=.f64 y #s(literal 3143850773938835/190536410541747572716161940294993060653600960856016305594430966774009505543198585212421026798308836130360530463953040948208494609331560382464 binary64)) (*.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal 1/2 binary64) y))

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

soundness722.0ms (32%)

Rules

1864×	`fnmadd-define`
1816×	`fma-lowering-fma.f32`
1816×	`fma-lowering-fma.f64`
1812×	`sum5-define`
1630×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	168
1	124	168
2	302	168
3	871	168
4	2404	168
5	4335	168
0	8030	168
0	8	5
1	18	5
2	23	5
3	25	5
0	25	5

Stop Event

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

Compiler

Compiled 63 to 42 computations (33.3% saved)

preprocess36.0ms (1.6%)

Remove: (sort x y)
Compiler: Compiled 100 to 64 computations (36% saved)

Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, G

analyze0.0ms (0%)

sample646.0ms (28.7%)

preprocess36.0ms (1.6%)

explain66.0ms (2.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize18.0ms (0.8%)

series2.0ms (0.1%)

rewrite389.0ms (17.2%)

simplify126.0ms (5.6%)

eval47.0ms (2.1%)

prune29.0ms (1.3%)

simplify4.0ms (0.2%)

localize54.0ms (2.4%)

series1.0ms (0.1%)

rewrite20.0ms (0.9%)

simplify5.0ms (0.2%)

eval3.0ms (0.1%)

prune2.0ms (0.1%)

regimes9.0ms (0.4%)

regimes3.0ms (0.1%)

regimes13.0ms (0.6%)

bsearch9.0ms (0.4%)

simplify7.0ms (0.3%)

soundness722.0ms (32%)

preprocess36.0ms (1.6%)

end0.0ms (0%)

Profiling