Metrics for Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A

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 8 to 5 computations (37.5% saved)

Precisions

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

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

const: 0.0ms (0% of total)

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

sample573.0ms (23%)

Results

363.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 166.0ms

ival-add: 156.0ms (94% of total)

const: 7.0ms (4.2% of total)

backward-pass: 3.0ms (1.8% of total)

Bogosity

preprocess22.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

90×	`distribute-rgt-in`
86×	`sub-neg`
68×	`associate-+l-`
64×	`cancel-sign-sub-inv`
60×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	41	30
2	101	30
3	261	30
4	471	30
5	564	30
6	580	30
0	4	5
1	7	5
2	10	5
3	12	5
4	13	5
0	13	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (+ x y) x)

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

Call 2

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

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

explain40.0ms (1.6%)

FPErrors

Click to see full error table

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

Results

23.0ms

512×

valid

Compiler

Compiled 33 to 14 computations (57.6% saved)

Precisions

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

ival-add: 7.0ms (94.2% of total)

const: 0.0ms (0% 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 y (*.f64 x #s(literal 2 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize32.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 y (*.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(+.f64 y (*.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))

Rules

4×	`+-lowering-+.f64`
4×	`-lowering-.f32`
4×	`-lowering-.f64`
4×	`+-lowering-+.f32`
4×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	7	11
0	7	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

Results

16.0ms

256×

valid

Compiler

Compiled 14 to 9 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 4.0ms (69.9% of total)

ival-add: 1.0ms (17.5% of total)

const: 1.0ms (17.5% of total)

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

series4.0ms (0.2%)

Counts

2 → 36

Calls

Call 1

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

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

Calls

9 calls:

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

rewrite1.0s (42%)

Algorithm

1×	batch-egg-rewrite

Rules

17104×	`accelerator-lowering-fma.f32`
17104×	`accelerator-lowering-fma.f64`
4514×	`-lowering-.f32`
4514×	`-lowering-.f64`
3904×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	20	8
2	158	8
3	1540	8
0	8399	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 236

Calls

Call 1

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

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

simplify362.0ms (14.6%)

Algorithm

1×	egg-herbie

Rules

4188×	`/-lowering-/.f32`
4188×	`/-lowering-/.f64`
3666×	`associate-/r*`
2352×	`accelerator-lowering-fma.f32`
2352×	`accelerator-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	138
1	64	138
2	141	138
3	398	138
4	1108	138
5	2539	138
6	3437	138
7	4311	138
8	4789	138
9	4964	138
10	5054	138
11	5752	138
12	6068	138
13	6070	138
14	6070	138
15	6070	138
0	8131	120

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

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

eval146.0ms (5.9%)

Compiler: Compiled 8978 to 4244 computations (52.7% saved)

prune110.0ms (4.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	270	2	272
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	270	3	273

Accuracy

100.0%

Counts

273 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 y (*.f64 x #s(literal 2 binary64)))
▶	52.8%	(*.f64 #s(literal 2 binary64) x)
▶	48.3%	y

Compiler

Compiled 15 to 11 computations (26.7% saved)

localize31.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	5	6
0	5	6

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
y
(* 2 x)
2
x

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

Results

12.0ms

256×

valid

Compiler

Compiled 9 to 6 computations (33.3% saved)

Precisions

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

ival-mult: 2.0ms (70% of total)

const: 1.0ms (35% of total)

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

series1.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (* 2 x)>

Outputs
#<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)>

Calls

3 calls:

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

rewrite9.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* 2 x)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

Outputs
(* 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)

eval2.0ms (0.1%)

Compiler: Compiled 44 to 30 computations (31.8% saved)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	14	3	17

Accuracy

100.0%

Counts

17 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 y (*.f64 x #s(literal 2 binary64)))
✓	52.8%	(*.f64 #s(literal 2 binary64) x)
✓	48.3%	y

Compiler

Compiled 31 to 20 computations (35.5% saved)

regimes7.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 13 to 8 computations (38.5% saved)

regimes8.0ms (0.3%)

Counts

2 → 5

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
79.2%	5	`x`
77.4%	5	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
y

Outputs
y

Calls

2 calls:

0.0ms	x
0.0ms	y

Results

Accuracy	Segments	Branch
48.3%	1	`y`
48.3%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch48.0ms (1.9%)

Algorithm

4×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	2.2629142593259365e-36	9.773677482306133e-33
13.0ms	-2.4127440410289463e-44	-1.375151294024721e-51
14.0ms	-4.433420845414632e+30	-17459657486198264.0
10.0ms	-2.9877310178996236e+85	-3.793549037372426e+79

Results

24.0ms

576×

valid

Compiler

Compiled 372 to 296 computations (20.4% saved)

Precisions

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

ival-add: 6.0ms (86.8% of total)

const: 0.0ms (0% of total)

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

soundness2.0ms (0.1%)

Stop Event

1×

done

Compiler

Compiled 35 to 23 computations (34.3% saved)

preprocess34.0ms (1.4%)

Compiler: Compiled 98 to 64 computations (34.7% saved)

Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A

analyze0.0ms (0%)

sample573.0ms (23%)

preprocess22.0ms (0.9%)

explain40.0ms (1.6%)

eval0.0ms (0%)

prune1.0ms (0%)

localize32.0ms (1.3%)

series4.0ms (0.2%)

rewrite1.0s (42%)

simplify362.0ms (14.6%)

eval146.0ms (5.9%)

prune110.0ms (4.4%)

localize31.0ms (1.2%)

series1.0ms (0%)

rewrite9.0ms (0.4%)

simplify4.0ms (0.1%)

eval2.0ms (0.1%)

prune3.0ms (0.1%)

regimes7.0ms (0.3%)

regimes8.0ms (0.3%)

regimes1.0ms (0%)

bsearch48.0ms (1.9%)

soundness2.0ms (0.1%)

preprocess34.0ms (1.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	14	32
1	41	30
2	101	30
3	261	30
4	471	30
5	564	30
6	580	30
0	4	5
1	7	5
2	10	5
3	12	5
4	13	5
0	13	4

Iter	Nodes	Cost
0	14	32
1	41	30
2	101	30
3	261	30
4	471	30
5	564	30
6	580	30
0	4	5
1	7	5
2	10	5
3	12	5
4	13	5
0	13	4

Iter	Nodes	Cost
0	14	32
1	41	30
2	101	30
3	261	30
4	471	30
5	564	30
6	580	30
0	4	5
1	7	5
2	10	5
3	12	5
4	13	5
0	13	4