Metrics for Optimisation.CirclePacking:place from circle-packing-0.1.0.4, A

analyze22.0ms (1.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
25%	25%	74.9%	0.1%	0%	0%	0%	3
28.6%	25%	62.4%	0.1%	0%	12.5%	0%	4
46.2%	37.5%	43.7%	0.1%	0%	18.7%	0%	5
52.2%	37.5%	34.3%	0.1%	0%	28.1%	0%	6
65.1%	43.7%	23.4%	0.1%	0%	32.8%	0%	7
70.9%	43.7%	18%	0.1%	0%	38.2%	0%	8
79.5%	46.8%	12.1%	0.1%	0%	41%	0%	9
83.6%	46.8%	9.2%	0.1%	0%	43.9%	0%	10
88.7%	48.4%	6.1%	0.1%	0%	45.4%	0%	11
91.3%	48.4%	4.6%	0.1%	0%	46.9%	0%	12

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions

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

ival-add: 5.0ms (59.1% of total)

ival-sqrt: 3.0ms (35.5% of total)

const: 0.0ms (0% of total)

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

sample590.0ms (31.2%)

Results

397.0ms	8256×	0	valid
17.0ms	507×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 148.0ms

ival-sqrt: 79.0ms (53.4% of total)

ival-add: 58.0ms (39.2% of total)

const: 7.0ms (4.7% of total)

backward-pass: 3.0ms (2% of total)

Bogosity

preprocess22.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

144×	`sum3-define`
144×	`sum5-define`
144×	`sum4-define`
136×	`fmsub-define`
128×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	27	26
2	44	26
3	70	26
4	191	26
5	410	26
6	597	26
7	682	26
8	700	26
9	704	26
0	4	4
1	5	4
0	5	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ x y))

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

Call 2

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

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

Symmetry

(sort x y)

explain45.0ms (2.4%)

FPErrors

Click to see full error table

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

Results

24.0ms

512×

valid

Compiler

Compiled 30 to 14 computations (53.3% saved)

Precisions

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

ival-add: 4.0ms (44.5% of total)

ival-sqrt: 4.0ms (44.5% of total)

const: 0.0ms (0% of total)

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

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify3.0ms (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	(sqrt.f64 (+.f64 x y))

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`sqrt-lowering-sqrt.f64`
2×	`sqrt-lowering-sqrt.f32`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
1	5	9
0	5	9

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ x y))
(+ x y)
x
y

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

localize18.0ms (0.9%)

Localize:

Found 2 expressions of interest:

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

Results

13.0ms

256×

valid

Compiler

Compiled 12 to 5 computations (58.3% saved)

Precisions

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

ival-add: 2.0ms (50.6% of total)

ival-sqrt: 2.0ms (50.6% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.3%)

Counts

2 → 48

Calls

Call 1

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

Outputs
#<alt (sqrt y)>
#<alt (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))>
#<alt (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))>
#<alt (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))>
#<alt (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))>
#<alt (sqrt y)>
#<alt (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))>
#<alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -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
1.0ms	x	@	-inf	(sqrt (+ x y))
1.0ms	y	@	-inf	(sqrt (+ x y))
1.0ms	y	@	inf	(sqrt (+ x y))
1.0ms	x	@	inf	(sqrt (+ x y))
0.0ms	y	@	0	(sqrt (+ x y))

rewrite310.0ms (16.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2796×	`/-lowering-/.f32`
2796×	`/-lowering-/.f64`
2488×	`-lowering-.f32`
2488×	`-lowering-.f64`
1966×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	20	7
2	157	7
3	1562	7
0	9159	7

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 216

Calls

Call 1

Inputs
(sqrt (+ x y))
(+ x y)

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

simplify222.0ms (11.7%)

Algorithm

1×	egg-herbie

Rules

4460×	`-lowering-.f32`
4460×	`-lowering-.f64`
2462×	`fma-lowering-fma.f32`
2462×	`fma-lowering-fma.f64`
1876×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	606
1	486	568
2	1689	541
3	6147	539
0	8118	539

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(sqrt x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -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
(sqrt y)
(sqrt.f64 y)
(+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))
(+.f64 (sqrt.f64 y) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 #s(literal 1/2 binary64) x)))
(+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+.f64 (sqrt.f64 y) (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 x #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))))))
(+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(+.f64 (sqrt.f64 y) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x #s(literal 1/16 binary64))))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 y #s(literal 1/2 binary64)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 y (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (*.f64 y #s(literal -1/8 binary64)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow y 3))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 y #s(literal 1/2 binary64)))) (.f64 (.f64 y y) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 y #s(literal 1/16 binary64))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 y #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (+.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 y #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 y y)) #s(literal 1/8 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 y #s(literal 1/2 binary64))) (+.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 y y)) #s(literal 1/8 binary64)) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) y) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 0 binary64) x))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))
(+.f64 (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 y #s(literal 1/2 binary64))))
(+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))
(+.f64 (sqrt.f64 x) (.f64 y (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 y #s(literal -1/8 binary64))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))
(+.f64 (sqrt.f64 x) (.f64 y (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 y (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 y #s(literal 1/16 binary64))))))))
(sqrt y)
(sqrt.f64 y)
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(.f64 y (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(.f64 y (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x #s(literal -1/8 binary64))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
(.f64 y (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 x (.f64 x #s(literal -1/8 binary64)))) (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (*.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (-.f64 #s(literal 0 binary64) y))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) x)) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) (-.f64 #s(literal 0 binary64) y))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (.f64 (.f64 x x) #s(literal 1/8 binary64))) (+.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))))) (-.f64 #s(literal 0 binary64) y))
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
x
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.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 (+.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)))

eval29.0ms (1.5%)

Compiler: Compiled 7773 to 906 computations (88.3% saved)

prune61.0ms (3.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	263	2	265

Accuracy

100.0%

Counts

265 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	97.4%	(sqrt.f64 y)

Compiler

Compiled 10 to 7 computations (30% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 y)

Rules

2×	`sqrt-lowering-sqrt.f64`
2×	`sqrt-lowering-sqrt.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	3
0	2	3

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt y)
y

Outputs
(sqrt y)
(sqrt.f64 y)
y

localize12.0ms (0.6%)

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 y)

Results

8.0ms

256×

valid

Compiler

Compiled 6 to 4 computations (33.3% saved)

Precisions

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

ival-sqrt: 2.0ms (85.5% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0.1%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (sqrt y)>

Outputs
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(sqrt y)
0.0ms	y	@	-inf	(sqrt y)
0.0ms	y	@	0	(sqrt y)

rewrite124.0ms (6.6%)

Algorithm

1×	batch-egg-rewrite

Rules

362×	`-lowering-.f32`
362×	`-lowering-.f64`
166×	`prod-exp`
154×	`pow-lowering-pow.f64`
154×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	2
1	4	2
2	12	2
3	26	2
4	65	2
5	168	2
0	875	2

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

1 → 35

Calls

Call 1

Inputs
(sqrt y)

Outputs
(exp.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 y (.f64 y (.f64 y y)))) #s(literal 1/8 binary64)))
(sqrt.f64 y)
(pow.f64 y #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 y #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 y) #s(literal 1 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(pow.f64 (pow.f64 y #s(literal 1/16 binary64)) #s(literal 8 binary64))
(pow.f64 (.f64 y (.f64 y (*.f64 y y))) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (*.f64 (log.f64 y) #s(literal 2 binary64)))
(pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 2 binary64))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/4 binary64)) (exp.f64 #s(literal 1/4 binary64))) (log.f64 y))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 y) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(*.f64 (pow.f64 y #s(literal 1/8 binary64)) (pow.f64 y #s(literal 3/8 binary64)))
(*.f64 (pow.f64 y #s(literal 1/8 binary64)) (pow.f64 (pow.f64 y #s(literal 3/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1/16 binary64)) (pow.f64 y #s(literal 7/16 binary64)))
(*.f64 (pow.f64 y #s(literal 3/8 binary64)) (pow.f64 y #s(literal 1/8 binary64)))
(.f64 (pow.f64 y #s(literal 1/32 binary64)) (.f64 (pow.f64 y #s(literal 1/32 binary64)) (pow.f64 y #s(literal 7/16 binary64))))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))))
(*.f64 (pow.f64 y #s(literal 3/16 binary64)) (pow.f64 y #s(literal 5/16 binary64)))
(*.f64 (pow.f64 y #s(literal 7/16 binary64)) (pow.f64 y #s(literal 1/16 binary64)))
(*.f64 (pow.f64 y #s(literal 5/16 binary64)) (pow.f64 y #s(literal 3/16 binary64)))
(*.f64 (pow.f64 (pow.f64 y #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 y #s(literal 7/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 y #s(literal 3/8 binary64)) #s(literal 1 binary64)) (pow.f64 y #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 y #s(literal 7/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 y #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 1 binary64)) (pow.f64 (exp.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) #s(literal 1 binary64)))
(.f64 (.f64 (pow.f64 y #s(literal 7/16 binary64)) (pow.f64 y #s(literal 1/32 binary64))) (pow.f64 y #s(literal 1/32 binary64)))

simplify16.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

120×	`fma-define`
112×	`fma-lowering-fma.f32`
112×	`fma-lowering-fma.f64`
104×	`fnmadd-define`
80×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	14	24
2	36	24
3	66	24
4	163	24
5	250	24
6	408	24
7	493	24
8	513	24
9	521	24
0	521	24

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))

Outputs
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)

eval5.0ms (0.2%)

Compiler: Compiled 295 to 85 computations (71.2% saved)

prune10.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	47	2	49

Accuracy

100.0%

Counts

49 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	97.4%	(sqrt.f64 y)

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes6.0ms (0.3%)

Counts

2 → 1

Calls

Call 1

Inputs
(sqrt.f64 y)
(sqrt.f64 (+.f64 x y))

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

Calls

4 calls:

2.0ms	(sqrt.f64 (+.f64 x y))
2.0ms	(+.f64 x y)
1.0ms	x
1.0ms	y

Results

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

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 y)

Outputs
(sqrt.f64 y)

Calls

2 calls:

1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
97.4%	1	`x`
97.4%	1	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 y)

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

soundness352.0ms (18.6%)

Rules

4460×	`-lowering-.f32`
4460×	`-lowering-.f64`
2462×	`fma-lowering-fma.f32`
2462×	`fma-lowering-fma.f64`
1876×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	606
1	486	568
2	1689	541
3	6147	539
0	8118	539

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 12 to 8 computations (33.3% saved)

preprocess20.0ms (1.1%)

Remove: (sort x y)
Compiler: Compiled 52 to 34 computations (34.6% saved)

Optimisation.CirclePacking:place from circle-packing-0.1.0.4, A

analyze22.0ms (1.2%)

sample590.0ms (31.2%)

preprocess22.0ms (1.2%)

explain45.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.2%)

localize18.0ms (0.9%)

series5.0ms (0.3%)

rewrite310.0ms (16.4%)

simplify222.0ms (11.7%)

eval29.0ms (1.5%)

prune61.0ms (3.2%)

simplify8.0ms (0.4%)

localize12.0ms (0.6%)

series1.0ms (0.1%)

rewrite124.0ms (6.6%)

simplify16.0ms (0.8%)

eval5.0ms (0.2%)

prune10.0ms (0.5%)

regimes6.0ms (0.3%)

regimes3.0ms (0.1%)

simplify7.0ms (0.4%)

soundness352.0ms (18.6%)

preprocess20.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	14	28
1	27	26
2	44	26
3	70	26
4	191	26
5	410	26
6	597	26
7	682	26
8	700	26
9	704	26
0	4	4
1	5	4
0	5	4

Iter	Nodes	Cost
0	8	24
1	14	24
2	36	24
3	66	24
4	163	24
5	250	24
6	408	24
7	493	24
8	513	24
9	521	24
0	521	24

Iter	Nodes	Cost
0	14	28
1	27	26
2	44	26
3	70	26
4	191	26
5	410	26
6	597	26
7	682	26
8	700	26
9	704	26
0	4	4
1	5	4
0	5	4

Iter	Nodes	Cost
0	8	24
1	14	24
2	36	24
3	66	24
4	163	24
5	250	24
6	408	24
7	493	24
8	513	24
9	521	24
0	521	24

Iter	Nodes	Cost
0	14	28
1	27	26
2	44	26
3	70	26
4	191	26
5	410	26
6	597	26
7	682	26
8	700	26
9	704	26
0	4	4
1	5	4
0	5	4

Iter	Nodes	Cost
0	8	24
1	14	24
2	36	24
3	66	24
4	163	24
5	250	24
6	408	24
7	493	24
8	513	24
9	521	24
0	521	24