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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze25.0ms (2.2%)

Memory

-14.2MiB live, 30.6MiB allocated; 10ms collecting garbage

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 6 to 6 computations (0% saved)

sample746.0ms (64.3%)

Memory

-1.7MiB live, 781.5MiB allocated; 258ms collecting garbage

Samples

437.0ms	8 256×	0	valid
23.0ms	508×	0	invalid

Precisions

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

ival-sqrt: 87.0ms (58.7% of total)

ival-add: 56.0ms (37.8% of total)

ival-assert: 3.0ms (2% of total)

adjust: 2.0ms (1.3% of total)

Bogosity

explain51.0ms (4.4%)

Memory

-11.8MiB live, 39.9MiB allocated; 10ms collecting garbage

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

31.0ms

512×

valid

Compiler

Compiled 26 to 16 computations (38.5% saved)

Precisions

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

ival-sqrt: 16.0ms (79.8% of total)

ival-add: 3.0ms (15% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess13.0ms (1.1%)

Memory

25.1MiB live, 25.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	16	30
0	4	4
0	6	4
1	7	4
0	7	4

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Symmetry

(sort x y)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 4 to 4 computations (0% saved)

series6.0ms (0.6%)

Memory

11.7MiB live, 11.7MiB allocated; 0ms collecting garbage

Counts

4 → 31

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))))
#s(approx (sqrt (+ x y)) #s(hole 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))))))))
#s(approx (+ x y) #s(hole binary64 x))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))))
#s(approx y #s(hole binary64 y))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ x y)) #s(hole 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)))))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Calls

6 calls:

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

rewrite68.0ms (5.8%)

Memory

-23.7MiB live, 99.9MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	190	780
0	191	666
0	1062	634

Stop Event

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

Counts

35 → 39

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 x y))
(+.f64 x y)
x
y
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))))
#s(approx (sqrt (+ x y)) #s(hole 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))))))))
#s(approx (+ x y) #s(hole binary64 x))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))))
#s(approx y #s(hole binary64 y))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ x y)) #s(hole 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)))))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Outputs
(pow.f64 (+.f64 y x) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 y x))
(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (-.f64 x y))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 y y) (.f64 x y))))
(+.f64 y x)
(+.f64 x y)
x
y
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x) #s(literal 1/2 binary64) (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (.f64 (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) #s(literal -1/8 binary64))) x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) #s(literal 1/2 binary64))) x (sqrt.f64 y)))
#s(approx (+ x y) y)
#s(approx (+ x y) (+.f64 y x))
#s(approx x x)
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (.f64 (.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1/8 binary64) (.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) (.f64 y y) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/16 binary64) (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ x y) x)
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) x))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 (/.f64 (.f64 y y) #s(literal -1 binary64)) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64)))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) (/.f64 (.f64 y y) #s(literal -1 binary64)) (fma.f64 (.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1 binary64)) (sqrt.f64 (pow.f64 x #s(literal -7 binary64)))) #s(literal 1/16 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64))))) x)))
#s(approx (+ x y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 y x)) #s(literal 1 binary64)) x)))
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal -1/8 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) y) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) #s(literal -1/8 binary64))) y (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)))
#s(approx y y)
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (pow.f64 y #s(literal -7 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 y))))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))) y)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))))) y)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -7 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))) y)))
#s(approx (+ x y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 x y)) #s(literal 1 binary64)) y)))

eval5.0ms (0.5%)

Memory: 15.4MiB live, 15.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 694 to 185 computations (73.3% saved)

prune2.0ms (0.2%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Accuracy

100.0%

Counts

40 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	100.0%	(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
▶	96.7%	(sqrt.f64 #s(approx (+ x y) y))
▶	98.5%	#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x) #s(literal 1/2 binary64) (sqrt.f64 y)))

Compiler

Compiled 37 to 29 computations (21.6% saved)

series23.0ms (2%)

Memory

-20.7MiB live, 42.7MiB allocated; 16ms collecting garbage

Counts

16 → 57

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (sqrt y)))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (* (/ 1 (sqrt y)) x) #s(hole binary64 (* x (sqrt (/ 1 y)))))
#s(approx x #s(hole binary64 x))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 y))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (+ x y)))
#s(approx (+ (/ x y) 1) #s(hole binary64 1))
#s(approx (+ (/ x y) 1) #s(hole binary64 (+ 1 (/ x y))))
#s(approx (/ x y) #s(hole binary64 (/ x y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))))
#s(approx (sqrt (+ x y)) #s(hole 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))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* 1/2 (* x (sqrt (/ 1 y))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))))
#s(approx (+ x y) #s(hole binary64 x))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 x))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (+ (/ x y) 1) #s(hole binary64 (/ x y)))
#s(approx (+ (/ x y) 1) #s(hole binary64 (* x (+ (/ 1 x) (/ 1 y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)))
#s(approx (/ 1 (sqrt y)) #s(hole binary64 (sqrt (/ 1 y))))
#s(approx (sqrt y) #s(hole binary64 (sqrt y)))
#s(approx y #s(hole binary64 y))
#s(approx (+ (/ x y) 1) #s(hole binary64 (/ (+ x y) y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ x y)) #s(hole 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)))))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt y) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	y	@	inf	((sqrt (+ x y)) (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (* (/ 1 (sqrt y)) x) (/ 1 (sqrt y)) 1 (sqrt y) y x 1/2 (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
3.0ms	y	@	-inf	((sqrt (+ x y)) (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (* (/ 1 (sqrt y)) x) (/ 1 (sqrt y)) 1 (sqrt y) y x 1/2 (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
2.0ms	y	@	0	((sqrt (+ x y)) (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (* (/ 1 (sqrt y)) x) (/ 1 (sqrt y)) 1 (sqrt y) y x 1/2 (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
2.0ms	x	@	-inf	((sqrt (+ x y)) (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (* (/ 1 (sqrt y)) x) (/ 1 (sqrt y)) 1 (sqrt y) y x 1/2 (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
2.0ms	x	@	0	((sqrt (+ x y)) (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (* (/ 1 (sqrt y)) x) (/ 1 (sqrt y)) 1 (sqrt y) y x 1/2 (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))

rewrite60.0ms (5.2%)

Memory

8.4MiB live, 99.4MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	252	1274
0	268	1135
0	1302	1099

Stop Event

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

Counts

73 → 103

Calls

Call 1

Inputs
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x) #s(literal 1/2 binary64) (sqrt.f64 y)))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x) #s(literal 1/2 binary64) (sqrt.f64 y))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x)
(/.f64 #s(literal 1 binary64) (sqrt.f64 y))
#s(literal 1 binary64)
(sqrt.f64 y)
y
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) y)
(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
(*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(+.f64 (/.f64 x y) #s(literal 1 binary64))
(/.f64 x y)
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (* x (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* 1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* x (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (sqrt y)))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (* x (sqrt (/ 1 y)))))))
#s(approx (* (/ 1 (sqrt y)) x) #s(hole binary64 (* x (sqrt (/ 1 y)))))
#s(approx x #s(hole binary64 x))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 y))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (+ x y)))
#s(approx (+ (/ x y) 1) #s(hole binary64 1))
#s(approx (+ (/ x y) 1) #s(hole binary64 (+ 1 (/ x y))))
#s(approx (/ x y) #s(hole binary64 (/ x y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)))))))
#s(approx (sqrt (+ x y)) #s(hole 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))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* 1/2 (* x (sqrt (/ 1 y))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* x (+ (* 1/2 (sqrt (/ 1 y))) (* (/ 1 x) (sqrt y))))))
#s(approx (+ x y) #s(hole binary64 x))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 x))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (+ (/ x y) 1) #s(hole binary64 (/ x y)))
#s(approx (+ (/ x y) 1) #s(hole binary64 (* x (+ (/ 1 x) (/ 1 y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* -1 (* x (+ (* -1 (* (/ 1 x) (sqrt y))) (* -1/2 (sqrt (/ 1 y))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) y)) (* 1/2 (sqrt (/ 1 x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* 1/2 (sqrt (/ 1 x))) (* y (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) y)))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (/ (+ (sqrt (pow y 3)) (* 1/2 (* x (sqrt y)))) y)))
#s(approx (/ 1 (sqrt y)) #s(hole binary64 (sqrt (/ 1 y))))
#s(approx (sqrt y) #s(hole binary64 (sqrt y)))
#s(approx y #s(hole binary64 y))
#s(approx (+ (/ x y) 1) #s(hole binary64 (/ (+ x y) y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* x (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ x y)) #s(hole 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)))))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* x (sqrt (/ 1 (pow y 3)))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -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)))))))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) #s(hole binary64 (* -1 (* y (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt y) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))
#s(approx (* (+ (/ x y) 1) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Outputs
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) (sqrt.f64 y)))
(/.f64 (-.f64 (.f64 (sqrt.f64 y) (sqrt.f64 y)) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))))) (-.f64 (sqrt.f64 y) (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)))) (.f64 (sqrt.f64 y) (sqrt.f64 y))) (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) (sqrt.f64 y)))
(/.f64 (+.f64 (pow.f64 (sqrt.f64 y) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) #s(literal 3 binary64))) (fma.f64 (sqrt.f64 y) (sqrt.f64 y) (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)))) (.f64 (sqrt.f64 y) (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 y) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) (-.f64 (.f64 (sqrt.f64 y) (sqrt.f64 y)) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) (sqrt.f64 y)))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) (sqrt.f64 y))
(fma.f64 (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) (*.f64 x #s(literal 1/2 binary64)) (sqrt.f64 y))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) x) (sqrt.f64 y))
(fma.f64 (*.f64 (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) x) #s(literal 1/2 binary64) (sqrt.f64 y))
(-.f64 (sqrt.f64 y) (.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) x)))
(+.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) (sqrt.f64 y))
(+.f64 (sqrt.f64 y) (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))))
(*.f64 (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) x)
(*.f64 x (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) x) (sqrt.f64 y))
(pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 y) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 y)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 y))
(sqrt.f64 (pow.f64 y #s(literal -1 binary64)))
#s(literal 1 binary64)
(pow.f64 y #s(literal 1/2 binary64))
(sqrt.f64 y)
y
x
#s(literal 1/2 binary64)
(pow.f64 #s(approx (+ x y) y) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) y)
(pow.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
(*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)
(*.f64 y (+.f64 (/.f64 x y) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) y (*.f64 (/.f64 x y) y))
(fma.f64 y #s(literal 1 binary64) (*.f64 y (/.f64 x y)))
(+.f64 (.f64 y #s(literal 1 binary64)) (.f64 y (/.f64 x y)))
(+.f64 (.f64 #s(literal 1 binary64) y) (.f64 (/.f64 x y) y))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 x y) (/.f64 x y))) (-.f64 #s(literal 1 binary64) (/.f64 x y)))
(/.f64 (-.f64 (*.f64 (/.f64 x y) (/.f64 x y)) #s(literal 1 binary64)) (-.f64 (/.f64 x y) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 x y) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (/.f64 x y) (/.f64 x y)) (.f64 #s(literal 1 binary64) (/.f64 x y)))))
(/.f64 (+.f64 (pow.f64 (/.f64 x y) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (/.f64 x y) (/.f64 x y) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 x y) #s(literal 1 binary64)))))
(+.f64 (/.f64 x y) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 (neg.f64 x) (neg.f64 y))
(/.f64 x y)
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (.f64 (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (.f64 (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) #s(literal -1/8 binary64))) x (*.f64 (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) #s(literal 1/2 binary64))) x (sqrt.f64 y)))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (sqrt.f64 y))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (fma.f64 (*.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) (sqrt.f64 y)))
#s(approx (* (/ 1 (sqrt y)) x) (*.f64 (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) x))
#s(approx x x)
#s(approx (+ x y) y)
#s(approx (+ x y) (+.f64 y x))
#s(approx (* (+ (/ x y) 1) y) y)
#s(approx (* (+ (/ x y) 1) y) (+.f64 y x))
#s(approx (+ (/ x y) 1) #s(literal 1 binary64))
#s(approx (+ (/ x y) 1) (+.f64 (/.f64 x y) #s(literal 1 binary64)))
#s(approx (/ x y) (/.f64 x y))
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (.f64 (.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1/8 binary64) (.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) (.f64 y y) (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) (pow.f64 y #s(literal 3 binary64))) #s(literal 1/16 binary64) (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (.f64 (.f64 #s(literal 1/2 binary64) x) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (.f64 (fma.f64 (pow.f64 x #s(literal -1 binary64)) (sqrt.f64 y) (.f64 (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (+ x y) x)
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) x))
#s(approx (* (+ (/ x y) 1) y) x)
#s(approx (* (+ (/ x y) 1) y) (*.f64 (+.f64 (/.f64 y x) #s(literal 1 binary64)) x))
#s(approx (+ (/ x y) 1) (/.f64 x y))
#s(approx (+ (/ x y) 1) (*.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 y #s(literal -1 binary64))) x))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 (/.f64 (.f64 y y) #s(literal -1 binary64)) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (*.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64)))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) (/.f64 (.f64 y y) #s(literal -1 binary64)) (fma.f64 (.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1 binary64)) (sqrt.f64 (pow.f64 x #s(literal -7 binary64)))) #s(literal 1/16 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal 1/2 binary64))))) x)))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (neg.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)) (neg.f64 (.f64 (pow.f64 x #s(literal -1 binary64)) (sqrt.f64 y)))) x)))
#s(approx (+ x y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 y x)) #s(literal 1 binary64)) x)))
#s(approx (* (+ (/ x y) 1) y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 y x)) #s(literal 1 binary64)) x)))
#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) y) #s(literal -1/8 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) y) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (pow.f64 x #s(literal -3 binary64))) #s(literal -1/8 binary64))) y (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))) y (sqrt.f64 x)))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (/.f64 (fma.f64 (*.f64 (sqrt.f64 y) x) #s(literal 1/2 binary64) (pow.f64 y #s(literal 3/2 binary64))) y))
#s(approx (/ 1 (sqrt y)) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)))
#s(approx (sqrt y) (sqrt.f64 y))
#s(approx y y)
#s(approx (+ (/ x y) 1) (/.f64 (+.f64 y x) y))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) y))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (.f64 (.f64 #s(literal -1/8 binary64) (*.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))))) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) y))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (pow.f64 y #s(literal -7 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64)))))) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) y))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))) y))
#s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
#s(approx (* (+ (/ x y) 1) y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y))
#s(approx (sqrt (+ x y)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 y))))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (*.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)))) y)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (*.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64))))) y)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -7 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)))))) y)))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 y))))
#s(approx (+ (* (* (/ 1 (sqrt y)) x) 1/2) (sqrt y)) (neg.f64 (.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (*.f64 #s(literal -1 binary64) (pow.f64 (sqrt.f64 y) #s(literal -1 binary64)))) y)))
#s(approx (sqrt y) (neg.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 y))))
#s(approx (+ x y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 x y)) #s(literal 1 binary64)) y)))
#s(approx (* (+ (/ x y) 1) y) (neg.f64 (*.f64 (-.f64 (neg.f64 (/.f64 x y)) #s(literal 1 binary64)) y)))

eval14.0ms (1.2%)

Memory: -16.7MiB live, 29.4MiB allocated; 4ms collecting garbage
Compiler: Compiled 2 209 to 442 computations (80% saved)

prune4.0ms (0.3%)

Memory

11.1MiB live, 11.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	115	4	119

Accuracy

100.0%

Counts

119 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	100.0%	(sqrt.f64 #s(approx (+ x y) (*.f64 (+.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
✓	96.7%	(sqrt.f64 #s(approx (+ x y) y))
✓	98.5%	#s(approx (sqrt (+ x y)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) x) #s(literal 1/2 binary64) (sqrt.f64 y)))

Compiler

Compiled 74 to 49 computations (33.8% saved)

regimes7.0ms (0.6%)

Memory

16.8MiB live, 16.8MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes5.0ms (0.5%)

Memory

13.1MiB live, 13.1MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (+ x y) y))
(sqrt.f64 (+.f64 x y))

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes47.0ms (4.1%)

Memory

-38.7MiB live, 16.1MiB allocated; 5ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (+ x y) y))

Outputs
(sqrt.f64 #s(approx (+ x y) y))

Calls

4 calls:

44.0ms	x
1.0ms	(sqrt.f64 (+.f64 x y))
1.0ms	(+.f64 x y)
1.0ms	y

Results

Accuracy	Segments	Branch
96.7%	1	`(+.f64 x y)`
96.7%	1	`(sqrt.f64 (+.f64 x y))`
96.7%	1	`x`
96.7%	1	`y`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify51.0ms (4.4%)

Memory

7.5MiB live, 54.2MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	16	22
2	19	22
3	27	22
4	50	22
5	223	22
6	2148	22
7	5281	22

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations5.0ms (0.4%)

Memory

9.8MiB live, 9.8MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 22 to 13 computations (40.9% saved)

preprocess27.0ms (2.3%)

Memory: 13.4MiB live, 57.7MiB allocated; 6ms collecting garbage
Compiler: Compiled 100 to 70 computations (30% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze25.0ms (2.2%)

sample746.0ms (64.3%)

explain51.0ms (4.4%)

preprocess13.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

series6.0ms (0.6%)

rewrite68.0ms (5.8%)

eval5.0ms (0.5%)

prune2.0ms (0.2%)

series23.0ms (2%)

rewrite60.0ms (5.2%)

eval14.0ms (1.2%)

prune4.0ms (0.3%)

regimes7.0ms (0.6%)

regimes5.0ms (0.5%)

regimes47.0ms (4.1%)

simplify51.0ms (4.4%)

derivations5.0ms (0.4%)

preprocess27.0ms (2.3%)

end0.0ms (0%)

Profiling