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

analyze16.0ms (1.3%)

Memory

32.0MiB live, 32.0MiB allocated; 0ms 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)

sample811.0ms (64%)

Memory

62.6MiB live, 1 112.0MiB allocated; 286ms collecting garbage

Samples

399.0ms	8 255×	0	valid
22.0ms	516×	0	invalid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 183.0ms

ival-sqrt: 107.0ms (58.3% of total)

ival-add!: 74.0ms (40.3% of total)

adjust: 2.0ms (1.1% of total)

Bogosity

preprocess35.0ms (2.8%)

Memory

-35.6MiB live, 10.3MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	17	26
2	19	26
3	23	26
4	31	26
5	37	26
6	44	26
7	46	26

Stop Event

1×

saturated

Alt Table

Click to see full alt table

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

Symmetry

(sort x y)

Compiler

Compiled 8 to 8 computations (0% saved)

series12.0ms (0.9%)

Memory

14.5MiB live, 14.5MiB 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
3.0ms	x	@	-inf	((sqrt (+ x y)) (+ x y) x y)
3.0ms	y	@	-inf	((sqrt (+ x y)) (+ x y) x y)
2.0ms	x	@	inf	((sqrt (+ x y)) (+ x y) x y)
2.0ms	y	@	inf	((sqrt (+ x y)) (+ x y) x y)
1.0ms	x	@	0	((sqrt (+ x y)) (+ x y) x y)

rewrite95.0ms (7.5%)

Memory

7.8MiB live, 64.2MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	190	780
0	191	666
0	1068	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 (fma.f64 (.f64 x x) x (.f64 (.f64 y y) y)) (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 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (.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 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) #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 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) 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 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) 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))) (.f64 (.f64 y y) y)) #s(literal 1/16 binary64) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) 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 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (/.f64 (.f64 (.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x))) y) #s(literal 1/2 binary64)))) x)))
#s(approx (sqrt (+ x y)) (neg.f64 (.f64 (fma.f64 (/.f64 (.f64 (.f64 y y) (sqrt.f64 (pow.f64 x #s(literal -5 binary64)))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (.f64 (/.f64 (.f64 (.f64 y y) y) #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 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) 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 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) 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 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) #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 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (/.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 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 y y) y))))) (/.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 (sqrt.f64 (pow.f64 y #s(literal -7 binary64))) (.f64 (.f64 x x) x)) #s(literal 1/16 binary64) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y)))))) (/.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 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (*.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 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (*.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 (.f64 (.f64 x x) (sqrt.f64 (pow.f64 y #s(literal -5 binary64)))) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (.f64 (/.f64 (.f64 (.f64 x x) x) #s(literal 1 binary64)) (sqrt.f64 (pow.f64 y #s(literal -7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) y))) (.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)))

eval4.0ms (0.3%)

Memory: 6.4MiB live, 6.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 405 to 182 computations (55.1% saved)

prune2.0ms (0.2%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	5	37

Accuracy

100.0%

Counts

37 → 5

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)))
▶	98.5%	(sqrt.f64 #s(approx (+ x y) y))
▶	3.1%	(sqrt.f64 #s(approx (+ x y) x))
▶	3.1%	#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)))

Compiler

Compiled 35 to 34 computations (2.9% saved)

series41.0ms (3.2%)

Memory

-25.5MiB live, 23.4MiB allocated; 3ms collecting garbage

Counts

18 → 57

Calls

Call 1

Inputs
#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)))
(fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y)
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
x
y
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (+ x y) x))
#s(approx (+ x y) x)
(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 x)) y) 1/2) (sqrt x)) #s(hole binary64 (* 1/2 (* (sqrt (/ 1 x)) y))))
#s(approx (+ (* (* (/ 1 (sqrt x)) y) 1/2) (sqrt x)) #s(hole binary64 (/ (+ (sqrt (pow x 3)) (* 1/2 (* (sqrt x) y))) x)))
#s(approx (* (/ 1 (sqrt x)) y) #s(hole binary64 (* (sqrt (/ 1 x)) y)))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (sqrt (/ 1 x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#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 x)) y) 1/2) (sqrt x)) #s(hole binary64 (sqrt x)))
#s(approx (+ (* (* (/ 1 (sqrt x)) y) 1/2) (sqrt x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 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 (* (+ (/ 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 x)) y) 1/2) (sqrt x)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (+ (* (* (/ 1 (sqrt x)) y) 1/2) (sqrt x)) #s(hole binary64 (* -1 (* x (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) y)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#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 x)) y) 1/2) (sqrt x)) #s(hole binary64 (+ (sqrt x) (* 1/2 (* (sqrt (/ 1 x)) 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 x)) y) 1/2) (sqrt x)) #s(hole binary64 (* y (+ (* 1/2 (sqrt (/ 1 x))) (* (sqrt x) (/ 1 y))))))
#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 x)) y) 1/2) (sqrt x)) #s(hole binary64 (* -1 (* y (+ (* -1 (* (sqrt x) (/ 1 y))) (* -1/2 (sqrt (/ 1 x))))))))
#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
28.0ms	x	@	inf	((sqrt (+ x y)) (+ (* (* (/ 1 (sqrt x)) y) 1/2) (sqrt x)) (* (/ 1 (sqrt x)) y) (/ 1 (sqrt x)) 1 (sqrt x) x y 1/2 (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
5.0ms	x	@	-inf	((sqrt (+ x y)) (+ (* (* (/ 1 (sqrt x)) y) 1/2) (sqrt x)) (* (/ 1 (sqrt x)) y) (/ 1 (sqrt x)) 1 (sqrt x) x y 1/2 (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))
2.0ms	y	@	-inf	((sqrt (+ x y)) (+ (* (* (/ 1 (sqrt x)) y) 1/2) (sqrt x)) (* (/ 1 (sqrt x)) y) (/ 1 (sqrt x)) 1 (sqrt x) x y 1/2 (sqrt (+ x y)) (+ x y) (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 x)) y) 1/2) (sqrt x)) (* (/ 1 (sqrt x)) y) (/ 1 (sqrt x)) 1 (sqrt x) x y 1/2 (sqrt (+ x y)) (+ x y) (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 x)) y) 1/2) (sqrt x)) (* (/ 1 (sqrt x)) y) (/ 1 (sqrt x)) 1 (sqrt x) x y 1/2 (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (sqrt (+ x y)) (+ x y) (* (+ (/ x y) 1) y) (+ (/ x y) 1) (/ x y))

rewrite62.0ms (4.9%)

Memory

20.9MiB live, 67.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	253	1285
0	270	1146
0	1310	1110

Stop Event

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

Counts

75 → 106

Calls

Call 1

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

eval12.0ms (1%)

Memory: -23.7MiB live, 20.7MiB allocated; 5ms collecting garbage
Compiler: Compiled 970 to 436 computations (55.1% saved)

prune4.0ms (0.3%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	94	5	99

Accuracy

100.0%

Counts

99 → 5

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)))
✓	98.5%	(sqrt.f64 #s(approx (+ x y) y))
✓	3.1%	(sqrt.f64 #s(approx (+ x y) x))
✓	3.1%	#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)))

Compiler

Compiled 61 to 56 computations (8.2% saved)

regimes9.0ms (0.7%)

Memory

20.4MiB live, 20.4MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 x 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)

regimes128.0ms (10.1%)

Memory

-37.8MiB live, 22.2MiB allocated; 161ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

124.0ms	(sqrt.f64 (+.f64 x y))
1.0ms	(+.f64 x y)
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
98.5%	1	`(+.f64 x y)`
98.5%	1	`(sqrt.f64 (+.f64 x y))`
98.5%	1	`x`
98.5%	1	`y`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes4.0ms (0.3%)

Memory

12.1MiB live, 12.1MiB allocated; 0ms 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) x))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
3.1%	1	`(+.f64 x y)`
3.1%	1	`(sqrt.f64 (+.f64 x y))`
3.1%	1	`y`
3.1%	1	`x`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

derivations4.0ms (0.3%)

Memory

6.3MiB live, 6.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 10 to 9 computations (10% saved)

preprocess28.0ms (2.2%)

Memory: 0.3MiB live, 53.1MiB allocated; 14ms collecting garbage
Remove: (sort x y)
Compiler: Compiled 42 to 41 computations (2.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze16.0ms (1.3%)

sample811.0ms (64%)

preprocess35.0ms (2.8%)

series12.0ms (0.9%)

rewrite95.0ms (7.5%)

eval4.0ms (0.3%)

prune2.0ms (0.2%)

series41.0ms (3.2%)

rewrite62.0ms (4.9%)

eval12.0ms (1%)

prune4.0ms (0.3%)

regimes9.0ms (0.7%)

regimes128.0ms (10.1%)

regimes4.0ms (0.3%)

derivations4.0ms (0.3%)

preprocess28.0ms (2.2%)

end0.0ms (0%)

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