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

start0.0ms (0%)

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

analyze50.0ms (3%)

Memory

-5.6MiB live, 39.3MiB allocated; 9ms 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)

sample670.0ms (40.9%)

Memory

55.1MiB live, 642.8MiB allocated; 243ms collecting garbage

Samples

423.0ms	8 256×	0	valid
16.0ms	509×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 137.0ms

ival-sqrt: 104.0ms (75.8% of total)

ival-add!: 31.0ms (22.6% of total)

adjust: 2.0ms (1.5% of total)

Bogosity

preprocess43.0ms (2.6%)

Memory

-26.9MiB live, 24.6MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	21	30

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)

series5.0ms (0.3%)

Memory

9.0MiB live, 9.0MiB 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 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (/ x (pow (sqrt y) 3))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt y) 5))) (* 1/8 (/ 1 (pow (sqrt y) 3))))) (* 1/2 (/ 1 (sqrt y))))))))
#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 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (/ y (sqrt x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (/ y (pow (sqrt x) 3))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* y (- (* 1/16 (/ y (pow (sqrt x) 5))) (* 1/8 (/ 1 (pow (sqrt x) 3))))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (sqrt (/ 1 y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (sqrt (/ 1 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Calls

6 calls:

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

rewrite168.0ms (10.3%)

Memory

33.8MiB live, 304.4MiB allocated; 56ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	168	792
0	169	750
1	879	690
0	8253	656

Stop Event

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

Counts

35 → 49

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 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (/ x (pow (sqrt y) 3))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt y) 5))) (* 1/8 (/ 1 (pow (sqrt y) 3))))) (* 1/2 (/ 1 (sqrt y))))))))
#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 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (/ y (sqrt x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (/ y (pow (sqrt x) 3))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* y (- (* 1/16 (/ y (pow (sqrt x) 5))) (* 1/8 (/ 1 (pow (sqrt x) 3))))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (sqrt (/ 1 y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (sqrt (/ 1 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Outputs
(*.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)))
(pow.f64 (+.f64 y x) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
(/.f64 (sqrt.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))) (sqrt.f64 (fma.f64 y (-.f64 y x) (.f64 x x))))
(sqrt.f64 (+.f64 y x))
(exp.f64 (*.f64 (log.f64 (+.f64 y x)) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (-.f64 y x))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 y (-.f64 y x) (.f64 x x))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 x y)) (-.f64 x y))
(/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (fma.f64 y y (-.f64 (.f64 x x) (*.f64 y x))))
(/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (fma.f64 y (-.f64 y x) (.f64 x x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))
(+.f64 (/.f64 (.f64 (.f64 x x) x) (fma.f64 y (-.f64 y x) (.f64 x x))) (/.f64 (.f64 (.f64 y y) y) (fma.f64 y (-.f64 y x) (.f64 x x))))
(+.f64 y x)
(+.f64 x y)
x
y
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (/.f64 x (*.f64 (sqrt.f64 y) y)) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) x (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (/.f64 x (pow.f64 y #s(literal 5/2 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 y) y))) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) 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)) (/.f64 x (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 y (.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 (.f64 x x) x) x))) #s(literal -1/8 binary64) (.f64 (/.f64 y (.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64))) x (/.f64 x (sqrt.f64 x))))
#s(approx (sqrt (+ x y)) (fma.f64 x (fma.f64 (/.f64 (.f64 (.f64 y y) y) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 (.f64 x x) x) x))) #s(literal -1/8 binary64) (.f64 (/.f64 y (*.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64)))) (/.f64 x (sqrt.f64 x))))
#s(approx (+ x y) (fma.f64 (/.f64 y x) x x))
#s(approx (sqrt (+ x y)) (neg.f64 (/.f64 x (sqrt.f64 x))))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 x) (fma.f64 (/.f64 y (.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 x) (fma.f64 (/.f64 (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 (.f64 x x) x) x))) #s(literal -1/8 binary64) (fma.f64 (/.f64 y (.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))))
#s(approx (sqrt (+ x y)) (neg.f64 (fma.f64 x (fma.f64 (/.f64 (.f64 (.f64 y y) y) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 (.f64 x x) x) x))) #s(literal -1/8 binary64) (.f64 (/.f64 y (*.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64)))) (/.f64 x (sqrt.f64 x)))))
#s(approx (+ x y) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 y) x) #s(literal 1 binary64))))
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (/.f64 y (*.f64 (sqrt.f64 x) x)) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) y (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (fma.f64 (/.f64 y (pow.f64 x #s(literal 5/2 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) x))) y (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) y (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (/.f64 y (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 x (.f64 (/.f64 y (sqrt.f64 y)) y)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 (.f64 y y) y) y))) #s(literal -1/8 binary64) (.f64 (/.f64 x (.f64 (/.f64 y (sqrt.f64 y)) y)) #s(literal 1/2 binary64))) y (/.f64 y (sqrt.f64 y))))
#s(approx (sqrt (+ x y)) (fma.f64 y (fma.f64 (/.f64 (.f64 (.f64 x x) x) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 y))) #s(literal 5 binary64) (.f64 (log.f64 y) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 (.f64 y y) y) y))) #s(literal -1/8 binary64) (.f64 (/.f64 x (*.f64 (/.f64 y (sqrt.f64 y)) y)) #s(literal 1/2 binary64)))) (/.f64 y (sqrt.f64 y))))
#s(approx (+ x y) (fma.f64 (/.f64 x y) y y))
#s(approx (sqrt (+ x y)) (neg.f64 (/.f64 y (sqrt.f64 y))))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 y) (fma.f64 (/.f64 x (.f64 (/.f64 y (sqrt.f64 y)) y)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 y) (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 (.f64 y y) y) y))) #s(literal -1/8 binary64) (fma.f64 (/.f64 x (.f64 (/.f64 y (sqrt.f64 y)) y)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))))))
#s(approx (sqrt (+ x y)) (neg.f64 (fma.f64 y (fma.f64 (/.f64 (.f64 (.f64 x x) x) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 y))) #s(literal 5 binary64) (.f64 (log.f64 y) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 (.f64 y y) y) y))) #s(literal -1/8 binary64) (.f64 (/.f64 x (*.f64 (/.f64 y (sqrt.f64 y)) y)) #s(literal 1/2 binary64)))) (/.f64 y (sqrt.f64 y)))))
#s(approx (+ x y) (*.f64 (neg.f64 y) (-.f64 (/.f64 (neg.f64 x) y) #s(literal 1 binary64))))

eval8.0ms (0.5%)

Memory: -30.2MiB live, 15.6MiB allocated; 5ms collecting garbage
Compiler: Compiled 953 to 196 computations (79.4% saved)

prune2.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Accuracy

100.0%

Counts

47 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	98.0%	(sqrt.f64 #s(approx (+ x y) y))
▶	3.3%	#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 y (.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
▶	3.5%	#s(approx (sqrt (+ x y)) (sqrt.f64 x))

Compiler

Compiled 38 to 29 computations (23.7% saved)

series77.0ms (4.7%)

Memory

-12.7MiB live, 39.6MiB allocated; 14ms collecting garbage

Counts

15 → 57

Calls

Call 1

Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 y (.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
(.f64 (fma.f64 (/.f64 y (.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(fma.f64 (/.f64 y (*.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 y (*.f64 (/.f64 x (sqrt.f64 x)) x))
y
(*.f64 (/.f64 x (sqrt.f64 x)) x)
(/.f64 x (sqrt.f64 x))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) 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 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (/ x (pow (sqrt y) 3))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt y) 5))) (* 1/8 (/ 1 (pow (sqrt y) 3))))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* 1/2 (/ (* y (sqrt x)) x))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt x))) (/ (pow x 2) (sqrt x))) x)))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* 1/2 (/ (* y (sqrt x)) (pow x 2)))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt x))) (/ (pow x 2) (sqrt x))) (pow x 2))))
#s(approx (/ y (* (/ x (sqrt x)) x)) #s(hole binary64 (/ (* y (sqrt x)) (pow x 2))))
#s(approx (* (/ x (sqrt x)) x) #s(hole binary64 (/ (pow x 2) (sqrt x))))
#s(approx (/ x (sqrt x)) #s(hole binary64 (/ x (sqrt x))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ 1 (sqrt x))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x))))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x)))) x)))
#s(approx (/ y (* (/ x (sqrt x)) x)) #s(hole binary64 (/ (* y (sqrt (/ 1 x))) x)))
#s(approx (* (/ x (sqrt x)) x) #s(hole binary64 (/ x (sqrt (/ 1 x)))))
#s(approx (/ x (sqrt x)) #s(hole binary64 (/ 1 (sqrt (/ 1 x)))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ 1 (* x (sqrt (/ 1 x))))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x)))))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* -1 (/ (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x)))) x))))
#s(approx (/ y (* (/ x (sqrt x)) x)) #s(hole binary64 (* -1 (/ (* y (sqrt (/ 1 x))) x))))
#s(approx (* (/ x (sqrt x)) x) #s(hole binary64 (* -1 (/ x (sqrt (/ 1 x))))))
#s(approx (/ x (sqrt x)) #s(hole binary64 (/ -1 (sqrt (/ 1 x)))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ -1 (* x (sqrt (/ 1 x))))))
#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 (/ y (sqrt x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (/ y (pow (sqrt x) 3))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* y (- (* 1/16 (/ y (pow (sqrt x) 5))) (* 1/8 (/ 1 (pow (sqrt x) 3))))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (+ (* 1/2 (/ (* y (sqrt x)) x)) (/ x (sqrt x)))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (+ (* 1/2 (/ (* y (sqrt x)) (pow x 2))) (/ 1 (sqrt x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (sqrt (/ 1 y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* y (+ (* 1/2 (/ (sqrt x) x)) (/ x (* y (sqrt x)))))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* y (+ (* 1/2 (/ (sqrt x) (pow x 2))) (/ 1 (* y (sqrt x)))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (sqrt (/ 1 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* y (+ (* -1 (/ x (* y (sqrt x)))) (* -1/2 (/ (sqrt x) x)))))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* -1 (* y (- (* -1/2 (/ (sqrt x) (pow x 2))) (/ 1 (* y (sqrt x))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
63.0ms	y	@	0	((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (/ y (* (/ x (sqrt x)) x)) y (* (/ x (sqrt x)) x) (/ x (sqrt x)) 1/2 (/ 1 (sqrt x)) 1 (sqrt (+ x y)) (+ x y))
4.0ms	x	@	-inf	((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (/ y (* (/ x (sqrt x)) x)) y (* (/ x (sqrt x)) x) (/ x (sqrt x)) 1/2 (/ 1 (sqrt x)) 1 (sqrt (+ x y)) (+ x y))
3.0ms	x	@	0	((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (/ y (* (/ x (sqrt x)) x)) y (* (/ x (sqrt x)) x) (/ x (sqrt x)) 1/2 (/ 1 (sqrt x)) 1 (sqrt (+ x y)) (+ x y))
2.0ms	x	@	inf	((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (/ y (* (/ x (sqrt x)) x)) y (* (/ x (sqrt x)) x) (/ x (sqrt x)) 1/2 (/ 1 (sqrt x)) 1 (sqrt (+ x y)) (+ x y))
2.0ms	y	@	-inf	((sqrt (+ x y)) (sqrt x) x (sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (/ y (* (/ x (sqrt x)) x)) y (* (/ x (sqrt x)) x) (/ x (sqrt x)) 1/2 (/ 1 (sqrt x)) 1 (sqrt (+ x y)) (+ x y))

rewrite200.0ms (12.2%)

Memory

35.7MiB live, 305.7MiB allocated; 96ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	254	1478
0	272	1429
1	1230	1229
0	8261	1190

Stop Event

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

Counts

72 → 150

Calls

Call 1

Inputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(sqrt.f64 x)
x
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 y (.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
(.f64 (fma.f64 (/.f64 y (.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(fma.f64 (/.f64 y (*.f64 (/.f64 x (sqrt.f64 x)) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 y (*.f64 (/.f64 x (sqrt.f64 x)) x))
y
(*.f64 (/.f64 x (sqrt.f64 x)) x)
(/.f64 x (sqrt.f64 x))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (+ x y) y))
#s(approx (+ x y) 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 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (/ x (pow (sqrt y) 3))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt y) 5))) (* 1/8 (/ 1 (pow (sqrt y) 3))))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* 1/2 (/ (* y (sqrt x)) x))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt x))) (/ (pow x 2) (sqrt x))) x)))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* 1/2 (/ (* y (sqrt x)) (pow x 2)))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt x))) (/ (pow x 2) (sqrt x))) (pow x 2))))
#s(approx (/ y (* (/ x (sqrt x)) x)) #s(hole binary64 (/ (* y (sqrt x)) (pow x 2))))
#s(approx (* (/ x (sqrt x)) x) #s(hole binary64 (/ (pow x 2) (sqrt x))))
#s(approx (/ x (sqrt x)) #s(hole binary64 (/ x (sqrt x))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ 1 (sqrt x))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x))))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x)))) x)))
#s(approx (/ y (* (/ x (sqrt x)) x)) #s(hole binary64 (/ (* y (sqrt (/ 1 x))) x)))
#s(approx (* (/ x (sqrt x)) x) #s(hole binary64 (/ x (sqrt (/ 1 x)))))
#s(approx (/ x (sqrt x)) #s(hole binary64 (/ 1 (sqrt (/ 1 x)))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ 1 (* x (sqrt (/ 1 x))))))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x)))))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* -1 (/ (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x)))) x))))
#s(approx (/ y (* (/ x (sqrt x)) x)) #s(hole binary64 (* -1 (/ (* y (sqrt (/ 1 x))) x))))
#s(approx (* (/ x (sqrt x)) x) #s(hole binary64 (* -1 (/ x (sqrt (/ 1 x))))))
#s(approx (/ x (sqrt x)) #s(hole binary64 (/ -1 (sqrt (/ 1 x)))))
#s(approx (/ 1 (sqrt x)) #s(hole binary64 (/ -1 (* x (sqrt (/ 1 x))))))
#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 (/ y (sqrt x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (/ y (pow (sqrt x) 3))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* y (- (* 1/16 (/ y (pow (sqrt x) 5))) (* 1/8 (/ 1 (pow (sqrt x) 3))))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (+ (* 1/2 (/ (* y (sqrt x)) x)) (/ x (sqrt x)))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (+ (* 1/2 (/ (* y (sqrt x)) (pow x 2))) (/ 1 (sqrt x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (sqrt (/ 1 y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* y (+ (* 1/2 (/ (sqrt x) x)) (/ x (* y (sqrt x)))))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* y (+ (* 1/2 (/ (sqrt x) (pow x 2))) (/ 1 (* y (sqrt x)))))))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (sqrt (/ 1 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* y (+ (* -1 (/ x (* y (sqrt x)))) (* -1/2 (/ (sqrt x) x)))))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) #s(hole binary64 (* -1 (* y (- (* -1/2 (/ (sqrt x) (pow x 2))) (/ 1 (* y (sqrt x))))))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Outputs
#s(approx (sqrt (+ x y)) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(neg.f64 (neg.f64 (sqrt.f64 x)))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal -1 binary64)))
x
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 y (.f64 (sqrt.f64 x) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
(.f64 (fma.f64 (/.f64 y (.f64 (sqrt.f64 x) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x)
(.f64 x (fma.f64 (/.f64 y (.f64 (sqrt.f64 x) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) x))) (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (.f64 y #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x))))
(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (pow.f64 (/.f64 y (.f64 (sqrt.f64 x) x)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) x)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (.f64 y #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x))))))
(/.f64 (fma.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 x) x) (.f64 (neg.f64 (sqrt.f64 x)) (.f64 y #s(literal 1/2 binary64)))) (.f64 (neg.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) x)))
(/.f64 (fma.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x) (.f64 (sqrt.f64 x) (.f64 y #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x)))
(/.f64 (fma.f64 (.f64 y #s(literal 1/2 binary64)) (neg.f64 (sqrt.f64 x)) (.f64 (.f64 (sqrt.f64 x) x) #s(literal -1 binary64))) (.f64 (*.f64 (sqrt.f64 x) x) (neg.f64 (sqrt.f64 x))))
(/.f64 (fma.f64 (.f64 y #s(literal 1/2 binary64)) (sqrt.f64 x) (.f64 (.f64 (sqrt.f64 x) x) #s(literal 1 binary64))) (.f64 (*.f64 (sqrt.f64 x) x) (sqrt.f64 x)))
(/.f64 (neg.f64 (-.f64 (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (/.f64 (.f64 y #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 (sqrt.f64 x) x)) #s(literal 3 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)))) (neg.f64 (+.f64 (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) x)) (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 (sqrt.f64 x) x) (sqrt.f64 x)))))))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) x)) (-.f64 (/.f64 (.f64 y #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(/.f64 (fma.f64 (pow.f64 (/.f64 y (.f64 (sqrt.f64 x) x)) #s(literal 3 binary64)) #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x))) (+.f64 (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) x)) (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 (sqrt.f64 x) x) (sqrt.f64 x))))))
(fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (/.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) x)))
(fma.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) x)))
(fma.f64 (/.f64 y (/.f64 x (sqrt.f64 x))) (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 y x) (/.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 y (*.f64 (sqrt.f64 x) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 y (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) x)) (-.f64 (/.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 (/.f64 (.f64 y #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (neg.f64 (/.f64 y (.f64 (sqrt.f64 x) x))) #s(literal 1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (/.f64 y (.f64 (sqrt.f64 x) x))))
(+.f64 (/.f64 (.f64 (pow.f64 (/.f64 y (.f64 (sqrt.f64 x) x)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) x)) (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (.f64 (sqrt.f64 x) x) (sqrt.f64 x)))))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (+.f64 (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 y #s(literal 1/2 binary64))) (.f64 (.f64 x x) x)) (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 (.f64 y #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 (*.f64 (sqrt.f64 x) x) (sqrt.f64 x)))))))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) x)))
(+.f64 (/.f64 (.f64 y #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 (neg.f64 (/.f64 y (/.f64 x (sqrt.f64 x)))) (neg.f64 x))
(/.f64 (neg.f64 (neg.f64 y)) (*.f64 (sqrt.f64 x) x))
(/.f64 (/.f64 y (/.f64 x (sqrt.f64 x))) x)
(/.f64 (neg.f64 y) (*.f64 (neg.f64 x) (sqrt.f64 x)))
(/.f64 y (*.f64 (sqrt.f64 x) x))
(neg.f64 (/.f64 y (*.f64 (neg.f64 x) (sqrt.f64 x))))
(neg.f64 (/.f64 (neg.f64 y) (*.f64 (sqrt.f64 x) x)))
y
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/4 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) (neg.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (/.f64 x (sqrt.f64 x)) x)
(*.f64 (sqrt.f64 x) x)
(*.f64 x (/.f64 x (sqrt.f64 x)))
(*.f64 x (sqrt.f64 x))
(pow.f64 (exp.f64 (log.f64 (sqrt.f64 x))) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 3 binary64))
(pow.f64 x #s(literal 3/2 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) x)) (sqrt.f64 x))
(/.f64 (*.f64 (neg.f64 x) x) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))
(/.f64 (*.f64 x x) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) x)))
(neg.f64 (*.f64 (neg.f64 x) (sqrt.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 3 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (sqrt.f64 x)) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 (sqrt.f64 x)) #s(literal 3 binary64))))
(/.f64 (neg.f64 (neg.f64 x)) (sqrt.f64 x))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 x)))
(/.f64 x (sqrt.f64 x))
(neg.f64 (/.f64 x (neg.f64 (sqrt.f64 x))))
(neg.f64 (/.f64 (neg.f64 x) (sqrt.f64 x)))
#s(literal 1/2 binary64)
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 x #s(literal -1/2 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64)))
#s(literal 1 binary64)
(*.f64 (pow.f64 #s(approx (+ x y) y) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ x y) y) #s(literal 1/4 binary64)))
(pow.f64 #s(approx (+ x y) y) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(approx (+ x y) y) #s(literal -1/2 binary64)))
(sqrt.f64 #s(approx (+ x y) y))
(exp.f64 (*.f64 (log.f64 #s(approx (+ x y) y)) #s(literal 1/2 binary64)))
#s(approx (+ x y) y)
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (/.f64 x (*.f64 (sqrt.f64 y) y)) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) x (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (-.f64 (.f64 (/.f64 x (pow.f64 y #s(literal 5/2 binary64))) #s(literal 1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 y) y))) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) x (sqrt.f64 y)))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx x x)
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (.f64 (/.f64 (.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) x)) x))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (/.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (/.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) x)) (*.f64 x x)))
#s(approx (/ y (* (/ x (sqrt x)) x)) (.f64 y (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x))))
#s(approx (* (/ x (sqrt x)) x) (*.f64 (sqrt.f64 x) x))
#s(approx (/ x (sqrt x)) (/.f64 x (sqrt.f64 x)))
#s(approx (/ 1 (sqrt x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(approx (+ x y) y)
#s(approx (+ x y) (+.f64 y x))
#s(approx (sqrt (+ x y)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) #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) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/8 binary64) (.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))) #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) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 y y) y) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (/.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64) (sqrt.f64 x)) x))
#s(approx (/ y (* (/ x (sqrt x)) x)) (/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) x))
#s(approx (* (/ x (sqrt x)) x) (/.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (/ x (sqrt x)) (sqrt.f64 x))
#s(approx (/ 1 (sqrt x)) (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
#s(approx (+ x y) (*.f64 (-.f64 (/.f64 y x) #s(literal -1 binary64)) x))
#s(approx (sqrt (+ x y)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) x))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 x) (fma.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/8 binary64) (.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 y y) y) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (neg.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64) (sqrt.f64 x))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (/.f64 (neg.f64 (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) #s(literal 1/2 binary64) (sqrt.f64 x))) x))
#s(approx (/ y (* (/ x (sqrt x)) x)) (/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) y) x))
#s(approx (* (/ x (sqrt x)) x) (/.f64 x (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (/ x (sqrt x)) (neg.f64 (sqrt.f64 x)))
#s(approx (/ 1 (sqrt x)) (neg.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x))))
#s(approx (+ x y) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 y) x) #s(literal 1 binary64))))
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (/.f64 y (*.f64 (sqrt.f64 x) x)) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) y (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (-.f64 (.f64 (/.f64 y (pow.f64 x #s(literal 5/2 binary64))) #s(literal 1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x))) y (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) y (sqrt.f64 x)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (fma.f64 (/.f64 (*.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (fma.f64 (.f64 y (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (+ x y)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) y))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 y y))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (.f64 y y))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 x x) x) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 y))) #s(literal 5 binary64) (.f64 (log.f64 y) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 y y))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (.f64 (fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64) (/.f64 x (.f64 (sqrt.f64 x) y))) y))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) y))) y))
#s(approx (+ x y) (*.f64 (-.f64 (/.f64 x y) #s(literal -1 binary64)) y))
#s(approx (sqrt (+ x y)) (*.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 y) (fma.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 y y))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 y) (+.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (.f64 y y))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))
#s(approx (sqrt (+ x y)) (.f64 (neg.f64 y) (+.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 x x) x) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 y))) #s(literal 5 binary64) (.f64 (log.f64 y) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 y y))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y)))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (.f64 (neg.f64 y) (fma.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 x) x) (/.f64 (neg.f64 x) (.f64 (sqrt.f64 x) y)))))
#s(approx (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) (.f64 (neg.f64 y) (-.f64 (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x))) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) y)))))
#s(approx (+ x y) (*.f64 (neg.f64 y) (-.f64 (/.f64 (neg.f64 x) y) #s(literal 1 binary64))))

eval18.0ms (1.1%)

Memory: 4.6MiB live, 49.9MiB allocated; 5ms collecting garbage
Compiler: Compiled 3 904 to 765 computations (80.4% saved)

prune4.0ms (0.3%)

Memory

11.5MiB live, 11.5MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	152	4	156

Accuracy

100.0%

Counts

156 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.0%	(sqrt.f64 #s(approx (+ x y) y))
✓	3.5%	#s(approx (sqrt (+ x y)) (sqrt.f64 x))
▶	3.4%	#s(approx (sqrt (+ x y)) #s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) x)) x)))

Compiler

Compiled 52 to 37 computations (28.8% saved)

series67.0ms (4.1%)

Memory

-24.6MiB live, 30.4MiB allocated; 13ms collecting garbage

Counts

10 → 52

Calls

Call 1

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

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 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (/ x (pow (sqrt y) 3))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt y) 5))) (* 1/8 (/ 1 (pow (sqrt y) 3))))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* 1/2 (/ (* y (sqrt x)) x))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt x))) (/ (pow x 2) (sqrt x))) x)))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt x))) (* x (sqrt x))) x)))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* 1/2 (* y (sqrt x)))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (+ (* 1/2 (* y (sqrt x))) (* x (sqrt x)))))
#s(approx (* (sqrt x) y) #s(hole binary64 (* y (sqrt x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (sqrt x) x) #s(hole binary64 (* x (sqrt x))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x))))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ (* y (sqrt (/ 1 x))) x))))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* (pow x 2) (sqrt (/ 1 x)))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* (pow x 2) (+ (sqrt (/ 1 x)) (* 1/2 (/ (* y (sqrt (/ 1 x))) x))))))
#s(approx (* (sqrt x) y) #s(hole binary64 (* x (* y (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x)))))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ (* y (sqrt (/ 1 x))) x)))))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* -1 (* (pow x 2) (sqrt (/ 1 x))))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* (pow x 2) (+ (* -1 (sqrt (/ 1 x))) (* -1/2 (/ (* y (sqrt (/ 1 x))) x))))))
#s(approx (* (sqrt x) y) #s(hole binary64 (* -1 (* x (* y (sqrt (/ 1 x)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (/ y (sqrt x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (/ y (pow (sqrt x) 3))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* y (- (* 1/16 (/ y (pow (sqrt x) 5))) (* 1/8 (/ 1 (pow (sqrt x) 3))))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (/ x (sqrt x))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (+ (* 1/2 (/ (* y (sqrt x)) x)) (/ x (sqrt x)))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (+ (sqrt x) (* 1/2 (/ (* y (sqrt x)) x)))))
#s(approx y #s(hole binary64 y))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (sqrt (/ 1 y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* y (+ (* 1/2 (/ (sqrt x) x)) (/ x (* y (sqrt x)))))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (* y (+ (* 1/2 (/ (sqrt x) x)) (/ (sqrt x) y)))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* y (+ (* 1/2 (sqrt x)) (/ (* x (sqrt x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (sqrt (/ 1 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* y (+ (* -1 (/ x (* y (sqrt x)))) (* -1/2 (/ (sqrt x) x)))))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (* -1 (* y (+ (* -1 (/ (sqrt x) y)) (* -1/2 (/ (sqrt x) x)))))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* -1 (* y (+ (* -1 (/ (* x (sqrt x)) y)) (* -1/2 (sqrt x)))))))

Calls

6 calls:

Time	Variable		Point	Expression
58.0ms	x	@	inf	((sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (* (sqrt x) y) (sqrt x) x y 1/2 (* (sqrt x) x))
2.0ms	x	@	-inf	((sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (* (sqrt x) y) (sqrt x) x y 1/2 (* (sqrt x) x))
2.0ms	y	@	-inf	((sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (* (sqrt x) y) (sqrt x) x y 1/2 (* (sqrt x) x))
1.0ms	y	@	inf	((sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (* (sqrt x) y) (sqrt x) x y 1/2 (* (sqrt x) x))
1.0ms	x	@	0	((sqrt (+ x y)) (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (* (sqrt x) y) (sqrt x) x y 1/2 (* (sqrt x) x))

rewrite169.0ms (10.3%)

Memory

30.7MiB live, 299.3MiB allocated; 46ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	248	1477
0	260	1423
1	1270	1291
0	8342	1239

Stop Event

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

Counts

62 → 145

Calls

Call 1

Inputs
#s(approx (sqrt (+ x y)) #s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) x)) x)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) x)) x))
(/.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) x)) x)
(fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) x))
(*.f64 (sqrt.f64 x) y)
(sqrt.f64 x)
x
y
#s(literal 1/2 binary64)
(*.f64 (sqrt.f64 x) x)
#s(approx (sqrt (+ x y)) #s(hole binary64 (sqrt y)))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* 1/2 (/ x (sqrt y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* -1/8 (/ x (pow (sqrt y) 3))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt y) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt y) 5))) (* 1/8 (/ 1 (pow (sqrt y) 3))))) (* 1/2 (/ 1 (sqrt y))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* 1/2 (/ (* y (sqrt x)) x))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt x))) (/ (pow x 2) (sqrt x))) x)))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (/ (+ (* 1/2 (* y (sqrt x))) (* x (sqrt x))) x)))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* 1/2 (* y (sqrt x)))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (+ (* 1/2 (* y (sqrt x))) (* x (sqrt x)))))
#s(approx (* (sqrt x) y) #s(hole binary64 (* y (sqrt x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (sqrt x) x) #s(hole binary64 (* x (sqrt x))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x))))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ (* y (sqrt (/ 1 x))) x))))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* (pow x 2) (sqrt (/ 1 x)))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* (pow x 2) (+ (sqrt (/ 1 x)) (* 1/2 (/ (* y (sqrt (/ 1 x))) x))))))
#s(approx (* (sqrt x) y) #s(hole binary64 (* x (* y (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (/ (pow y 2) (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))) (+ (* 1/16 (/ (pow y 3) (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))) (* 1/2 (/ y (* (pow x 2) (sqrt (/ 1 x))))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (+ (* 1/2 (* y (sqrt (/ 1 x)))) (/ 1 (sqrt (/ 1 x)))))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ (* y (sqrt (/ 1 x))) x)))))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* -1 (* (pow x 2) (sqrt (/ 1 x))))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* (pow x 2) (+ (* -1 (sqrt (/ 1 x))) (* -1/2 (/ (* y (sqrt (/ 1 x))) x))))))
#s(approx (* (sqrt x) y) #s(hole binary64 (* -1 (* x (* y (sqrt (/ 1 x)))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* 1/2 (/ y (sqrt x))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* -1/8 (/ y (pow (sqrt x) 3))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (+ (sqrt x) (* y (+ (* y (- (* 1/16 (/ y (pow (sqrt x) 5))) (* 1/8 (/ 1 (pow (sqrt x) 3))))) (* 1/2 (/ 1 (sqrt x))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (/ x (sqrt x))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (+ (* 1/2 (/ (* y (sqrt x)) x)) (/ x (sqrt x)))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (+ (sqrt x) (* 1/2 (/ (* y (sqrt x)) x)))))
#s(approx y #s(hole binary64 y))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (sqrt (/ 1 y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* y (+ (* 1/2 (/ (sqrt x) x)) (/ x (* y (sqrt x)))))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (* y (+ (* 1/2 (/ (sqrt x) x)) (/ (sqrt x) y)))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* y (+ (* 1/2 (sqrt x)) (/ (* x (sqrt x)) y)))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (sqrt (/ 1 y))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y)))))))))))
#s(approx (sqrt (+ x y)) #s(hole binary64 (* -1 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (/ (pow x 2) (* (pow y 4) (pow (sqrt (/ 1 y)) 3)))) (+ (* 1/16 (/ (pow x 3) (* (pow y 6) (pow (sqrt (/ 1 y)) 5)))) (* 1/2 (/ x (* (pow y 2) (sqrt (/ 1 y))))))))))))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) #s(hole binary64 (* -1 (* y (+ (* -1 (/ x (* y (sqrt x)))) (* -1/2 (/ (sqrt x) x)))))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) #s(hole binary64 (* -1 (* y (+ (* -1 (/ (sqrt x) y)) (* -1/2 (/ (sqrt x) x)))))))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) #s(hole binary64 (* -1 (* y (+ (* -1 (/ (* x (sqrt x)) y)) (* -1/2 (sqrt x)))))))

Outputs
#s(approx (sqrt (+ x y)) #s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/.f64 (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))) x)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/.f64 (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))) x))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 x x)) (.f64 (/.f64 (.f64 (sqrt.f64 x) x) x) (/.f64 (.f64 (sqrt.f64 x) x) x))) (-.f64 (.f64 (/.f64 (.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64)) (/.f64 (*.f64 (sqrt.f64 x) x) x)))
(/.f64 (fma.f64 (pow.f64 (/.f64 (.f64 (sqrt.f64 x) y) x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (/.f64 (.f64 (sqrt.f64 x) x) x) #s(literal 3 binary64))) (+.f64 (/.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 x x)) (-.f64 (.f64 (/.f64 (.f64 (sqrt.f64 x) x) x) (/.f64 (.f64 (sqrt.f64 x) x) x)) (.f64 (.f64 (/.f64 (.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64)) (/.f64 (.f64 (sqrt.f64 x) x) x)))))
(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) x (.f64 x (.f64 (sqrt.f64 x) x))) (*.f64 x x))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))) (neg.f64 x))
(/.f64 (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))) x)
(neg.f64 (/.f64 (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))) (neg.f64 x)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))) x))
(fma.f64 (/.f64 (.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 x) x) x))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 x) y) x) (/.f64 (.f64 (sqrt.f64 x) x) x))
(-.f64 (.f64 (/.f64 (.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64)) (/.f64 (*.f64 (neg.f64 x) (sqrt.f64 x)) x))
(+.f64 (/.f64 (.f64 (sqrt.f64 x) x) x) (.f64 (/.f64 (*.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64)))
(+.f64 (.f64 (/.f64 (.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64)) (/.f64 (*.f64 (sqrt.f64 x) x) x))
(/.f64 (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x)) (-.f64 (.f64 (sqrt.f64 x) x) (.f64 (*.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (sqrt.f64 x) x) (.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))) (fma.f64 (.f64 x x) x (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 (.f64 (sqrt.f64 x) x) (.f64 (*.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))) (pow.f64 (.f64 (neg.f64 x) (sqrt.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x (fma.f64 (.f64 x x) x (.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (.f64 (neg.f64 x) (sqrt.f64 x))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 (.f64 x x) x)) (-.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x)))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 (.f64 x x) x))) (neg.f64 (-.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 x x) x) (.f64 (sqrt.f64 x) x)))) (neg.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x))))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 x x) x) (.f64 (sqrt.f64 x) x))) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x)))))
(fma.f64 (fabs.f64 (pow.f64 x #s(literal 3/4 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/4 binary64))) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) x))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x) (.f64 (neg.f64 (neg.f64 x)) (sqrt.f64 x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x) (.f64 (sqrt.f64 x) x))
(fma.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))
(fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) x))
(fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (neg.f64 (neg.f64 x)) (sqrt.f64 x)))
(fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) x))
(fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) y) (.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) x))
(fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) y) (.f64 (neg.f64 (neg.f64 x)) (sqrt.f64 x)))
(fma.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) y) (.f64 (sqrt.f64 x) x))
(fma.f64 (/.f64 x (sqrt.f64 x)) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))
(fma.f64 (sqrt.f64 x) (.f64 y #s(literal 1/2 binary64)) (.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) x))
(fma.f64 (sqrt.f64 x) (.f64 y #s(literal 1/2 binary64)) (.f64 (neg.f64 (neg.f64 x)) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 x) (.f64 y #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) x))
(fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))
(fma.f64 x (/.f64 x (sqrt.f64 x)) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))
(fma.f64 x (sqrt.f64 x) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (-.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) x))) (/.f64 (.f64 (.f64 x x) x) (-.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) x))))
(-.f64 (.f64 (sqrt.f64 x) x) (.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) y)) (sqrt.f64 x)))
(-.f64 (.f64 (sqrt.f64 x) x) (.f64 (*.f64 (sqrt.f64 x) (neg.f64 y)) #s(literal 1/2 binary64)))
(-.f64 (.f64 (sqrt.f64 x) x) (.f64 #s(literal -1/2 binary64) (*.f64 (sqrt.f64 x) y)))
(-.f64 (.f64 (sqrt.f64 x) x) (.f64 (neg.f64 (sqrt.f64 x)) (*.f64 y #s(literal 1/2 binary64))))
(-.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (neg.f64 (/.f64 x (sqrt.f64 x))) x))
(-.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (neg.f64 x) (/.f64 x (sqrt.f64 x))))
(-.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (neg.f64 x) (sqrt.f64 x)))
(+.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 x) x))))) (/.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (sqrt.f64 x) x)) (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) y) (.f64 #s(literal 1/2 binary64) y)) x (-.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x))))))
(+.f64 (.f64 (sqrt.f64 x) x) (.f64 (*.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) x))
(+.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (neg.f64 (neg.f64 x)) (sqrt.f64 x)))
(+.f64 (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 x) x))
(*.f64 (sqrt.f64 x) y)
(*.f64 y (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(neg.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(sqrt.f64 x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal -1 binary64)))
x
y
#s(literal 1/2 binary64)
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/4 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) (neg.f64 (pow.f64 x #s(literal 3/4 binary64))))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (/.f64 x (sqrt.f64 x)) x)
(*.f64 (sqrt.f64 x) x)
(*.f64 x (/.f64 x (sqrt.f64 x)))
(*.f64 x (sqrt.f64 x))
(pow.f64 (exp.f64 (log.f64 (sqrt.f64 x))) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 3 binary64))
(pow.f64 x #s(literal 3/2 binary64))
(/.f64 (neg.f64 (*.f64 x (neg.f64 x))) (neg.f64 (neg.f64 (sqrt.f64 x))))
(/.f64 (*.f64 x (neg.f64 x)) (neg.f64 (sqrt.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) x))))
(/.f64 (*.f64 x x) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 x) x)))
(neg.f64 (*.f64 (neg.f64 x) (sqrt.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 3 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (sqrt.f64 x)) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 (sqrt.f64 x)) #s(literal 3 binary64))))
#s(approx (sqrt (+ x y)) (sqrt.f64 y))
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 x (sqrt.f64 y)) #s(literal 1/2 binary64) (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (/.f64 x (*.f64 (sqrt.f64 y) y)) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) x (sqrt.f64 y)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (-.f64 (.f64 (/.f64 x (pow.f64 y #s(literal 5/2 binary64))) #s(literal 1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 y) y))) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) x (sqrt.f64 y)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (.f64 (/.f64 (.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/.f64 (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))) x))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) (/.f64 (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))) x))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64)))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (fma.f64 (sqrt.f64 x) x (.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64))))
#s(approx (* (sqrt x) y) (*.f64 (sqrt.f64 x) y))
#s(approx (sqrt x) (sqrt.f64 x))
#s(approx x x)
#s(approx (* (sqrt x) x) (*.f64 (sqrt.f64 x) x))
#s(approx (sqrt (+ x y)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) #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) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/8 binary64) (.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))) #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) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 y y) y) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (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) 1/2) (* (sqrt x) x)) x) (.f64 (fma.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) x) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x)))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (.f64 (fma.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) x) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (* (sqrt x) y) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) x))
#s(approx (sqrt (+ x y)) (*.f64 x (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 x)))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/8 binary64) (.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 x)))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 x) x)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 y y) y) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 y (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 x)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (neg.f64 (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) 1/2) (* (sqrt x) x)) x) (.f64 (fma.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) x) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (neg.f64 x)))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (.f64 x x)))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) y) x) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))) (*.f64 x x)))
#s(approx (* (sqrt x) y) (.f64 (.f64 x y) (/.f64 #s(literal -1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (+ x y)) (fma.f64 (/.f64 y (sqrt.f64 x)) #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (/.f64 y (*.f64 (sqrt.f64 x) x)) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) y (sqrt.f64 x)))
#s(approx (sqrt (+ x y)) (fma.f64 (fma.f64 (-.f64 (.f64 (/.f64 y (pow.f64 x #s(literal 5/2 binary64))) #s(literal 1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 x) x))) y (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) y (sqrt.f64 x)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/.f64 x (sqrt.f64 x)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (fma.f64 (/.f64 (*.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x))))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) (fma.f64 (/.f64 (*.f64 (sqrt.f64 x) y) x) #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(approx y y)
#s(approx (sqrt (+ x y)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) y))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 y y))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (.f64 y y))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 x x) x) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 y))) #s(literal 5 binary64) (.f64 (log.f64 y) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 y y))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (.f64 (fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64) (/.f64 x (.f64 (sqrt.f64 x) y))) y))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) (*.f64 (fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) y)) y))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (.f64 x (/.f64 (sqrt.f64 x) y))) y))
#s(approx (sqrt (+ x y)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (neg.f64 y)))
#s(approx (sqrt (+ x y)) (.f64 (fma.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 y y))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) (neg.f64 y)))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (.f64 y y))) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) (neg.f64 y)))
#s(approx (sqrt (+ x y)) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 y) y)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 x x) x) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 y))) #s(literal 5 binary64) (.f64 (log.f64 y) #s(literal 6 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 y)) (*.f64 y y))) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) (neg.f64 y)))
#s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (.f64 (fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal -1/2 binary64) (/.f64 (neg.f64 x) (.f64 (sqrt.f64 x) y))) (neg.f64 y)))
#s(approx (/ (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) x) (*.f64 (fma.f64 (/.f64 (sqrt.f64 x) x) #s(literal -1/2 binary64) (/.f64 (sqrt.f64 x) (neg.f64 y))) (neg.f64 y)))
#s(approx (+ (* (* (sqrt x) y) 1/2) (* (sqrt x) x)) (.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (.f64 x (/.f64 (sqrt.f64 x) (neg.f64 y)))) (neg.f64 y)))

eval15.0ms (0.9%)

Memory: 2.1MiB live, 48.8MiB allocated; 1ms collecting garbage
Compiler: Compiled 5 596 to 759 computations (86.4% saved)

prune7.0ms (0.4%)

Memory

-38.0MiB live, 20.0MiB allocated; 5ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	137	4	141

Accuracy

100.0%

Counts

141 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.0%	(sqrt.f64 #s(approx (+ x y) y))
✓	3.5%	#s(approx (sqrt (+ x y)) (sqrt.f64 x))
✓	3.4%	#s(approx (sqrt (+ x y)) #s(approx (* (+ (* (/ y (* (/ x (sqrt x)) x)) 1/2) (/ 1 (sqrt x))) x) (/.f64 (fma.f64 (.f64 (sqrt.f64 x) y) #s(literal 1/2 binary64) (.f64 (sqrt.f64 x) x)) x)))

Compiler

Compiled 125 to 72 computations (42.4% saved)

regimes8.0ms (0.5%)

Memory

27.5MiB live, 27.5MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

regimes6.0ms (0.4%)

Memory

-27.0MiB live, 19.5MiB allocated; 2ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.0%	1	`(+.f64 x y)`
98.0%	1	`(sqrt.f64 (+.f64 x y))`
98.0%	1	`x`
98.0%	1	`y`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes4.0ms (0.3%)

Memory

16.3MiB live, 16.3MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
3.5%	1	`(+.f64 x y)`
3.5%	1	`(sqrt.f64 (+.f64 x y))`
3.5%	1	`x`
3.5%	1	`y`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

derivations75.0ms (4.6%)

Memory

-21.0MiB live, 73.2MiB allocated; 4ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 17 to 10 computations (41.2% saved)

preprocess41.0ms (2.5%)

Memory: -14.2MiB live, 58.4MiB allocated; 16ms collecting garbage
Remove: (sort x y)
Compiler: Compiled 55 to 44 computations (20% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze50.0ms (3%)

sample670.0ms (40.9%)

preprocess43.0ms (2.6%)

series5.0ms (0.3%)

rewrite168.0ms (10.3%)

eval8.0ms (0.5%)

prune2.0ms (0.1%)

series77.0ms (4.7%)

rewrite200.0ms (12.2%)

eval18.0ms (1.1%)

prune4.0ms (0.3%)

series67.0ms (4.1%)

rewrite169.0ms (10.3%)

eval15.0ms (0.9%)

prune7.0ms (0.4%)

regimes8.0ms (0.5%)

regimes6.0ms (0.4%)

regimes4.0ms (0.3%)

derivations75.0ms (4.6%)

preprocess41.0ms (2.5%)

end0.0ms (0%)

Profiling