Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

start0.0ms (0%)

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

analyze35.0ms (1.6%)

Memory

33.9MiB live, 70.0MiB allocated; 33ms 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
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample865.0ms (39.7%)

Memory

0.5MiB live, 1 432.4MiB allocated; 595ms collecting garbage

Samples

441.0ms	8 256×	0	valid
13.0ms	361×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 195.0ms

ival-mult!: 92.0ms (47.2% of total)

ival-sqrt: 81.0ms (41.5% of total)

ival-add!: 21.0ms (10.8% of total)

adjust: 2.0ms (1% of total)

Bogosity

preprocess102.0ms (4.7%)

Memory

-9.3MiB live, 37.0MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	42	40
2	107	40
3	185	40
4	418	40
5	2020	40
6	4663	40

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.7%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series6.0ms (0.3%)

Memory

13.6MiB live, 13.6MiB allocated; 0ms collecting garbage

Counts

5 → 30

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite153.0ms (7%)

Memory

26.3MiB live, 267.3MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	795
0	159	761
1	831	704
0	8176	638

Stop Event

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

Counts

35 → 97

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)))
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (sqrt.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x)))) (sqrt.f64 (-.f64 y (*.f64 x x))))
(/.f64 (hypot.f64 (.f64 (sqrt.f64 y) y) (.f64 x (.f64 x x))) (sqrt.f64 (fma.f64 (.f64 x (.f64 x x)) x (.f64 y (-.f64 y (*.f64 x x))))))
(/.f64 (hypot.f64 (.f64 (sqrt.f64 y) y) (.f64 x (.f64 x x))) (sqrt.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))))
(sqrt.f64 (fma.f64 x x y))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (neg.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x)))) (neg.f64 (-.f64 y (*.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x x) (.f64 (.f64 y y) y))) (neg.f64 (fma.f64 (.f64 x (.f64 x x)) x (.f64 y (-.f64 y (.f64 x x))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x x) (.f64 (.f64 y y) y))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) y))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 y (.f64 x x))) (-.f64 y (*.f64 x x)))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x x) (.f64 (.f64 y y) y)) (fma.f64 (.f64 x (.f64 x x)) x (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x x) (.f64 (.f64 y y) y)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y)))
(fma.f64 (*.f64 (neg.f64 x) #s(literal -1 binary64)) x y)
(fma.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (.f64 #s(literal 1 binary64) (neg.f64 x)) y)
(fma.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x) y)
(fma.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (.f64 (neg.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) y)
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) y)
(fma.f64 (*.f64 (neg.f64 x) x) #s(literal -1 binary64) y)
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 1 binary64)) y)
(fma.f64 (neg.f64 x) (neg.f64 x) y)
(fma.f64 x (*.f64 #s(literal -1 binary64) (neg.f64 x)) y)
(fma.f64 x x y)
(fma.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x) y)
(fma.f64 #s(literal 1 binary64) (*.f64 x x) y)
(fma.f64 (*.f64 x x) #s(literal 1 binary64) y)
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) x) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (/.f64 (.f64 (.f64 x (.f64 x x)) x) (-.f64 y (.f64 x x))))
(-.f64 y (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) x (.f64 y (-.f64 y (.f64 x x))))) (/.f64 (.f64 (.f64 y y) y) (fma.f64 (.f64 x (.f64 x x)) x (.f64 y (-.f64 y (*.f64 x x))))))
(+.f64 (/.f64 (.f64 (.f64 y y) y) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (.f64 y y))) (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 x x)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) y) (*.f64 y y))))
(+.f64 (*.f64 x x) y)
(+.f64 y (*.f64 x x))
(.f64 (.f64 (neg.f64 x) #s(literal -1 binary64)) x)
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (*.f64 #s(literal 1 binary64) (neg.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (neg.f64 x) #s(literal 1 binary64)) (*.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 (neg.f64 x) x) #s(literal -1 binary64))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 1 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 x (.f64 #s(literal -1 binary64) (neg.f64 x)))
(*.f64 x x)
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x (*.f64 x x)) x) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 x x)) #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (.f64 (.f64 x (*.f64 x x)) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
x
y
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y)) x) x (sqrt.f64 y)))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (.f64 (fma.f64 (.f64 x (/.f64 x (*.f64 (sqrt.f64 y) y))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) x) x (sqrt.f64 y)))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x (/.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) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 y))) x) x (sqrt.f64 y)))
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (fma.f64 x x y))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (sqrt (+ (* x x) y)) (.f64 x (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* x x) y)) (.f64 x (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) (fma.f64 (.f64 y (/.f64 y (.f64 (.f64 x (.f64 x x)) x))) #s(literal -1/8 binary64) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 x (fma.f64 (.f64 y (/.f64 y (.f64 (.f64 x (.f64 x x)) x))) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal 3 binary64)) #s(literal 1/16 binary64) (.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64)))) x))
#s(approx (+ (* x x) y) (.f64 (.f64 (-.f64 (/.f64 y (*.f64 x x)) #s(literal -1 binary64)) x) x))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
#s(approx (sqrt (+ (* x x) y)) (.f64 (neg.f64 x) (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* x x) y)) (.f64 (neg.f64 x) (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) (fma.f64 (.f64 y (/.f64 y (.f64 (.f64 x (.f64 x x)) x))) #s(literal -1/8 binary64) #s(literal 1 binary64)))))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 (fma.f64 x (fma.f64 (.f64 y (/.f64 y (.f64 (.f64 x (.f64 x x)) x))) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (/.f64 y (.f64 x x)) #s(literal 3 binary64)) #s(literal 1/16 binary64) (.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64)))) x)))
#s(approx (sqrt (+ (* x x) y)) x)
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (/.f64 y (.f64 x (.f64 x x))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) y x))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (fma.f64 (/.f64 y (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) y (/.f64 #s(literal 1/2 binary64) x)) y x))
#s(approx (sqrt (+ (* x x) y)) (/.f64 y (sqrt.f64 y)))
#s(approx (sqrt (+ (* x x) y)) (.f64 (fma.f64 (.f64 x (/.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 x) y)) (.f64 y (fma.f64 (/.f64 (.f64 (.f64 x (.f64 x 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 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 x) y)) (fma.f64 y (fma.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 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 (.f64 x (.f64 x 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 x (*.f64 (/.f64 y (sqrt.f64 y)) y))) #s(literal 1/2 binary64)))) (/.f64 y (sqrt.f64 y))))
#s(approx (+ (* x x) y) (fma.f64 (/.f64 (*.f64 x x) y) y y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 (/.f64 y (sqrt.f64 y))))
#s(approx (sqrt (+ (* x x) y)) (.f64 (neg.f64 y) (fma.f64 (.f64 x (/.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 x) y)) (neg.f64 (.f64 y (fma.f64 (/.f64 (.f64 (.f64 x (.f64 x 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 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 x) y)) (neg.f64 (fma.f64 y (fma.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 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 (.f64 x (.f64 x 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 x (*.f64 (/.f64 y (sqrt.f64 y)) y))) #s(literal 1/2 binary64)))) (/.f64 y (sqrt.f64 y)))))
#s(approx (+ (* x x) y) (.f64 (neg.f64 y) (-.f64 (/.f64 (.f64 (neg.f64 x) x) y) #s(literal 1 binary64))))

eval18.0ms (0.8%)

Memory: -18.8MiB live, 24.9MiB allocated; 9ms collecting garbage
Compiler: Compiled 832 to 340 computations (59.1% saved)

prune4.0ms (0.2%)

Memory

10.7MiB live, 10.7MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	6	94

Accuracy

100.0%

Counts

94 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.7%	(sqrt.f64 (fma.f64 x x y))
▶	35.5%	(sqrt.f64 #s(approx (+ (* x x) y) y))
▶	35.3%	#s(approx (sqrt (+ (* x x) y)) (/.f64 y (sqrt.f64 y)))
	0.8%	#s(approx (sqrt (+ (* x x) y)) (.f64 (neg.f64 x) (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64))))
▶	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
▶	66.9%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 88 to 88 computations (0% saved)

series6.0ms (0.3%)

Memory

12.9MiB live, 12.9MiB allocated; 0ms collecting garbage

Counts

12 → 33

Calls

Call 1

Inputs
(sqrt.f64 (fma.f64 x x y))
(fma.f64 x x y)
x
y
#s(approx (sqrt (+ (* x x) y)) x)
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (+ (* x x) y) y)
#s(approx (sqrt (+ (* x x) y)) (/.f64 y (sqrt.f64 y)))
(/.f64 y (sqrt.f64 y))
(sqrt.f64 y)

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

Calls

6 calls:

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

rewrite142.0ms (6.5%)

Memory

-18.2MiB live, 213.1MiB allocated; 35ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	169	837
0	175	797
1	851	738
0	8257	703

Stop Event

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

Counts

45 → 104

Calls

Call 1

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

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

eval8.0ms (0.4%)

Memory: 18.6MiB live, 18.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 819 to 334 computations (59.2% saved)

prune4.0ms (0.2%)

Memory

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	91	6	97

Accuracy

100.0%

Counts

97 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.7%	(sqrt.f64 (fma.f64 x x y))
✓	35.5%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	35.3%	#s(approx (sqrt (+ (* x x) y)) (/.f64 y (sqrt.f64 y)))
▶	0.8%	#s(approx (sqrt (+ (* x x) y)) (.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 x)))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
✓	66.9%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 44 to 44 computations (0% saved)

series83.0ms (3.8%)

Memory

-24.5MiB live, 22.6MiB allocated; 2ms collecting garbage

Counts

10 → 39

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
75.0ms	x	@	inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) y (* x x) x 1/2 1 (neg x))
2.0ms	y	@	0	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) y (* x x) x 1/2 1 (neg x))
1.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) y (* x x) x 1/2 1 (neg x))
1.0ms	y	@	inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) y (* x x) x 1/2 1 (neg x))
1.0ms	x	@	0	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) y (* x x) x 1/2 1 (neg x))

rewrite200.0ms (9.2%)

Memory

10.0MiB live, 258.8MiB allocated; 61ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	192	1013
0	201	969
1	999	894
0	8872	840

Stop Event

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

Counts

49 → 181

Calls

Call 1

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

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

eval20.0ms (0.9%)

Memory: -1.2MiB live, 44.5MiB allocated; 2ms collecting garbage
Compiler: Compiled 1 780 to 718 computations (59.7% saved)

prune5.0ms (0.2%)

Memory

10.0MiB live, 10.0MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	168	6	174

Accuracy

100.0%

Counts

174 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.7%	(sqrt.f64 (fma.f64 x x y))
✓	35.5%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	35.3%	#s(approx (sqrt (+ (* x x) y)) (/.f64 y (sqrt.f64 y)))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
▶	0.8%	#s(approx (sqrt (+ (* x x) y)) #s(approx (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 x x)) x)))
✓	66.9%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 51 to 50 computations (2% saved)

series24.0ms (1.1%)

Memory

-28.6MiB live, 18.0MiB allocated; 2ms collecting garbage

Counts

9 → 39

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
17.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (/ (- (* -1/2 y) (* x x)) x) (- (* -1/2 y) (* x x)) (* -1/2 y) -1/2 y (* x x) x)
1.0ms	y	@	inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (/ (- (* -1/2 y) (* x x)) x) (- (* -1/2 y) (* x x)) (* -1/2 y) -1/2 y (* x x) x)
1.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (/ (- (* -1/2 y) (* x x)) x) (- (* -1/2 y) (* x x)) (* -1/2 y) -1/2 y (* x x) x)
1.0ms	x	@	inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (/ (- (* -1/2 y) (* x x)) x) (- (* -1/2 y) (* x x)) (* -1/2 y) -1/2 y (* x x) x)
1.0ms	x	@	0	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (/ (- (* -1/2 y) (* x x)) x) (- (* -1/2 y) (* x x)) (* -1/2 y) -1/2 y (* x x) x)

rewrite161.0ms (7.4%)

Memory

35.5MiB live, 263.7MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	193	1050
0	197	1006
1	995	942
0	8839	875

Stop Event

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

Counts

48 → 122

Calls

Call 1

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

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

eval14.0ms (0.7%)

Memory: -27.6MiB live, 36.5MiB allocated; 4ms collecting garbage
Compiler: Compiled 1 331 to 581 computations (56.3% saved)

prune5.0ms (0.2%)

Memory

9.0MiB live, 9.0MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	110	6	116

Accuracy

100.0%

Counts

116 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.7%	(sqrt.f64 (fma.f64 x x y))
✓	35.5%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	35.3%	#s(approx (sqrt (+ (* x x) y)) (/.f64 y (sqrt.f64 y)))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
✓	0.8%	#s(approx (sqrt (+ (* x x) y)) #s(approx (* (+ (* (/ y (* x x)) 1/2) 1) (neg x)) (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) y) (.f64 x x)) x)))
✓	66.9%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 114 to 89 computations (21.9% saved)

regimes106.0ms (4.9%)

Memory

-17.3MiB live, 29.6MiB allocated; 2ms collecting garbage

Counts

9 → 2

Calls

Call 1

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

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

Calls

5 calls:

94.0ms	(+.f64 (*.f64 x x) y)
3.0ms	x
3.0ms	y
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`(*.f64 x x)`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`x`
83.8%	2	`y`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

regimes8.0ms (0.3%)

Memory

18.9MiB live, 18.9MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
91.6%	2	`(*.f64 x x)`
74.7%	2	`(+.f64 (*.f64 x x) y)`
74.7%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
91.6%	2	`x`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

regimes6.0ms (0.3%)

Memory

13.8MiB live, 13.8MiB allocated; 0ms collecting garbage

Accuracy

Total -42.0b remaining (-198.2%)

Threshold costs -42b (-198.2%)

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) y)) x)

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
66.9%	1	`(+.f64 (*.f64 x x) y)`
66.9%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
66.9%	1	`y`
66.9%	1	`(*.f64 x x)`
66.9%	1	`x`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

bsearch27.0ms (1.2%)

Memory

-43.0MiB live, 4.1MiB allocated; 1ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
26.0ms	4.536961030802584e+138	3.7126615168365815e+140

Samples

25.0ms

48×

valid

Compiler

Compiled 39 to 46 computations (-17.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sqrt: 23.0ms (97.5% of total)

adjust: 0.0ms (0% of total)

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

ival-mult!: 0.0ms (0% of total)

bsearch12.0ms (0.6%)

Memory

18.4MiB live, 18.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	7.518407714268317e-79	2.3333463687962122e-74

Samples

5.0ms	128×	0	valid
1.0ms	38×	0	invalid

Compiler

Compiled 105 to 122 computations (-16.2% saved)

Precisions

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

ival-sqrt: 1.0ms (40.2% of total)

ival-mult!: 1.0ms (40.2% of total)

adjust: 0.0ms (0% of total)

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

derivations103.0ms (4.7%)

Memory

-15.9MiB live, 132.7MiB allocated; 12ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 18 to 16 computations (11.1% saved)

preprocess64.0ms (2.9%)

Memory: 13.0MiB live, 58.8MiB allocated; 5ms collecting garbage
Compiler: Compiled 83 to 77 computations (7.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze35.0ms (1.6%)

sample865.0ms (39.7%)

preprocess102.0ms (4.7%)

series6.0ms (0.3%)

rewrite153.0ms (7%)

eval18.0ms (0.8%)

prune4.0ms (0.2%)

series6.0ms (0.3%)

rewrite142.0ms (6.5%)

eval8.0ms (0.4%)

prune4.0ms (0.2%)

series83.0ms (3.8%)

rewrite200.0ms (9.2%)

eval20.0ms (0.9%)

prune5.0ms (0.2%)

series24.0ms (1.1%)

rewrite161.0ms (7.4%)

eval14.0ms (0.7%)

prune5.0ms (0.2%)

regimes106.0ms (4.9%)

regimes8.0ms (0.3%)

regimes6.0ms (0.3%)

bsearch27.0ms (1.2%)

bsearch12.0ms (0.6%)

derivations103.0ms (4.7%)

preprocess64.0ms (2.9%)

end0.0ms (0%)

Profiling