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

start0.0ms (0%)

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

analyze24.0ms (1.2%)

Memory

-42.4MiB live, 51.1MiB allocated; 9ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
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)

sample1.3s (68.1%)

Memory

-2.3MiB live, 1 162.2MiB allocated; 1.2s collecting garbage

Samples

1.1s	8 256×	0	valid
43.0ms	303×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 207.0ms

ival-sqrt: 85.0ms (41% of total)

ival-mult!: 69.0ms (33.3% of total)

ival-add!: 52.0ms (25.1% of total)

adjust: 2.0ms (1% of total)

Bogosity

preprocess140.0ms (7.1%)

Memory

-10.2MiB live, 40.3MiB allocated; 63ms 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
▶	71.9%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series7.0ms (0.3%)

Memory

21.7MiB live, 21.7MiB allocated; 0ms collecting garbage

Counts

5 → 28

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 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))))
#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 (+ x (* 1/2 (/ y x)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-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	x	@	-inf	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x y)
1.0ms	x	@	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)

rewrite54.0ms (2.7%)

Memory

-9.0MiB live, 78.4MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	167	745
0	170	678
0	929	619

Stop Event

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

Counts

33 → 48

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 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))))
#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 (+ x (* 1/2 (/ y x)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

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

eval5.0ms (0.2%)

Memory: 14.9MiB live, 14.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 482 to 198 computations (58.9% saved)

prune2.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	4	45

Accuracy

100.0%

Counts

45 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.9%	(sqrt.f64 (fma.f64 x x y))
▶	39.3%	(sqrt.f64 #s(approx (+ (* x x) y) y))
▶	63.6%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
▶	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 26 to 26 computations (0% saved)

series11.0ms (0.6%)

Memory

-23.4MiB live, 21.1MiB allocated; 10ms collecting garbage

Counts

12 → 34

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
x
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x)
(/.f64 y x)
y
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (+ (* x x) y) y)
(sqrt.f64 (fma.f64 x x y))
(fma.f64 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 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (* 1/2 (/ y x))))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (/ (+ (* 1/2 y) (pow x 2)) x)))
#s(approx (/ y x) #s(hole binary64 (/ y x)))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#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 (+ (* (/ y x) 1/2) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* 1/2 (/ y x)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (* y (+ (* 1/2 (/ 1 x)) (/ x 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 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) y 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) y 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	y	@	inf	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) y 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	x	@	inf	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) y 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	x	@	0	((sqrt (+ (* x x) y)) (neg x) x (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) y 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* x x) y))

rewrite157.0ms (7.9%)

Memory

25.8MiB live, 123.1MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	852
0	201	776
0	1042	746

Stop Event

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

Counts

46 → 68

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
x
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
(fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x)
(/.f64 y x)
y
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (+ (* x x) y) y))
#s(approx (+ (* x x) y) y)
(sqrt.f64 (fma.f64 x x y))
(fma.f64 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 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (* 1/2 (/ y x))))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (/ (+ (* 1/2 y) (pow x 2)) x)))
#s(approx (/ y x) #s(hole binary64 (/ y x)))
#s(approx (+ (* x x) y) #s(hole binary64 y))
#s(approx (+ (* x x) y) #s(hole binary64 (+ y (pow x 2))))
#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 (+ (* (/ y x) 1/2) x) #s(hole binary64 (* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* 1/2 (/ y x)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (* y (+ (* 1/2 (/ 1 x)) (/ x 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 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

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

eval6.0ms (0.3%)

Memory: 17.7MiB live, 17.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 599 to 254 computations (57.6% saved)

prune6.0ms (0.3%)

Memory

-37.7MiB live, 7.5MiB allocated; 5ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	55	5	60

Accuracy

100.0%

Counts

60 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.9%	(sqrt.f64 (fma.f64 x x y))
▶	35.2%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	39.3%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	63.6%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 33 to 33 computations (0% saved)

series3.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated; 0ms collecting garbage

Counts

4 → 28

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
#s(approx (+ (* x x) y) (*.f64 x x))
(*.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 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))))
#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 (+ x (* 1/2 (/ y x)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))))
#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)
1.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x)
0.0ms	x	@	0	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x)
0.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x)
0.0ms	y	@	inf	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x)

rewrite45.0ms (2.3%)

Memory

28.5MiB live, 74.4MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	167	752
0	169	685
0	929	626

Stop Event

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

Counts

32 → 38

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
#s(approx (+ (* x x) y) (*.f64 x x))
(*.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 (/ 1 y)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ (sqrt y) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 y))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* 1/16 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))))
#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 (+ x (* 1/2 (/ y x)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (pow x 6) (sqrt (/ 1 (pow y 7))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* (sqrt y) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ (* x x) y)) #s(hole binary64 (* -1 (* y (+ (* -1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 6) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))))
#s(approx (+ (* x x) y) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

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

eval25.0ms (1.3%)

Memory: -27.5MiB live, 21.2MiB allocated; 14ms collecting garbage
Compiler: Compiled 407 to 162 computations (60.2% saved)

prune3.0ms (0.1%)

Memory

8.0MiB live, 8.0MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	31	5	36

Accuracy

100.0%

Counts

36 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.9%	(sqrt.f64 (fma.f64 x x y))
✓	35.2%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	39.3%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	63.6%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 61 to 53 computations (13.1% saved)

regimes38.0ms (1.9%)

Memory

-12.8MiB live, 32.8MiB allocated; 5ms collecting garbage

Counts

6 → 2

Calls

Call 1

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

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

Calls

5 calls:

28.0ms	(*.f64 x x)
2.0ms	x
2.0ms	y
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	(+.f64 (*.f64 x x) y)

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`
88.8%	2	`y`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

regimes11.0ms (0.5%)

Memory

37.6MiB live, 37.6MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
71.9%	1	`y`
71.9%	1	`(*.f64 x x)`
71.9%	1	`(+.f64 (*.f64 x x) y)`
71.9%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
71.9%	1	`x`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

regimes10.0ms (0.5%)

Memory

-17.9MiB live, 27.6MiB allocated; 3ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
61.2%	2	`x`
61.2%	2	`(*.f64 x x)`
45.7%	2	`(+.f64 (*.f64 x x) y)`
45.7%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
56.6%	2	`y`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

regimes9.0ms (0.4%)

Memory

-23.2MiB live, 23.0MiB allocated; 3ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

1.0ms	y
1.0ms	x
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
39.3%	1	`(+.f64 (*.f64 x x) y)`
39.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
39.3%	1	`y`
39.3%	1	`(*.f64 x x)`
39.3%	1	`x`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

regimes5.0ms (0.3%)

Memory

21.2MiB live, 21.2MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
1.3%	1	`y`
1.3%	1	`(*.f64 x x)`
1.3%	1	`(+.f64 (*.f64 x x) y)`
1.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.3%	1	`x`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

bsearch2.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	4.642439373391793e+130	3.2496440490466324e+131

Samples

1.0ms

16×

valid

Compiler

Compiled 22 to 25 computations (-13.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0% of total)

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

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

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

bsearch17.0ms (0.9%)

Memory

-13.9MiB live, 38.3MiB allocated; 7ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	1.0688835684589056e-58	1.2097000069971969e-54

Samples

9.0ms	128×	0	valid
1.0ms	36×	0	invalid

Compiler

Compiled 113 to 130 computations (-15% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 1.0ms (39.2% of total)

ival-mult!: 1.0ms (39.2% of total)

adjust: 0.0ms (0% of total)

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

derivations10.0ms (0.5%)

Memory

29.5MiB live, 29.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 31 to 24 computations (22.6% saved)

preprocess42.0ms (2.1%)

Memory: 3.7MiB live, 139.8MiB allocated; 12ms collecting garbage
Remove: (abs x)
Compiler: Compiled 126 to 115 computations (8.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze24.0ms (1.2%)

sample1.3s (68.1%)

preprocess140.0ms (7.1%)

series7.0ms (0.3%)

rewrite54.0ms (2.7%)

eval5.0ms (0.2%)

prune2.0ms (0.1%)

series11.0ms (0.6%)

rewrite157.0ms (7.9%)

eval6.0ms (0.3%)

prune6.0ms (0.3%)

series3.0ms (0.1%)

rewrite45.0ms (2.3%)

eval25.0ms (1.3%)

prune3.0ms (0.1%)

regimes38.0ms (1.9%)

regimes11.0ms (0.5%)

regimes10.0ms (0.5%)

regimes9.0ms (0.4%)

regimes5.0ms (0.3%)

bsearch2.0ms (0.1%)

bsearch17.0ms (0.9%)

derivations10.0ms (0.5%)

preprocess42.0ms (2.1%)

end0.0ms (0%)

Profiling