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

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze28.0ms (2.2%)

Memory

-14.0MiB live, 29.0MiB allocated; 20ms 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)

sample823.0ms (63.7%)

Memory

30.0MiB live, 742.6MiB allocated; 187ms collecting garbage

Samples

491.0ms	8 256×	0	valid
12.0ms	316×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 164.0ms

ival-mult!: 80.0ms (48.7% of total)

ival-sqrt: 63.0ms (38.4% of total)

ival-add!: 20.0ms (12.2% of total)

adjust: 2.0ms (1.2% of total)

Bogosity

preprocess136.0ms (10.5%)

Memory

-45.5MiB live, 56.0MiB allocated; 16ms 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
▶	65.9%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series7.0ms (0.5%)

Memory

14.3MiB live, 14.3MiB allocated; 0ms collecting garbage

Counts

5 → 31

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))
#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)))
#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 y #s(hole binary64 y))
#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	y	@	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)

rewrite89.0ms (6.9%)

Memory

13.1MiB live, 56.5MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	170	765
0	173	698
0	932	637

Stop Event

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

Counts

36 → 51

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))
#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)))
#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 y #s(hole binary64 y))
#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)) 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 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)) (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 y y)
#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 (0.4%)

Memory: 8.8MiB live, 8.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 495 to 204 computations (58.8% saved)

prune2.0ms (0.2%)

Memory

3.1MiB live, 3.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	4	48

Accuracy

100.0%

Counts

48 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.9%	(sqrt.f64 (fma.f64 x x y))
▶	31.2%	(sqrt.f64 #s(approx (+ (* x x) y) y))
▶	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
▶	71.4%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 23 to 23 computations (0% saved)

series4.0ms (0.3%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Counts

9 → 31

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) x)
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)
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 x #s(hole binary64 x))
#s(approx (neg x) #s(hole binary64 (* -1 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))
#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)))
#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 y #s(hole binary64 y))
#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 (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	y	@	-inf	((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	x	@	inf	((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))
0.0ms	y	@	inf	((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))
0.0ms	x	@	0	((sqrt (+ (* x x) y)) x (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (+ (* x x) y) y (sqrt (+ (* x x) y)) (+ (* x x) y))

rewrite88.0ms (6.8%)

Memory

-11.8MiB live, 75.5MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	173	761
0	176	692
0	933	662

Stop Event

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

Counts

40 → 53

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) x)
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)
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 x #s(hole binary64 x))
#s(approx (neg x) #s(hole binary64 (* -1 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))
#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)))
#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 y #s(hole binary64 y))
#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
#s(approx (sqrt (+ (* x x) y)) x)
x
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
(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)
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 x x)
#s(approx (neg x) (neg.f64 x))
#s(approx (+ (* x x) y) y)
#s(approx (+ (* x x) y) (fma.f64 x x y))
#s(approx (sqrt (+ (* x x) y)) 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 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)) (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 y y)
#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 (0.3%)

Memory: 9.7MiB live, 9.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 478 to 193 computations (59.6% saved)

prune3.0ms (0.2%)

Memory

6.0MiB live, 6.0MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	44	4	48

Accuracy

100.0%

Counts

48 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.9%	(sqrt.f64 (fma.f64 x x y))
✓	31.2%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
✓	71.4%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 43 to 38 computations (11.6% saved)

regimes44.0ms (3.4%)

Memory

-15.9MiB live, 40.4MiB allocated; 9ms collecting garbage

Counts

5 → 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))
(sqrt.f64 (fma.f64 x x y))
(sqrt.f64 (+.f64 (*.f64 x x) y))

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

Calls

5 calls:

36.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	y
2.0ms	(+.f64 (*.f64 x x) y)
2.0ms	(*.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`
83.1%	2	`y`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

regimes9.0ms (0.7%)

Memory

-25.9MiB live, 18.4MiB allocated; 6ms collecting garbage

Counts

3 → 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))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
90.8%	2	`(*.f64 x x)`
75.4%	2	`(+.f64 (*.f64 x x) y)`
75.4%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
90.8%	2	`x`

Compiler

Compiled 12 to 14 computations (-16.7% saved)

regimes6.0ms (0.5%)

Memory

19.2MiB live, 19.2MiB allocated; 0ms collecting garbage

Accuracy

Total -44.9b remaining (-245.4%)

Threshold costs -44.9b (-245.4%)

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	(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
71.4%	1	`(+.f64 (*.f64 x x) y)`
71.4%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
71.4%	1	`y`
71.4%	1	`(*.f64 x x)`
71.4%	1	`x`

Compiler

Compiled 13 to 16 computations (-23.1% saved)

bsearch2.0ms (0.1%)

Memory

3.2MiB live, 3.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.565778635954416e+150	1.617514820245893e+150

Samples

1.0ms

16×

valid

Compiler

Compiled 19 to 22 computations (-15.8% 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)

bsearch14.0ms (1.1%)

Memory

-19.8MiB live, 26.5MiB allocated; 2ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	1.0335955308272722e-76	4.1166303207276054e-70

Samples

5.0ms	144×	0	valid
1.0ms	35×	0	invalid

Compiler

Compiled 117 to 136 computations (-16.2% saved)

Precisions

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

ival-sqrt: 1.0ms (37.9% of total)

ival-mult!: 1.0ms (37.9% of total)

adjust: 0.0ms (0% of total)

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

derivations7.0ms (0.5%)

Memory

11.9MiB live, 11.9MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 18 to 16 computations (11.1% saved)

preprocess23.0ms (1.8%)

Memory: 14.6MiB live, 58.1MiB allocated; 6ms 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%)

analyze28.0ms (2.2%)

sample823.0ms (63.7%)

preprocess136.0ms (10.5%)

series7.0ms (0.5%)

rewrite89.0ms (6.9%)

eval5.0ms (0.4%)

prune2.0ms (0.2%)

series4.0ms (0.3%)

rewrite88.0ms (6.8%)

eval5.0ms (0.3%)

prune3.0ms (0.2%)

regimes44.0ms (3.4%)

regimes9.0ms (0.7%)

regimes6.0ms (0.5%)

bsearch2.0ms (0.1%)

bsearch14.0ms (1.1%)

derivations7.0ms (0.5%)

preprocess23.0ms (1.8%)

end0.0ms (0%)

Profiling