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

start0.0ms (0%)

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

analyze17.0ms (1.3%)

Memory

17.1MiB live, 17.1MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

sample787.0ms (60.2%)

Memory

-33.1MiB live, 914.3MiB allocated; 223ms collecting garbage

Samples

507.0ms	8 256×	0	valid
16.0ms	316×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 343.0ms

ival-sqrt: 148.0ms (43.2% of total)

ival-mult!: 123.0ms (35.9% of total)

ival-add!: 70.0ms (20.4% of total)

adjust: 1.0ms (0.3% of total)

Bogosity

explain61.0ms (4.7%)

Memory

28.5MiB live, 75.8MiB allocated; 3ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
92	-	-	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
0	-	-	`(+.f64 (*.f64 x x) y)`
0	-	-	`y`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) y))`	oflow-rescue	92	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	92
↳	`(*.f64 x x)`	overflow	92

Confusion

	Predicted +	Predicted -
+	92	0
-	0	164

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	92	0	0
-	0	0	164

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	164
1	92

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sqrt: 4.0ms (46.8% of total)

ival-mult!: 3.0ms (35.1% of total)

ival-add!: 1.0ms (11.7% of total)

adjust: 0.0ms (0% of total)

preprocess15.0ms (1.2%)

Memory

14.5MiB live, 14.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	33	40
2	87	40
3	133	40
4	179	40
5	181	40
0	5	6
0	8	6
1	13	6
2	32	6
3	59	6
4	74	6
0	74	5

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.5%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series83.0ms (6.4%)

Memory

-38.0MiB live, 14.0MiB allocated; 6ms 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
76.0ms	y	@	0	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x y)
2.0ms	y	@	inf	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x y)
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)

rewrite54.0ms (4.1%)

Memory

29.9MiB live, 73.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	170	765
0	174	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 (pow.f64 x #s(literal 4 binary64)) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (-.f64 y (.f64 x x)))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 y y) (.f64 (.f64 x x) y))))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 y y (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 y (*.f64 x x)))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) y)
(fma.f64 (neg.f64 x) (neg.f64 x) y)
(fma.f64 (fabs.f64 x) (fabs.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 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.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 #s(literal -1/8 binary64) (.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -3 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 (pow.f64 y #s(literal -3 binary64))) #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) (pow.f64 x #s(literal 4 binary64))) #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 (+.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) x))
#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) (pow.f64 x #s(literal 4 binary64))) #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)) (.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #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 (pow.f64 x #s(literal 3 binary64))) #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) (pow.f64 x #s(literal -3 binary64)))) y (/.f64 #s(literal 1/2 binary64) x)) y x))
#s(approx y y)
#s(approx (sqrt (+ (* x x) y)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ (* x x) y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 y))) y))
#s(approx (sqrt (+ (* x x) y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -3 binary64))) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (sqrt.f64 (pow.f64 y #s(literal -7 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 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -3 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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -3 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 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 y #s(literal -7 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 (pow.f64 y #s(literal -3 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)))

eval6.0ms (0.4%)

Memory: 11.9MiB live, 11.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 868 to 212 computations (75.6% saved)

prune6.0ms (0.5%)

Memory

-30.9MiB live, 13.7MiB allocated; 4ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	48	5	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	5	54

Accuracy

100.0%

Counts

54 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.5%	(sqrt.f64 (fma.f64 x x y))
▶	40.6%	(sqrt.f64 #s(approx (+ (* x x) y) (.f64 (+.f64 (/.f64 y (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))))
▶	39.0%	(sqrt.f64 #s(approx (+ (* x x) y) y))
▶	63.9%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
▶	63.7%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 104 to 72 computations (30.8% saved)

series13.0ms (1%)

Memory

27.9MiB live, 27.9MiB allocated; 0ms collecting garbage

Counts

18 → 52

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

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 #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 (* (+ (/ y (* x x)) 1) (* x x)) #s(hole binary64 y))
#s(approx (* (+ (/ y (* x x)) 1) (* x x)) #s(hole binary64 (+ y (pow x 2))))
#s(approx (+ (/ y (* x x)) 1) #s(hole binary64 (/ y (pow x 2))))
#s(approx (+ (/ y (* x x)) 1) #s(hole binary64 (/ (+ 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 (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 (+ (* (/ y x) 1/2) x) #s(hole binary64 x))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (* x (+ 1 (* 1/2 (/ y (pow x 2)))))))
#s(approx (* (+ (/ y (* x x)) 1) (* x x)) #s(hole binary64 (pow x 2)))
#s(approx (* (+ (/ y (* x x)) 1) (* x x)) #s(hole binary64 (* (pow x 2) (+ 1 (/ y (pow x 2))))))
#s(approx (+ (/ y (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (/ y (* x x)) 1) #s(hole binary64 (+ 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 (+ (* (/ 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 y #s(hole binary64 y))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (+ x (* 1/2 (/ y 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 (+ (* (/ y x) 1/2) x) #s(hole binary64 (* y (+ (* 1/2 (/ 1 x)) (/ x y)))))
#s(approx (* (+ (/ y (* x x)) 1) (* x x)) #s(hole binary64 (* y (+ 1 (/ (pow x 2) y)))))
#s(approx (+ (/ y (* x x)) 1) #s(hole binary64 (* y (+ (/ 1 y) (/ 1 (pow x 2))))))
#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)))))
#s(approx (+ (* (/ y x) 1/2) x) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))))
#s(approx (* (+ (/ y (* x x)) 1) (* x x)) #s(hole binary64 (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	inf	((sqrt (+ (* x x) y)) (+ (* x x) y) x y (sqrt (+ (* x x) y)) (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (/ y (* x x)) 1) (* x x)) (+ (/ y (* x x)) 1) (/ y (* x x)) (* x x) 1)
2.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (+ (* x x) y) x y (sqrt (+ (* x x) y)) (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (/ y (* x x)) 1) (* x x)) (+ (/ y (* x x)) 1) (/ y (* x x)) (* x x) 1)
2.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (+ (* x x) y) x y (sqrt (+ (* x x) y)) (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (/ y (* x x)) 1) (* x x)) (+ (/ y (* x x)) 1) (/ y (* x x)) (* x x) 1)
2.0ms	x	@	inf	((sqrt (+ (* x x) y)) (+ (* x x) y) x y (sqrt (+ (* x x) y)) (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (/ y (* x x)) 1) (* x x)) (+ (/ y (* x x)) 1) (/ y (* x x)) (* x x) 1)
1.0ms	y	@	0	((sqrt (+ (* x x) y)) (+ (* x x) y) x y (sqrt (+ (* x x) y)) (sqrt (+ (* x x) y)) (+ (* x x) y) (sqrt (+ (* x x) y)) (+ (* (/ y x) 1/2) x) (/ y x) 1/2 (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (/ y (* x x)) 1) (* x x)) (+ (/ y (* x x)) 1) (/ y (* x x)) (* x x) 1)

rewrite85.0ms (6.5%)

Memory

-27.7MiB live, 111.7MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	224	1167
0	237	1084
0	1143	1053

Stop Event

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

Counts

70 → 109

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

eval13.0ms (1%)

Memory: 24.0MiB live, 24.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 599 to 474 computations (81.8% saved)

prune6.0ms (0.5%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	134	5	139

Accuracy

100.0%

Counts

139 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.5%	(sqrt.f64 (fma.f64 x x y))
✓	40.6%	(sqrt.f64 #s(approx (+ (* x x) y) (.f64 (+.f64 (/.f64 y (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))))
✓	39.0%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	63.9%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
✓	63.7%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 110 to 59 computations (46.4% saved)

regimes62.0ms (4.7%)

Memory

-28.5MiB live, 18.7MiB allocated; 4ms collecting garbage

Counts

6 → 2

Calls

Call 1

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

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

Calls

5 calls:

52.0ms	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`
85.9%	2	`y`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes7.0ms (0.5%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

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

Calls

4 calls:

2.0ms	x
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
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`

Compiler

Compiled 15 to 14 computations (6.7% saved)

regimes5.0ms (0.4%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) 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:

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

Results

Accuracy	Segments	Branch
92.1%	2	`(*.f64 x x)`
75.7%	2	`(+.f64 (*.f64 x x) y)`
75.7%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
92.1%	2	`x`

Compiler

Compiled 15 to 14 computations (6.7% saved)

regimes19.0ms (1.5%)

Memory

-32.8MiB live, 14.1MiB allocated; 1ms 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)) x)

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

Calls

5 calls:

15.0ms	(+.f64 (*.f64 x x) y)
1.0ms	x
1.0ms	y
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
63.7%	1	`(+.f64 (*.f64 x x) y)`
63.7%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
63.7%	1	`y`
63.7%	1	`(*.f64 x x)`
63.7%	1	`x`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch2.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
1.0ms	4.4056938811305765e+144	7.027436300226442e+145

Samples

1.0ms

16×

valid

Compiler

Compiled 23 to 23 computations (0% 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)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
0.0ms	4.4056938811305765e+144	7.027436300226442e+145

Compiler

Compiled 22 to 22 computations (0% saved)

bsearch10.0ms (0.8%)

Memory

18.3MiB live, 18.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	1.8724596737328945e-27	1.6552324723728175e-25

Samples

4.0ms	112×	0	valid
1.0ms	25×	0	invalid

Compiler

Compiled 121 to 108 computations (10.7% saved)

Precisions

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

ival-sqrt: 1.0ms (46.5% of total)

ival-mult!: 1.0ms (46.5% of total)

adjust: 0.0ms (0% of total)

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

simplify11.0ms (0.8%)

Memory

17.7MiB live, 17.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	63
1	25	63
2	44	63
3	71	63
4	86	63

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #s(approx (sqrt (+ ( x x) y)) x))
(if (<=.f64 x #s(literal 4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) x))
(if (<=.f64 x #s(literal 6690223559559187/2787593149816327892691964784081045188247552 binary64)) (sqrt.f64 #s(approx (+ (* x x) y) y)) #s(approx (sqrt (+ (* x x) y)) x))
#s(approx (sqrt (+ (* x x) y)) x)

Outputs
(if (<=.f64 x #s(literal 4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #s(approx (sqrt (+ ( x x) y)) x))
(if (<=.f64 x #s(literal 4999999999999999945435305910704598063392403130200679472590007732362651199555129074427056403228815030648329464160476949292016380761727168556302336 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) x))
(if (<=.f64 x #s(literal 6690223559559187/2787593149816327892691964784081045188247552 binary64)) (sqrt.f64 #s(approx (+ (* x x) y) y)) #s(approx (sqrt (+ (* x x) y)) x))
#s(approx (sqrt (+ (* x x) y)) x)

derivations25.0ms (1.9%)

Memory

-39.2MiB live, 9.3MiB allocated; 22ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 63 to 20 computations (68.3% saved)

preprocess20.0ms (1.5%)

Memory: 41.9MiB live, 41.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 174 to 74 computations (57.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze17.0ms (1.3%)

sample787.0ms (60.2%)

explain61.0ms (4.7%)

preprocess15.0ms (1.2%)

eval0.0ms (0%)

prune0.0ms (0%)

series83.0ms (6.4%)

rewrite54.0ms (4.1%)

eval6.0ms (0.4%)

prune6.0ms (0.5%)

series13.0ms (1%)

rewrite85.0ms (6.5%)

eval13.0ms (1%)

prune6.0ms (0.5%)

regimes62.0ms (4.7%)

regimes7.0ms (0.5%)

regimes5.0ms (0.4%)

regimes19.0ms (1.5%)

bsearch2.0ms (0.1%)

bsearch0.0ms (0%)

bsearch10.0ms (0.8%)

simplify11.0ms (0.8%)

derivations25.0ms (1.9%)

preprocess20.0ms (1.5%)

end0.0ms (0%)

Profiling