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

start0.0ms (0%)

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

analyze44.0ms (3.5%)

Memory

-10.5MiB live, 32.0MiB allocated; 13ms 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)

sample840.0ms (67%)

Memory

34.3MiB live, 1 355.8MiB allocated; 283ms collecting garbage

Samples

519.0ms	8 256×	0	valid
14.0ms	318×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 339.0ms

ival-mult: 156.0ms (46.1% of total)

ival-sqrt: 98.0ms (28.9% of total)

ival-add: 80.0ms (23.6% of total)

ival-assert: 3.0ms (0.9% of total)

adjust: 2.0ms (0.6% of total)

Bogosity

explain109.0ms (8.7%)

Memory

-3.6MiB live, 93.7MiB allocated; 26ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
94	-	-	`(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	94	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	94
↳	`(*.f64 x x)`	overflow	94

Confusion

	Predicted +	Predicted -
+	94	0
-	0	162

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	94	0	0
-	0	0	162

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	162
1	94

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

72.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 21.0ms (75.7% of total)

ival-add: 3.0ms (10.8% of total)

ival-sqrt: 3.0ms (10.8% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess14.0ms (1.2%)

Memory

22.0MiB live, 22.0MiB 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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.8%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series24.0ms (1.9%)

Memory

-34.2MiB live, 12.5MiB allocated; 5ms 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
17.0ms	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)
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)

rewrite56.0ms (4.5%)

Memory

14.8MiB live, 61.6MiB allocated; 3ms 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 (0.5%)

Memory: 11.0MiB live, 11.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 868 to 212 computations (75.6% saved)

prune2.0ms (0.2%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	3	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Accuracy

100.0%

Counts

54 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.8%	(sqrt.f64 (fma.f64 x x y))
▶	32.7%	(sqrt.f64 #s(approx (+ (* x x) y) y))
▶	70.2%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 21 to 16 computations (23.8% saved)

series3.0ms (0.3%)

Memory

4.9MiB live, 4.9MiB allocated; 0ms collecting garbage

Counts

7 → 30

Calls

Call 1

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

rewrite47.0ms (3.7%)

Memory

-16.0MiB live, 33.7MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	169	745
0	172	677
0	929	647

Stop Event

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

Counts

37 → 48

Calls

Call 1

Inputs
#s(approx (sqrt (+ (* x x) y)) x)
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 (+ (* 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
(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 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))
#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)
#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) (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 -1/8 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 1/2 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)))

eval5.0ms (0.4%)

Memory: 9.6MiB live, 9.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 859 to 193 computations (77.5% saved)

prune3.0ms (0.2%)

Memory

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

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	52	3	55

Accuracy

100.0%

Counts

55 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	65.8%	(sqrt.f64 (fma.f64 x x y))
✓	32.7%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	70.2%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 48 to 29 computations (39.6% saved)

regimes23.0ms (1.8%)

Memory

-22.5MiB live, 24.7MiB allocated; 2ms 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))
(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:

16.0ms	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
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`
86.5%	2	`y`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes5.0ms (0.4%)

Memory

15.2MiB live, 15.2MiB 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	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
92.1%	2	`(*.f64 x x)`
74.9%	2	`(+.f64 (*.f64 x x) y)`
74.9%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
92.1%	2	`x`

Compiler

Compiled 15 to 14 computations (6.7% saved)

regimes7.0ms (0.5%)

Memory

-30.6MiB live, 16.3MiB allocated; 2ms 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:

2.0ms	(+.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
70.2%	1	`(+.f64 (*.f64 x x) y)`
70.2%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
70.2%	1	`y`
70.2%	1	`(*.f64 x x)`
70.2%	1	`x`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch2.0ms (0.2%)

Memory

3.3MiB live, 3.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.5274399056667329e+137	1.610509146215248e+137

Samples

1.0ms

16×

valid

Compiler

Compiled 22 to 22 computations (0% saved)

Precisions

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

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

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

adjust: 0.0ms (0% of total)

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

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

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

bsearch14.0ms (1.1%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	6.766603354607342e-73	4.02828066723465e-67

Samples

6.0ms	144×	0	valid
1.0ms	28×	0	invalid

Compiler

Compiled 153 to 136 computations (11.1% saved)

Precisions

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

ival-add: 1.0ms (29.1% of total)

ival-mult: 1.0ms (29.1% of total)

ival-sqrt: 1.0ms (29.1% of total)

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

adjust: 0.0ms (0% of total)

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

simplify13.0ms (1.1%)

Memory

-25.2MiB live, 21.3MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	45
1	21	45
2	40	45
3	67	45
4	82	45

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 x #s(literal 160000000000000009386249803211841916087392685822356870209499416728157141632861049752076405727382297436864486013712119990028833657869828096 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) x))

(if (<=.f64 x #s(literal 331999078261233/948568795032094272909893509191171341133987714380927500611236528192824358010355712 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 160000000000000009386249803211841916087392685822356870209499416728157141632861049752076405727382297436864486013712119990028833657869828096 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) x))

(if (<=.f64 x #s(literal 331999078261233/948568795032094272909893509191171341133987714380927500611236528192824358010355712 binary64)) (sqrt.f64 #s(approx (+ (* x x) y) y)) #s(approx (sqrt (+ (* x x) y)) x))

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

derivations5.0ms (0.4%)

Memory

9.6MiB live, 9.6MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 45 to 16 computations (64.4% saved)

preprocess30.0ms (2.4%)

Memory: 14.0MiB live, 61.3MiB allocated; 8ms collecting garbage
Compiler: Compiled 194 to 96 computations (50.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze44.0ms (3.5%)

sample840.0ms (67%)

explain109.0ms (8.7%)

preprocess14.0ms (1.2%)

eval0.0ms (0%)

prune0.0ms (0%)

series24.0ms (1.9%)

rewrite56.0ms (4.5%)

eval6.0ms (0.5%)

prune2.0ms (0.2%)

series3.0ms (0.3%)

rewrite47.0ms (3.7%)

eval5.0ms (0.4%)

prune3.0ms (0.2%)

regimes23.0ms (1.8%)

regimes5.0ms (0.4%)

regimes7.0ms (0.5%)

bsearch2.0ms (0.2%)

bsearch14.0ms (1.1%)

simplify13.0ms (1.1%)

derivations5.0ms (0.4%)

preprocess30.0ms (2.4%)

end0.0ms (0%)

Profiling