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

start0.0ms (0%)

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

analyze29.0ms (2.8%)

Memory

-19.6MiB live, 28.5MiB allocated; 12ms 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)

sample695.0ms (65.9%)

Memory

-0.5MiB live, 907.4MiB allocated; 186ms collecting garbage

Samples

408.0ms	8 256×	0	valid
15.0ms	311×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 243.0ms

ival-mult: 82.0ms (33.7% of total)

ival-add: 80.0ms (32.9% of total)

ival-sqrt: 75.0ms (30.8% of total)

adjust: 3.0ms (1.2% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain91.0ms (8.7%)

Memory

-11.6MiB live, 92.7MiB allocated; 46ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
75	-	-	`(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	75	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	75
↳	`(*.f64 x x)`	overflow	75

Confusion

	Predicted +	Predicted -
+	75	0
-	0	181

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	75	0	0
-	0	0	181

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	181
1	75

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

54.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-sqrt: 31.0ms (79.7% of total)

ival-mult: 4.0ms (10.3% of total)

ival-add: 2.0ms (5.1% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess16.0ms (1.5%)

Memory

23.5MiB live, 23.5MiB 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

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

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.7%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series9.0ms (0.9%)

Memory

-36.8MiB live, 9.7MiB 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
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)

rewrite62.0ms (5.9%)

Memory

16.8MiB live, 62.6MiB allocated; 5ms 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))) (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 (pow.f64 y #s(literal 1 binary64)) (pow.f64 y #s(literal 1 binary64)) (-.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 (.f64 #s(literal -1 binary64) x) (.f64 #s(literal -1 binary64) 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 (.f64 #s(literal -1 binary64) x) (*.f64 #s(literal -1 binary64) 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)) (pow.f64 y #s(literal 1/2 binary64)))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) (pow.f64 (pow.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (.f64 x x) (pow.f64 y #s(literal 1/2 binary64))))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 (pow.f64 (pow.f64 y #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 (pow.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64))) (.f64 x x) (.f64 (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (.f64 x x) (pow.f64 y #s(literal 1/2 binary64))))
#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 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 y y)) (pow.f64 x #s(literal 4 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)))) 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)) (*.f64 #s(literal -1 binary64) x))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(literal -1 binary64) (.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 #s(literal -1 binary64) 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 (.f64 #s(literal -1 binary64) x) (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 y y)) (pow.f64 x #s(literal 4 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(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 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64) (.f64 (/.f64 y (.f64 (*.f64 x x) x)) #s(literal -1/8 binary64))) 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 (.f64 (.f64 x x) x) #s(literal -1 binary64)))) y (.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) y x))
#s(approx y y)
#s(approx (sqrt (+ (* x x) y)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) (pow.f64 (pow.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))) y))
#s(approx (sqrt (+ (* x x) y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (pow.f64 (pow.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (pow.f64 (pow.f64 y #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))) y))
#s(approx (sqrt (+ (* x x) y)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (pow.f64 (pow.f64 y #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (pow.f64 (pow.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (pow.f64 (pow.f64 y #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64))))) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))) y))
#s(approx (+ (* x x) y) (.f64 (+.f64 (/.f64 (.f64 x x) y) #s(literal 1 binary64)) y))
#s(approx (sqrt (+ (* x x) y)) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 1/2 binary64))) #s(literal -1 binary64)))
#s(approx (sqrt (+ (* x x) y)) (.f64 (.f64 #s(literal -1 binary64) y) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (pow.f64 (pow.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 (.f64 #s(literal -1 binary64) y) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (pow.f64 (pow.f64 (pow.f64 y #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (pow.f64 (pow.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (sqrt (+ (* x x) y)) (.f64 (.f64 #s(literal -1 binary64) y) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (pow.f64 (pow.f64 (pow.f64 y #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (pow.f64 (pow.f64 y #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (pow.f64 (pow.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1/2 binary64))))))))
#s(approx (+ (* x x) y) (.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 x x) y) #s(literal -1 binary64)) #s(literal 1 binary64)) y) #s(literal -1 binary64)))

eval6.0ms (0.6%)

Memory: 9.1MiB live, 9.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 961 to 216 computations (77.5% saved)

prune10.0ms (1%)

Memory

13.9MiB live, 13.9MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	2	54

Accuracy

100.0%

Counts

54 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	72.7%	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	67.0%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))

Compiler

Compiled 19 to 14 computations (26.3% saved)

series6.0ms (0.5%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Counts

6 → 33

Calls

Call 1

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

Calls

6 calls:

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

rewrite52.0ms (4.9%)

Memory

-1.7MiB live, 46.7MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	179	824
0	181	750
0	957	696

Stop Event

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

Counts

39 → 48

Calls

Call 1

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

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

eval12.0ms (1.1%)

Memory: -34.8MiB live, 11.3MiB allocated; 4ms collecting garbage
Compiler: Compiled 1 189 to 210 computations (82.3% saved)

prune13.0ms (1.2%)

Memory

18.2MiB live, 18.2MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	49	2	51

Accuracy

100.0%

Counts

51 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	72.7%	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	67.0%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))

Compiler

Compiled 38 to 26 computations (31.6% saved)

regimes7.0ms (0.7%)

Memory

13.5MiB live, 13.5MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

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

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

Calls

5 calls:

1.0ms	y
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	x
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.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`
87.0%	2	`y`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes7.0ms (0.7%)

Memory

-35.4MiB live, 11.1MiB allocated; 3ms 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)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
67.0%	1	`y`
67.0%	1	`(*.f64 x x)`
67.0%	1	`(+.f64 (*.f64 x x) y)`
67.0%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
67.0%	1	`x`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch9.0ms (0.8%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
8.0ms	5.357459509483117e+113	3.2715014434758585e+125

Samples

4.0ms	96×	0	valid
0.0ms	1×	0	invalid

Compiler

Compiled 123 to 106 computations (13.8% saved)

Precisions

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

ival-mult: 1.0ms (47.9% of total)

ival-sqrt: 1.0ms (47.9% of total)

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

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

adjust: 0.0ms (0% of total)

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

simplify11.0ms (1%)

Memory

13.0MiB live, 13.0MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	36
1	20	36
2	39	36
3	66	36
4	81	36

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 199999999999999984973552323798576408508934173966967692287845194445058839995158605320632698752563530750306011682731106456567808 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #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 (/.f64 y x) #s(literal 1/2 binary64) x))

Inputs

(if (<=.f64 x #s(literal 199999999999999984973552323798576408508934173966967692287845194445058839995158605320632698752563530750306011682731106456567808 binary64)) (sqrt.f64 (+.f64 (*.f64 x x) y)) #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 (/.f64 y x) #s(literal 1/2 binary64) x))

Outputs
(if (<=.f64 x #s(literal 199999999999999984973552323798576408508934173966967692287845194445058839995158605320632698752563530750306011682731106456567808 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #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 (/.f64 y x) #s(literal 1/2 binary64) x))

Outputs

(if (<=.f64 x #s(literal 199999999999999984973552323798576408508934173966967692287845194445058839995158605320632698752563530750306011682731106456567808 binary64)) (sqrt.f64 (+.f64 (*.f64 x x) y)) #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 (/.f64 y x) #s(literal 1/2 binary64) x))

derivations3.0ms (0.3%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 36 to 15 computations (58.3% saved)

preprocess17.0ms (1.6%)

Memory: 19.8MiB live, 19.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 130 to 70 computations (46.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze29.0ms (2.8%)

sample695.0ms (65.9%)

explain91.0ms (8.7%)

preprocess16.0ms (1.5%)

eval0.0ms (0%)

prune0.0ms (0%)

series9.0ms (0.9%)

rewrite62.0ms (5.9%)

eval6.0ms (0.6%)

prune10.0ms (1%)

series6.0ms (0.5%)

rewrite52.0ms (4.9%)

eval12.0ms (1.1%)

prune13.0ms (1.2%)

regimes7.0ms (0.7%)

regimes7.0ms (0.7%)

bsearch9.0ms (0.8%)

simplify11.0ms (1%)

derivations3.0ms (0.3%)

preprocess17.0ms (1.6%)

end0.0ms (0%)

Profiling