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

start0.0ms (0%)

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

analyze33.0ms (2.7%)

Memory

-15.5MiB live, 29.3MiB allocated; 9ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample817.0ms (67.3%)

Memory

39.2MiB live, 1 013.4MiB allocated; 288ms collecting garbage

Samples

462.0ms	8 256×	0	valid
13.0ms	315×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 241.0ms

ival-sqrt: 85.0ms (35.3% of total)

ival-add: 76.0ms (31.6% of total)

ival-mult: 75.0ms (31.2% of total)

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

adjust: 2.0ms (0.8% of total)

Bogosity

explain66.0ms (5.5%)

Memory

3.0MiB live, 100.7MiB allocated; 18ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
88	-	-	`(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	88	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	88
↳	`(*.f64 x x)`	overflow	88

Confusion

	Predicted +	Predicted -
+	88	0
-	0	168

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	88	0	0
-	0	0	168

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	168
1	88

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 4.0ms (38.4% of total)

ival-sqrt: 3.0ms (28.8% of total)

ival-add: 2.0ms (19.2% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess29.0ms (2.4%)

Memory

-27.6MiB live, 18.9MiB allocated; 4ms 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: 0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.0%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series8.0ms (0.6%)

Memory

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

Counts

5 → 31

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) x y)
2.0ms	x	@	0	((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)

rewrite53.0ms (4.3%)

Memory

4.7MiB live, 56.2MiB 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))) (+.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: 8.9MiB live, 8.9MiB 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

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	4	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Accuracy

100.0%

Counts

54 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.0%	(sqrt.f64 (fma.f64 x x y))
▶	33.0%	(sqrt.f64 #s(approx (+ (* x x) y) y))
▶	69.7%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
▶	69.0%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 34 to 25 computations (26.5% saved)

series7.0ms (0.6%)

Memory

10.7MiB live, 10.7MiB allocated; 0ms collecting garbage

Counts

11 → 39

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite50.0ms (4.1%)

Memory

1.6MiB live, 48.5MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	198	902
0	203	825
0	1046	794

Stop Event

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

Counts

50 → 70

Calls

Call 1

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

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

eval20.0ms (1.6%)

Memory: -31.7MiB live, 15.2MiB allocated; 2ms collecting garbage
Compiler: Compiled 1 393 to 273 computations (80.4% saved)

prune4.0ms (0.4%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	79	4	83

Accuracy

100.0%

Counts

83 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.0%	(sqrt.f64 (fma.f64 x x y))
✓	33.0%	(sqrt.f64 #s(approx (+ (* x x) y) y))
✓	69.7%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
✓	69.0%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 74 to 42 computations (43.2% saved)

regimes10.0ms (0.8%)

Memory

19.0MiB live, 19.0MiB allocated; 0ms collecting garbage

Counts

5 → 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))

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

Calls

5 calls:

2.0ms	y
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`
87.6%	2	`y`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes18.0ms (1.5%)

Memory

-34.1MiB live, 13.3MiB 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))
#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:

12.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	x
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

9.9MiB live, 9.9MiB 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	(+.f64 (*.f64 x x) y)
1.0ms	x
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
87.7%	2	`(*.f64 x x)`
73.2%	2	`(+.f64 (*.f64 x x) y)`
73.2%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
87.7%	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

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:

1.0ms	x
1.0ms	y
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
69.0%	1	`(+.f64 (*.f64 x x) y)`
69.0%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
69.0%	1	`y`
69.0%	1	`(*.f64 x x)`
69.0%	1	`x`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch4.0ms (0.4%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
4.0ms	2.8658143057137426e+137	9.824596619407523e+140

Samples

2.0ms	48×	0	valid
0.0ms	1×	0	invalid

Compiler

Compiled 51 to 49 computations (3.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
0.0ms	2.8658143057137426e+137	9.824596619407523e+140

Compiler

Compiled 48 to 46 computations (4.2% saved)

bsearch9.0ms (0.8%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	1.634652869416524e-41	1.4892611222734442e-40

Samples

4.0ms	96×	0	valid
1.0ms	19×	0	invalid

Compiler

Compiled 105 to 94 computations (10.5% saved)

Precisions

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

ival-add: 1.0ms (43.2% of total)

ival-mult: 1.0ms (43.2% of total)

ival-sqrt: 1.0ms (43.2% of total)

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

adjust: 0.0ms (0% of total)

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

simplify18.0ms (1.5%)

Memory

-31.0MiB live, 17.5MiB allocated; 4ms 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 200000000000000011856760248162974007412724977534090657729700148965999155656947961304046593016036249138303584474586765896459394327029164802048 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #s(approx (sqrt (+ ( x x) y)) x))
(if (<=.f64 x #s(literal 200000000000000011856760248162974007412724977534090657729700148965999155656947961304046593016036249138303584474586765896459394327029164802048 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) x))
(if (<=.f64 x #s(literal 1225996432692711/49039857307708443467467104868809893875799651909875269632 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 200000000000000011856760248162974007412724977534090657729700148965999155656947961304046593016036249138303584474586765896459394327029164802048 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #s(approx (sqrt (+ ( x x) y)) x))
(if (<=.f64 x #s(literal 200000000000000011856760248162974007412724977534090657729700148965999155656947961304046593016036249138303584474586765896459394327029164802048 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) x))
(if (<=.f64 x #s(literal 1225996432692711/49039857307708443467467104868809893875799651909875269632 binary64)) (sqrt.f64 #s(approx (+ (* x x) y) y)) #s(approx (sqrt (+ (* x x) y)) x))
#s(approx (sqrt (+ (* x x) y)) x)

derivations6.0ms (0.5%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 63 to 20 computations (68.3% saved)

preprocess41.0ms (3.4%)

Memory: -4.6MiB live, 41.7MiB allocated; 4ms collecting garbage
Compiler: Compiled 232 to 106 computations (54.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze33.0ms (2.7%)

sample817.0ms (67.3%)

explain66.0ms (5.5%)

preprocess29.0ms (2.4%)

eval0.0ms (0%)

prune0.0ms (0%)

series8.0ms (0.6%)

rewrite53.0ms (4.3%)

eval6.0ms (0.5%)

prune2.0ms (0.2%)

series7.0ms (0.6%)

rewrite50.0ms (4.1%)

eval20.0ms (1.6%)

prune4.0ms (0.4%)

regimes10.0ms (0.8%)

regimes18.0ms (1.5%)

regimes5.0ms (0.4%)

regimes5.0ms (0.4%)

bsearch4.0ms (0.4%)

bsearch0.0ms (0%)

bsearch9.0ms (0.8%)

simplify18.0ms (1.5%)

derivations6.0ms (0.5%)

preprocess41.0ms (3.4%)

end0.0ms (0%)

Profiling