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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze21.0ms (0.6%)

Memory

2.2MiB live, 39.6MiB allocated

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)

sample717.0ms (22.1%)

Memory

-19.8MiB live, 1 177.4MiB allocated

Samples

438.0ms	8 256×	0	valid
15.0ms	304×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 203.0ms

ival-mult: 87.0ms (42.9% of total)

ival-sqrt: 61.0ms (30.1% of total)

ival-add: 45.0ms (22.2% of total)

ival-true: 6.0ms (3% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain62.0ms (1.9%)

Memory

15.0MiB live, 130.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
85	-	-	`(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	85	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	85
↳	`(*.f64 x x)`	overflow	85

Confusion

	Predicted +	Predicted -
+	85	0
-	0	171

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	85	0	0
-	0	0	171

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	171
1	85

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms

512×

valid

Compiler

Compiled 58 to 24 computations (58.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 4.0ms (37.2% of total)

ival-sqrt: 4.0ms (37.2% of total)

ival-add: 2.0ms (18.6% of total)

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

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

preprocess374.0ms (11.5%)

Memory

-23.2MiB live, 340.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	46	32
2	128	32
3	410	32
4	1207	32
5	1638	32
6	1997	32
7	4040	32
8	4660	32
9	5130	32
10	5656	32
11	6034	32
12	6510	32
13	6798	32
14	7580	32
0	5	6
0	8	6
1	14	6
2	38	6
3	128	6
4	443	6
5	739	6
6	1331	6
7	3315	6
8	4082	6
9	4871	6
10	5223	6
11	5577	6
12	6118	6
13	6375	6
14	7978	6
0	8057	5

Stop Event

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

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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	69.1%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify227.0ms (7%)

Memory

16.7MiB live, 207.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 (*.f64 x x) y))
cost-diff	128	(+.f64 (*.f64 x x) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	14	16
2	38	16
3	128	16
4	443	16
5	739	16
6	1331	16
7	3315	16
8	4082	16
9	4871	16
10	5223	16
11	5577	16
12	6118	16
13	6375	16
14	7978	16
0	8057	14

Stop Event

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

Calls

Call 1

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

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

localize15.0ms (0.5%)

Memory

24.5MiB live, 24.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(+.f64 (*.f64 x x) y)
accuracy	19.773575176949787	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

11.0ms

256×

valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (39.3% of total)

ival-sqrt: 2.0ms (39.3% of total)

ival-add: 1.0ms (19.7% of total)

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

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

series6.0ms (0.2%)

Memory

-30.2MiB live, 8.9MiB allocated

Counts

3 → 28

Calls

Call 1

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

Outputs
y
(+ y (pow x 2))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (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))))))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -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))))))))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* 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)))))))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))

Calls

6 calls:

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

simplify24.0ms (0.7%)

Memory

34.4MiB live, 34.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	530
0	422	500

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

28 → 26

Calls

Call 1

Inputs
y
(+ y (pow x 2))
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (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))))))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -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))))))))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* 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)))))))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))

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

rewrite140.0ms (4.3%)

Memory

-14.4MiB live, 137.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	31	14
2	235	14
3	2618	14
0	9576	11

Stop Event

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

Counts

3 → 340

Calls

Call 1

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

Outputs
(*.f64 (exp.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x y)))))
(*.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 x x y) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 x x y) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (*.f64 (fma.f64 x x y) y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) (fma.f64 x x y))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 x x y) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 (fma.f64 x x y) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))
(*.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 x x y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 x x y) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 #s(literal -1 binary64) (fma.f64 x x y))
(*.f64 (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (pow.f64 (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))
(*.f64 #s(literal 1 binary64) (fma.f64 x x y))
(*.f64 (fma.f64 x x y) (/.f64 (fma.f64 x x y) (fma.f64 x x y)))
(.f64 (fma.f64 x x y) (.f64 (fma.f64 x x y) (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (fma.f64 x x y) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) #s(literal 2 binary64)) (pow.f64 (*.f64 y (/.f64 y (fma.f64 x x y))) #s(literal 2 binary64)))) (fma.f64 x x y))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)))) (fma.f64 x x y))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 y (/.f64 y (fma.f64 x x y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (*.f64 y (/.f64 y (fma.f64 x x y))))))))
(/.f64 (neg.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64)))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (fma.f64 x x y))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (.f64 (fma.f64 x x y) (*.f64 y y)))) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))))) (neg.f64 (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))))
(/.f64 (neg.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))))
(/.f64 (neg.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (.f64 y y) (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 x x y) #s(literal 1 binary64))) (.f64 (fma.f64 x x y) (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 y y) (fma.f64 x x y)) (*.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))
(/.f64 (-.f64 (fma.f64 x x y) (.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (.f64 (neg.f64 y) y))) (*.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x y)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x y) (.f64 y y))) (.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 x x y) (*.f64 y y))))
(/.f64 (-.f64 (fma.f64 x x y) (.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (.f64 y y))) (*.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x y)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (fma.f64 x x y) (.f64 y y))) (.f64 (fma.f64 x x y) #s(literal 1 binary64))) (.f64 (fma.f64 x x y) (/.f64 (fma.f64 x x y) (*.f64 y y))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (.f64 (fma.f64 x x y) (*.f64 (neg.f64 y) y))) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64)))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64)))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (*.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64)))) (.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (*.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x y) (.f64 y y)) (.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 x x y) (.f64 y y))))
(/.f64 (+.f64 (fma.f64 x x y) (.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (.f64 y y))) (*.f64 (/.f64 (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x y)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (fma.f64 x x y) (.f64 y y)) (.f64 (fma.f64 x x y) #s(literal 1 binary64))) (.f64 (fma.f64 x x y) (/.f64 (fma.f64 x x y) (.f64 y y))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y) (.f64 (fma.f64 x x y) (.f64 y y))) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64)))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) #s(literal 1 binary64))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) (.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64))) (.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) (pow.f64 y #s(literal 3 binary64)))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (.f64 (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 6 binary64))) (/.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64)))))
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(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) #s(literal 2 binary64)) (pow.f64 (*.f64 y (/.f64 y (fma.f64 x x y))) #s(literal 2 binary64)))) (hypot.f64 (sqrt.f64 y) x))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)))) (hypot.f64 (sqrt.f64 y) x))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 y (/.f64 y (fma.f64 x x y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (*.f64 y (/.f64 y (fma.f64 x x y))))))))
(/.f64 (sqrt.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))))))
(/.f64 (sqrt.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 (pow.f64 (*.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (fma.f64 x x y))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (.f64 (fma.f64 x x y) (.f64 y y)))) (hypot.f64 y (.f64 x x)))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))) (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (hypot.f64 y (*.f64 x x))) (neg.f64 (hypot.f64 (sqrt.f64 y) x)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x y) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (fma.f64 x x y))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (*.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9 binary64))) (sqrt.f64 (*.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal 3 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (fabs.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64)))
(/.f64 (hypot.f64 y (.f64 x x)) (sqrt.f64 (-.f64 (.f64 x x) (neg.f64 y))))
(/.f64 (hypot.f64 y (*.f64 x x)) (hypot.f64 (sqrt.f64 y) x))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (hypot.f64 y (*.f64 x x)))
(sqrt.f64 (fma.f64 x x y))
(fabs.f64 (neg.f64 (hypot.f64 (sqrt.f64 y) x)))
(fabs.f64 (hypot.f64 (sqrt.f64 y) x))
(hypot.f64 (sqrt.f64 (neg.f64 (neg.f64 y))) (-.f64 x #s(literal 0 binary64)))
(hypot.f64 (sqrt.f64 (neg.f64 (neg.f64 y))) x)
(hypot.f64 (sqrt.f64 (neg.f64 y)) (-.f64 x #s(literal 0 binary64)))
(hypot.f64 (sqrt.f64 (neg.f64 y)) x)
(hypot.f64 (sqrt.f64 y) (-.f64 x #s(literal 0 binary64)))
(hypot.f64 (sqrt.f64 y) x)
(hypot.f64 (-.f64 x #s(literal 0 binary64)) (sqrt.f64 (neg.f64 (neg.f64 y))))
(hypot.f64 (-.f64 x #s(literal 0 binary64)) (sqrt.f64 (neg.f64 y)))
(hypot.f64 (-.f64 x #s(literal 0 binary64)) (sqrt.f64 y))
(hypot.f64 x (sqrt.f64 (neg.f64 (neg.f64 y))))
(hypot.f64 x (sqrt.f64 (neg.f64 y)))
(hypot.f64 x (sqrt.f64 y))
(exp.f64 (fma.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/4 binary64) (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 y) x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (hypot.f64 (sqrt.f64 y) x)))
(+.f64 (cosh.f64 (log.f64 (hypot.f64 (sqrt.f64 y) x))) (sinh.f64 (log.f64 (hypot.f64 (sqrt.f64 y) x))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (.f64 x x))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (-.f64 x #s(literal 0 binary64)) (-.f64 x #s(literal 0 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x))
(.f64 #s(literal -1 binary64) (.f64 x x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(fabs.f64 (-.f64 (*.f64 x x) #s(literal 0 binary64)))
(fabs.f64 (*.f64 (-.f64 x #s(literal 0 binary64)) x))
(fabs.f64 (*.f64 x (-.f64 x #s(literal 0 binary64))))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval129.0ms (4%)

Memory: 18.8MiB live, 141.2MiB allocated
Compiler: Compiled 7 938 to 1 139 computations (85.7% saved)

prune9.0ms (0.3%)

Memory

-18.1MiB live, 20.9MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	362	4	366
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	363	4	367

Accuracy

100.0%

Counts

367 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	69.1%	(sqrt.f64 (fma.f64 x x y))
▶	68.3%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
▶	34.7%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 36 to 27 computations (25% saved)

simplify231.0ms (7.1%)

Memory

-7.4MiB live, 191.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 x x y)
cost-diff	0	(sqrt.f64 (fma.f64 x x y))
cost-diff	0	(/.f64 y x)
cost-diff	0	(fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x)
cost-diff	0	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
0	21	57
1	34	57
2	73	57
3	222	57
4	667	57
5	1139	57
6	1994	57
7	4071	57
8	4868	57
9	5658	57
10	6014	57
11	6368	57
12	6909	57
13	7166	57
0	8270	57

Stop Event

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

Calls

Call 1

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

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

localize106.0ms (3.3%)

Memory

-4.2MiB live, 83.6MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x y)
accuracy	10.476073992605635	(sqrt.f64 (fma.f64 x x y))
accuracy	0	(fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x)
accuracy	0	(/.f64 y x)
accuracy	20.22005981386745	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 y x) #s(literal 1/2 binary64) x))
accuracy	0	(sqrt.f64 y)
accuracy	20.56933891148905	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0	(neg.f64 x)
accuracy	42.11135774825348	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Samples

61.0ms	171×	0	valid
37.0ms	85×	0	invalid

Compiler

Compiled 112 to 28 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 33.0ms (57.1% of total)

ival-sqrt: 19.0ms (32.9% of total)

ival-div: 2.0ms (3.5% of total)

ival-add: 2.0ms (3.5% of total)

ival-neg: 1.0ms (1.7% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

15.3MiB live, 15.3MiB allocated

Counts

9 → 34

Calls

Call 1

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

Outputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (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))))))))))
(* -1 x)
(* 1/2 (/ y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ y x)
y
(+ y (pow x 2))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -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))))))))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* 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)))))))))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

Calls

6 calls:

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

simplify27.0ms (0.8%)

Memory

8.4MiB live, 44.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	579
0	463	547

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

34 → 32

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (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))))))))))
(* -1 x)
(* 1/2 (/ y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ y x)
y
(+ y (pow x 2))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -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))))))))
(* -1 (* x (- (* -1/2 (/ y (pow x 2))) 1)))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* 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)))))))))
(* y (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ 1 (/ (pow x 2) y)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) (* 1/2 (/ 1 x)))))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))

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

rewrite152.0ms (4.7%)

Memory

-23.3MiB live, 136.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	50
0	21	50
1	69	50
2	489	48
3	6852	48
0	8076	48

Stop Event

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

Counts

9 → 339

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) y)) x)
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 #s(literal 1 binary64) x)
(.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 x x) (pow.f64 x #s(literal -1 binary64)))
(*.f64 x #s(literal -1 binary64))
(*.f64 x #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 x x))
(/.f64 (*.f64 x x) x)
(/.f64 x #s(literal -1 binary64))
(/.f64 x #s(literal 1 binary64))
(neg.f64 x)
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) #s(literal 0 binary64))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x #s(literal 0 binary64))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) x #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) x #s(literal 0 binary64))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 0 binary64))
(fma.f64 (*.f64 x x) (pow.f64 x #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 x #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 x #s(literal 1 binary64) #s(literal 0 binary64))
(sqrt.f64 (*.f64 x x))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 x x)) x)
(-.f64 (/.f64 #s(literal 0 binary64) x) x)
(-.f64 #s(literal 0 binary64) x)
(fabs.f64 (-.f64 x #s(literal 0 binary64)))
(fabs.f64 x)
(exp.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(+.f64 (cosh.f64 (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))) (sinh.f64 (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 1 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 1 binary64))))
(+.f64 #s(literal 0 binary64) x)
(+.f64 x #s(literal 0 binary64))
x
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
(*.f64 (neg.f64 (pow.f64 y #s(literal 1/4 binary64))) (neg.f64 (pow.f64 y #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 y #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 y #s(literal 1/4 binary64))))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 y #s(literal 1/2 binary64))
(sqrt.f64 y)
(fabs.f64 (sqrt.f64 y))
(exp.f64 (log.f64 (sqrt.f64 y)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 y))) (sinh.f64 (log.f64 (sqrt.f64 y))))
#s(approx (sqrt (+ (* x x) y)) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))
(.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 x y) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 4 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) x) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) x)))
(.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 x y) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 6 binary64)))) (fma.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) x) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) x)) (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 x x (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 2 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 x x (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 2 binary64))) (fma.f64 x x (pow.f64 (*.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 2 binary64)))) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))
(.f64 (/.f64 (fma.f64 x x (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 2 binary64))) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 x y) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1/4 binary64) (*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) x)))
(.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 x y) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) (pow.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) x)) #s(literal -1 binary64))))
(.f64 (pow.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal -2 binary64)) #s(literal 1/4 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) x)) #s(literal -1 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 x y) #s(literal -3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) #s(literal -1 binary64)) (fma.f64 x x (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 2 binary64))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x)))
(.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) (.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) #s(literal -1 binary64))))
(.f64 (fma.f64 x x (pow.f64 (.f64 #s(literal -1/2 binary64) (/.f64 y x)) #s(literal 2 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1/2 binary64) (/.f64 y x) x))
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(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (*.f64 x x) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x x y)) (neg.f64 (*.f64 y (/.f64 y (fma.f64 x x (neg.f64 y))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x x y)) (/.f64 (*.f64 (neg.f64 y) y) (fma.f64 x x (neg.f64 y))))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 y (/.f64 (*.f64 y y) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 y #s(literal 1 binary64) (*.f64 x x))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 x x (neg.f64 y))) (neg.f64 (*.f64 y (/.f64 y (fma.f64 x x (neg.f64 y))))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 x x (neg.f64 y))) (/.f64 (*.f64 (neg.f64 y) y) (fma.f64 x x (neg.f64 y))))
(fma.f64 (*.f64 x x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (*.f64 x x) #s(literal -1 binary64) y)
(fma.f64 (*.f64 x x) #s(literal 1 binary64) y)
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (neg.f64 y))) (neg.f64 (*.f64 y (/.f64 y (fma.f64 x x (neg.f64 y))))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (neg.f64 y))) (/.f64 (*.f64 (neg.f64 y) y) (fma.f64 x x (neg.f64 y))))
(fma.f64 x x y)
(-.f64 (/.f64 (*.f64 y y) (fma.f64 x x y)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (*.f64 y (/.f64 y (fma.f64 x x (neg.f64 y)))))
(-.f64 #s(literal 0 binary64) (fma.f64 x x (neg.f64 y)))
(-.f64 y (*.f64 x x))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 x x y) y (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (neg.f64 (*.f64 y (/.f64 y (fma.f64 x x (neg.f64 y))))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x y)) (/.f64 (*.f64 (neg.f64 y) y) (fma.f64 x x (neg.f64 y))))
(+.f64 y (*.f64 x x))
(+.f64 (*.f64 x x) y)

eval47.0ms (1.4%)

Memory: 19.2MiB live, 55.1MiB allocated
Compiler: Compiled 9 033 to 1 176 computations (87% saved)

prune33.0ms (1%)

Memory

-37.3MiB live, 25.8MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	369	1	370
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	371	3	374

Accuracy

100.0%

Counts

374 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	69.1%	(sqrt.f64 (fma.f64 x x y))
✓	34.7%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	67.9%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 22 to 17 computations (22.7% saved)

simplify283.0ms (8.7%)

Memory

19.9MiB live, 211.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (sqrt (+ (* x x) y)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
0	6	9
1	12	9
2	36	9
3	126	9
4	447	9
5	740	9
6	1334	9
7	3318	9
8	4085	9
9	4874	9
10	5226	9
11	5580	9
12	6121	9
13	6378	9
14	7981	9
0	8060	8

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Calls

Call 1

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

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

localize14.0ms (0.4%)

Memory

15.7MiB live, 15.7MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
accuracy	20.573435173178197	#s(approx (sqrt (+ (* x x) y)) x)

Samples

10.0ms

256×

valid

Compiler

Compiled 18 to 13 computations (27.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (39.9% of total)

ival-sqrt: 2.0ms (39.9% of total)

ival-add: 1.0ms (20% of total)

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

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

series1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Counts

1 → 22

Calls

Call 1

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

Outputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (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))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -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))))))))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* 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)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	((sqrt (+ (* x x) y)))
0.0ms	y	@	-inf	((sqrt (+ (* x x) y)))
0.0ms	x	@	-inf	((sqrt (+ (* x x) y)))
0.0ms	x	@	inf	((sqrt (+ (* x x) y)))
0.0ms	y	@	inf	((sqrt (+ (* x x) y)))

simplify24.0ms (0.7%)

Memory

-14.8MiB live, 23.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	123	490
0	385	461

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

22 → 21

Calls

Call 1

Inputs
(sqrt y)
(+ (sqrt y) (* 1/2 (* (pow x 2) (sqrt (/ 1 y)))))
(+ (sqrt y) (* (pow x 2) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* 1/2 (sqrt (/ 1 y))))))
(+ (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))))))))))
x
(* x (+ 1 (* 1/2 (/ y (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (+ (* 1/16 (/ (pow y 3) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ y (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 2) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -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))))))))
(+ x (* 1/2 (/ y x)))
(+ x (* y (+ (* -1/8 (/ y (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* y (+ (* y (- (* 1/16 (/ y (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ (sqrt (/ 1 y)) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/8 (* (pow x 4) (sqrt (/ 1 (pow y 5))))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))))))
(* 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)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))

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

rewrite122.0ms (3.8%)

Memory

-5.5MiB live, 113.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
0	6	8
1	29	8
2	233	8
3	2623	8
0	9563	6

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Counts

1 → 1

Calls

Call 1

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

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

eval3.0ms (0.1%)

Memory: 4.2MiB live, 4.2MiB allocated
Compiler: Compiled 615 to 129 computations (79% saved)

prune3.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	22	3	25

Accuracy

100.0%

Counts

25 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	69.1%	(sqrt.f64 (fma.f64 x x y))
✓	34.7%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	67.9%	#s(approx (sqrt (+ (* x x) y)) x)

Compiler

Compiled 72 to 36 computations (50% saved)

regimes13.0ms (0.4%)

Memory

13.3MiB live, 13.3MiB allocated

Counts

6 → 2

Calls

Call 1

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

Calls

5 calls:

3.0ms	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	`x`
83.5%	2	`y`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes28.0ms (0.9%)

Memory

-28.4MiB live, 10.5MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

23.0ms	(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
92.4%	2	`x`
75.4%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
75.4%	2	`(+.f64 (*.f64 x x) y)`
92.4%	2	`(*.f64 x x)`

Compiler

Compiled 15 to 14 computations (6.7% saved)

regimes8.0ms (0.2%)

Memory

14.7MiB live, 14.7MiB allocated

Accuracy

Total -42.6b remaining (-207.2%)

Threshold costs -42.6b (-207.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

1.0ms	x
1.0ms	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
67.9%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
67.9%	1	`(+.f64 (*.f64 x x) y)`
67.9%	1	`y`
67.9%	1	`x`
67.9%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.316874680599413e+263	1.7601223362326704e+264

Compiler

Compiled 9 to 10 computations (-11.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.129590018030353e-137	3.171421291825711e-129

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify54.0ms (1.7%)

Memory

18.4MiB live, 55.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	50

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (*.f64 x x) #s(literal 500000000000000022070259451447643889643195698691290637281503086641722198041511804637241833845925416199409849438773805515698556484214352937342799866667017096235890326785935022607598869817624603345407231591885929026416516254957774801286987505083286521920239280586752 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) x))

(if (<=.f64 (*.f64 x x) #s(literal 8379879956214123/418993997810706159361688281193932691483730181893512293053861295116305125939798343025058571817715732115313495568327689089179808837873330310826051531440128 binary64)) #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #s(approx (sqrt (+ (* x x) y)) x))

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

Outputs

(if (<=.f64 (*.f64 x x) #s(literal 500000000000000022070259451447643889643195698691290637281503086641722198041511804637241833845925416199409849438773805515698556484214352937342799866667017096235890326785935022607598869817624603345407231591885929026416516254957774801286987505083286521920239280586752 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) x))

(if (<=.f64 (*.f64 x x) #s(literal 8379879956214123/418993997810706159361688281193932691483730181893512293053861295116305125939798343025058571817715732115313495568327689089179808837873330310826051531440128 binary64)) #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) #s(approx (sqrt (+ (* x x) y)) x))

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

soundness273.0ms (8.4%)

Memory

-20.4MiB live, 133.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	530
0	422	500
0	5	14
0	8	14
1	31	14
2	235	14
3	2618	14
0	9576	11
0	15	50
0	21	50
1	69	50
2	489	48
3	6852	48
0	8076	48

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Compiler

Compiled 96 to 57 computations (40.6% saved)

preprocess97.0ms (3%)

Memory: -7.4MiB live, 118.3MiB allocated
Compiler: Compiled 208 to 100 computations (51.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze21.0ms (0.6%)

sample717.0ms (22.1%)

explain62.0ms (1.9%)

preprocess374.0ms (11.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify227.0ms (7%)

localize15.0ms (0.5%)

series6.0ms (0.2%)

simplify24.0ms (0.7%)

rewrite140.0ms (4.3%)

eval129.0ms (4%)

prune9.0ms (0.3%)

simplify231.0ms (7.1%)

localize106.0ms (3.3%)

series7.0ms (0.2%)

simplify27.0ms (0.8%)

rewrite152.0ms (4.7%)

eval47.0ms (1.4%)

prune33.0ms (1%)

simplify283.0ms (8.7%)

localize14.0ms (0.4%)

series1.0ms (0%)

simplify24.0ms (0.7%)

rewrite122.0ms (3.8%)

eval3.0ms (0.1%)

prune3.0ms (0.1%)

regimes13.0ms (0.4%)

regimes28.0ms (0.9%)

regimes8.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify54.0ms (1.7%)

soundness273.0ms (8.4%)

preprocess97.0ms (3%)

end0.0ms (0%)

Profiling