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

start0.0ms (0%)

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

analyze21.0ms (0.6%)

Memory

35.5MiB live, 81.5MiB allocated; 2ms 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)

sample909.0ms (25.5%)

Memory

1.7MiB live, 1 420.7MiB allocated; 375ms collecting garbage

Samples

554.0ms	8 256×	0	valid
15.0ms	342×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 286.0ms

ival-mult: 173.0ms (60.6% of total)

ival-sqrt: 56.0ms (19.6% of total)

ival-add: 44.0ms (15.4% of total)

ival-true: 6.0ms (2.1% of total)

ival-assert: 4.0ms (1.4% of total)

adjust: 3.0ms (1.1% of total)

Bogosity

explain68.0ms (1.9%)

Memory

-4.5MiB live, 132.1MiB allocated; 16ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
77	-	-	`(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	77	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	77
↳	`(*.f64 x x)`	overflow	77

Confusion

	Predicted +	Predicted -
+	77	0
-	0	179

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	77	0	0
-	0	0	179

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	179
1	77

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-add: 5.0ms (37.1% of total)

ival-mult: 4.0ms (29.7% of total)

ival-sqrt: 3.0ms (22.3% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess15.0ms (0.4%)

Memory

33.3MiB live, 33.3MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	32	34
2	86	34
3	132	34
4	178	34
5	180	34
0	5	6
0	8	6
1	13	6
2	32	6
3	59	6
4	74	6
0	74	5

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

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

prune5.0ms (0.1%)

Memory

-51.9MiB live, 0.9MiB allocated; 10ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.1%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated; 0ms collecting garbage

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	1	(+.f64 (*.f64 x x) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	13	16
2	32	16
3	59	16
4	74	16
0	74	14

Stop Event

1×	iter limit
1×	saturated
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 (0.4%)

Memory

35.8MiB live, 35.8MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (*.f64 x x) y)
accuracy	17.87319659203106	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

11.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

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

ival-mult: 2.0ms (40.5% of total)

ival-sqrt: 2.0ms (40.5% of total)

ival-add: 1.0ms (20.2% of total)

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

adjust: 0.0ms (0% of total)

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

series9.0ms (0.3%)

Memory

-32.2MiB live, 13.6MiB allocated; 5ms collecting garbage

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
5.0ms	x	@	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	y	@	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))

simplify158.0ms (4.4%)

Memory

2.3MiB live, 237.8MiB allocated; 36ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	524
1	418	509
2	1636	496
3	7219	494
0	8672	456

Stop Event

1×	iter limit
1×	node limit

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

rewrite232.0ms (6.5%)

Memory

8.1MiB live, 239.0MiB allocated; 42ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	30	14
2	215	14
3	2423	14
0	9078	11

Stop Event

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

Counts

3 → 234

Calls

Call 1

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

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

eval89.0ms (2.5%)

Memory: 18.4MiB live, 110.2MiB allocated; 19ms collecting garbage
Compiler: Compiled 7 790 to 868 computations (88.9% saved)

prune6.0ms (0.2%)

Memory

20.1MiB live, 20.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	255	4	259
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	256	4	260

Accuracy

100.0%

Counts

260 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.1%	(sqrt.f64 (fma.f64 x x y))
▶	61.2%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
▶	42.3%	#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)

simplify41.0ms (1.2%)

Memory

-26.7MiB live, 12.0MiB allocated; 11ms collecting garbage

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 #s(literal 1/2 binary64) x)
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
cost-diff	0	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y 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	29	57
2	58	57
3	103	57
4	151	57
5	192	57
6	196	57
0	196	57

Stop Event

1×	iter limit
1×	saturated
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 #s(literal 1/2 binary64) x) y x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
y
(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 #s(literal 1/2 binary64) x) y x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
y
(sqrt.f64 (fma.f64 x x y))
(fma.f64 x x y)
x
y

localize106.0ms (3%)

Memory

6.7MiB live, 112.9MiB allocated; 36ms collecting garbage

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 x x y)
accuracy	9.9769310956209	(sqrt.f64 (fma.f64 x x y))
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.05859375	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
accuracy	24.810813375089253	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
accuracy	0.0	(sqrt.f64 y)
accuracy	18.922264075903673	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0.0	(neg.f64 x)
accuracy	45.300760984511236	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Samples

89.0ms	184×	0	valid
7.0ms	72×	0	invalid

Compiler

Compiled 52 to 13 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-sqrt: 51.0ms (61.2% of total)

ival-mult: 25.0ms (30% of total)

ival-add: 3.0ms (3.6% of total)

ival-div: 2.0ms (2.4% of total)

ival-neg: 1.0ms (1.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.2%)

Memory

20.5MiB live, 20.5MiB allocated; 0ms collecting garbage

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 #s(literal 1/2 binary64) x) y x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(/.f64 #s(literal 1/2 binary64) 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)
(/ 1/2 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
1.0ms	x	@	0	((sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 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)) (+ (* (/ 1/2 x) y) x) (/ 1/2 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)) (+ (* (/ 1/2 x) y) x) (/ 1/2 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)) (+ (* (/ 1/2 x) y) x) (/ 1/2 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)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (+ (* x x) y))

simplify343.0ms (9.6%)

Memory

-3.2MiB live, 265.8MiB allocated; 145ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	571
1	456	556
2	1736	524
3	7700	524
0	8187	485

Stop Event

1×	iter limit
1×	node limit

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

rewrite228.0ms (6.4%)

Memory

23.7MiB live, 263.6MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
0	21	50
1	60	50
2	394	50
3	4683	50
0	8155	50

Stop Event

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

Counts

9 → 188

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 #s(literal 1/2 binary64) x) y x))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
(/.f64 #s(literal 1/2 binary64) x)
(sqrt.f64 (fma.f64 x x y))
(fma.f64 x x y)

Outputs
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
(*.f64 (pow.f64 (pow.f64 y #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 y #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (neg.f64 (neg.f64 y)) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 (neg.f64 y)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (neg.f64 (fabs.f64 y)) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 (fabs.f64 y)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (fabs.f64 (fabs.f64 y)) #s(literal 1/4 binary64)) (pow.f64 (fabs.f64 (fabs.f64 y)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (neg.f64 y) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 y) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (fabs.f64 y) #s(literal 1/4 binary64)) (pow.f64 (fabs.f64 y) #s(literal 1/4 binary64)))
(*.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 (neg.f64 (pow.f64 y #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (pow.f64 y #s(literal 1/4 binary64))) #s(literal 2 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 (neg.f64 y) #s(literal 1/2 binary64))
(pow.f64 (fabs.f64 y) #s(literal 1/2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 y #s(literal 1/2 binary64))
(sqrt.f64 y)
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 y))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 y #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 y)) #s(literal 1/4 binary64)))
(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 (/.f64 #s(literal 1/2 binary64) x) y x))
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))))
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (fma.f64 (neg.f64 x) x (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
(.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 4 binary64)) (pow.f64 (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (.f64 (-.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x)))
(.f64 (/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (/.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 6 binary64)) #s(literal 1/64 binary64) (pow.f64 (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x) #s(literal 3 binary64)))) (fma.f64 (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x) (-.f64 (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))) (pow.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 4 binary64))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y (neg.f64 x)) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) (neg.f64 x)) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)))
(.f64 (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x)) (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x) (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)) #s(literal 2 binary64)) (pow.f64 (.f64 x (/.f64 x (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)) (.f64 x (/.f64 x (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x))) #s(literal 2 binary64))) (-.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64))) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)) #s(literal 3 binary64)) (pow.f64 (.f64 x (/.f64 x (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)) (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)) (.f64 x (/.f64 x (-.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) y) x)))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x))) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) x) y)) x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64)))) (neg.f64 (-.f64 x (*.f64 (/.f64 #s(literal 1/2 binary64) x) y))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) x) y) x))))
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(*.f64 (pow.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 y (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y (*.f64 x x)) y))))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (.f64 (-.f64 y (.f64 x x)) y) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x y)))
(*.f64 (neg.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 x x y)) (pow.f64 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (*.f64 x x) y)) #s(literal 1/2 binary64)))
(pow.f64 (neg.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 x x y))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) y))))
(/.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 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (hypot.f64 y (.f64 x x)) (sqrt.f64 (-.f64 y (.f64 x x))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (fma.f64 x x y))
(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 (exp.f64 (log.f64 (fma.f64 x x y)))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x y))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (fma.f64 x x y)))) (sinh.f64 (log.f64 (sqrt.f64 (fma.f64 x x y)))))
(*.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x y))
(.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y (*.f64 x x)) y)))
(.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (-.f64 y (.f64 x x)) y) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 x x y) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (fma.f64 x x y) (/.f64 (-.f64 (.f64 x x) y) (-.f64 (*.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (.f64 x x))) #s(literal 2 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (.f64 x x))) (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64))) (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (.f64 x x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (.f64 x x))) (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) 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 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (fma.f64 y y (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 y (*.f64 x x))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 y y))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 3 binary64)))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))
(/.f64 (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (-.f64 y (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) (.f64 (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (fma.f64 (.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (-.f64 (*.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (.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 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 x x) y))
(/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))
(neg.f64 (/.f64 (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 x x) y)))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(neg.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 y (*.f64 x x))))
(neg.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 x x) y)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x y) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (.f64 x x) y)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y (.f64 x x)) y)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (-.f64 y (.f64 x x)) y) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y (.f64 x x)) y)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (-.f64 y (.f64 x x)) y) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) y)
(fma.f64 (.f64 (neg.f64 x) x) (/.f64 (.f64 (neg.f64 x) x) (-.f64 (.f64 x x) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (*.f64 x x) y)))
(fma.f64 (pow.f64 y #s(literal 3/2 binary64)) (/.f64 (pow.f64 y #s(literal 3/2 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (neg.f64 x) (-.f64 (.f64 x x) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (*.f64 x x) y)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (-.f64 (.f64 x x) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (*.f64 x x) y)))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (.f64 y y) (/.f64 y (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (.f64 x x) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (neg.f64 x) (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 x x) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (*.f64 x x) y)))
(fma.f64 (neg.f64 x) (neg.f64 x) y)
(fma.f64 y (/.f64 (.f64 y y) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (*.f64 x x) y)))
(fma.f64 (.f64 x x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 x x) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (*.f64 x x) y)))
(fma.f64 x x y)
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (.f64 x x))) (.f64 y (/.f64 y (-.f64 (*.f64 x x) y))))
(-.f64 y (*.f64 (neg.f64 x) x))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (.f64 x x))) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (*.f64 x x) y)))
(+.f64 y (*.f64 x x))
(+.f64 (*.f64 x x) y)

eval70.0ms (2%)

Memory: -9.8MiB live, 96.0MiB allocated; 8ms collecting garbage
Compiler: Compiled 6 217 to 802 computations (87.1% saved)

prune19.0ms (0.5%)

Memory

-28.7MiB live, 18.2MiB allocated; 2ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	215	5	220

Accuracy

100.0%

Counts

220 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	72.1%	(sqrt.f64 (fma.f64 x x y))
▶	32.9%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	61.2%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	42.3%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 46 to 34 computations (26.1% saved)

simplify4.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x x) y) (*.f64 x x))
cost-diff	0	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	9	23
1	14	23
2	33	23
3	60	23
4	75	23
0	75	21

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize15.0ms (0.4%)

Memory

21.9MiB live, 21.9MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	17.87319659203106	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
accuracy	25.23941232679431	#s(approx (+ (* x x) y) (*.f64 x x))

Samples

11.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-mult: 2.0ms (40.7% of total)

ival-sqrt: 2.0ms (40.7% of total)

ival-add: 1.0ms (20.4% of total)

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

adjust: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

3.3MiB live, 3.2MiB allocated; 0ms collecting garbage

Counts

3 → 28

Calls

Call 1

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

Calls

6 calls:

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

simplify173.0ms (4.9%)

Memory

-24.8MiB live, 157.0MiB allocated; 30ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	524
1	418	509
2	1631	496
3	7210	494
0	8672	456

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 26

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))))))))))
y
(+ y (pow x 2))
(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) (+ 1 (/ 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)))))))))
(* 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 (/ (pow x 2) y)) 1)))

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

rewrite220.0ms (6.2%)

Memory

9.8MiB live, 205.2MiB allocated; 63ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
0	9	22
1	31	22
2	210	22
3	2352	22
0	8907	20

Stop Event

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

Counts

3 → 38

Calls

Call 1

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

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

eval8.0ms (0.2%)

Memory: 21.1MiB live, 21.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 428 to 250 computations (82.5% saved)

prune23.0ms (0.6%)

Memory

-39.3MiB live, 7.9MiB allocated; 2ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	63	5	68

Accuracy

100.0%

Counts

68 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	72.1%	(sqrt.f64 (fma.f64 x x y))
✓	32.9%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	61.2%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	42.3%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 98 to 54 computations (44.9% saved)

regimes12.0ms (0.3%)

Memory

23.5MiB live, 23.5MiB allocated; 0ms collecting garbage

Counts

6 → 2

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	y
2.0ms	(+.f64 (*.f64 x x) y)
2.0ms	x
2.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`(*.f64 x x)`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`x`
85.1%	2	`y`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes9.0ms (0.2%)

Memory

16.9MiB live, 16.9MiB allocated; 0ms collecting garbage

Counts

5 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

regimes20.0ms (0.6%)

Memory

-36.1MiB live, 19.4MiB allocated; 3ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
72.1%	1	`y`
72.1%	1	`(*.f64 x x)`
72.1%	1	`(+.f64 (*.f64 x x) y)`
72.1%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
72.1%	1	`x`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes8.0ms (0.2%)

Memory

15.1MiB live, 15.1MiB allocated; 0ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
60.4%	2	`x`
59.2%	2	`y`
60.4%	2	`(*.f64 x x)`
44.5%	2	`(+.f64 (*.f64 x x) y)`
44.5%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes7.0ms (0.2%)

Memory

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

Counts

2 → 1

Calls

Call 1

Inputs
#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))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
42.3%	1	`(+.f64 (*.f64 x x) y)`
42.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
42.3%	1	`y`
42.3%	1	`(*.f64 x x)`
42.3%	1	`x`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes18.0ms (0.5%)

Memory

-36.0MiB live, 11.2MiB allocated; 2ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

13.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	y
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	x
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
1.3%	1	`y`
1.3%	1	`(*.f64 x x)`
1.3%	1	`(+.f64 (*.f64 x x) y)`
1.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.3%	1	`x`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch3.0ms (0.1%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
3.0ms	1.4869732102187018e+116	1.0826947349666688e+117

Samples

1.0ms

32×

valid

Compiler

Compiled 47 to 42 computations (10.6% 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)

bsearch1.0ms (0%)

Memory

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

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
0.0ms	1.4869732102187018e+116	1.0826947349666688e+117

Compiler

Compiled 45 to 40 computations (11.1% saved)

bsearch12.0ms (0.3%)

Memory

12.0MiB live, 12.0MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	3.1539769782726063e-84	1.7771390479382865e-82

Samples

5.0ms	112×	0	valid
1.0ms	26×	0	invalid

Compiler

Compiled 142 to 122 computations (14.1% saved)

Precisions

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

ival-add: 1.0ms (37.4% of total)

ival-mult: 1.0ms (37.4% of total)

ival-sqrt: 1.0ms (37.4% of total)

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

adjust: 0.0ms (0% of total)

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

simplify11.0ms (0.3%)

Memory

14.2MiB live, 14.2MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	91
1	36	91
2	56	91
3	83	91
4	98	91

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 500000000000000025277713862997516907114118515401501639510240737361116381988542702912116688552531109626208556618350592 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(if (<=.f64 x #s(literal 500000000000000025277713862997516907114118515401501639510240737361116381988542702912116688552531109626208556618350592 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 x #s(literal 640796110776273/4271974071841820164790043412339104229205409044713305539894083215644439451561281100045924173873152 binary64)) #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Outputs
(if (<=.f64 x #s(literal 500000000000000025277713862997516907114118515401501639510240737361116381988542702912116688552531109626208556618350592 binary64)) (sqrt.f64 (+.f64 (.f64 x x) y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(if (<=.f64 x #s(literal 500000000000000025277713862997516907114118515401501639510240737361116381988542702912116688552531109626208556618350592 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 x #s(literal 640796110776273/4271974071841820164790043412339104229205409044713305539894083215644439451561281100045924173873152 binary64)) #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

derivations626.0ms (17.6%)

Memory

-44.5MiB live, 588.2MiB allocated; 211ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	524
1	418	509
2	1636	496
3	7219	494
0	8672	456
0	149	571
1	456	556
2	1736	524
3	7700	524
0	8187	485
0	5	14
0	8	14
1	30	14
2	215	14
3	2423	14
0	9078	11

Stop Event

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

Compiler

Compiled 91 to 27 computations (70.3% saved)

preprocess46.0ms (1.3%)

Memory: 12.9MiB live, 111.3MiB allocated; 17ms collecting garbage
Compiler: Compiled 298 to 126 computations (57.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze21.0ms (0.6%)

sample909.0ms (25.5%)

explain68.0ms (1.9%)

preprocess15.0ms (0.4%)

eval0.0ms (0%)

prune5.0ms (0.1%)

simplify4.0ms (0.1%)

localize15.0ms (0.4%)

series9.0ms (0.3%)

simplify158.0ms (4.4%)

rewrite232.0ms (6.5%)

eval89.0ms (2.5%)

prune6.0ms (0.2%)

simplify41.0ms (1.2%)

localize106.0ms (3%)

series7.0ms (0.2%)

simplify343.0ms (9.6%)

rewrite228.0ms (6.4%)

eval70.0ms (2%)

prune19.0ms (0.5%)

simplify4.0ms (0.1%)

localize15.0ms (0.4%)

series2.0ms (0.1%)

simplify173.0ms (4.9%)

rewrite220.0ms (6.2%)

eval8.0ms (0.2%)

prune23.0ms (0.6%)

regimes12.0ms (0.3%)

regimes9.0ms (0.2%)

regimes20.0ms (0.6%)

regimes8.0ms (0.2%)

regimes7.0ms (0.2%)

regimes18.0ms (0.5%)

bsearch3.0ms (0.1%)

bsearch1.0ms (0%)

bsearch12.0ms (0.3%)

simplify11.0ms (0.3%)

derivations626.0ms (17.6%)

preprocess46.0ms (1.3%)

end0.0ms (0%)

Profiling