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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze22.0ms (0.6%)

Memory

-1.3MiB live, 43.9MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample794.0ms (22.3%)

Memory

50.0MiB live, 1 168.0MiB allocated

Samples

488.0ms	8 256×	0	valid
16.0ms	358×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 300.0ms

ival-mult: 169.0ms (56.4% of total)

ival-sqrt: 78.0ms (26% of total)

ival-add: 42.0ms (14% of total)

ival-true: 6.0ms (2% of total)

ival-assert: 4.0ms (1.3% of total)

Bogosity

explain67.0ms (1.9%)

Memory

0.5MiB live, 144.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
91	-	-	`(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	91	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	91
↳	`(*.f64 x x)`	overflow	91

Confusion

	Predicted +	Predicted -
+	91	0
-	0	165

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	91	0	0
-	0	0	165

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	165
1	91

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-add: 7.0ms (38.1% of total)

ival-mult: 7.0ms (38.1% of total)

ival-sqrt: 4.0ms (21.8% of total)

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

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

preprocess17.0ms (0.5%)

Memory

-16.1MiB live, 31.0MiB allocated

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, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.0%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Memory

7.3MiB live, 7.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

localize79.0ms (2.2%)

Memory

-27.7MiB live, 30.0MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 (*.f64 x x) y)
accuracy	0.0	(*.f64 x x)
accuracy	21.1315602634943	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

75.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 2.0ms (32.9% of total)

ival-mult: 2.0ms (32.9% of total)

ival-sqrt: 2.0ms (32.9% of total)

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

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

series5.0ms (0.2%)

Memory

7.3MiB live, 7.3MiB allocated

Counts

3 → 28

Calls

Call 1

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

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

Calls

6 calls:

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

simplify156.0ms (4.4%)

Memory

11.3MiB live, 207.4MiB allocated

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)

rewrite110.0ms (3.1%)

Memory

18.9MiB live, 156.9MiB allocated

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))))
(*.f64 (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) (fma.f64 x x y))
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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))))

eval37.0ms (1%)

Memory: -31.8MiB live, 67.9MiB allocated
Compiler: Compiled 7 790 to 868 computations (88.9% saved)

prune5.0ms (0.2%)

Memory

18.7MiB live, 18.7MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	254	5	259
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	255	5	260

Accuracy

100.0%

Counts

260 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.0%	(sqrt.f64 (fma.f64 x x y))
▶	68.6%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
▶	68.3%	#s(approx (sqrt (+ (* x x) y)) (.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
▶	34.6%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 106 to 78 computations (26.4% saved)

simplify166.0ms (4.7%)

Memory

13.2MiB live, 105.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 y (*.f64 x x))
cost-diff	0	(fma.f64 (/.f64 y (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64))
cost-diff	0	#s(approx (sqrt (+ (* x x) y)) (.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
cost-diff	4	(.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
cost-diff	0	(fma.f64 x x y)
cost-diff	0	(sqrt.f64 (fma.f64 x x y))
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))
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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	103
0	32	95
1	49	95
2	111	95
3	294	95
4	944	95
5	2737	95
6	3896	95
7	4206	95
8	4301	95
9	4343	95
10	4359	95
11	4359	95
12	4507	95
13	4771	95
14	4839	95
15	4839	95
16	4863	95
17	6037	95
18	6189	95
19	6189	95
20	6189	95
21	7401	95
0	8141	95

Stop Event

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

Calls

Call 1

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

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

localize58.0ms (1.6%)

Memory

-1.9MiB live, 96.4MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	5.186458932719023	(.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
accuracy	7.7689987961848965	(/.f64 y (*.f64 x x))
accuracy	20.106553827618576	#s(approx (sqrt (+ (* x x) y)) (.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
accuracy	0.0	(fma.f64 x x y)
accuracy	10.91256931103844	(sqrt.f64 (fma.f64 x x y))
accuracy	0.0	(sqrt.f64 y)
accuracy	21.344285016178763	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0.0	(neg.f64 x)
accuracy	42.851246949074245	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.09375	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
accuracy	20.106553827618576	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))

Samples

30.0ms	174×	0	valid
10.0ms	82×	0	invalid

Compiler

Compiled 90 to 18 computations (80% saved)

Precisions

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

ival-mult: 16.0ms (56.8% of total)

ival-div: 4.0ms (14.2% of total)

ival-add: 3.0ms (10.7% of total)

ival-sqrt: 3.0ms (10.7% of total)

ival-neg: 1.0ms (3.6% of total)

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

exact: 0.0ms (0% of total)

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

series19.0ms (0.5%)

Memory

-23.9MiB live, 23.2MiB allocated

Counts

14 → 41

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (* (/ y (* x x)) 1/2) 1) x) (sqrt (+ (* x x) y)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) (* x x))
2.0ms	y	@	0	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (* (/ y (* x x)) 1/2) 1) x) (sqrt (+ (* x x) y)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) (* x x))
2.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (* (/ y (* x x)) 1/2) 1) x) (sqrt (+ (* x x) y)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) (* x x))
2.0ms	x	@	0	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (* (/ y (* x x)) 1/2) 1) x) (sqrt (+ (* x x) y)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) (* x x))
2.0ms	y	@	inf	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (* (+ (* (/ y (* x x)) 1/2) 1) x) (sqrt (+ (* x x) y)) (+ (* (/ y (* x x)) 1/2) 1) (/ y (* x x)) (* x x))

simplify311.0ms (8.7%)

Memory

66.0MiB live, 251.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	615
1	479	592
2	1790	556
3	7021	556
0	8770	510

Stop Event

1×	iter limit
1×	node limit

Counts

41 → 39

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

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

rewrite374.0ms (10.5%)

Memory

-23.2MiB live, 326.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	92
0	32	92
1	96	92
2	612	92
3	7622	92
0	8372	92

Stop Event

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

Counts

14 → 306

Calls

Call 1

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

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

eval57.0ms (1.6%)

Memory: 11.3MiB live, 111.2MiB allocated
Compiler: Compiled 11 043 to 1 311 computations (88.1% saved)

prune16.0ms (0.4%)

Memory

-22.1MiB live, 24.7MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	332	1	333
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	333	5	338

Accuracy

100.0%

Counts

338 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	67.0%	(sqrt.f64 (fma.f64 x x y))
✓	68.3%	#s(approx (sqrt (+ (* x x) y)) (.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
▶	68.4%	#s(approx (sqrt (+ (* x x) y)) (.f64 #s(approx (+ ( (/ y (* x x)) 1/2) 1) #s(literal 1 binary64)) x))
✓	34.6%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 60 to 44 computations (26.7% saved)

simplify10.0ms (0.3%)

Memory

15.1MiB live, 15.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

cost-diff

#s(approx (+ (* (/ y (* x x)) 1/2) 1) #s(literal 1 binary64))

cost-diff

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

cost-diff

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	46
0	14	46
1	28	46
2	78	46
3	186	46
4	367	46
5	457	46
6	469	46
7	476	46
0	476	42

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize46.0ms (1.3%)

Memory

6.4MiB live, 52.7MiB allocated

Localize:

Found 3 expressions of interest:

New

Metric

Score

Program

accuracy

5.186458932719023

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

accuracy

20.106553827618576

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

accuracy

20.464119380956866

#s(approx (+ (* (/ y (* x x)) 1/2) 1) #s(literal 1 binary64))

Samples

40.0ms

256×

valid

Compiler

Compiled 30 to 13 computations (56.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 27.0ms (81.7% of total)

ival-div: 2.0ms (6.1% of total)

ival-add: 2.0ms (6.1% of total)

ival-sqrt: 2.0ms (6.1% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

3 → 33

Calls

Call 1

Inputs

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

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

#s(approx (+ (* (/ y (* x x)) 1/2) 1) #s(literal 1 binary64))

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) x) (+ (* (/ y (* x x)) 1/2) 1))
1.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) x) (+ (* (/ y (* x x)) 1/2) 1))
0.0ms	y	@	inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) x) (+ (* (/ y (* x x)) 1/2) 1))
0.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) x) (+ (* (/ y (* x x)) 1/2) 1))
0.0ms	x	@	inf	((sqrt (+ (* x x) y)) (* (+ (* (/ y (* x x)) 1/2) 1) x) (+ (* (/ y (* x x)) 1/2) 1))

simplify333.0ms (9.3%)

Memory

-25.0MiB live, 214.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	145	577
1	444	554
2	1706	518
3	7193	518
0	8017	475

Stop Event

1×	iter limit
1×	node limit

Counts

33 → 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))))))))))
(* 1/2 (/ y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(* 1/2 (/ y (pow x 2)))
(/ (+ (* 1/2 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)))))))
1
(+ 1 (* 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))))))))
(* -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 y) (* 1/2 (/ 1 (pow x 2)))))
(* -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)))))
(* y (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 y)))

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

rewrite175.0ms (4.9%)

Memory

8.7MiB live, 157.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
0	14	44
1	60	44
2	412	44
3	5394	44
0	8546	40

Stop Event

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

Counts

3 → 4

Calls

Call 1

Inputs

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

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

#s(approx (+ (* (/ y (* x x)) 1/2) 1) #s(literal 1 binary64))

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

eval3.0ms (0.1%)

Memory: 6.0MiB live, 6.0MiB allocated
Compiler: Compiled 712 to 135 computations (81% saved)

prune4.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	27	5	32

Accuracy

100.0%

Counts

32 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	67.0%	(sqrt.f64 (fma.f64 x x y))
✓	68.3%	#s(approx (sqrt (+ (* x x) y)) (.f64 (fma.f64 (/.f64 y (.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x))
✓	68.4%	#s(approx (sqrt (+ (* x x) y)) (.f64 #s(approx (+ ( (/ y (* x x)) 1/2) 1) #s(literal 1 binary64)) x))
✓	34.6%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 139 to 75 computations (46% saved)

regimes48.0ms (1.3%)

Memory

-15.3MiB live, 31.6MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

5 calls:

36.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
3.0ms	(+.f64 (*.f64 x x) y)
3.0ms	y
3.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
83.3%	2	`y`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes7.0ms (0.2%)

Memory

22.3MiB live, 22.3MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
91.5%	2	`x`
75.7%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
75.7%	2	`(+.f64 (*.f64 x x) y)`
91.5%	2	`(*.f64 x x)`

Compiler

Compiled 15 to 14 computations (6.7% saved)

regimes23.0ms (0.6%)

Memory

-12.5MiB live, 37.3MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

17.0ms	x
2.0ms	y
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
68.4%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
68.4%	1	`(+.f64 (*.f64 x x) y)`
68.4%	1	`y`
68.4%	1	`x`
68.4%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes8.0ms (0.2%)

Memory

-28.0MiB live, 18.3MiB allocated

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:

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
1.2%	1	`(*.f64 x x)`
1.2%	1	`x`
1.2%	1	`y`
1.2%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.2%	1	`(+.f64 (*.f64 x x) y)`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.1315947606626716e+164	9.761757338214929e+165

Compiler

Compiled 9 to 10 computations (-11.1% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	5.3062174611928927e-64	8.604771902106136e-63

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify16.0ms (0.5%)

Memory

44.7MiB live, 44.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	95
1	42	95
2	92	95
3	202	95
4	381	95
5	465	95
6	472	95
7	474	95

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) #s(literal 400000000000000000713339979435167346058254570241205570842806111080518011391159814248187483197137184399507588144883912942575230584126514493815012733010253789624532992 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (.f64 #s(approx (+ ( (/ y (* x x)) 1/2) 1) #s(literal 1 binary64)) x)))
(if (<=.f64 (.f64 x x) #s(literal 7410693711188237/7410693711188236507108543040556026102609279018600996098525285376506440296955904 binary64)) #s(approx (sqrt (+ ( x x) y)) (sqrt.f64 y)) #s(approx (sqrt (+ (* x x) y)) (.f64 #s(approx (+ ( (/ y (* x x)) 1/2) 1) #s(literal 1 binary64)) x)))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(approx (+ ( (/ y (* x x)) 1/2) 1) #s(literal 1 binary64)) x))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Outputs
(if (<=.f64 (.f64 x x) #s(literal 400000000000000000713339979435167346058254570241205570842806111080518011391159814248187483197137184399507588144883912942575230584126514493815012733010253789624532992 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (.f64 #s(approx (+ ( (/ y (* x x)) 1/2) 1) #s(literal 1 binary64)) x)))
(if (<=.f64 (.f64 x x) #s(literal 7410693711188237/7410693711188236507108543040556026102609279018600996098525285376506440296955904 binary64)) #s(approx (sqrt (+ ( x x) y)) (sqrt.f64 y)) #s(approx (sqrt (+ (* x x) y)) (.f64 #s(approx (+ ( (/ y (* x x)) 1/2) 1) #s(literal 1 binary64)) x)))
#s(approx (sqrt (+ (* x x) y)) (.f64 #s(approx (+ ( (/ y (* x x)) 1/2) 1) #s(literal 1 binary64)) x))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

soundness529.0ms (14.9%)

Memory

-7.1MiB live, 559.2MiB allocated

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	5	14
0	8	14
1	30	14
2	215	14
3	2423	14
0	9078	11
0	156	615
1	479	592
2	1790	556
3	7021	556
0	8770	510

Stop Event

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

Compiler

Compiled 170 to 88 computations (48.2% saved)

preprocess55.0ms (1.6%)

Memory: -9.5MiB live, 83.1MiB allocated
Compiler: Compiled 322 to 136 computations (57.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze22.0ms (0.6%)

sample794.0ms (22.3%)

explain67.0ms (1.9%)

preprocess17.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize79.0ms (2.2%)

series5.0ms (0.2%)

simplify156.0ms (4.4%)

rewrite110.0ms (3.1%)

eval37.0ms (1%)

prune5.0ms (0.2%)

simplify166.0ms (4.7%)

localize58.0ms (1.6%)

series19.0ms (0.5%)

simplify311.0ms (8.7%)

rewrite374.0ms (10.5%)

eval57.0ms (1.6%)

prune16.0ms (0.4%)

simplify10.0ms (0.3%)

localize46.0ms (1.3%)

series3.0ms (0.1%)

simplify333.0ms (9.3%)

rewrite175.0ms (4.9%)

eval3.0ms (0.1%)

prune4.0ms (0.1%)

regimes48.0ms (1.3%)

regimes7.0ms (0.2%)

regimes23.0ms (0.6%)

regimes8.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify16.0ms (0.5%)

soundness529.0ms (14.9%)

preprocess55.0ms (1.6%)

end0.0ms (0%)

Profiling