Metrics for Optimisation.CirclePacking:place from circle-packing-0.1.0.4, C

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 7 to 7 computations (0% saved)

sample919.0ms (17.8%)

Memory

-111.9MiB live, 861.4MiB allocated

Samples

644.0ms

8 256×

valid

Precisions

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

ival-fabs: 99.0ms (40.8% of total)

ival-sub: 74.0ms (30.5% of total)

ival-sqrt: 61.0ms (25.1% of total)

ival-true: 6.0ms (2.5% of total)

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

Bogosity

explain70.0ms (1.4%)

Memory

-19.2MiB live, 69.6MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`y`
-	-	`(fabs.f64 (-.f64 x y))`
-	-	`(-.f64 x y)`
-	-	`(sqrt.f64 (fabs.f64 (-.f64 x y)))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

24.0ms

512×

valid

Compiler

Compiled 39 to 19 computations (51.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sqrt: 6.0ms (48.1% of total)

ival-sub: 3.0ms (24.1% of total)

ival-fabs: 3.0ms (24.1% of total)

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

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

preprocess56.0ms (1.1%)

Memory

-8.0MiB live, 30.5MiB allocated

Algorithm

1×	egg-herbie

Rules

40×	`lower-fma.f64`
40×	`lower-fma.f32`
26×	`lower-*.f64`
26×	`lower-*.f32`
25×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	35	27
2	72	27
3	137	27
4	185	27
5	197	27
6	199	27
0	5	5
0	8	5
1	12	5
2	19	5
3	27	5
4	46	5
5	93	5
6	144	5
7	165	5
8	173	5
0	173	5

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))

Outputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))

Symmetry

(sort x y)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(-.f64 x y)
cost-diff	0	(fabs.f64 (-.f64 x y))
cost-diff	0	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Rules

40×	`lower-fma.f64`
40×	`lower-fma.f32`
26×	`lower-*.f64`
26×	`lower-*.f32`
17×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	12	14
2	19	14
3	27	14
4	46	14
5	93	14
6	144	14
7	165	14
8	173	14
0	173	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(fabs.f64 (-.f64 x y))
(-.f64 x y)
x
y

Outputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(fabs.f64 (-.f64 x y))
(fabs.f64 (-.f64 y x))
(-.f64 x y)
x
y

localize16.0ms (0.3%)

Memory

15.6MiB live, 15.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x y)
accuracy	0	(fabs.f64 (-.f64 x y))
accuracy	0.01953125	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Samples

10.0ms

256×

valid

Compiler

Compiled 16 to 7 computations (56.3% saved)

Precisions

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

ival-sqrt: 2.0ms (41.7% of total)

ival-sub: 1.0ms (20.9% of total)

ival-fabs: 1.0ms (20.9% of total)

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

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

series188.0ms (3.6%)

Memory

-31.3MiB live, 5.2MiB allocated

Counts

3 → 72

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())
#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())
#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())

Inputs

#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())

#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())

#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())

Outputs
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (neg (+ y (* -1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (neg (+ y (* -1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (neg (+ y (* -1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (neg (+ y (* -1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (+ x (* -1 y)))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (+ x (* -1 y)))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (+ x (* -1 y)))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (+ x (* -1 y)))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 (-.f64 x y))) (patch (sqrt.f64 (fabs.f64 (-.f64 x y))) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (neg (+ y (* -1 x)))) (taylor -inf x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (neg (+ y (* -1 x)))) (taylor -inf x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (neg (+ y (* -1 x)))) (taylor -inf x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (neg (+ y (* -1 x)))) (taylor -inf x) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (+ x (* -1 y))) (taylor -inf y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (+ x (* -1 y))) (taylor -inf y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (+ x (* -1 y))) (taylor -inf y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (fabs (+ x (* -1 y))) (taylor -inf y) (#s(alt (fabs.f64 (-.f64 x y)) (patch (fabs.f64 (-.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (- x y) (taylor 0 x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ y x)))) (taylor inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ y x) 1))) (taylor -inf x) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ x y) 1)) (taylor inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ x y))))) (taylor -inf y) (#s(alt (-.f64 x y) (patch (-.f64 x y) #<representation binary64>) () ())) ())

Calls

18 calls:

Time	Variable		Point	Expression
183.0ms	y	@	inf	(sqrt (fabs (- x y)))
1.0ms	y	@	-inf	(sqrt (fabs (- x y)))
0.0ms	x	@	-inf	(sqrt (fabs (- x y)))
0.0ms	x	@	0	(sqrt (fabs (- x y)))
0.0ms	x	@	inf	(sqrt (fabs (- x y)))

simplify141.0ms (2.7%)

Memory

3.3MiB live, 121.1MiB allocated

Algorithm

1×	egg-herbie

Rules

1 329×	`lower-fma.f64`
1 329×	`lower-fma.f32`
1 270×	`lower-*.f64`
1 270×	`lower-*.f32`
982×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	279
1	79	279
2	186	279
3	544	279
4	1600	279
5	2441	279
6	3322	279
7	4909	279
8	5417	279
9	5793	279
10	6314	279
11	6979	279
12	7716	279
0	8093	279

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 69

Calls

Call 1

Inputs
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(* -1 y)
(- x y)
(- x y)
(- x y)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))

Outputs
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (- x y)))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (+ x (* -1 y))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (+ x (* -1 y))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (+ x (* -1 y))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(sqrt (fabs (+ x (* -1 y))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (neg (+ y (* -1 x))))
(fabs.f64 (-.f64 y x))
(fabs (neg (+ y (* -1 x))))
(fabs.f64 (-.f64 y x))
(fabs (neg (+ y (* -1 x))))
(fabs.f64 (-.f64 y x))
(fabs (neg (+ y (* -1 x))))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (- x y))
(fabs.f64 (-.f64 y x))
(fabs (+ x (* -1 y)))
(fabs.f64 (-.f64 y x))
(fabs (+ x (* -1 y)))
(fabs.f64 (-.f64 y x))
(fabs (+ x (* -1 y)))
(fabs.f64 (-.f64 y x))
(fabs (+ x (* -1 y)))
(fabs.f64 (-.f64 y x))
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
x
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)

rewrite308.0ms (6%)

Memory

5.1MiB live, 271.2MiB allocated

Rules

2 321×	`lower-/.f64`
2 321×	`lower-/.f32`
2 153×	`lower-fma.f64`
2 153×	`lower-fma.f32`
1 628×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	12
0	8	12
1	29	12
2	181	12
3	1675	12
0	8378	12

Stop Event

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

Counts

3 → 322

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(fabs.f64 (-.f64 x y))
(-.f64 x y)

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

eval52.0ms (1%)

Memory: 4.5MiB live, 111.8MiB allocated
Compiler: Compiled 12 615 to 1 388 computations (89% saved)

prune93.0ms (1.8%)

Memory

-14.0MiB live, 112.0MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	389	2	391
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	389	3	392

Accuracy

100.0%

Counts

392 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))))
✓	100.0%	(sqrt.f64 (fabs.f64 (-.f64 x y)))
▶	52.6%	(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))

Compiler

Compiled 25 to 18 computations (28% saved)

simplify9.0ms (0.2%)

Memory

14.2MiB live, 14.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

48×	`lower-fma.f64`
48×	`lower-fma.f32`
36×	`lower-*.f64`
36×	`lower-*.f32`
21×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	57
0	21	57
1	32	57
2	41	57
3	54	57
4	83	57
5	133	57
6	164	57
7	195	57
8	211	57
9	214	57
0	214	57

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))
(fabs.f64 #s(approx (- x y) (neg.f64 y)))
#s(approx (- x y) (neg.f64 y))
(neg.f64 y)
y
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))))
#s(literal 1 binary64)
(sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))))
(fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))
(/.f64 #s(literal 1 binary64) (-.f64 y x))
(-.f64 y x)
y
x

Outputs
(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))
(fabs.f64 #s(approx (- x y) (neg.f64 y)))
#s(approx (- x y) (neg.f64 y))
(neg.f64 y)
y
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))))
#s(literal 1 binary64)
(sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x))))
(fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))
(/.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))
(/.f64 #s(literal 1 binary64) (-.f64 y x))
(/.f64 #s(literal -1 binary64) (-.f64 x y))
(-.f64 y x)
y
x

localize82.0ms (1.6%)

Memory

-9.1MiB live, 69.5MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))
accuracy	0.015625	(/.f64 #s(literal 1 binary64) (-.f64 y x))
accuracy	0.13671875	(sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))))
accuracy	0.2890625	(/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))))
accuracy	0	(neg.f64 y)
accuracy	0	(fabs.f64 #s(approx (- x y) (neg.f64 y)))
accuracy	0.01953125	(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))
accuracy	31.39067447435182	#s(approx (- x y) (neg.f64 y))

Samples

70.0ms

256×

valid

Compiler

Compiled 50 to 14 computations (72% saved)

Precisions

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

ival-neg: 27.0ms (68.9% of total)

ival-sub: 3.0ms (7.7% of total)

ival-div: 3.0ms (7.7% of total)

ival-sqrt: 3.0ms (7.7% of total)

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

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.3%)

Memory

-8.6MiB live, 28.3MiB allocated

Counts

8 → 180

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y)))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y)))) #<representation binary64>) () ())
#s(alt (fabs.f64 #s(approx (- x y) (neg.f64 y))) (patch (fabs.f64 #s(approx (- x y) (neg.f64 y))) #<representation binary64>) () ())
#s(alt #s(approx (- x y) (neg.f64 y)) (patch #s(approx (- x y) (neg.f64 y)) #<representation binary64>) () ())
#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))))) (patch (/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))) (patch (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))) #<representation binary64>) () ())
#s(alt (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))) (patch (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (-.f64 y x)) (patch (/.f64 #s(literal 1 binary64) (-.f64 y x)) #<representation binary64>) () ())

Outputs
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y)))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y)))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y)))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y)))) #<representation binary64>) () ())) ())
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Calls

45 calls:

Time	Variable		Point	Expression
3.0ms	y	@	-inf	(/ 1 (- y x))
1.0ms	x	@	inf	(/ 1 (sqrt (fabs (/ 1 (- y x)))))
1.0ms	x	@	-inf	(/ 1 (sqrt (fabs (/ 1 (- y x)))))
1.0ms	y	@	inf	(/ 1 (sqrt (fabs (/ 1 (- y x)))))
1.0ms	y	@	-inf	(/ 1 (sqrt (fabs (/ 1 (- y x)))))

simplify232.0ms (4.5%)

Memory

0.2MiB live, 203.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4 675×	`lower-fma.f64`
4 675×	`lower-fma.f32`
2 002×	`lower-*.f64`
2 002×	`lower-*.f32`
1 088×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	1055
1	414	1032
2	1071	995
3	4174	995
0	8198	978

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 177

Calls

Call 1

Inputs
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(* -1 y)
(- x y)
(- x y)
(- x y)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ -1 (+ x (* -1 y))))))
(sqrt (/ 1 (fabs (/ -1 (+ x (* -1 y))))))
(sqrt (/ 1 (fabs (/ -1 (+ x (* -1 y))))))
(sqrt (/ 1 (fabs (/ -1 (+ x (* -1 y))))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (- y x)))))
(sqrt (/ 1 (fabs (/ 1 (+ y (* -1 x))))))
(sqrt (/ 1 (fabs (/ 1 (+ y (* -1 x))))))
(sqrt (/ 1 (fabs (/ 1 (+ y (* -1 x))))))
(sqrt (/ 1 (fabs (/ 1 (+ y (* -1 x))))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ -1 (+ x (* -1 y)))))
(sqrt (fabs (/ -1 (+ x (* -1 y)))))
(sqrt (fabs (/ -1 (+ x (* -1 y)))))
(sqrt (fabs (/ -1 (+ x (* -1 y)))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (- y x))))
(sqrt (fabs (/ 1 (+ y (* -1 x)))))
(sqrt (fabs (/ 1 (+ y (* -1 x)))))
(sqrt (fabs (/ 1 (+ y (* -1 x)))))
(sqrt (fabs (/ 1 (+ y (* -1 x)))))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ -1 (+ x (* -1 y))))
(fabs (/ -1 (+ x (* -1 y))))
(fabs (/ -1 (+ x (* -1 y))))
(fabs (/ -1 (+ x (* -1 y))))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (- y x)))
(fabs (/ 1 (+ y (* -1 x))))
(fabs (/ 1 (+ y (* -1 x))))
(fabs (/ 1 (+ y (* -1 x))))
(fabs (/ 1 (+ y (* -1 x))))
(/ -1 x)
(- (* -1 (/ y (pow x 2))) (/ 1 x))
(- (* y (- (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))
(- (* y (- (* y (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(/ 1 y)
(/ (+ 1 (/ x y)) y)
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (* -1 (/ x y))) y)
(/ (- (+ 1 (/ (pow x 3) (pow y 3))) (+ (* -1 (/ x y)) (* -1 (/ (pow x 2) (pow y 2))))) y)
(/ 1 y)
(* -1 (/ (- (* -1 (/ x y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) (* -1 x)) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 3) y)) (pow x 2)) y)) (* -1 x)) y)) 1) y))
(/ 1 y)
(+ (/ 1 y) (/ x (pow y 2)))
(+ (* x (+ (/ 1 (pow y 2)) (/ x (pow y 3)))) (/ 1 y))
(+ (* x (+ (* x (+ (/ 1 (pow y 3)) (/ x (pow y 4)))) (/ 1 (pow y 2)))) (/ 1 y))
(/ -1 x)
(/ (- (* -1 (/ y x)) 1) x)
(/ (- (* -1 (/ (pow y 2) (pow x 2))) (+ 1 (/ y x))) x)
(/ (- (* -1 (/ (pow y 3) (pow x 3))) (+ 1 (+ (/ y x) (/ (pow y 2) (pow x 2))))) x)
(/ -1 x)
(* -1 (/ (+ 1 (/ y x)) x))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) y) x))) x))
(* -1 (/ (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (* -1 (pow y 2))) x)) y) x))) x))

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

rewrite155.0ms (3%)

Memory

18.8MiB live, 203.3MiB allocated

Rules

1 360×	`lower-fma.f64`
1 360×	`lower-fma.f32`
1 190×	`lower-*.f64`
1 190×	`lower-*.f32`
831×	`lower-pow.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	50
0	21	51
1	73	50
2	409	42
3	3969	38
0	9298	38

Stop Event

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

Counts

8 → 388

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))
(fabs.f64 #s(approx (- x y) (neg.f64 y)))
#s(approx (- x y) (neg.f64 y))
(neg.f64 y)
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))))
(sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))))
(fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))
(/.f64 #s(literal 1 binary64) (-.f64 y x))

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

eval83.0ms (1.6%)

Memory: -1.3MiB live, 156.9MiB allocated
Compiler: Compiled 9 909 to 1 248 computations (87.4% saved)

prune87.0ms (1.7%)

Memory

6.8MiB live, 129.3MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	562	3	565
Fresh	0	0	0
Picked	2	0	2
Done	1	0	1
Total	565	3	568

Accuracy

100.0%

Counts

568 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x)))
▶	100.0%	(sqrt.f64 (-.f64 y x))
▶	52.6%	(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))

Compiler

Compiled 22 to 13 computations (40.9% saved)

simplify23.0ms (0.4%)

Memory

-7.5MiB live, 28.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

136×	`lower-fma.f64`
136×	`lower-fma.f32`
88×	`lower-*.f64`
88×	`lower-*.f32`
76×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	45
0	14	45
1	21	45
2	31	45
3	47	45
4	83	45
5	157	45
6	238	45
7	424	45
8	738	45
9	803	45
10	819	45
11	820	45
0	820	45

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))
(fabs.f64 #s(approx (- x y) y))
#s(approx (- x y) y)
y
(sqrt.f64 (-.f64 y x))
(-.f64 y x)
y
x
(/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x)))
(-.f64 y x)
y
x
(sqrt.f64 (-.f64 y x))

Outputs
(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))
(fabs.f64 #s(approx (- x y) y))
#s(approx (- x y) y)
y
(sqrt.f64 (-.f64 y x))
(-.f64 y x)
y
x
(/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x)))
(-.f64 y x)
y
x
(sqrt.f64 (-.f64 y x))

localize58.0ms (1.1%)

Memory

-21.4MiB live, 68.3MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 y x)
accuracy	0.01953125	(sqrt.f64 (-.f64 y x))
accuracy	0.5390625	(/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x)))
accuracy	0	(-.f64 y x)
accuracy	0.01953125	(sqrt.f64 (-.f64 y x))
accuracy	0	(fabs.f64 #s(approx (- x y) y))
accuracy	0.01953125	(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))
accuracy	62.54513549234422	#s(approx (- x y) y)

Samples

44.0ms

256×

valid

Compiler

Compiled 41 to 10 computations (75.6% saved)

Precisions

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

ival-sub: 12.0ms (66.9% of total)

ival-sqrt: 3.0ms (16.7% of total)

ival-div: 2.0ms (11.2% of total)

ival-fabs: 1.0ms (5.6% of total)

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

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

series10.0ms (0.2%)

Memory

21.1MiB live, 21.1MiB allocated

Counts

6 → 144

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())
#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())
#s(alt #s(approx (- x y) y) (patch #s(approx (- x y) y) #<representation binary64>) () ())
#s(alt (sqrt.f64 (-.f64 y x)) (patch (sqrt.f64 (-.f64 y x)) #<representation binary64>) () ())
#s(alt (-.f64 y x) (patch (-.f64 y x) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())

Outputs
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (neg (+ y (* -1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (neg (+ y (* -1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (neg (+ y (* -1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (neg (+ y (* -1 x))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (- x y))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (+ x (* -1 y)))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (+ x (* -1 y)))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (+ x (* -1 y)))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (+ x (* -1 y)))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) (patch (sqrt.f64 (fabs.f64 #s(approx (- x y) y))) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 x) (#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 x) (#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 x) (#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor 0 x) (#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf x) (#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf x) (#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf x) (#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())) ())
#s(alt (fabs (- x y)) (taylor inf x) (#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())) ())
#s(alt (fabs (neg (+ y (* -1 x)))) (taylor -inf x) (#s(alt (fabs.f64 #s(approx (- x y) y)) (patch (fabs.f64 #s(approx (- x y) y)) #<representation binary64>) () ())) ())
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#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) (patch (/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x))) #<representation binary64>) () ())) ())

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(sqrt (- y x))
1.0ms	y	@	-inf	(sqrt (- y x))
1.0ms	y	@	-inf	(/ (- y x) (sqrt (- y x)))
1.0ms	x	@	inf	(sqrt (- y x))
1.0ms	x	@	-inf	(sqrt (- y x))

simplify181.0ms (3.5%)

Memory

-8.3MiB live, 300.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 482×	`lower-fma.f64`
7 482×	`lower-fma.f32`
2 620×	`lower-*.f64`
2 620×	`lower-*.f32`
954×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	201	1670
1	597	1568
2	2170	1528
3	4852	1520
0	8173	1450

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 138

Calls

Call 1

Inputs
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(* -1 y)
(- x y)
(- x y)
(- x y)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7)))))))))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(sqrt y)
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3))))))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 x)
(- y x)
(- y x)
(- y x)
y
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
(* y (+ 1 (* -1 (/ x y))))
y
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
(* -1 (* y (- (/ x y) 1)))
y
(+ y (* -1 x))
(+ y (* -1 x))
(+ y (* -1 x))
(* -1 x)
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* x (- (/ y x) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1)))
(sqrt y)
(* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))
(* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7)))))))))
(sqrt y)
(* -1 (* y (+ (* -1 (sqrt (/ 1 y))) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))))
(* -1 (* y (+ (* -1 (sqrt (/ 1 y))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))
(* -1 (* y (+ (* -1 (sqrt (/ 1 y))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))))
(sqrt y)
(+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y)))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3))))))))
(+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5))))))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))

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

rewrite141.0ms (2.7%)

Memory

37.4MiB live, 269.6MiB allocated

Rules

1 495×	`lower-fma.f64`
1 495×	`lower-fma.f32`
1 267×	`lower-*.f64`
1 267×	`lower-*.f32`
911×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
0	14	29
1	55	29
2	377	29
3	4460	29
0	9579	29

Stop Event

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

Counts

6 → 510

Calls

Call 1

Inputs
(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))
(fabs.f64 #s(approx (- x y) y))
#s(approx (- x y) y)
(sqrt.f64 (-.f64 y x))
(-.f64 y x)
(/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x)))

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

eval344.0ms (6.7%)

Memory: -22.9MiB live, 229.5MiB allocated
Compiler: Compiled 28 108 to 1 552 computations (94.5% saved)

prune282.0ms (5.5%)

Memory

15.0MiB live, 213.8MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1 234	2	1 236
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	1 235	4	1 239

Accuracy

100.0%

Counts

1 239 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x)))
✓	100.0%	(sqrt.f64 (-.f64 y x))
▶	49.7%	(sqrt.f64 #s(approx (- y x) (neg.f64 x)))
▶	51.0%	#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))

Compiler

Compiled 27 to 16 computations (40.7% saved)

simplify48.0ms (0.9%)

Memory

-24.4MiB live, 14.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Rules

136×	`lower-fma.f64`
136×	`lower-fma.f32`
88×	`lower-*.f64`
88×	`lower-*.f32`
69×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
0	13	30
1	21	30
2	28	30
3	43	30
4	66	30
5	105	30
6	159	30
7	241	30
8	417	30
9	711	30
10	739	30
11	777	30
12	806	30
0	806	30

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))
(sqrt.f64 y)
y
(sqrt.f64 #s(approx (- y x) (neg.f64 x)))
#s(approx (- y x) (neg.f64 x))
(neg.f64 x)
x

Outputs
#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))
(sqrt.f64 y)
y
(sqrt.f64 #s(approx (- y x) (neg.f64 x)))
#s(approx (- y x) (neg.f64 x))
(neg.f64 x)
x

localize44.0ms (0.8%)

Memory

-7.1MiB live, 33.4MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.015625	(sqrt.f64 #s(approx (- y x) (neg.f64 x)))
accuracy	31.97206578361353	#s(approx (- y x) (neg.f64 x))
accuracy	0	(sqrt.f64 y)
accuracy	15.37086627563164	#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))

Samples

11.0ms	192×	0	valid
4.0ms	64×	0	invalid

Compiler

Compiled 23 to 9 computations (60.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sqrt: 3.0ms (39.2% of total)

ival-div: 2.0ms (26.2% of total)

ival-sub: 1.0ms (13.1% of total)

ival-neg: 1.0ms (13.1% of total)

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

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

series4.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated

Counts

5 → 96

Calls

Call 1

Inputs
#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())
#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) (taylor inf y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) (taylor inf y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor -inf y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 (sqrt (/ 1 y))) (* -1/2 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor -inf y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 (sqrt (/ 1 y))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* 1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))))))) (taylor -inf y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1 (sqrt (/ 1 y))) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))) (* 1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))))) (taylor -inf y) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor 0 x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor inf x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) (patch #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 y) (patch (sqrt.f64 y) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (sqrt (/ 1 x)) (/ y (sqrt -1)))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ y (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* y (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ y (pow (sqrt -1) 5)))))))) (* (sqrt x) (sqrt -1))) (taylor 0 y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (* -1/2 (* x (sqrt (/ 1 (pow y 3))))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5)))))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* y (+ (sqrt (/ 1 y)) (+ (* -1/2 (* x (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (pow x 2) (sqrt (/ 1 (pow y 5))))) (* -1/16 (* (pow x 3) (sqrt (/ 1 (pow y 7))))))))) (taylor inf y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt y) (pow (sqrt -1) 2))) (taylor -inf y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))) (taylor -inf y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))) (taylor -inf y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ (* -1/8 (* (* (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))) (taylor -inf y) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (sqrt y) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* -1/2 (* x (sqrt (/ 1 y))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* -1/8 (* x (sqrt (/ 1 (pow y 3)))))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (sqrt y) (* x (+ (* -1/2 (sqrt (/ 1 y))) (* x (+ (* -1/8 (sqrt (/ 1 (pow y 3)))) (* -1/16 (* x (sqrt (/ 1 (pow y 5)))))))))) (taylor 0 x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt -1)) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 3) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor inf x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 2) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 3) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* y (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (- y x) (neg.f64 x))) (patch (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (- y x) (taylor 0 y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (* -1 (/ x y)))) (taylor inf y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (/ x y) 1))) (taylor -inf y) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ y (* -1 x)) (taylor 0 x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ y x) 1)) (taylor inf x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ y x))))) (taylor -inf x) (#s(alt #s(approx (- y x) (neg.f64 x)) (patch #s(approx (- y x) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	y	@	-inf	(sqrt y)
0.0ms	y	@	0	(sqrt y)
0.0ms	x	@	inf	(neg x)
0.0ms	y	@	inf	(sqrt y)
0.0ms	y	@	0	(/ (- y x) (sqrt (- y x)))

simplify637.0ms (12.3%)

Memory

1.8MiB live, 276.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 368×	`lower-fma.f64`
10 368×	`lower-fma.f32`
2 597×	`lower-*.f64`
2 597×	`lower-*.f32`
2 153×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	189	1355
1	570	1337
2	2087	1297
3	4402	1279
0	8229	1209

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 93

Calls

Call 1

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

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

rewrite173.0ms (3.4%)

Memory

12.0MiB live, 247.0MiB allocated

Rules

1 620×	`lower-*.f64`
1 620×	`lower-*.f32`
1 128×	`lower-pow.f64`
1 128×	`lower-pow.f32`
1 120×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	28
0	13	28
1	46	28
2	282	24
3	3191	21
0	9219	21

Stop Event

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

Counts

5 → 54

Calls

Call 1

Inputs
#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))
(sqrt.f64 y)
(sqrt.f64 #s(approx (- y x) (neg.f64 x)))
#s(approx (- y x) (neg.f64 x))
(neg.f64 x)

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

eval14.0ms (0.3%)

Memory: -0.1MiB live, 37.2MiB allocated
Compiler: Compiled 1 809 to 230 computations (87.3% saved)

prune20.0ms (0.4%)

Memory

30.0MiB live, 64.8MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	147	4	151

Accuracy

100.0%

Counts

151 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x)))
✓	100.0%	(sqrt.f64 (-.f64 y x))
✓	49.7%	(sqrt.f64 #s(approx (- y x) (neg.f64 x)))
✓	51.0%	#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))

Compiler

Compiled 71 to 37 computations (47.9% saved)

regimes20.0ms (0.4%)

Memory

1.2MiB live, 45.9MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))
(sqrt.f64 #s(approx (- y x) (neg.f64 x)))
(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))
(sqrt.f64 (-.f64 y x))
(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))
(sqrt.f64 (fabs.f64 (-.f64 x y)))
(/.f64 (-.f64 y x) (sqrt.f64 (-.f64 y x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))))

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

Calls

5 calls:

8.0ms	(-.f64 x y)
3.0ms	(fabs.f64 (-.f64 x y))
3.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))
3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(sqrt.f64 (fabs.f64 (-.f64 x y)))`
100.0%	1	`(fabs.f64 (-.f64 x y))`
100.0%	1	`(-.f64 x y)`

Compiler

Compiled 24 to 16 computations (33.3% saved)

regimes11.0ms (0.2%)

Memory

-7.4MiB live, 31.7MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))
(sqrt.f64 #s(approx (- y x) (neg.f64 x)))
(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))

Outputs
(sqrt.f64 #s(approx (- y x) (neg.f64 x)))
#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))

Calls

5 calls:

3.0ms	(-.f64 x y)
2.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))
2.0ms	(fabs.f64 (-.f64 x y))
2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
81.7%	2	`x`
89.6%	2	`y`
63.0%	4	`(sqrt.f64 (fabs.f64 (-.f64 x y)))`
63.0%	4	`(fabs.f64 (-.f64 x y))`
63.0%	4	`(-.f64 x y)`

Compiler

Compiled 24 to 16 computations (33.3% saved)

regimes8.0ms (0.2%)

Memory

-18.5MiB live, 19.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))

Outputs
#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))

Calls

5 calls:

3.0ms	(-.f64 x y)
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))
1.0ms	(fabs.f64 (-.f64 x y))
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
51.0%	1	`(sqrt.f64 (fabs.f64 (-.f64 x y)))`
51.0%	1	`(fabs.f64 (-.f64 x y))`
51.0%	1	`(-.f64 x y)`
51.0%	1	`x`
51.0%	1	`y`

Compiler

Compiled 24 to 16 computations (33.3% saved)

bsearch5.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
5.0ms	7.938432993302024e-47	1.511412609110183e-46

Samples

2.0ms

64×

valid

Compiler

Compiled 62 to 46 computations (25.8% saved)

Precisions

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

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

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

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

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

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

simplify5.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	20	37
2	23	37
3	24	37

Stop Event

1×

saturated

Calls

Call 1

Inputs

(sqrt.f64 (-.f64 y x))

(if (<=.f64 y #s(literal 8741742960768907/102844034832575377634685573909834406561420991602098741459288064 binary64)) (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)))

#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))

Outputs

(sqrt.f64 (-.f64 y x))

(if (<=.f64 y #s(literal 8741742960768907/102844034832575377634685573909834406561420991602098741459288064 binary64)) (sqrt.f64 #s(approx (- y x) (neg.f64 x))) #s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y)))

#s(approx (/ (- y x) (sqrt (- y x))) (sqrt.f64 y))

soundness565.0ms (10.9%)

Memory

-45.0MiB live, 381.3MiB allocated

Rules

7 482×	`lower-fma.f64`
7 482×	`lower-fma.f32`
2 620×	`lower-*.f64`
2 620×	`lower-*.f32`
2 321×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	12
0	8	12
1	29	12
2	181	12
3	1675	12
0	8378	12
0	13	50
0	21	51
1	73	50
2	409	42
3	3969	38
0	9298	38
0	201	1670
1	597	1568
2	2170	1528
3	4852	1520
0	8173	1450

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
1×	iter limit

Compiler

Compiled 91 to 58 computations (36.3% saved)

preprocess59.0ms (1.1%)

Memory: 1.8MiB live, 77.1MiB allocated
Compiler: Compiled 66 to 38 computations (42.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	15	31
1	35	27
2	72	27
3	137	27
4	185	27
5	197	27
6	199	27
0	5	5
0	8	5
1	12	5
2	19	5
3	27	5
4	46	5
5	93	5
6	144	5
7	165	5
8	173	5
0	173	5

Iter	Nodes	Cost
0	13	57
0	21	57
1	32	57
2	41	57
3	54	57
4	83	57
5	133	57
6	164	57
7	195	57
8	211	57
9	214	57
0	214	57

Iter	Nodes	Cost
0	9	45
0	14	45
1	21	45
2	31	45
3	47	45
4	83	45
5	157	45
6	238	45
7	424	45
8	738	45
9	803	45
10	819	45
11	820	45
0	820	45

Iter	Nodes	Cost
0	10	30
0	13	30
1	21	30
2	28	30
3	43	30
4	66	30
5	105	30
6	159	30
7	241	30
8	417	30
9	711	30
10	739	30
11	777	30
12	806	30
0	806	30

Iter	Nodes	Cost
0	15	31
1	35	27
2	72	27
3	137	27
4	185	27
5	197	27
6	199	27
0	5	5
0	8	5
1	12	5
2	19	5
3	27	5
4	46	5
5	93	5
6	144	5
7	165	5
8	173	5
0	173	5

Iter	Nodes	Cost
0	13	57
0	21	57
1	32	57
2	41	57
3	54	57
4	83	57
5	133	57
6	164	57
7	195	57
8	211	57
9	214	57
0	214	57

Iter	Nodes	Cost
0	9	45
0	14	45
1	21	45
2	31	45
3	47	45
4	83	45
5	157	45
6	238	45
7	424	45
8	738	45
9	803	45
10	819	45
11	820	45
0	820	45

Iter	Nodes	Cost
0	10	30
0	13	30
1	21	30
2	28	30
3	43	30
4	66	30
5	105	30
6	159	30
7	241	30
8	417	30
9	711	30
10	739	30
11	777	30
12	806	30
0	806	30

start0.0ms (0%)

analyze0.0ms (0%)

sample919.0ms (17.8%)

explain70.0ms (1.4%)

preprocess56.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize16.0ms (0.3%)

series188.0ms (3.6%)

simplify141.0ms (2.7%)

rewrite308.0ms (6%)

eval52.0ms (1%)

prune93.0ms (1.8%)

simplify9.0ms (0.2%)

localize82.0ms (1.6%)

series14.0ms (0.3%)

simplify232.0ms (4.5%)

rewrite155.0ms (3%)

eval83.0ms (1.6%)

prune87.0ms (1.7%)

simplify23.0ms (0.4%)

localize58.0ms (1.1%)

series10.0ms (0.2%)

simplify181.0ms (3.5%)

rewrite141.0ms (2.7%)

eval344.0ms (6.7%)

prune282.0ms (5.5%)

simplify48.0ms (0.9%)

localize44.0ms (0.8%)

series4.0ms (0.1%)

simplify637.0ms (12.3%)

rewrite173.0ms (3.4%)

eval14.0ms (0.3%)

prune20.0ms (0.4%)

regimes20.0ms (0.4%)

regimes11.0ms (0.2%)

regimes8.0ms (0.2%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

soundness565.0ms (10.9%)

preprocess59.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	31
1	35	27
2	72	27
3	137	27
4	185	27
5	197	27
6	199	27
0	5	5
0	8	5
1	12	5
2	19	5
3	27	5
4	46	5
5	93	5
6	144	5
7	165	5
8	173	5
0	173	5

Iter	Nodes	Cost
0	13	57
0	21	57
1	32	57
2	41	57
3	54	57
4	83	57
5	133	57
6	164	57
7	195	57
8	211	57
9	214	57
0	214	57

Iter	Nodes	Cost
0	9	45
0	14	45
1	21	45
2	31	45
3	47	45
4	83	45
5	157	45
6	238	45
7	424	45
8	738	45
9	803	45
10	819	45
11	820	45
0	820	45

Iter	Nodes	Cost
0	10	30
0	13	30
1	21	30
2	28	30
3	43	30
4	66	30
5	105	30
6	159	30
7	241	30
8	417	30
9	711	30
10	739	30
11	777	30
12	806	30
0	806	30