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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB 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)

sample820.0ms (16.3%)

Memory

37.1MiB live, 835.2MiB allocated

Samples

522.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 250.0ms

ival-sub: 104.0ms (41.6% of total)

ival-fabs: 79.0ms (31.6% of total)

ival-sqrt: 56.0ms (22.4% of total)

ival-true: 7.0ms (2.8% of total)

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

Bogosity

explain69.0ms (1.4%)

Memory

-42.8MiB live, 133.8MiB 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

22.0ms

512×

valid

Compiler

Compiled 37 to 19 computations (48.6% saved)

Precisions

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

ival-sub: 3.0ms (30.4% of total)

ival-fabs: 3.0ms (30.4% of total)

ival-sqrt: 3.0ms (30.4% of total)

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

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

preprocess62.0ms (1.2%)

Memory

-6.8MiB live, 30.6MiB allocated

Algorithm

1×	egg-herbie

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 5 to 5 computations (0% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 5 computations (0% saved)

simplify6.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB 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)))

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

localize17.0ms (0.3%)

Memory

13.1MiB live, 50.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x y)
accuracy	0	(fabs.f64 (-.f64 x y))
accuracy	0.0078125	(sqrt.f64 (fabs.f64 (-.f64 x y)))

Samples

13.0ms

256×

valid

Compiler

Compiled 16 to 7 computations (56.3% saved)

Precisions

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

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

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

ival-fabs: 1.0ms (20.8% of total)

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

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

series53.0ms (1.1%)

Memory

-24.2MiB live, 12.4MiB 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 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 (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 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 (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 (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 (* -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 (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 (* -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 -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>) () ())) ())
#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 (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 (* -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 (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 (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 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 (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 (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 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>) () ())) ())

Calls

6 calls:

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

simplify128.0ms (2.5%)

Memory

21.4MiB live, 140.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	279
1	79	279
2	186	279
3	541	279
4	1596	279
5	2435	279
6	3316	279
7	4901	279
8	5409	279
9	5785	279
10	6306	279
11	6970	279
12	7705	279
0	8082	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)))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(sqrt (fabs (+ x (* -1 y))))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(fabs (+ x (* -1 y)))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(* -1 y)
(- x y)
(- x y)
(- x y)
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(sqrt (fabs (- x y)))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
(fabs (- x y))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(sqrt (fabs (neg (+ y (* -1 x)))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
(fabs (neg (+ y (* -1 x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 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)))
(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))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.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)))
(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))
(* -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)
(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 (* -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)
(* -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 (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)))
(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))
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.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)))
(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))
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)
(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)))
(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))
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)

rewrite209.0ms (4.2%)

Memory

-2.7MiB live, 190.4MiB allocated

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
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eval90.0ms (1.8%)

Memory: 21.3MiB live, 104.2MiB allocated
Compiler: Compiled 9 124 to 1 402 computations (84.6% saved)

prune20.0ms (0.4%)

Memory

-7.0MiB live, 29.4MiB 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
✓	100.0%	(sqrt.f64 (fabs.f64 (-.f64 x y)))
▶	100.0%	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x)))))
▶	47.0%	(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify111.0ms (2.2%)

Memory

-8.0MiB live, 159.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 y x)
cost-diff	0	(fabs.f64 (*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x))))
cost-diff	0	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x)))))
cost-diff	1408	(*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.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))))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	75
0	22	83
1	37	83
2	67	83
3	155	59
4	430	51
5	892	51
6	2223	51
7	6429	51
0	8092	51

Stop Event

1×	iter limit
1×	node limit
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
(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x)))))
(fabs.f64 (*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x))))
(*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x)))
(+.f64 y x)
y
x
(/.f64 (-.f64 x y) (+.f64 y x))
(-.f64 x y)

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

localize46.0ms (0.9%)

Memory

7.0MiB live, 93.2MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(fabs.f64 (*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x))))
accuracy	0.0078125	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x)))))
accuracy	0.041347509768442016	(/.f64 (-.f64 x y) (+.f64 y x))
accuracy	0.046875	(*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x)))
accuracy	0	(neg.f64 y)
accuracy	0	(fabs.f64 #s(approx (- x y) (neg.f64 y)))
accuracy	0.0078125	(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))
accuracy	34.81807211167532	#s(approx (- x y) (neg.f64 y))

Samples

37.0ms	255×	0	valid
0.0ms	1×	5	exit

Compiler

Compiled 68 to 13 computations (80.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 6.0ms (34.5% of total)

ival-fabs: 3.0ms (17.3% of total)

ival-sqrt: 3.0ms (17.3% of total)

ival-div: 2.0ms (11.5% of total)

ival-sub: 2.0ms (11.5% of total)

ival-add: 1.0ms (5.8% of total)

ival-neg: 1.0ms (5.8% of total)

adjust: 0.0ms (0% of total)

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

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

series11.0ms (0.2%)

Memory

-15.4MiB live, 21.8MiB allocated

Counts

9 → 204

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

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	inf	((sqrt (fabs (- x y))) (fabs (- x y)) (- x y) (neg y) (* (+ y x) (/ (- x y) (+ y x))) (sqrt (fabs (* (+ y x) (/ (- x y) (+ y x))))) (fabs (* (+ y x) (/ (- x y) (+ y x)))) (+ y x) (/ (- x y) (+ y x)))
1.0ms	x	@	-inf	((sqrt (fabs (- x y))) (fabs (- x y)) (- x y) (neg y) (* (+ y x) (/ (- x y) (+ y x))) (sqrt (fabs (* (+ y x) (/ (- x y) (+ y x))))) (fabs (* (+ y x) (/ (- x y) (+ y x)))) (+ y x) (/ (- x y) (+ y x)))
1.0ms	x	@	inf	((sqrt (fabs (- x y))) (fabs (- x y)) (- x y) (neg y) (* (+ y x) (/ (- x y) (+ y x))) (sqrt (fabs (* (+ y x) (/ (- x y) (+ y x))))) (fabs (* (+ y x) (/ (- x y) (+ y x)))) (+ y x) (/ (- x y) (+ y x)))
1.0ms	y	@	-inf	((sqrt (fabs (- x y))) (fabs (- x y)) (- x y) (neg y) (* (+ y x) (/ (- x y) (+ y x))) (sqrt (fabs (* (+ y x) (/ (- x y) (+ y x))))) (fabs (* (+ y x) (/ (- x y) (+ y x)))) (+ y x) (/ (- x y) (+ y x)))
1.0ms	y	@	0	((sqrt (fabs (- x y))) (fabs (- x y)) (- x y) (neg y) (* (+ y x) (/ (- x y) (+ y x))) (sqrt (fabs (* (+ y x) (/ (- x y) (+ y x))))) (fabs (* (+ y x) (/ (- x y) (+ y x)))) (+ y x) (/ (- x y) (+ y x)))

simplify182.0ms (3.6%)

Memory

19.7MiB live, 201.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	153	981
1	464	960
2	1257	906
3	4780	894
0	8365	870

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 192

Calls

Call 1

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

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

rewrite353.0ms (7%)

Memory

-14.9MiB live, 188.4MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	69
0	22	69
1	73	45
2	533	45
3	7885	45
0	8253	45

Stop Event

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

Counts

9 → 697

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

Outputs
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eval276.0ms (5.5%)

Memory: -2.5MiB live, 207.7MiB allocated
Compiler: Compiled 22 570 to 3 625 computations (83.9% saved)

prune94.0ms (1.9%)

Memory

-8.6MiB live, 66.2MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1 034	1	1 035
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	1 034	4	1 038

Accuracy

100.0%

Counts

1 038 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (fabs.f64 (-.f64 x y)))
▶	100.0%	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))))
✓	100.0%	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (+.f64 y x)))))
✓	47.0%	(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify480.0ms (9.5%)

Memory

18.9MiB live, 207.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(fabs.f64 (*.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))
cost-diff	0	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))))
cost-diff	768	(fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))
cost-diff	1728	(*.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	10	79
0	18	79
1	33	79
2	78	79
3	188	49
4	305	39
5	651	39
6	2715	37
7	7051	37
0	8355	37

Stop Event

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

Calls

Call 1

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

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

localize152.0ms (3%)

Memory

-19.7MiB live, 113.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))))
accuracy	0.01171875	(/.f64 x (+.f64 y x))
accuracy	0.046875	(*.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))
accuracy	0.09765625	(fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))

Samples

142.0ms	255×	0	valid
0.0ms	1×	5	exit

Compiler

Compiled 85 to 13 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 134.0ms

ival-mult: 93.0ms (69.2% of total)

ival-div: 35.0ms (26% of total)

ival-add: 3.0ms (2.2% of total)

ival-sqrt: 2.0ms (1.5% of total)

ival-fabs: 1.0ms (0.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.4%)

Memory

12.1MiB live, 48.8MiB allocated

Counts

5 → 120

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt (+ x (* -1 y)) (taylor 0 y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -2 (/ y x))) (taylor 0 y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* 2 (/ y (pow x 2))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -2 (/ y (pow x 3))) (* 2 (/ 1 (pow x 2))))) (* 2 (/ 1 x))))) (taylor 0 y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ x y) (+ (* -1 (/ y (+ x y))) (/ x (+ x y)))))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ x y) (+ (* -1 (/ y (+ x y))) (/ x (+ x y)))))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ x y) (+ (* -1 (/ y (+ x y))) (/ x (+ x y)))))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ x y) (+ (* -1 (/ y (+ x y))) (/ x (+ x y)))))) (taylor 0 y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (+ x y) (+ (* -1 (/ y (+ x y))) (/ x (+ x y))))) (taylor 0 y) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (+ x y) (+ (* -1 (/ y (+ x y))) (/ x (+ x y))))) (taylor 0 y) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (+ x y) (+ (* -1 (/ y (+ x y))) (/ x (+ x y))))) (taylor 0 y) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (+ x y) (+ (* -1 (/ y (+ x y))) (/ x (+ x y))))) (taylor 0 y) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor 0 y) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (/ y (pow x 2)) (/ 1 x)))) (taylor 0 y) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x)))) (taylor 0 y) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor inf y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt (* y (- (+ (* -1 (/ x y)) (* 2 (/ x y))) 1)) (taylor inf y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt (* y (- (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 2) (pow y 2))) (+ (* 2 (/ x y)) (* 2 (/ (pow x 2) (pow y 2)))))) (+ 1 (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt (* y (- (+ (* -1 (/ x y)) (+ (* -1 (/ (pow x 2) (pow y 2))) (+ (* 2 (/ x y)) (+ (* 2 (/ (pow x 2) (pow y 2))) (+ (/ (* x (- (* -1 (pow x 2)) (pow x 2))) (pow y 3)) (/ (pow x 3) (pow y 3))))))) (+ 1 (+ (* -1 (/ (pow x 3) (pow y 3))) (/ (pow x 2) (pow y 2)))))) (taylor inf y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (- (* 2 (/ x y)) 1) (taylor inf y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ (pow x 2) (pow y 2))) (* 2 (/ x y))) (+ 1 (/ (pow x 2) (pow y 2)))) (taylor inf y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (/ (pow x 2) (pow y 2))) (+ (* 2 (/ x y)) (/ (pow x 3) (pow y 3)))) (+ 1 (+ (* -1 (/ (pow x 3) (pow y 3))) (/ (pow x 2) (pow y 2))))) (taylor inf y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ x y) (- (/ x (+ x y)) (/ y (+ x y)))))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ x y) (- (/ x (+ x y)) (/ y (+ x y)))))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ x y) (- (/ x (+ x y)) (/ y (+ x y)))))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ x y) (- (/ x (+ x y)) (/ y (+ x y)))))) (taylor inf y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (+ x y) (- (/ x (+ x y)) (/ y (+ x y))))) (taylor inf y) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (+ x y) (- (/ x (+ x y)) (/ y (+ x y))))) (taylor inf y) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (+ x y) (- (/ x (+ x y)) (/ y (+ x y))))) (taylor inf y) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (+ x y) (- (/ x (+ x y)) (/ y (+ x y))))) (taylor inf y) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (/ x y) (taylor inf y) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ x (* -1 (/ (pow x 2) y))) y) (taylor inf y) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ x (/ (pow x 3) (pow y 2))) (/ (pow x 2) y)) y) (taylor inf y) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ x (* -1 (/ (pow x 4) (pow y 3)))) (+ (* -1 (/ (pow x 3) (pow y 2))) (/ (pow x 2) y))) y) (taylor inf y) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor -inf y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ (+ (* -1 x) (* -1 (- (* -1 x) x))) y))))) (taylor -inf y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ (+ (* -1 x) (+ (* -1 (- (* -1 x) x)) (* -1 (/ (+ (* 2 (pow x 2)) (* x (- (* -1 x) x))) y)))) y))))) (taylor -inf y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (+ 1 (* -1 (/ (+ (* -1 x) (+ (* -1 (- (* -1 x) x)) (* -1 (/ (+ (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) y)) (+ (* 2 (pow x 2)) (* x (- (* -1 x) x)))) y)))) y))))) (taylor -inf y) (#s(alt (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) (patch (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (* -1 x) x) y)) 1) (taylor -inf y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (+ (* -1 x) (* 2 (/ (pow x 2) y))) x) y)) 1) (taylor -inf y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (- (+ (* -1 x) (* -1 (/ (- (* 2 (/ (pow x 3) y)) (* 2 (pow x 2))) y))) x) y)) 1) (taylor -inf y) (#s(alt (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) (patch (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ (* -1 (/ y (- x (* -1 y)))) (/ x (- x (* -1 y)))) (- x (* -1 y))))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (+ (* -1 (/ y (- x (* -1 y)))) (/ x (- x (* -1 y)))) (- x (* -1 y))))) (taylor -inf y) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
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#s(alt (sqrt (fabs (* (- y (* -1 x)) (- (* -1 (/ y (- y (* -1 x)))) (* -1 (/ x (- y (* -1 x)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (- y (* -1 x)) (- (* -1 (/ y (- y (* -1 x)))) (* -1 (/ x (- y (* -1 x)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (- y (* -1 x)) (- (* -1 (/ y (- y (* -1 x)))) (* -1 (/ x (- y (* -1 x)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (fabs (* (- y (* -1 x)) (- (* -1 (/ y (- y (* -1 x)))) (* -1 (/ x (- y (* -1 x)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) (patch (sqrt.f64 (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x)))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (- y (* -1 x)) (- (* -1 (/ y (- y (* -1 x)))) (* -1 (/ x (- y (* -1 x))))))) (taylor -inf x) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (- y (* -1 x)) (- (* -1 (/ y (- y (* -1 x)))) (* -1 (/ x (- y (* -1 x))))))) (taylor -inf x) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (- y (* -1 x)) (- (* -1 (/ y (- y (* -1 x)))) (* -1 (/ x (- y (* -1 x))))))) (taylor -inf x) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt (fabs (* (- y (* -1 x)) (- (* -1 (/ y (- y (* -1 x)))) (* -1 (/ x (- y (* -1 x))))))) (taylor -inf x) (#s(alt (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) (patch (fabs.f64 (.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ y x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) (* -1 y)) x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) (* -1 y)) x))) (taylor -inf x) (#s(alt (/.f64 x (+.f64 y x)) (patch (/.f64 x (+.f64 y x)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	((* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (/ x (+ y x)))
3.0ms	y	@	0	((* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (/ x (+ y x)))
3.0ms	x	@	-inf	((* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (/ x (+ y x)))
3.0ms	y	@	inf	((* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (/ x (+ y x)))
1.0ms	x	@	inf	((* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (/ x (+ y x)))

simplify145.0ms (2.9%)

Memory

15.8MiB live, 280.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	336	1749
1	1031	1669
2	3212	1445
0	8364	1399

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 117

Calls

Call 1

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

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

rewrite531.0ms (10.6%)

Memory

-172.1MiB live, 287.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	68
0	18	68
1	75	68
2	726	56
0	8674	53

Stop Event

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

Counts

5 → 746

Calls

Call 1

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

Outputs
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eval220.0ms (4.4%)

Memory: 17.5MiB live, 293.8MiB allocated
Compiler: Compiled 35 086 to 3 939 computations (88.8% saved)

prune31.0ms (0.6%)

Memory

-18.6MiB live, 58.3MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	862	1	863
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	863	4	867

Accuracy

100.0%

Counts

867 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (fabs.f64 (-.f64 x y)))
✓	100.0%	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))))
✓	47.0%	(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))
▶	89.1%	(sqrt.f64 (fabs.f64 #s(approx (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))))

Compiler

Compiled 38 to 30 computations (21.1% saved)

simplify153.0ms (3%)

Memory

19.4MiB live, 208.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))
cost-diff	0	(fabs.f64 #s(approx (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)))
cost-diff	0	(sqrt.f64 (fabs.f64 #s(approx (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))))
cost-diff	1024	(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	96
0	21	96
1	38	96
2	88	93
3	203	63
4	331	38
5	680	38
6	3043	38
0	8101	38

Stop Event

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

Calls

Call 1

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

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

localize58.0ms (1.2%)

Memory

-3.1MiB live, 128.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))
accuracy	0.00390625	(-.f64 (/.f64 x y) #s(literal 1 binary64))
accuracy	0.0078125	(sqrt.f64 (fabs.f64 #s(approx (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))))
accuracy	6.8283868928423015	(*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y)

Samples

31.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 74 to 17 computations (77% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 6.0ms (30.2% of total)

ival-div: 5.0ms (25.1% of total)

ival-sqrt: 3.0ms (15.1% of total)

ival-add: 3.0ms (15.1% of total)

ival-sub: 1.0ms (5% of total)

ival-fabs: 1.0ms (5% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.3%)

Memory

-0.7MiB live, 37.2MiB allocated

Counts

5 → 120

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	y	@	-inf	((* (- (/ x y) 1) y) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (- (/ x y) 1))
1.0ms	y	@	0	((* (- (/ x y) 1) y) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (- (/ x y) 1))
1.0ms	x	@	0	((* (- (/ x y) 1) y) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (- (/ x y) 1))
1.0ms	x	@	inf	((* (- (/ x y) 1) y) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (- (/ x y) 1))
1.0ms	x	@	-inf	((* (- (/ x y) 1) y) (sqrt (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))))) (fabs (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x))))) (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (- (/ x y) 1))

simplify173.0ms (3.4%)

Memory

11.0MiB live, 315.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	187	1327
1	552	1280
2	1973	1122
0	8387	1115

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 114

Calls

Call 1

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

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

rewrite148.0ms (2.9%)

Memory

17.5MiB live, 288.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	90
0	21	90
1	97	87
2	904	81
0	8367	78

Stop Event

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

Counts

5 → 72

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval59.0ms (1.2%)

Memory: -57.4MiB live, 94.2MiB allocated
Compiler: Compiled 2 850 to 493 computations (82.7% saved)

prune6.0ms (0.1%)

Memory

18.0MiB live, 18.0MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	186	4	190

Accuracy

100.0%

Counts

190 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (fabs.f64 (-.f64 x y)))
✓	100.0%	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 y x) (fma.f64 y (/.f64 #s(literal -1 binary64) (+.f64 y x)) (/.f64 x (+.f64 y x))))))
✓	47.0%	(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))
✓	89.1%	(sqrt.f64 (fabs.f64 #s(approx (* (+ y x) (+ (* y (/ -1 (+ y x))) (/ x (+ y x)))) (*.f64 (-.f64 (/.f64 x y) #s(literal 1 binary64)) y))))

Compiler

Compiled 89 to 58 computations (34.8% saved)

regimes15.0ms (0.3%)

Memory

-12.5MiB live, 26.1MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	y
2.0ms	x
2.0ms	(fabs.f64 (-.f64 x y))
2.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))
2.0ms	(-.f64 x 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 14 to 16 computations (-14.3% saved)

regimes7.0ms (0.1%)

Memory

17.3MiB live, 17.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
47.0%	1	`x`
47.0%	1	`y`
47.0%	1	`(sqrt.f64 (fabs.f64 (-.f64 x y)))`
47.0%	1	`(fabs.f64 (-.f64 x y))`
47.0%	1	`(-.f64 x y)`

Compiler

Compiled 14 to 16 computations (-14.3% saved)

simplify24.0ms (0.5%)

Memory

11.6MiB live, 50.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	22	13
3	26	13
4	28	13
5	29	13

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness222.0ms (4.4%)

Memory

-32.7MiB live, 48.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	279
1	79	279
2	186	279
3	541	279
4	1596	279
5	2435	279
6	3316	279
7	4901	279
8	5409	279
9	5785	279
10	6306	279
11	6970	279
12	7705	279
0	8082	279

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 14 to 14 computations (0% saved)

preprocess25.0ms (0.5%)

Memory: 31.7MiB live, 70.5MiB allocated
Remove: (sort x y)
Compiler: Compiled 50 to 48 computations (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	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

start0.0ms (0%)

analyze0.0ms (0%)

sample820.0ms (16.3%)

explain69.0ms (1.4%)

preprocess62.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize17.0ms (0.3%)

series53.0ms (1.1%)

simplify128.0ms (2.5%)

rewrite209.0ms (4.2%)

eval90.0ms (1.8%)

prune20.0ms (0.4%)

simplify111.0ms (2.2%)

localize46.0ms (0.9%)

series11.0ms (0.2%)

simplify182.0ms (3.6%)

rewrite353.0ms (7%)

eval276.0ms (5.5%)

prune94.0ms (1.9%)

simplify480.0ms (9.5%)

localize152.0ms (3%)

series19.0ms (0.4%)

simplify145.0ms (2.9%)

rewrite531.0ms (10.6%)

eval220.0ms (4.4%)

prune31.0ms (0.6%)

simplify153.0ms (3%)

localize58.0ms (1.2%)

series13.0ms (0.3%)

simplify173.0ms (3.4%)

rewrite148.0ms (2.9%)

eval59.0ms (1.2%)

prune6.0ms (0.1%)

regimes15.0ms (0.3%)

regimes7.0ms (0.1%)

simplify24.0ms (0.5%)

soundness222.0ms (4.4%)

preprocess25.0ms (0.5%)

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