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

0.3MiB live, 0.3MiB 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)

sample1.0s (35%)

Memory

-153.2MiB live, 925.0MiB allocated

Samples

412.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 225.0ms

ival-sub: 90.0ms (40.1% of total)

ival-fabs: 69.0ms (30.7% of total)

ival-sqrt: 57.0ms (25.4% of total)

ival-true: 5.0ms (2.2% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

explain48.0ms (1.7%)

Memory

-5.7MiB live, 77.0MiB 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

21.0ms

512×

valid

Compiler

Compiled 37 to 19 computations (48.6% saved)

Precisions

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

ival-sqrt: 4.0ms (41.1% of total)

ival-sub: 3.0ms (30.8% of total)

ival-fabs: 3.0ms (30.8% of total)

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

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

preprocess23.0ms (0.8%)

Memory

9.2MiB live, 46.3MiB allocated

Algorithm

1×	egg-herbie

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
52×	`lower-*.f64`
52×	`lower-*.f32`
50×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort x y)

Compiler

Compiled 5 to 5 computations (0% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB 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 (0.2%)

Memory

13.7MiB live, 13.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
52×	`lower-*.f64`
52×	`lower-*.f32`
34×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize19.0ms (0.7%)

Memory

-0.5MiB live, 36.4MiB allocated

Localize:

Found 3 expressions of interest:

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

Samples

15.0ms

256×

valid

Compiler

Compiled 16 to 7 computations (56.3% saved)

Precisions

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

ival-sqrt: 3.0ms (54.2% of total)

ival-sub: 1.0ms (18.1% of total)

ival-fabs: 1.0ms (18.1% of total)

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

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

series4.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB 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))

simplify168.0ms (5.9%)

Memory

-2.8MiB live, 117.0MiB allocated

Algorithm

1×	egg-herbie

Rules

2 658×	`lower-fma.f64`
2 658×	`lower-fma.f32`
2 540×	`lower-*.f64`
2 540×	`lower-*.f32`
1 962×	`div-sub`

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)

rewrite284.0ms (9.9%)

Memory

-6.4MiB live, 248.3MiB allocated

Rules

4 642×	`lower-/.f64`
4 642×	`lower-/.f32`
4 306×	`lower-fma.f64`
4 306×	`lower-fma.f32`
3 256×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 322

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fabs.f64 (-.f64 y x))))
(.f64 (sqrt.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (+.f64 y x)))))
(.f64 (sqrt.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (.f64 x x)))) (sqrt.f64 (fabs.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)))))
(.f64 (sqrt.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (.f64 x x)))) (pow.f64 (fabs.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (fma.f64 y x (hypot.f64 y x))))))
(*.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (fabs.f64 (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (pow.f64 (fabs.f64 (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/4 binary64)) (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (-.f64 y x))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (fabs.f64 (-.f64 y x))))
(pow.f64 (pow.f64 (-.f64 x y) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))) (neg.f64 (sqrt.f64 (fabs.f64 (+.f64 y x)))))
(/.f64 (neg.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))) (neg.f64 (sqrt.f64 (fabs.f64 (fma.f64 y x (hypot.f64 y x))))))
(/.f64 (sqrt.f64 (neg.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))) (sqrt.f64 (neg.f64 (fabs.f64 (+.f64 y x)))))
(/.f64 (sqrt.f64 (neg.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))) (sqrt.f64 (neg.f64 (fabs.f64 (fma.f64 y x (hypot.f64 y x))))))
(/.f64 (sqrt.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (*.f64 x x)))) (sqrt.f64 (fabs.f64 (+.f64 y x))))
(/.f64 (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (fabs.f64 (fma.f64 y x (hypot.f64 y x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fabs.f64 (+.f64 y x))) (sqrt.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fabs.f64 (fma.f64 y x (hypot.f64 y x)))) (sqrt.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x)))))
(sqrt.f64 (fabs.f64 (-.f64 y x)))
(exp.f64 (fma.f64 (log.f64 (fabs.f64 (-.f64 y x))) #s(literal 1/4 binary64) (*.f64 (log.f64 (fabs.f64 (-.f64 y x))) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (fabs.f64 (-.f64 y x))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 x y) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fabs.f64 (-.f64 y x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fabs.f64 (-.f64 y x))) #s(literal 1/2 binary64)))
(.f64 (fabs.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fabs.f64 (-.f64 (hypot.f64 y x) (*.f64 y x))))
(.f64 (fabs.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (fabs.f64 (-.f64 (hypot.f64 y x) (*.f64 y x))))
(.f64 (fabs.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 y x)) (fma.f64 (neg.f64 y) y (*.f64 x x)))) (fabs.f64 (-.f64 y x)))
(.f64 (fabs.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 y x) y) #s(literal 2 binary64))))) (fabs.f64 (-.f64 (.f64 (+.f64 y x) y) (.f64 x x))))
(.f64 (fabs.f64 (/.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (fabs.f64 (fma.f64 (.f64 (+.f64 y x) y) (-.f64 (.f64 (+.f64 y x) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (fabs.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 y x) y) #s(literal 2 binary64))))) (fabs.f64 (-.f64 (.f64 (+.f64 y x) y) (.f64 x x))))
(.f64 (fabs.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (fabs.f64 (fma.f64 (.f64 (+.f64 y x) y) (-.f64 (.f64 (+.f64 y x) y) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (fabs.f64 (/.f64 (.f64 (+.f64 y x) (-.f64 y x)) (*.f64 (+.f64 y x) (-.f64 y x)))) (fabs.f64 (-.f64 y x)))
(.f64 (neg.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fabs.f64 (+.f64 y x)))))
(*.f64 (neg.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fabs.f64 (fma.f64 y x (hypot.f64 y x))))))
(.f64 (fabs.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))) (fabs.f64 (fma.f64 (neg.f64 y) y (.f64 x x))))
(*.f64 (fabs.f64 (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64))) (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(*.f64 #s(literal 1 binary64) (fabs.f64 (-.f64 y x)))
(*.f64 (fabs.f64 (+.f64 y x)) (fabs.f64 (/.f64 (-.f64 x y) (neg.f64 (+.f64 y x)))))
(*.f64 (fabs.f64 (+.f64 y x)) (fabs.f64 (/.f64 (-.f64 x y) (+.f64 y x))))
(.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (fabs.f64 (pow.f64 (neg.f64 (+.f64 y x)) #s(literal -1 binary64))))
(.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (.f64 x x))) (fabs.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))))
(*.f64 (fabs.f64 (fma.f64 y x (hypot.f64 y x))) (fabs.f64 (/.f64 (-.f64 x y) (neg.f64 (fma.f64 y x (hypot.f64 y x))))))
(*.f64 (fabs.f64 (fma.f64 y x (hypot.f64 y x))) (fabs.f64 (/.f64 (-.f64 x y) (fma.f64 y x (hypot.f64 y x)))))
(*.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fabs.f64 (pow.f64 (neg.f64 (fma.f64 y x (hypot.f64 y x))) #s(literal -1 binary64))))
(*.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fabs.f64 (pow.f64 (fma.f64 y x (hypot.f64 y x)) #s(literal -1 binary64))))
(*.f64 (fabs.f64 (-.f64 y x)) #s(literal 1 binary64))
(pow.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) (-.f64 y x))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))) (neg.f64 (neg.f64 (fabs.f64 (+.f64 y x)))))
(/.f64 (neg.f64 (neg.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))) (neg.f64 (neg.f64 (fabs.f64 (fma.f64 y x (hypot.f64 y x))))))
(/.f64 (fabs.f64 (.f64 #s(literal -1 binary64) (.f64 (+.f64 y x) (-.f64 y x)))) (fabs.f64 (+.f64 y x)))
(/.f64 (fabs.f64 (*.f64 #s(literal -1 binary64) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (fabs.f64 (fma.f64 y x (hypot.f64 y x))))
(/.f64 (fabs.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 x y) #s(literal 2 binary64)))) (fabs.f64 (+.f64 #s(literal 0 binary64) (-.f64 x y))))
(/.f64 (fabs.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 x y) #s(literal 3 binary64)))) (fabs.f64 (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (-.f64 x y) #s(literal 2 binary64)) (*.f64 #s(literal 0 binary64) (-.f64 x y))))))
(/.f64 (fabs.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (+.f64 y x))) (fabs.f64 (hypot.f64 y x)))
(/.f64 (fabs.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (+.f64 y x))) (fabs.f64 (fma.f64 (*.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (fabs.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 y x (hypot.f64 y x)))) (fabs.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (fabs.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) (fma.f64 y x (hypot.f64 y x)))) (fabs.f64 (hypot.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3/2 binary64)))))
(/.f64 (fabs.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) #s(literal 1 binary64))) (fabs.f64 (fma.f64 y x (hypot.f64 y x))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (+.f64 y x))) #s(literal 2 binary64)) (pow.f64 (.f64 y (/.f64 y (+.f64 y x))) #s(literal 2 binary64)))) (fabs.f64 (fma.f64 x (/.f64 x (+.f64 y x)) (*.f64 y (/.f64 y (+.f64 y x))))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))) #s(literal 2 binary64)))) (fabs.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))))))
(/.f64 (fabs.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (+.f64 y x) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (+.f64 y x) #s(literal 3 binary64))))) (fabs.f64 (+.f64 (pow.f64 (.f64 x (/.f64 x (+.f64 y x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 y (/.f64 y (+.f64 y x))) #s(literal 2 binary64)) (.f64 (.f64 x (/.f64 x (+.f64 y x))) (*.f64 y (/.f64 y (+.f64 y x))))))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))) #s(literal 3 binary64)))) (fabs.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y x (hypot.f64 y x))))))))
(/.f64 (fabs.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64))) (fabs.f64 (.f64 (hypot.f64 y x) (+.f64 y x))))
(/.f64 (fabs.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (fabs.f64 (.f64 (fma.f64 (*.f64 y y) (hypot.f64 y x) (pow.f64 x #s(literal 4 binary64))) (+.f64 y x))))
(/.f64 (fabs.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64))) (fabs.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y x (hypot.f64 y x)))))
(/.f64 (fabs.f64 (.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 y #s(literal 9 binary64))) #s(literal 1 binary64))) (fabs.f64 (.f64 (hypot.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (pow.f64 (*.f64 y x) #s(literal 3/2 binary64))) (fma.f64 y x (hypot.f64 y x)))))
(/.f64 (fabs.f64 (-.f64 (.f64 (.f64 x x) (+.f64 y x)) (.f64 (+.f64 y x) (.f64 y y)))) (fabs.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64))))
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(/.f64 (exp.f64 (log.f64 (fabs.f64 (fma.f64 (neg.f64 y) y (*.f64 x x))))) (exp.f64 (log.f64 (fabs.f64 (+.f64 y x)))))
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(-.f64 x y)
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eval103.0ms (3.6%)

Memory: -5.3MiB live, 104.1MiB allocated
Compiler: Compiled 8 510 to 1 401 computations (83.5% saved)

prune12.0ms (0.4%)

Memory

-16.4MiB live, 32.9MiB allocated

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	390	1	391
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	390	2	392

Accuracy

100.0%

Counts

392 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (fabs.f64 (-.f64 x y)))
▶	53.0%	(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))

Compiler

Compiled 10 to 11 computations (-10% saved)

simplify7.0ms (0.3%)

Memory

17.4MiB live, 17.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
32×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
0	10	24
1	15	24
2	20	24
3	27	24
4	36	24
5	53	24
6	80	24
7	107	24
8	151	24
9	166	24
10	174	24
0	174	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (0.6%)

Memory

-5.3MiB live, 32.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 (fabs.f64 #s(approx (- x y) (neg.f64 y))))
accuracy	0	(neg.f64 y)
accuracy	0	(fabs.f64 #s(approx (- x y) (neg.f64 y)))
accuracy	31.095535886191673	#s(approx (- x y) (neg.f64 y))

Samples

14.0ms

256×

valid

Compiler

Compiled 17 to 8 computations (52.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-fabs: 3.0ms (41.3% of total)

ival-sqrt: 2.0ms (27.5% of total)

ival-sub: 1.0ms (13.8% of total)

ival-neg: 1.0ms (13.8% of total)

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

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

series3.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

4 → 84

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>) () ())

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

Calls

6 calls:

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

simplify181.0ms (6.3%)

Memory

9.1MiB live, 124.4MiB allocated

Algorithm

1×	egg-herbie

Rules

2 658×	`lower-fma.f64`
2 658×	`lower-fma.f32`
2 540×	`lower-*.f64`
2 540×	`lower-*.f32`
1 962×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	303
1	79	303
2	186	303
3	541	303
4	1596	303
5	2435	303
6	3316	303
7	4901	303
8	5409	303
9	5785	303
10	6306	303
11	6970	303
12	7705	303
0	8082	303

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 81

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)
(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)
(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)
(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)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 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)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 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)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 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)

rewrite133.0ms (4.6%)

Memory

-0.2MiB live, 165.4MiB allocated

Rules

3 818×	`lower-fma.f64`
3 818×	`lower-fma.f32`
3 386×	`lower-/.f64`
3 386×	`lower-/.f32`
2 450×	`lower-*.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	10	23
1	32	23
2	170	23
3	1599	19
0	9594	19

Stop Event

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

Counts

4 → 63

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)

Outputs
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fabs.f64 #s(approx (- x y) y))))
(*.f64 (pow.f64 (fabs.f64 #s(approx (- x y) y)) #s(literal 1/4 binary64)) (pow.f64 (fabs.f64 #s(approx (- x y) y)) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fabs.f64 #s(approx (- x y) y))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (fabs.f64 #s(approx (- x y) y))))
(pow.f64 (pow.f64 #s(approx (- x y) y) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fabs.f64 #s(approx (- x y) y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 #s(approx (- x y) y)) #s(literal 1/2 binary64))
(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))
(exp.f64 (fma.f64 (log.f64 (fabs.f64 #s(approx (- x y) y))) #s(literal 1/4 binary64) (*.f64 (log.f64 (fabs.f64 #s(approx (- x y) y))) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (fabs.f64 #s(approx (- x y) y))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(approx (- x y) y) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fabs.f64 #s(approx (- x y) y)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fabs.f64 #s(approx (- x y) y))) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1 binary64) (fabs.f64 #s(approx (- x y) y)))
(*.f64 (fabs.f64 #s(approx (- x y) y)) #s(literal 1 binary64))
(/.f64 (fabs.f64 (neg.f64 (pow.f64 #s(approx (- x y) y) #s(literal 2 binary64)))) (fabs.f64 #s(approx (- x y) y)))
(/.f64 (fabs.f64 (neg.f64 (pow.f64 #s(approx (- x y) y) #s(literal 3 binary64)))) (fabs.f64 (fma.f64 #s(approx (- x y) y) #s(approx (- x y) y) #s(literal 0 binary64))))
(fabs.f64 (-.f64 (neg.f64 #s(approx (- x y) y)) #s(literal 0 binary64)))
(fabs.f64 (neg.f64 #s(approx (- x y) y)))
(fabs.f64 #s(approx (- x y) y))
(exp.f64 (log.f64 (fabs.f64 #s(approx (- x y) y))))
(*.f64 #s(literal 1 binary64) #s(approx (- x y) y))
(*.f64 #s(literal -1 binary64) (neg.f64 #s(approx (- x y) y)))
#s(approx (- x y) y)
(/.f64 (-.f64 (pow.f64 #s(approx (- x y) y) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 #s(approx (- x y) y) #s(approx (- x y) y) (+.f64 #s(literal 0 binary64) (*.f64 #s(approx (- x y) y) #s(literal 0 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (neg.f64 #s(approx (- x y) y)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 #s(approx (- x y) y) #s(approx (- x y) y) (*.f64 #s(literal 0 binary64) (neg.f64 #s(approx (- x y) y))))))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 #s(approx (- x y) y) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 #s(approx (- x y) y) #s(literal 2 binary64)) #s(literal 0 binary64))))
(/.f64 (neg.f64 (pow.f64 #s(approx (- x y) y) #s(literal 2 binary64))) (neg.f64 #s(approx (- x y) y)))
(neg.f64 (neg.f64 #s(approx (- x y) y)))
(fma.f64 #s(literal 1 binary64) #s(approx (- x y) y) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (neg.f64 #s(approx (- x y) y)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (- x y) y)))
(-.f64 #s(approx (- x y) y) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) #s(approx (- x y) y))
(+.f64 #s(approx (- x y) y) #s(literal 0 binary64))
(*.f64 #s(literal 1 binary64) y)
(*.f64 #s(literal -1 binary64) y)
(.f64 (.f64 y y) (pow.f64 y #s(literal -1 binary64)))
(*.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 y #s(literal -2 binary64)))
(*.f64 y #s(literal -1 binary64))
(pow.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 y #s(literal 1 binary64))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 0 binary64)) (*.f64 y y))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 y #s(literal 5 binary64))) (pow.f64 y #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 y #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 y #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal -1 binary64)))
(/.f64 (*.f64 y y) (-.f64 y #s(literal 0 binary64)))
(/.f64 (*.f64 y y) y)
(/.f64 (pow.f64 y #s(literal 3 binary64)) (*.f64 y y))
(neg.f64 y)
(fma.f64 #s(literal 1 binary64) y #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) y #s(literal 0 binary64))
(fma.f64 (*.f64 y y) (pow.f64 y #s(literal -1 binary64)) #s(literal 0 binary64))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 y #s(literal -2 binary64)) #s(literal 0 binary64))
(fma.f64 y #s(literal -1 binary64) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) y)
(exp.f64 (*.f64 (log.f64 y) #s(literal 1 binary64)))
(exp.f64 (log.f64 y))
(+.f64 #s(literal 0 binary64) y)
(+.f64 y #s(literal 0 binary64))
y

eval36.0ms (1.2%)

Memory: -29.2MiB live, 46.6MiB allocated
Compiler: Compiled 999 to 248 computations (75.2% saved)

prune6.0ms (0.2%)

Memory

24.7MiB live, 24.7MiB allocated

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	144	2	146

Accuracy

100.0%

Counts

146 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (fabs.f64 (-.f64 x y)))
▶	53.0%	(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify9.0ms (0.3%)

Memory

-17.5MiB live, 20.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
32×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	8	19
1	10	19
2	15	19
3	21	19
4	30	19
5	45	19
6	78	19
7	105	19
8	148	19
9	163	19
10	171	19
0	171	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.7%)

Memory

2.5MiB live, 42.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))
accuracy	0	(fabs.f64 #s(approx (- x y) y))
accuracy	62.571071371385855	#s(approx (- x y) y)

Samples

11.0ms

256×

valid

Compiler

Compiled 15 to 7 computations (53.3% saved)

Precisions

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

ival-fabs: 2.0ms (36.5% of total)

ival-sqrt: 2.0ms (36.5% of total)

ival-sub: 1.0ms (18.3% of total)

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

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

series3.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

3 → 72

Calls

Call 1

Inputs

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

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

#s(alt #s(approx (- x y) y) (patch #s(approx (- x y) y) #<representation:binary64>) () ())

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

Calls

6 calls:

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

simplify159.0ms (5.5%)

Memory

5.5MiB live, 118.7MiB allocated

Algorithm

1×	egg-herbie

Rules

2 658×	`lower-fma.f64`
2 658×	`lower-fma.f32`
2 540×	`lower-*.f64`
2 540×	`lower-*.f32`
1 962×	`div-sub`

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)

rewrite174.0ms (6.1%)

Memory

-10.5MiB live, 226.2MiB allocated

Rules

4 940×	`lower-fma.f64`
4 940×	`lower-fma.f32`
3 038×	`lower-/.f64`
3 038×	`lower-/.f32`
2 820×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	8	18
1	27	18
2	155	18
3	1398	18
0	9745	18

Stop Event

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

Counts

3 → 43

Calls

Call 1

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

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

eval11.0ms (0.4%)

Memory: 26.6MiB live, 26.6MiB allocated
Compiler: Compiled 784 to 149 computations (81% saved)

prune27.0ms (0.9%)

Memory

-13.7MiB live, 21.6MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	112	2	114

Accuracy

100.0%

Counts

114 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (fabs.f64 (-.f64 x y)))
✓	53.0%	(sqrt.f64 (fabs.f64 #s(approx (- x y) y)))

Compiler

Compiled 23 to 22 computations (4.3% saved)

regimes9.0ms (0.3%)

Memory

27.1MiB live, 27.1MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 14 to 16 computations (-14.3% saved)

regimes9.0ms (0.3%)

Memory

-10.4MiB live, 27.6MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	(-.f64 x y)
2.0ms	(sqrt.f64 (fabs.f64 (-.f64 x y)))
1.0ms	(fabs.f64 (-.f64 x y))
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
53.0%	1	`x`
53.0%	1	`y`
53.0%	1	`(sqrt.f64 (fabs.f64 (-.f64 x y)))`
53.0%	1	`(fabs.f64 (-.f64 x y))`
53.0%	1	`(-.f64 x y)`

Compiler

Compiled 14 to 16 computations (-14.3% saved)

simplify42.0ms (1.5%)

Memory

-25.9MiB live, 72.3MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative-binary64-+.f64`
8×	`sub-neg-binary64-neg.f64-+.f64--.f64`
4×	`-commutative-binary64-.f64`
4×	`neg-sub0-binary64--.f64-neg.f64`
4×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	20	12
3	25	12
4	28	12
5	29	12

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness303.0ms (10.6%)

Memory

-11.8MiB live, 186.0MiB allocated

Rules

3 818×	`lower-fma.f64`
3 818×	`lower-fma.f32`
3 386×	`lower-/.f64`
3 386×	`lower-/.f32`
2 658×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	10	23
1	32	23
2	170	23
3	1599	19
0	9594	19
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
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 18 to 19 computations (-5.6% saved)

preprocess47.0ms (1.6%)

Memory: 17.7MiB live, 55.9MiB allocated
Remove: (sort x y)
Compiler: Compiled 48 to 46 computations (4.2% 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	7	24
0	10	24
1	15	24
2	20	24
3	27	24
4	36	24
5	53	24
6	80	24
7	107	24
8	151	24
9	166	24
10	174	24
0	174	24

Iter	Nodes	Cost
0	6	19
0	8	19
1	10	19
2	15	19
3	21	19
4	30	19
5	45	19
6	78	19
7	105	19
8	148	19
9	163	19
10	171	19
0	171	19

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	7	24
0	10	24
1	15	24
2	20	24
3	27	24
4	36	24
5	53	24
6	80	24
7	107	24
8	151	24
9	166	24
10	174	24
0	174	24

Iter	Nodes	Cost
0	6	19
0	8	19
1	10	19
2	15	19
3	21	19
4	30	19
5	45	19
6	78	19
7	105	19
8	148	19
9	163	19
10	171	19
0	171	19

start0.0ms (0%)

analyze0.0ms (0%)

sample1.0s (35%)

explain48.0ms (1.7%)

preprocess23.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.2%)

localize19.0ms (0.7%)

series4.0ms (0.1%)

simplify168.0ms (5.9%)

rewrite284.0ms (9.9%)

eval103.0ms (3.6%)

prune12.0ms (0.4%)

simplify7.0ms (0.3%)

localize18.0ms (0.6%)

series3.0ms (0.1%)

simplify181.0ms (6.3%)

rewrite133.0ms (4.6%)

eval36.0ms (1.2%)

prune6.0ms (0.2%)

simplify9.0ms (0.3%)

localize20.0ms (0.7%)

series3.0ms (0.1%)

simplify159.0ms (5.5%)

rewrite174.0ms (6.1%)

eval11.0ms (0.4%)

prune27.0ms (0.9%)

regimes9.0ms (0.3%)

regimes9.0ms (0.3%)

simplify42.0ms (1.5%)

soundness303.0ms (10.6%)

preprocess47.0ms (1.6%)

end0.0ms (0%)

Profiling

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

Iter	Nodes	Cost
0	7	24
0	10	24
1	15	24
2	20	24
3	27	24
4	36	24
5	53	24
6	80	24
7	107	24
8	151	24
9	166	24
10	174	24
0	174	24

Iter	Nodes	Cost
0	6	19
0	8	19
1	10	19
2	15	19
3	21	19
4	30	19
5	45	19
6	78	19
7	105	19
8	148	19
9	163	19
10	171	19
0	171	19