Metrics for System.Random.MWC.Distributions:standard from mwc-random-0.13.3.2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze1.0ms (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 9 to 8 computations (11.1% saved)

sample640.0ms (18.2%)

Memory

31.1MiB live, 730.0MiB allocated

Samples

370.0ms	8 255×	0	valid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 209.0ms

ival-mult: 145.0ms (69.5% of total)

ival-sub: 49.0ms (23.5% of total)

ival-true: 6.0ms (2.9% of total)

exact: 5.0ms (2.4% of total)

ival-assert: 3.0ms (1.4% of total)

adjust: 0.0ms (0% of total)

Bogosity

explain194.0ms (5.5%)

Memory

5.5MiB live, 81.2MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`y`
-	-	`(-.f64 (*.f64 x x) y)`
-	-	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
-	-	`#s(literal 1/2 binary64)`
-	-	`(*.f64 x x)`
-	-	`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

154.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 131.0ms

ival-mult: 127.0ms (97.3% of total)

ival-sub: 3.0ms (2.3% of total)

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

exact: 0.0ms (0% of total)

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

preprocess42.0ms (1.2%)

Memory

-2.1MiB live, 34.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	46	35
2	129	35
3	381	35
4	678	35
5	844	35
6	882	35
7	882	35
0	6	7
0	9	7
1	12	7
2	23	7
3	45	7
4	71	7
5	99	7
6	169	7
7	266	7
8	410	7
9	466	7
10	496	7
0	496	7

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))

Outputs
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(.f64 (-.f64 (.f64 x x) y) #s(literal 1/2 binary64))

Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify15.0ms (0.4%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) y)
cost-diff	0	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	12	18
2	23	18
3	45	18
4	71	18
5	99	18
6	169	18
7	266	18
8	410	18
9	466	18
10	496	18
0	496	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
#s(literal 1/2 binary64)
(-.f64 (*.f64 x x) y)
(*.f64 x x)
x
y

Outputs
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(.f64 (-.f64 (.f64 x x) y) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(-.f64 (*.f64 x x) y)
(*.f64 x x)
x
y

localize16.0ms (0.5%)

Memory

10.3MiB live, 10.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
accuracy	0.0078125	(-.f64 (*.f64 x x) y)

Samples

11.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-mult: 3.0ms (60.7% of total)

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

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

exact: 0.0ms (0% of total)

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

series44.0ms (1.2%)

Memory

-42.6MiB live, 4.3MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs
#s(alt (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y)) (patch (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y)) #<representation binary64>) () ())
#s(alt (-.f64 (.f64 x x) y) (patch (-.f64 (.f64 x x) y) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Inputs

#s(alt (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) (patch (*.f64 #s(literal 1/2 binary64) (-.f64 (*.f64 x x) y)) #<representation binary64>) () ())

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

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

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

Calls

6 calls:

Time	Variable		Point	Expression
36.0ms	x	@	-inf	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
1.0ms	x	@	0	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
1.0ms	x	@	inf	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
1.0ms	y	@	inf	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
1.0ms	y	@	0	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))

simplify109.0ms (3.1%)

Memory

39.7MiB live, 144.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	327
1	102	327
2	299	327
3	996	291
4	2501	291
5	4979	291
6	7157	291
0	8115	291

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

rewrite355.0ms (10.1%)

Memory

-21.9MiB live, 192.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	27	15
2	178	15
3	1645	15
0	8532	15

Stop Event

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

Counts

3 → 266

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(-.f64 (*.f64 x x) y)
(*.f64 x x)

Outputs
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eval46.0ms (1.3%)

Memory: 7.3MiB live, 44.6MiB allocated
Compiler: Compiled 8 156 to 910 computations (88.8% saved)

prune33.0ms (0.9%)

Memory

-18.7MiB live, 18.9MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	323	3	326
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	324	3	327

Accuracy

100.0%

Counts

327 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
▶	53.1%	(.f64 #s(literal 1/2 binary64) #s(approx (- ( x x) y) (*.f64 x x)))
▶	48.9%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))

Compiler

Compiled 17 to 17 computations (0% saved)

simplify14.0ms (0.4%)

Memory

18.8MiB live, 18.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	58
0	21	58
1	36	58
2	57	58
3	82	58
4	110	58
5	180	58
6	276	58
7	414	58
8	470	58
9	502	58
0	502	58

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize32.0ms (0.9%)

Memory

8.9MiB live, 44.2MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x (neg.f64 y))
accuracy	0	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
accuracy	0	(neg.f64 y)
accuracy	0	(*.f64 x x)
accuracy	0	(.f64 #s(literal 1/2 binary64) #s(approx (- ( x x) y) (*.f64 x x)))
accuracy	30.02422413835746	#s(approx (- (* x x) y) (*.f64 x x))
accuracy	0	(*.f64 y #s(literal -1/2 binary64))
accuracy	32.67792436528592	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))

Samples

23.0ms

256×

valid

Compiler

Compiled 50 to 13 computations (74% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 6.0ms (43.2% of total)

ival-neg: 5.0ms (36% of total)

ival-sub: 1.0ms (7.2% of total)

ival-add: 1.0ms (7.2% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

8 → 156

Calls

Call 1

Inputs
#s(alt #s(approx (* 1/2 (- (* x x) y)) (.f64 y #s(literal -1/2 binary64))) (patch #s(approx ( 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 y #s(literal -1/2 binary64)) (patch (.f64 y #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) #s(approx (- ( x x) y) (.f64 x x))) (patch (.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))) #<representation binary64>) () ())
#s(alt #s(approx (- (* x x) y) (.f64 x x)) (patch #s(approx (- ( x x) y) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y))) #<representation binary64>) () ())
#s(alt (fma.f64 x x (neg.f64 y)) (patch (fma.f64 x x (neg.f64 y)) #<representation binary64>) () ())
#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())

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

Calls

6 calls:

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

simplify114.0ms (3.2%)

Memory

-18.1MiB live, 68.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	864
1	102	864
2	299	864
3	996	756
4	2501	756
5	4979	756
6	7157	756
0	8115	756

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

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

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

rewrite270.0ms (7.7%)

Memory

6.6MiB live, 201.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	51
0	21	51
1	61	51
2	382	45
3	3700	45
0	8812	45

Stop Event

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

Counts

8 → 303

Calls

Call 1

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

Outputs
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eval375.0ms (10.7%)

Memory: 3.3MiB live, 84.2MiB allocated
Compiler: Compiled 7 887 to 1 050 computations (86.7% saved)

prune298.0ms (8.5%)

Memory

-1.7MiB live, 34.7MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	458	1	459
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	458	4	462

Accuracy

100.0%

Counts

462 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
✓	53.1%	(.f64 #s(literal 1/2 binary64) #s(approx (- ( x x) y) (*.f64 x x)))
▶	2.3%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal 1/2 binary64)))
✓	48.9%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))

Compiler

Compiled 21 to 22 computations (-4.8% saved)

simplify16.0ms (0.5%)

Memory

-7.8MiB live, 29.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
0	9	16
1	13	16
2	24	16
3	42	16
4	65	16
5	93	16
6	163	16
7	260	16
8	410	16
9	465	16
10	499	16
0	499	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.6%)

Memory

18.1MiB live, 54.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(*.f64 y #s(literal 1/2 binary64))
accuracy	62.52669625447974	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal 1/2 binary64)))

Samples

15.0ms

256×

valid

Compiler

Compiled 14 to 9 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 5.0ms (56.4% of total)

ival-sub: 4.0ms (45.2% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

12.4MiB live, 12.3MiB allocated

Counts

2 → 36

Calls

Call 1

Inputs

#s(alt #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal 1/2 binary64))) (patch #s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal 1/2 binary64))) #<representation binary64>) () ())

#s(alt (*.f64 y #s(literal 1/2 binary64)) (patch (*.f64 y #s(literal 1/2 binary64)) #<representation binary64>) () ())

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

Calls

6 calls:

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

simplify156.0ms (4.4%)

Memory

-19.7MiB live, 117.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	222
1	56	222
2	151	222
3	377	204
4	1028	186
5	3397	186
6	6121	186
0	8217	186

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

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

rewrite139.0ms (3.9%)

Memory

-10.8MiB live, 182.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
0	9	14
1	28	14
2	179	14
3	1646	14
0	8542	14

Stop Event

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

Counts

2 → 3

Calls

Call 1

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

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

eval4.0ms (0.1%)

Memory: 5.1MiB live, 5.1MiB allocated
Compiler: Compiled 246 to 18 computations (92.7% saved)

prune4.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	39	4	43

Accuracy

100.0%

Counts

43 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
✓	53.1%	(.f64 #s(literal 1/2 binary64) #s(approx (- ( x x) y) (*.f64 x x)))
✓	2.3%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal 1/2 binary64)))
✓	48.9%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))

Compiler

Compiled 49 to 38 computations (22.4% saved)

regimes33.0ms (0.9%)

Memory

-25.2MiB live, 21.5MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

23.0ms	y
2.0ms	x
2.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
2.0ms	(-.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
100.0%	1	`(-.f64 (*.f64 x x) y)`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 17 to 17 computations (0% saved)

regimes11.0ms (0.3%)

Memory

13.5MiB live, 13.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))

Calls

5 calls:

2.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
2.0ms	y
2.0ms	x
2.0ms	(-.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
100.0%	1	`(-.f64 (*.f64 x x) y)`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 17 to 17 computations (0% saved)

regimes14.0ms (0.4%)

Memory

-17.0MiB live, 19.4MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

5 calls:

6.0ms	x
2.0ms	y
2.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
2.0ms	(-.f64 (*.f64 x x) y)
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
89.4%	2	`x`
60.7%	3	`y`
82.9%	2	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
82.9%	2	`(-.f64 (*.f64 x x) y)`
89.4%	2	`(*.f64 x x)`

Compiler

Compiled 17 to 17 computations (0% saved)

regimes8.0ms (0.2%)

Memory

16.6MiB live, 16.6MiB allocated

Accuracy

Total -30.4b remaining (-92.9%)

Threshold costs -30.4b (-92.9%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
2.0ms	y
1.0ms	x
1.0ms	(-.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
48.9%	1	`y`
48.9%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
48.9%	1	`(-.f64 (*.f64 x x) y)`
48.9%	1	`x`
48.9%	1	`(*.f64 x x)`

Compiler

Compiled 17 to 17 computations (0% saved)

bsearch11.0ms (0.3%)

Memory

14.3MiB live, 14.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	3.532702535568562e-54	1.8246350555313693e-48

Samples

5.0ms

144×

valid

Compiler

Compiled 82 to 119 computations (-45.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-sub: 1.0ms (47.4% of total)

ival-mult: 1.0ms (47.4% of total)

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

exact: 0.0ms (0% of total)

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

simplify24.0ms (0.7%)

Memory

4.0MiB live, 40.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	53
1	29	53
2	32	53
3	33	53

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) #s(literal 806297233087391/1645504557321206042154969182557350504982735865633579863348609024 binary64)) #s(approx ( 1/2 (- (* x x) y)) (.f64 y #s(literal -1/2 binary64))) (.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))))
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))

Outputs
(*.f64 #s(literal 1/2 binary64) (fma.f64 x x (neg.f64 y)))
(*.f64 (fma.f64 x x (neg.f64 y)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
(.f64 (-.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(if (<=.f64 (.f64 x x) #s(literal 806297233087391/1645504557321206042154969182557350504982735865633579863348609024 binary64)) #s(approx ( 1/2 (- (* x x) y)) (.f64 y #s(literal -1/2 binary64))) (.f64 #s(literal 1/2 binary64) #s(approx (- (* x x) y) (*.f64 x x))))
(if (<=.f64 (.f64 x x) #s(literal 806297233087391/1645504557321206042154969182557350504982735865633579863348609024 binary64)) #s(approx ( 1/2 (- (* x x) y)) (.f64 #s(literal -1/2 binary64) y)) (.f64 #s(approx (- (* x x) y) (*.f64 x x)) #s(literal 1/2 binary64)))
#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))
#s(approx (* 1/2 (- (* x x) y)) (*.f64 #s(literal -1/2 binary64) y))

soundness408.0ms (11.6%)

Memory

-19.0MiB live, 171.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	327
1	102	327
2	299	327
3	996	291
4	2501	291
5	4979	291
6	7157	291
0	8115	291
0	6	15
0	9	15
1	27	15
2	178	15
3	1645	15
0	8532	15

Stop Event

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

Compiler

Compiled 59 to 39 computations (33.9% saved)

preprocess63.0ms (1.8%)

Memory: -18.0MiB live, 113.0MiB allocated
Remove: (abs x)
Compiler: Compiled 138 to 94 computations (31.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	37
1	46	35
2	129	35
3	381	35
4	678	35
5	844	35
6	882	35
7	882	35
0	6	7
0	9	7
1	12	7
2	23	7
3	45	7
4	71	7
5	99	7
6	169	7
7	266	7
8	410	7
9	466	7
10	496	7
0	496	7

Iter	Nodes	Cost
0	6	18
0	9	18
1	12	18
2	23	18
3	45	18
4	71	18
5	99	18
6	169	18
7	266	18
8	410	18
9	466	18
10	496	18
0	496	18

Iter	Nodes	Cost
0	15	58
0	21	58
1	36	58
2	57	58
3	82	58
4	110	58
5	180	58
6	276	58
7	414	58
8	470	58
9	502	58
0	502	58

Iter	Nodes	Cost
0	8	16
0	9	16
1	13	16
2	24	16
3	42	16
4	65	16
5	93	16
6	163	16
7	260	16
8	410	16
9	465	16
10	499	16
0	499	16

Iter	Nodes	Cost
0	16	37
1	46	35
2	129	35
3	381	35
4	678	35
5	844	35
6	882	35
7	882	35
0	6	7
0	9	7
1	12	7
2	23	7
3	45	7
4	71	7
5	99	7
6	169	7
7	266	7
8	410	7
9	466	7
10	496	7
0	496	7

Iter	Nodes	Cost
0	6	18
0	9	18
1	12	18
2	23	18
3	45	18
4	71	18
5	99	18
6	169	18
7	266	18
8	410	18
9	466	18
10	496	18
0	496	18

Iter	Nodes	Cost
0	15	58
0	21	58
1	36	58
2	57	58
3	82	58
4	110	58
5	180	58
6	276	58
7	414	58
8	470	58
9	502	58
0	502	58

Iter	Nodes	Cost
0	8	16
0	9	16
1	13	16
2	24	16
3	42	16
4	65	16
5	93	16
6	163	16
7	260	16
8	410	16
9	465	16
10	499	16
0	499	16

start0.0ms (0%)

analyze1.0ms (0%)

sample640.0ms (18.2%)

explain194.0ms (5.5%)

preprocess42.0ms (1.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify15.0ms (0.4%)

localize16.0ms (0.5%)

series44.0ms (1.2%)

simplify109.0ms (3.1%)

rewrite355.0ms (10.1%)

eval46.0ms (1.3%)

prune33.0ms (0.9%)

simplify14.0ms (0.4%)

localize32.0ms (0.9%)

series7.0ms (0.2%)

simplify114.0ms (3.2%)

rewrite270.0ms (7.7%)

eval375.0ms (10.7%)

prune298.0ms (8.5%)

simplify16.0ms (0.5%)

localize20.0ms (0.6%)

series3.0ms (0.1%)

simplify156.0ms (4.4%)

rewrite139.0ms (3.9%)

eval4.0ms (0.1%)

prune4.0ms (0.1%)

regimes33.0ms (0.9%)

regimes11.0ms (0.3%)

regimes14.0ms (0.4%)

regimes8.0ms (0.2%)

bsearch11.0ms (0.3%)

simplify24.0ms (0.7%)

soundness408.0ms (11.6%)

preprocess63.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	37
1	46	35
2	129	35
3	381	35
4	678	35
5	844	35
6	882	35
7	882	35
0	6	7
0	9	7
1	12	7
2	23	7
3	45	7
4	71	7
5	99	7
6	169	7
7	266	7
8	410	7
9	466	7
10	496	7
0	496	7

Iter	Nodes	Cost
0	6	18
0	9	18
1	12	18
2	23	18
3	45	18
4	71	18
5	99	18
6	169	18
7	266	18
8	410	18
9	466	18
10	496	18
0	496	18

Iter	Nodes	Cost
0	15	58
0	21	58
1	36	58
2	57	58
3	82	58
4	110	58
5	180	58
6	276	58
7	414	58
8	470	58
9	502	58
0	502	58

Iter	Nodes	Cost
0	8	16
0	9	16
1	13	16
2	24	16
3	42	16
4	65	16
5	93	16
6	163	16
7	260	16
8	410	16
9	465	16
10	499	16
0	499	16