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

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 9 to 8 computations (11.1% saved)

sample584.0ms (21.6%)

Memory

26.4MiB live, 750.3MiB allocated

Samples

360.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 175.0ms

ival-mult: 118.0ms (67.5% of total)

ival-sub: 43.0ms (24.6% of total)

ival-true: 6.0ms (3.4% of total)

exact: 5.0ms (2.9% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

explain210.0ms (7.8%)

Memory

-16.4MiB live, 70.8MiB 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

24.0ms

512×

valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 7.0ms (66.5% of total)

ival-sub: 3.0ms (28.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess42.0ms (1.5%)

Memory

16.7MiB live, 16.7MiB 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

simplify20.0ms (0.7%)

Memory

-13.3MiB live, 22.5MiB 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 (0.6%)

Memory

30.1MiB live, 30.1MiB allocated

Localize:

Found 3 expressions of interest:

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

Samples

11.0ms

256×

valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

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

ival-mult: 3.0ms (58.3% of total)

ival-sub: 1.0ms (19.4% 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

-29.8MiB live, 7.8MiB 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
2.0ms	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))
0.0ms	y	@	0	((* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))

simplify116.0ms (4.3%)

Memory

18.1MiB live, 62.1MiB 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)

rewrite159.0ms (5.9%)

Memory

20.4MiB live, 209.8MiB 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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eval35.0ms (1.3%)

Memory: 3.4MiB live, 79.0MiB allocated
Compiler: Compiled 8 156 to 910 computations (88.8% saved)

prune25.0ms (0.9%)

Memory

-31.6MiB live, 24.2MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	324	2	326
Fresh	0	0	0
Picked	0	1	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) (-.f64 (.f64 x x) y))
▶	53.6%	(.f64 #s(literal 1/2 binary64) #s(approx (- ( x x) y) (*.f64 x x)))
▶	48.6%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))

Compiler

Compiled 17 to 17 computations (0% saved)

simplify13.0ms (0.5%)

Memory

9.1MiB live, 9.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
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	12	41
0	15	41
1	20	41
2	31	41
3	52	41
4	77	41
5	105	41
6	175	41
7	274	41
8	414	41
9	469	41
10	501	41
0	501	41

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

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

localize132.0ms (4.9%)

Memory

-14.3MiB live, 24.5MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(.f64 #s(literal 1/2 binary64) #s(approx (- ( x x) y) (*.f64 x x)))
accuracy	29.71715824953389	#s(approx (- (* x x) y) (*.f64 x x))
accuracy	0	(*.f64 y #s(literal -1/2 binary64))
accuracy	32.91975428792022	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))

Samples

127.0ms

256×

valid

Compiler

Compiled 55 to 19 computations (65.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

ival-mult: 117.0ms (98.1% of total)

ival-sub: 1.0ms (0.8% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.2%)

Memory

3.9MiB live, 3.9MiB allocated

Counts

5 → 96

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>) () ())

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

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))
1.0ms	y	@	-inf	((* 1/2 (- (* x x) y)) (* y -1/2) (* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
0.0ms	y	@	0	((* 1/2 (- (* x x) y)) (* y -1/2) (* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
0.0ms	x	@	inf	((* 1/2 (- (* x x) y)) (* y -1/2) (* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))
0.0ms	x	@	-inf	((* 1/2 (- (* x x) y)) (* y -1/2) (* 1/2 (- (* x x) y)) (- (* x x) y) (* x x))

simplify114.0ms (4.2%)

Memory

16.7MiB live, 55.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	549
1	102	549
2	299	549
3	996	477
4	2501	477
5	4979	477
6	7157	477
0	8115	477

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

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 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)
(* -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)
(+ (* -1/2 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 (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)))))
(* 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))
(* -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 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))
(* -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))
(+ (* -1/2 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 (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))
(* 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)

rewrite161.0ms (5.9%)

Memory

12.8MiB live, 160.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	37
0	15	37
1	35	37
2	186	37
3	1656	37
0	8520	37

Stop Event

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

Counts

5 → 26

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)

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

eval13.0ms (0.5%)

Memory: -9.3MiB live, 27.0MiB allocated
Compiler: Compiled 864 to 98 computations (88.7% saved)

prune11.0ms (0.4%)

Memory

-29.5MiB live, 22.9MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	122	3	125

Accuracy

100.0%

Counts

125 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
✓	53.6%	(.f64 #s(literal 1/2 binary64) #s(approx (- ( x x) y) (*.f64 x x)))
✓	48.6%	#s(approx (* 1/2 (- (* x x) y)) (*.f64 y #s(literal -1/2 binary64)))

Compiler

Compiled 34 to 28 computations (17.6% saved)

regimes25.0ms (0.9%)

Memory

15.8MiB live, 52.8MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#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:

15.0ms	(*.f64 x x)
4.0ms	(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))
2.0ms	y
2.0ms	x
2.0ms	(-.f64 (*.f64 x x) y)

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)

regimes8.0ms (0.3%)

Memory

24.7MiB live, 24.7MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#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:

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

Results

Accuracy	Segments	Branch
86.9%	2	`x`
69.5%	3	`y`
82.9%	4	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
82.9%	4	`(-.f64 (*.f64 x x) y)`
86.9%	2	`(*.f64 x x)`

Compiler

Compiled 17 to 17 computations (0% saved)

regimes8.0ms (0.3%)

Memory

-15.0MiB live, 24.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

Results

Accuracy	Segments	Branch
48.6%	1	`y`
48.6%	1	`(.f64 #s(literal 1/2 binary64) (-.f64 (.f64 x x) y))`
48.6%	1	`(-.f64 (*.f64 x x) y)`
48.6%	1	`x`
48.6%	1	`(*.f64 x x)`

Compiler

Compiled 17 to 17 computations (0% saved)

bsearch14.0ms (0.5%)

Memory

-10.0MiB live, 28.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	3.1136588965695433e-15	1.9626350719171635

Samples

7.0ms

160×

valid

Compiler

Compiled 90 to 131 computations (-45.6% saved)

Precisions

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

ival-sub: 1.0ms (43.8% of total)

ival-mult: 1.0ms (43.8% of total)

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

exact: 0.0ms (0% of total)

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

simplify150.0ms (5.5%)

Memory

1.6MiB live, 45.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	46
1	22	46
2	27	46
3	29	46
4	30	46

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (*.f64 x x) #s(literal 5289050460814003/37778931862957161709568 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) (-.f64 (.f64 x x) y))
(.f64 (-.f64 (.f64 x x) y) #s(literal 1/2 binary64))
(if (<=.f64 (.f64 x x) #s(literal 5289050460814003/37778931862957161709568 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 5289050460814003/37778931862957161709568 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))

soundness735.0ms (27.2%)

Memory

0.3MiB live, 112.2MiB allocated

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×	done
1×	iter limit
1×	node limit

Compiler

Compiled 38 to 27 computations (28.9% saved)

preprocess99.0ms (3.7%)

Memory: -7.0MiB live, 56.7MiB allocated
Remove: (abs x)
Compiler: Compiled 110 to 76 computations (30.9% 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	12	41
0	15	41
1	20	41
2	31	41
3	52	41
4	77	41
5	105	41
6	175	41
7	274	41
8	414	41
9	469	41
10	501	41
0	501	41

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	12	41
0	15	41
1	20	41
2	31	41
3	52	41
4	77	41
5	105	41
6	175	41
7	274	41
8	414	41
9	469	41
10	501	41
0	501	41

start0.0ms (0%)

analyze0.0ms (0%)

sample584.0ms (21.6%)

explain210.0ms (7.8%)

preprocess42.0ms (1.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify20.0ms (0.7%)

localize16.0ms (0.6%)

series7.0ms (0.2%)

simplify116.0ms (4.3%)

rewrite159.0ms (5.9%)

eval35.0ms (1.3%)

prune25.0ms (0.9%)

simplify13.0ms (0.5%)

localize132.0ms (4.9%)

series5.0ms (0.2%)

simplify114.0ms (4.2%)

rewrite161.0ms (5.9%)

eval13.0ms (0.5%)

prune11.0ms (0.4%)

regimes25.0ms (0.9%)

regimes8.0ms (0.3%)

regimes8.0ms (0.3%)

bsearch14.0ms (0.5%)

simplify150.0ms (5.5%)

soundness735.0ms (27.2%)

preprocess99.0ms (3.7%)

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	12	41
0	15	41
1	20	41
2	31	41
3	52	41
4	77	41
5	105	41
6	175	41
7	274	41
8	414	41
9	469	41
10	501	41
0	501	41