Metrics for Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample755.0ms (24.3%)

Memory

-37.5MiB live, 1 016.8MiB allocated

Samples

482.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 212.0ms

ival-sub: 111.0ms (52.4% of total)

ival-mult: 91.0ms (43% of total)

ival-true: 6.0ms (2.8% of total)

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

Bogosity

explain134.0ms (4.3%)

Memory

-6.5MiB live, 70.1MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 x (*.f64 y y))`
-	-	`y`
-	-	`(*.f64 y y)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

18.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

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

ival-mult: 4.0ms (57.5% of total)

ival-sub: 2.0ms (28.8% of total)

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

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

preprocess22.0ms (0.7%)

Memory

36.7MiB live, 36.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	39	29
2	90	26
3	198	26
4	306	26
5	330	26
6	332	26
0	4	5
0	6	5
1	11	5
2	19	5
3	28	5
4	41	5
5	60	5
6	96	5
7	128	5
8	157	5
9	177	5
10	189	5
0	189	5

Stop Event

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

Calls

Call 1

Inputs
(-.f64 x (*.f64 y y))

Outputs
(-.f64 x (*.f64 y y))
(fma.f64 (neg.f64 y) y x)

Symmetry

(abs y)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

simplify30.0ms (1%)

Memory

-22.9MiB live, 12.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	11	10
2	19	10
3	28	10
4	41	10
5	60	10
6	96	10
7	128	10
8	157	10
9	177	10
10	189	10
0	189	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 x (*.f64 y y))
x
(*.f64 y y)
y

Outputs
(-.f64 x (*.f64 y y))
(fma.f64 (neg.f64 y) y x)
x
(*.f64 y y)
y

localize13.0ms (0.4%)

Memory

21.3MiB live, 21.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(*.f64 y y)
accuracy	0.01171875	(-.f64 x (*.f64 y y))

Samples

9.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (60.6% of total)

ival-sub: 1.0ms (30.3% of total)

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

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

series3.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

2 → 36

Calls

Call 1

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

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

Calls

6 calls:

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

simplify139.0ms (4.5%)

Memory

-18.5MiB live, 94.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	141
1	46	141
2	112	141
3	309	141
4	929	141
5	1915	141
6	3790	141
7	6274	141
0	8148	141

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 33

Calls

Call 1

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

Outputs
x
(+ x (* -1 (pow y 2)))
(-.f64 x (*.f64 y y))
(+ x (* -1 (pow y 2)))
(-.f64 x (*.f64 y y))
(+ x (* -1 (pow y 2)))
(-.f64 x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ x (pow y 2)) 1))
(-.f64 x (*.f64 y y))
(* (pow y 2) (- (/ x (pow y 2)) 1))
(-.f64 x (*.f64 y y))
(* (pow y 2) (- (/ x (pow y 2)) 1))
(-.f64 x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ x (pow y 2)) 1))
(-.f64 x (*.f64 y y))
(* (pow y 2) (- (/ x (pow y 2)) 1))
(-.f64 x (*.f64 y y))
(* (pow y 2) (- (/ x (pow y 2)) 1))
(-.f64 x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(- x (pow y 2))
(-.f64 x (*.f64 y y))
(- x (pow y 2))
(-.f64 x (*.f64 y y))
(- x (pow y 2))
(-.f64 x (*.f64 y y))
x
(* x (+ 1 (* -1 (/ (pow y 2) x))))
(-.f64 x (*.f64 y y))
(* x (+ 1 (* -1 (/ (pow y 2) x))))
(-.f64 x (*.f64 y y))
(* x (+ 1 (* -1 (/ (pow y 2) x))))
(-.f64 x (*.f64 y y))
x
(* -1 (* x (- (/ (pow y 2) x) 1)))
(-.f64 x (*.f64 y y))
(* -1 (* x (- (/ (pow y 2) x) 1)))
(-.f64 x (*.f64 y y))
(* -1 (* x (- (/ (pow y 2) x) 1)))
(-.f64 x (*.f64 y y))

rewrite373.0ms (12%)

Memory

-3.6MiB live, 266.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	26	8
2	179	8
3	1554	8
0	8483	8

Stop Event

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

Counts

2 → 201

Calls

Call 1

Inputs
(-.f64 x (*.f64 y y))
(*.f64 y y)

Outputs
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eval127.0ms (4.1%)

Memory: -4.6MiB live, 35.0MiB allocated
Compiler: Compiled 6 631 to 573 computations (91.4% saved)

prune62.0ms (2%)

Memory

-21.0MiB live, 16.3MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	232	2	234
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	233	2	235

Accuracy

100.0%

Counts

235 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (neg.f64 y) y x)
▶	48.2%	#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))

Compiler

Compiled 10 to 9 computations (10% saved)

simplify8.0ms (0.3%)

Memory

12.6MiB live, 12.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
0	11	26
1	19	26
2	24	26
3	36	26
4	48	26
5	66	26
6	105	26
7	133	26
8	160	26
9	180	26
10	192	26
0	192	26

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
y
(fma.f64 (neg.f64 y) y x)
(neg.f64 y)
y
x

Outputs
#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
y
(fma.f64 (neg.f64 y) y x)
(neg.f64 y)
y
x

localize25.0ms (0.8%)

Memory

-0.7MiB live, 36.1MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (neg.f64 y) y x)
accuracy	0	(neg.f64 y)
accuracy	0	(*.f64 (neg.f64 y) y)
accuracy	0	(neg.f64 y)
accuracy	33.15444209856144	#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))

Samples

19.0ms

256×

valid

Compiler

Compiled 24 to 9 computations (62.5% saved)

Precisions

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

ival-mult: 7.0ms (58.6% of total)

ival-sub: 2.0ms (16.8% of total)

ival-add: 1.0ms (8.4% of total)

ival-neg: 1.0ms (8.4% of total)

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

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

series4.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Counts

4 → 72

Calls

Call 1

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

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

Calls

6 calls:

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

simplify141.0ms (4.5%)

Memory

-7.2MiB live, 104.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	282
1	49	282
2	111	282
3	295	282
4	928	282
5	1962	282
6	3794	282
7	6291	282
0	8149	282

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 66

Calls

Call 1

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

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

rewrite182.0ms (5.9%)

Memory

2.9MiB live, 204.9MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	21
0	11	21
1	44	21
2	308	21
3	3230	16
0	9254	16

Stop Event

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

Counts

4 → 289

Calls

Call 1

Inputs
#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 y) y)
(neg.f64 y)
(fma.f64 (neg.f64 y) y x)

Outputs
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eval61.0ms (2%)

Memory: -5.2MiB live, 108.3MiB allocated
Compiler: Compiled 6 931 to 847 computations (87.8% saved)

prune13.0ms (0.4%)

Memory

1.5MiB live, 40.7MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	403	2	405
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	403	4	407

Accuracy

100.0%

Counts

407 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (neg.f64 y) y x)
▶	53.3%	(fma.f64 y y x)
✓	48.2%	#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))
▶	2.4%	#s(approx (- x (* y y)) (*.f64 y y))

Compiler

Compiled 18 to 16 computations (11.1% saved)

simplify10.0ms (0.3%)

Memory

12.6MiB live, 12.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
0	9	19
1	15	19
2	23	19
3	32	19
4	46	19
5	71	19
6	104	19
7	141	19
8	180	19
9	209	19
10	233	19
11	235	19
0	235	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- x (* y y)) (*.f64 y y))
(*.f64 y y)
y
(fma.f64 y y x)
y
x

Outputs
#s(approx (- x (* y y)) (*.f64 y y))
(*.f64 y y)
y
(fma.f64 y y x)
y
x

localize15.0ms (0.5%)

Memory

20.8MiB live, 20.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y x)
accuracy	0	(*.f64 y y)
accuracy	62.47074552011355	#s(approx (- x (* y y)) (*.f64 y y))

Samples

11.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 2.0ms (44.9% of total)

ival-sub: 1.0ms (22.4% of total)

ival-add: 1.0ms (22.4% of total)

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

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

series27.0ms (0.9%)

Memory

-36.1MiB live, 21.4MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs

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

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

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

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((- x (* y y)) (* y y) (+ (* y y) x))
0.0ms	y	@	-inf	((- x (* y y)) (* y y) (+ (* y y) x))
0.0ms	y	@	inf	((- x (* y y)) (* y y) (+ (* y y) x))
0.0ms	y	@	0	((- x (* y y)) (* y y) (+ (* y y) x))
0.0ms	x	@	inf	((- x (* y y)) (* y y) (+ (* y y) x))

simplify104.0ms (3.4%)

Memory

19.4MiB live, 133.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	243
1	74	243
2	181	243
3	531	243
4	1513	243
5	2969	243
6	5225	243
7	6553	243
0	8013	225

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 54

Calls

Call 1

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

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

rewrite192.0ms (6.2%)

Memory

-20.1MiB live, 251.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
0	9	16
1	37	16
2	274	16
3	3024	16
0	9009	16

Stop Event

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

Counts

3 → 152

Calls

Call 1

Inputs
#s(approx (- x (* y y)) (*.f64 y y))
(*.f64 y y)
(fma.f64 y y x)

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

eval22.0ms (0.7%)

Memory: 28.0MiB live, 64.8MiB allocated
Compiler: Compiled 4 009 to 447 computations (88.9% saved)

prune12.0ms (0.4%)

Memory

-15.8MiB live, 28.6MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	206	4	210

Accuracy

100.0%

Counts

210 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (neg.f64 y) y x)
✓	53.3%	(fma.f64 y y x)
✓	48.2%	#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))
✓	2.4%	#s(approx (- x (* y y)) (*.f64 y y))

Compiler

Compiled 41 to 26 computations (36.6% saved)

regimes12.0ms (0.4%)

Memory

-7.2MiB live, 29.2MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- x (* y y)) (*.f64 y y))
(fma.f64 y y x)
#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))
(-.f64 x (*.f64 y y))
(fma.f64 (neg.f64 y) y x)

Outputs
(fma.f64 (neg.f64 y) y x)

Calls

4 calls:

5.0ms	x
3.0ms	y
2.0ms	(-.f64 x (*.f64 y y))
2.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes9.0ms (0.3%)

Memory

32.8MiB live, 32.8MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- x (* y y)) (*.f64 y y))
(fma.f64 y y x)
#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))
(-.f64 x (*.f64 y y))

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

Calls

4 calls:

2.0ms	y
2.0ms	x
2.0ms	(-.f64 x (*.f64 y y))
2.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes9.0ms (0.3%)

Memory

-10.7MiB live, 28.0MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
#s(approx (- x (* y y)) (*.f64 y y))
(fma.f64 y y x)
#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))

Outputs
(fma.f64 y y x)
#s(approx (- x (* y y)) (*.f64 (neg.f64 y) y))

Calls

4 calls:

3.0ms	(*.f64 y y)
2.0ms	x
2.0ms	y
2.0ms	(-.f64 x (*.f64 y y))

Results

Accuracy	Segments	Branch
60.2%	3	`x`
89.2%	2	`y`
80.6%	2	`(-.f64 x (*.f64 y y))`
89.2%	2	`(*.f64 y y)`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes8.0ms (0.3%)

Memory

-16.4MiB live, 21.8MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (- x (* y y)) (*.f64 y y))
(fma.f64 y y x)

Outputs
(fma.f64 y y x)

Calls

4 calls:

3.0ms	(-.f64 x (*.f64 y y))
2.0ms	x
2.0ms	y
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
53.3%	1	`x`
53.3%	1	`(-.f64 x (*.f64 y y))`
53.3%	1	`y`
53.3%	1	`(*.f64 y y)`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes5.0ms (0.2%)

Memory

20.9MiB live, 20.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- x (* y y)) (*.f64 y y))

Outputs
#s(approx (- x (* y y)) (*.f64 y y))

Calls

4 calls:

1.0ms	x
1.0ms	y
1.0ms	(-.f64 x (*.f64 y y))
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
2.4%	1	`(-.f64 x (*.f64 y y))`
2.4%	1	`x`
2.4%	1	`y`
2.4%	1	`(*.f64 y y)`

Compiler

Compiled 10 to 11 computations (-10% saved)

bsearch0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	9.615558950685009e-37	1.8701817459229856e-36

Compiler

Compiled 8 to 9 computations (-12.5% saved)

simplify80.0ms (2.6%)

Memory

-22.6MiB live, 65.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	23	43
2	28	43
3	31	43
4	32	43

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (neg.f64 y) y x)
(-.f64 x (*.f64 y y))
(if (<=.f64 (.f64 y y) #s(literal 2993155353253689/2993155353253689176481146537402947624255349848014848 binary64)) (fma.f64 y y x) #s(approx (- x ( y y)) (*.f64 (neg.f64 y) y)))
(fma.f64 y y x)
#s(approx (- x (* y y)) (*.f64 y y))

Outputs
(fma.f64 (neg.f64 y) y x)
(-.f64 x (*.f64 y y))
(if (<=.f64 (.f64 y y) #s(literal 2993155353253689/2993155353253689176481146537402947624255349848014848 binary64)) (fma.f64 y y x) #s(approx (- x ( y y)) (*.f64 (neg.f64 y) y)))
(fma.f64 y y x)
#s(approx (- x (* y y)) (*.f64 y y))

soundness457.0ms (14.7%)

Memory

12.1MiB live, 396.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	141
1	46	141
2	112	141
3	309	141
4	929	141
5	1915	141
6	3790	141
7	6274	141
0	8148	141
0	4	8
0	6	8
1	26	8
2	179	8
3	1554	8
0	8483	8
0	8	21
0	11	21
1	44	21
2	308	21
3	3230	16
0	9254	16

Stop Event

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

Compiler

Compiled 94 to 54 computations (42.6% saved)

preprocess48.0ms (1.5%)

Memory: -5.4MiB live, 152.8MiB allocated
Remove: (abs y)
Compiler: Compiled 96 to 50 computations (47.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	29
1	39	29
2	90	26
3	198	26
4	306	26
5	330	26
6	332	26
0	4	5
0	6	5
1	11	5
2	19	5
3	28	5
4	41	5
5	60	5
6	96	5
7	128	5
8	157	5
9	177	5
10	189	5
0	189	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	11	10
2	19	10
3	28	10
4	41	10
5	60	10
6	96	10
7	128	10
8	157	10
9	177	10
10	189	10
0	189	10

Iter	Nodes	Cost
0	8	26
0	11	26
1	19	26
2	24	26
3	36	26
4	48	26
5	66	26
6	105	26
7	133	26
8	160	26
9	180	26
10	192	26
0	192	26

Iter	Nodes	Cost
0	7	19
0	9	19
1	15	19
2	23	19
3	32	19
4	46	19
5	71	19
6	104	19
7	141	19
8	180	19
9	209	19
10	233	19
11	235	19
0	235	19

Iter	Nodes	Cost
0	12	29
1	39	29
2	90	26
3	198	26
4	306	26
5	330	26
6	332	26
0	4	5
0	6	5
1	11	5
2	19	5
3	28	5
4	41	5
5	60	5
6	96	5
7	128	5
8	157	5
9	177	5
10	189	5
0	189	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	11	10
2	19	10
3	28	10
4	41	10
5	60	10
6	96	10
7	128	10
8	157	10
9	177	10
10	189	10
0	189	10

Iter	Nodes	Cost
0	8	26
0	11	26
1	19	26
2	24	26
3	36	26
4	48	26
5	66	26
6	105	26
7	133	26
8	160	26
9	180	26
10	192	26
0	192	26

Iter	Nodes	Cost
0	7	19
0	9	19
1	15	19
2	23	19
3	32	19
4	46	19
5	71	19
6	104	19
7	141	19
8	180	19
9	209	19
10	233	19
11	235	19
0	235	19

start0.0ms (0%)

analyze0.0ms (0%)

sample755.0ms (24.3%)

explain134.0ms (4.3%)

preprocess22.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify30.0ms (1%)

localize13.0ms (0.4%)

series3.0ms (0.1%)

simplify139.0ms (4.5%)

rewrite373.0ms (12%)

eval127.0ms (4.1%)

prune62.0ms (2%)

simplify8.0ms (0.3%)

localize25.0ms (0.8%)

series4.0ms (0.1%)

simplify141.0ms (4.5%)

rewrite182.0ms (5.9%)

eval61.0ms (2%)

prune13.0ms (0.4%)

simplify10.0ms (0.3%)

localize15.0ms (0.5%)

series27.0ms (0.9%)

simplify104.0ms (3.4%)

rewrite192.0ms (6.2%)

eval22.0ms (0.7%)

prune12.0ms (0.4%)

regimes12.0ms (0.4%)

regimes9.0ms (0.3%)

regimes9.0ms (0.3%)

regimes8.0ms (0.3%)

regimes5.0ms (0.2%)

bsearch0.0ms (0%)

simplify80.0ms (2.6%)

soundness457.0ms (14.7%)

preprocess48.0ms (1.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	29
1	39	29
2	90	26
3	198	26
4	306	26
5	330	26
6	332	26
0	4	5
0	6	5
1	11	5
2	19	5
3	28	5
4	41	5
5	60	5
6	96	5
7	128	5
8	157	5
9	177	5
10	189	5
0	189	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	11	10
2	19	10
3	28	10
4	41	10
5	60	10
6	96	10
7	128	10
8	157	10
9	177	10
10	189	10
0	189	10

Iter	Nodes	Cost
0	8	26
0	11	26
1	19	26
2	24	26
3	36	26
4	48	26
5	66	26
6	105	26
7	133	26
8	160	26
9	180	26
10	192	26
0	192	26

Iter	Nodes	Cost
0	7	19
0	9	19
1	15	19
2	23	19
3	32	19
4	46	19
5	71	19
6	104	19
7	141	19
8	180	19
9	209	19
10	233	19
11	235	19
0	235	19