Metrics for Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample641.0ms (75.9%)

Memory

31.2MiB live, 914.6MiB allocated

Samples

396.0ms

8 256×

valid

Precisions

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

ival-mult: 157.0ms (75.2% of total)

ival-sub: 38.0ms (18.2% of total)

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

exact: 5.0ms (2.4% of total)

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

Bogosity

explain89.0ms (10.5%)

Memory

-31.3MiB live, 178.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
2	-	-	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
0	-	-	`y`
0	-	-	`(*.f64 y #s(literal 4 binary64))`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`z`
0	-	-	`(*.f64 x x)`
0	-	-	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`	nan-rescue	2	0
↳	`(*.f64 x x)`	overflow	72
↳	`(*.f64 y #s(literal 4 binary64))`	overflow	2
↳	`(.f64 (.f64 y #s(literal 4 binary64)) z)`	overflow	35

Confusion

	Predicted +	Predicted -
+	2	0
-	0	254

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	0	0	254

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	254
1	2

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms

512×

valid

Compiler

Compiled 85 to 36 computations (57.6% saved)

Precisions

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

ival-mult: 9.0ms (73% of total)

ival-sub: 2.0ms (16.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess3.0ms (0.4%)

Memory

6.2MiB live, 6.2MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Outputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Compiler

Compiled 9 to 8 computations (11.1% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0.1%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y #s(literal 4 binary64))
cost-diff	0	(.f64 (.f64 y #s(literal 4 binary64)) z)
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
(*.f64 x x)
x
(.f64 (.f64 y #s(literal 4 binary64)) z)
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
z

Outputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
(*.f64 x x)
x
(.f64 (.f64 y #s(literal 4 binary64)) z)
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)
z

localize21.0ms (2.5%)

Memory

-5.4MiB live, 32.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f64 (.f64 y #s(literal 4 binary64)) z)
accuracy	0.0	(*.f64 y #s(literal 4 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.39843750000000006	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Samples

16.0ms

256×

valid

Compiler

Compiled 50 to 18 computations (64% saved)

Precisions

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

ival-mult: 5.0ms (81.4% of total)

ival-sub: 1.0ms (16.3% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.8%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

4 → 11

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
(*.f64 x x)
(.f64 (.f64 y #s(literal 4 binary64)) z)
(*.f64 y #s(literal 4 binary64))

Outputs
(* -4 (* y z))
(- (pow x 2) (* 4 (* y z)))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+ (* -4 (* y z)) (pow x 2))
(* 4 (* y z))
(* 4 y)
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))
1.0ms	z	@	0	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))
1.0ms	y	@	inf	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))
1.0ms	y	@	-inf	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))
1.0ms	x	@	inf	((- (* x x) (* (* y 4) z)) (* x x) (* (* y 4) z) (* y 4))

simplify0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	egg-herbie

Counts

11 → 4

Calls

Call 1

Inputs
(* -4 (* y z))
(- (pow x 2) (* 4 (* y z)))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+ (* -4 (* y z)) (pow x 2))
(* 4 (* y z))
(* 4 y)
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))

Outputs
(* -4 (* y z))
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
(- (pow x 2) (* 4 (* y z)))
(*.f64 x x)
(pow x 2)
(.f64 (.f64 y #s(literal 4 binary64)) z)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(*.f64 y #s(literal 4 binary64))

rewrite0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Counts

4 → 4

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
(*.f64 x x)
(.f64 (.f64 y #s(literal 4 binary64)) z)
(*.f64 y #s(literal 4 binary64))

Outputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
(*.f64 x x)
(.f64 (.f64 y #s(literal 4 binary64)) z)
(*.f64 y #s(literal 4 binary64))

eval1.0ms (0.1%)

Memory: 2.5MiB live, 2.5MiB allocated
Compiler: Compiled 96 to 18 computations (81.3% saved)

prune1.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	6	2	8
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	6	3	9

Accuracy

100.0%

Counts

9 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
▶	3.7%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
▶	53.3%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y #s(literal 4 binary64))
cost-diff	0	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Calls

Call 1

Inputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)

Outputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
(*.f64 y #s(literal 4 binary64))
y
#s(literal 4 binary64)

localize20.0ms (2.4%)

Memory

4.2MiB live, 42.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y #s(literal 4 binary64))
accuracy	61.65590186996078	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
accuracy	0.0	(*.f64 x x)
accuracy	29.868283196346155	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Samples

15.0ms

256×

valid

Compiler

Compiled 64 to 23 computations (64.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 7.0ms (84% of total)

ival-sub: 1.0ms (12% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.4%)

Memory

9.6MiB live, 9.6MiB allocated

Counts

4 → 10

Calls

Call 1

Inputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
(*.f64 x x)
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
(*.f64 y #s(literal 4 binary64))

Outputs
(* -4 (* y z))
(- (pow x 2) (* 4 (* y z)))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+ (* -4 (* y z)) (pow x 2))
(* 4 y)
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* y 4))
0.0ms	x	@	-inf	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* y 4))
0.0ms	y	@	-inf	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* y 4))
0.0ms	y	@	inf	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* y 4))
0.0ms	x	@	0	((- (* x x) (* (* y 4) z)) (* x x) (- (* x x) (* (* y 4) z)) (* y 4))

simplify2.0ms (0.2%)

Memory

-37.9MiB live, 1.0MiB allocated

Algorithm

1×	egg-herbie

Counts

10 → 4

Calls

Call 1

Inputs
(* -4 (* y z))
(- (pow x 2) (* 4 (* y z)))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(+ (* -4 (* y z)) (pow x 2))
(* 4 y)
(* y (- (/ (pow x 2) y) (* 4 z)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) (* -4 z))))
(* z (- (/ (pow x 2) z) (* 4 y)))
(* -1 (* z (- (* -1 (/ (pow x 2) z)) (* -4 y))))

Outputs
(* -4 (* y z))
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
(- (pow x 2) (* 4 (* y z)))
(*.f64 x x)
(pow x 2)
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(*.f64 y #s(literal 4 binary64))

rewrite0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Counts

4 → 4

Calls

Call 1

Inputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
(*.f64 x x)
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
(*.f64 y #s(literal 4 binary64))

Outputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
(*.f64 x x)
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
(*.f64 y #s(literal 4 binary64))

eval1.0ms (0.1%)

Memory: 2.1MiB live, 2.1MiB allocated
Compiler: Compiled 102 to 16 computations (84.3% saved)

prune2.0ms (0.2%)

Memory

6.2MiB live, 6.2MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	6	0	6
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	6	3	9

Accuracy

100.0%

Counts

9 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
✓	3.7%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
✓	53.3%	#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Compiler

Compiled 70 to 44 computations (37.1% saved)

regimes18.0ms (2.1%)

Memory

-44.4MiB live, 36.8MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Outputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Calls

7 calls:

7.0ms	y
2.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	x
2.0ms	z
2.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`y`
99.2%	1	`z`
99.2%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
99.2%	1	`(*.f64 x x)`
99.2%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
99.2%	1	`(*.f64 y #s(literal 4 binary64))`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

regimes10.0ms (1.2%)

Memory

29.2MiB live, 29.2MiB allocated

Accuracy

Total -32.6b remaining (-109.1%)

Threshold costs -32.6b (-109.1%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 y #s(literal 4 binary64)))

Outputs
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Calls

7 calls:

1.0ms	(*.f64 y #s(literal 4 binary64))
1.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
1.0ms	x
1.0ms	z
1.0ms	y

Results

Accuracy	Segments	Branch
53.3%	1	`x`
53.3%	1	`y`
53.3%	1	`z`
53.3%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
53.3%	1	`(*.f64 x x)`
53.3%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
53.3%	1	`(*.f64 y #s(literal 4 binary64))`

Compiler

Compiled 23 to 32 computations (-39.1% saved)

simplify6.0ms (0.7%)

Memory

-25.0MiB live, 13.4MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

Outputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
#s(approx (- (* x x) (* (* y 4) z)) (*.f64 x x))

soundness0.0ms (0.1%)

Memory

1.1MiB live, 1.1MiB allocated

Stop Event

1×

done

Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess17.0ms (2%)

Memory: 8.2MiB live, 46.7MiB allocated
Compiler: Compiled 62 to 44 computations (29% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample641.0ms (75.9%)

explain89.0ms (10.5%)

preprocess3.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0.1%)

simplify0.0ms (0%)

localize21.0ms (2.5%)

series7.0ms (0.8%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

simplify0.0ms (0%)

localize20.0ms (2.4%)

series3.0ms (0.4%)

simplify2.0ms (0.2%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune2.0ms (0.2%)

regimes18.0ms (2.1%)

regimes10.0ms (1.2%)

simplify6.0ms (0.7%)

soundness0.0ms (0.1%)

preprocess17.0ms (2%)

end0.0ms (0%)

Profiling