Metrics for Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, E

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze9.0ms (1.1%)

Memory

10.0MiB live, 10.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
50%	50%	50%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
66.7%	50%	25%	0.1%	0%	25%	0%	4
66.7%	50%	25%	0.1%	0%	25%	0%	5
80%	50%	12.5%	0.1%	0%	37.5%	0%	6
80%	50%	12.5%	0.1%	0%	37.5%	0%	7
88.9%	50%	6.2%	0.1%	0%	43.7%	0%	8
88.9%	50%	6.2%	0.1%	0%	43.7%	0%	9
94.1%	50%	3.1%	0.1%	0%	46.8%	0%	10
94.1%	50%	3.1%	0.1%	0%	46.8%	0%	11
97%	50%	1.6%	0.1%	0%	48.4%	0%	12

Compiler

Compiled 10 to 9 computations (10% saved)

sample640.0ms (79.4%)

Memory

23.4MiB live, 666.9MiB allocated

Samples

389.0ms	8 255×	0	valid
11.0ms	245×	0	invalid
0.0ms	1×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 224.0ms

ival-sqrt: 63.0ms (28.1% of total)

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

ival-sub: 51.0ms (22.7% of total)

ival-add: 39.0ms (17.4% of total)

ival-true: 7.0ms (3.1% of total)

exact: 5.0ms (2.2% of total)

ival-assert: 4.0ms (1.8% of total)

adjust: 0.0ms (0% of total)

Bogosity

explain72.0ms (8.9%)

Memory

11.6MiB live, 88.6MiB allocated

FPErrors

Click to see full error table

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

28.0ms

512×

valid

Compiler

Compiled 72 to 32 computations (55.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sqrt: 4.0ms (30.1% of total)

ival-sub: 3.0ms (22.6% of total)

ival-mult: 3.0ms (22.6% of total)

ival-add: 2.0ms (15.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess3.0ms (0.3%)

Memory

4.1MiB live, 4.1MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Outputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 8 to 7 computations (12.5% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0.1%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Calls

Call 1

Inputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 y (sqrt.f64 x))
y
(sqrt.f64 x)

Outputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 y (sqrt.f64 x))
y
(sqrt.f64 x)

localize21.0ms (2.6%)

Memory

-19.9MiB live, 21.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.0	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.1875	(*.f64 y (sqrt.f64 x))

Samples

16.0ms

256×

valid

Compiler

Compiled 42 to 16 computations (61.9% saved)

Precisions

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

ival-sub: 2.0ms (30.6% of total)

ival-mult: 2.0ms (30.6% of total)

ival-sqrt: 2.0ms (30.6% of total)

ival-add: 1.0ms (15.3% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.6%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

4 → 19

Calls

Call 1

Inputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) x)
(*.f64 y (sqrt.f64 x))
(sqrt.f64 x)

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((+ (- 1 x) (* y (sqrt x))) (- 1 x) (* y (sqrt x)) (sqrt x))
1.0ms	y	@	-inf	((+ (- 1 x) (* y (sqrt x))) (- 1 x) (* y (sqrt x)) (sqrt x))
1.0ms	x	@	inf	((+ (- 1 x) (* y (sqrt x))) (- 1 x) (* y (sqrt x)) (sqrt x))
1.0ms	x	@	0	((+ (- 1 x) (* y (sqrt x))) (- 1 x) (* y (sqrt x)) (sqrt x))
1.0ms	y	@	inf	((+ (- 1 x) (* y (sqrt x))) (- 1 x) (* y (sqrt x)) (sqrt x))

simplify0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Counts

19 → 4

Calls

Call 1

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

Outputs
(+ 1 (* (sqrt x) y))
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(-.f64 #s(literal 1 binary64) x)
1
(*.f64 y (sqrt.f64 x))
(+ 1 (* -1 x))
(sqrt.f64 x)

rewrite0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Counts

4 → 4

Calls

Call 1

Inputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) x)
(*.f64 y (sqrt.f64 x))
(sqrt.f64 x)

Outputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) x)
(*.f64 y (sqrt.f64 x))
(sqrt.f64 x)

eval1.0ms (0.1%)

Memory: 1.3MiB live, 1.3MiB allocated
Compiler: Compiled 85 to 18 computations (78.8% saved)

prune1.0ms (0.1%)

Memory

1.6MiB live, 1.6MiB allocated

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	7	1	8
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	7	2	9

Accuracy

99.9%

Counts

9 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
▶	63.2%	#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 20 to 17 computations (15% saved)

simplify0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Calls

Call 1

Inputs
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x

Outputs
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x

localize19.0ms (2.3%)

Memory

-18.7MiB live, 19.1MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(-.f64 #s(literal 1 binary64) x)
accuracy	23.58100545681254	#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))

Samples

14.0ms

256×

valid

Compiler

Compiled 32 to 19 computations (40.6% saved)

Precisions

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

ival-sqrt: 3.0ms (37.2% of total)

ival-mult: 2.0ms (24.8% of total)

ival-sub: 1.0ms (12.4% of total)

ival-add: 1.0ms (12.4% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.2%)

Memory

2.1MiB live, 2.1MiB allocated

Counts

2 → 16

Calls

Call 1

Inputs
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

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

Calls

6 calls:

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

simplify0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Counts

16 → 2

Calls

Call 1

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

Outputs
(+ 1 (* (sqrt x) y))
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
(+ 1 (+ (* -1 x) (* (sqrt x) y)))
(-.f64 #s(literal 1 binary64) x)

rewrite0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

Outputs
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

eval0.0ms (0.1%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 45 to 11 computations (75.6% saved)

prune2.0ms (0.2%)

Memory

2.4MiB live, 2.4MiB allocated

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	3	0	3
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	3	2	5

Accuracy

99.9%

Counts

5 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
✓	63.2%	#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 40 to 30 computations (25% saved)

regimes4.0ms (0.5%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Outputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))

Calls

3 calls:

1.0ms	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes4.0ms (0.4%)

Memory

7.1MiB live, 7.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))

Outputs
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))

Calls

3 calls:

1.0ms	(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
63.2%	1	`x`
63.2%	1	`y`
63.2%	1	`(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

simplify5.0ms (0.6%)

Memory

7.6MiB live, 7.6MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))

Outputs
(+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 y (sqrt.f64 x)))
#s(approx (+ (- 1 x) (* y (sqrt x))) (-.f64 #s(literal 1 binary64) x))

soundness0.0ms (0.1%)

Memory

0.6MiB live, 0.6MiB allocated

Stop Event

1×

done

Compiler

Compiled 20 to 13 computations (35% saved)

preprocess18.0ms (2.2%)

Memory: -14.3MiB live, 24.0MiB allocated
Compiler: Compiled 56 to 40 computations (28.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze9.0ms (1.1%)

sample640.0ms (79.4%)

explain72.0ms (8.9%)

preprocess3.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0.1%)

simplify0.0ms (0%)

localize21.0ms (2.6%)

series5.0ms (0.6%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

simplify0.0ms (0%)

localize19.0ms (2.3%)

series2.0ms (0.2%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval0.0ms (0.1%)

prune2.0ms (0.2%)

regimes4.0ms (0.5%)

regimes4.0ms (0.4%)

simplify5.0ms (0.6%)

soundness0.0ms (0.1%)

preprocess18.0ms (2.2%)

end0.0ms (0%)

Profiling