Metrics for Examples.Basics.ProofTests:f4 from sbv-4.4

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 15 to 11 computations (26.7% saved)

sample749.0ms (71.3%)

Memory

-16.1MiB live, 1 070.5MiB allocated

Samples

492.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 299.0ms

ival-mult: 216.0ms (72.3% of total)

ival-add: 68.0ms (22.8% of total)

ival-true: 6.0ms (2% of total)

exact: 5.0ms (1.7% of total)

ival-assert: 3.0ms (1% of total)

Bogosity

explain118.0ms (11.3%)

Memory

-5.1MiB live, 194.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
13	-	-	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`
8	-	-	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
1	-	-	`(.f64 (.f64 x #s(literal 2 binary64)) y)`
0	-	-	`(*.f64 x #s(literal 2 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`y`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(*.f64 y y)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f64`	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	nan-rescue	13	0
↳	`(*.f64 x x)`	overflow	72
↳	`(*.f64 x #s(literal 2 binary64))`	overflow	1
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	37
`+.f64`	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`	nan-rescue	8	0
↳	`(*.f64 x #s(literal 2 binary64))`	overflow	1
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	overflow	81
↳	`(*.f64 x x)`	overflow	72
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	37
↳	`(*.f64 y y)`	overflow	64
`*.f64`	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	18	0
-	0	238

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	18	0	0
-	0	0	238

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	238
1	14
2	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms

512×

valid

Compiler

Compiled 134 to 40 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 17.0ms (77.7% of total)

ival-add: 4.0ms (18.3% of total)

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

exact: 0.0ms (0% of total)

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

preprocess3.0ms (0.2%)

Memory

4.9MiB live, 4.9MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Outputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Compiler

Compiled 13 to 9 computations (30.8% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB 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
▶	93.0%	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
x
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
y
(*.f64 y y)

Outputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
x
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
y
(*.f64 y y)

localize27.0ms (2.6%)

Memory

-3.0MiB live, 39.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	0.22797736813742084	(.f64 (.f64 x #s(literal 2 binary64)) y)
accuracy	1.5976562500000002	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
accuracy	2.8007729933208236	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Samples

21.0ms

256×

valid

Compiler

Compiled 80 to 20 computations (75% saved)

Precisions

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

ival-add: 7.0ms (50.3% of total)

ival-mult: 6.0ms (43.1% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.7%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

5 → 17

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))

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

Calls

6 calls:

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

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Counts

17 → 5

Calls

Call 1

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

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

rewrite0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Counts

5 → 5

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))

Outputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))

eval1.0ms (0.1%)

Memory: 1.8MiB live, 1.8MiB allocated
Compiler: Compiled 168 to 23 computations (86.3% saved)

prune2.0ms (0.2%)

Memory

3.2MiB live, 3.2MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	6	4	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	6	5	11

Accuracy

100.0%

Counts

11 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	93.0%	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
▶	57.8%	(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
▶	50.3%	(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
▶	51.6%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
▶	55.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 89 to 60 computations (32.6% saved)

simplify1.0ms (0.1%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
x
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
y
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(*.f64 y y)
y
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
y
(*.f64 y y)

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 x x)
x
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
y
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(*.f64 y y)
y
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
y
(*.f64 y y)

localize35.0ms (3.4%)

Memory

-7.7MiB live, 67.8MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	0.22797736813742084	(.f64 (.f64 x #s(literal 2 binary64)) y)
accuracy	1.5976562500000002	(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
accuracy	25.26612310742896	#s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y))
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	1.5976562500000002	(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
accuracy	61.35188608507113	#s(approx (+ (* x x) (* (* x 2) y)) (*.f64 x #s(literal 2 binary64)))
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	0.22797736813742084	(.f64 (.f64 x #s(literal 2 binary64)) y)
accuracy	2.8007729933208236	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
accuracy	28.45996594541025	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
accuracy	0.0	(*.f64 x x)
accuracy	28.637982015929925	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Samples

26.0ms

256×

valid

Compiler

Compiled 276 to 32 computations (88.4% saved)

Precisions

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

ival-mult: 10.0ms (76.8% of total)

ival-add: 2.0ms (15.4% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.5%)

Memory

13.2MiB live, 13.2MiB allocated

Counts

11 → 17

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 y y)
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y))

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

Calls

6 calls:

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

simplify1.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated

Algorithm

1×	egg-herbie

Counts

17 → 11

Calls

Call 1

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

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

rewrite1.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Counts

11 → 11

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 y y)
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y))

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(.f64 (.f64 x #s(literal 2 binary64)) y)
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(*.f64 y y)
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
#s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y))

eval4.0ms (0.4%)

Memory: -30.6MiB live, 8.1MiB allocated
Compiler: Compiled 688 to 41 computations (94% saved)

prune2.0ms (0.2%)

Memory

8.9MiB live, 8.9MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	28	5	33

Accuracy

100.0%

Counts

33 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	93.0%	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
✓	57.8%	(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
✓	51.6%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
▶	60.6%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
✓	55.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 89 to 59 computations (33.7% saved)

simplify0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
y

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
y

localize23.0ms (2.2%)

Memory

-2.2MiB live, 53.6MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 y y)
accuracy	25.18923955898921	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Samples

15.0ms

256×

valid

Compiler

Compiled 40 to 22 computations (45% saved)

Precisions

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

ival-mult: 6.0ms (68.5% of total)

ival-add: 2.0ms (22.8% 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

4.1MiB live, 4.1MiB allocated

Counts

2 → 12

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)

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

Calls

6 calls:

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

simplify0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	egg-herbie

Counts

12 → 2

Calls

Call 1

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

Outputs
(pow y 2)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(+ (* 2 (* x y)) (pow y 2))
(*.f64 y y)

rewrite0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)

eval0.0ms (0%)

Memory: 1.0MiB live, 1.0MiB allocated
Compiler: Compiled 65 to 12 computations (81.5% saved)

prune4.0ms (0.4%)

Memory

-29.4MiB live, 9.4MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	3	0	3
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	3	5	8

Accuracy

100.0%

Counts

8 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	93.0%	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
✓	57.8%	(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
✓	51.6%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
✓	60.6%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
✓	55.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 195 to 82 computations (57.9% saved)

regimes8.0ms (0.7%)

Memory

16.5MiB live, 16.5MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Outputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Calls

3 calls:

2.0ms	y
2.0ms	x
2.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Results

Accuracy	Segments	Branch
98.5%	3	`x`
98.1%	3	`y`
98.5%	2	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes7.0ms (0.6%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

5 → 3

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 (.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))

Outputs

#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) (*.f64 y y))

#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Calls

3 calls:

2.0ms	x
2.0ms	y
2.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Results

Accuracy	Segments	Branch
83.9%	4	`y`
86.3%	3	`x`
66.4%	3	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes2.0ms (0.2%)

Memory

4.5MiB live, 4.5MiB allocated

Counts

4 → 3

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(+.f64 #s(approx (+ (* x x) (* (* x 2) y)) (.f64 x #s(literal 2 binary64))) (.f64 y y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y)))

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
85.9%	3	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes4.0ms (0.4%)

Memory

-30.5MiB live, 8.4MiB allocated

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Calls

3 calls:

2.0ms	x
1.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
1.0ms	y

Results

Accuracy	Segments	Branch
55.3%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
55.3%	1	`y`
55.3%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN

Compiler

Compiled 16 to 14 computations (12.5% saved)

bsearch33.0ms (3.2%)

Memory

25.3MiB live, 64.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
15.0ms	641113486843.5437	9.708113303267447e+20
15.0ms	-1.5460526395187075e+30	-209391915899225.94

Samples

17.0ms

304×

valid

Compiler

Compiled 700 to 508 computations (27.4% saved)

Precisions

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

ival-mult: 8.0ms (75.3% of total)

ival-add: 2.0ms (18.8% of total)

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

exact: 0.0ms (0% of total)

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

bsearch2.0ms (0.2%)

Memory

4.0MiB live, 4.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	641113486843.5437	9.708113303267447e+20
1.0ms	-1.5460526395187075e+30	-209391915899225.94

Compiler

Compiled 662 to 470 computations (29% saved)

simplify6.0ms (0.6%)

Memory: -32.6MiB live, 9.8MiB allocated

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample749.0ms (71.3%)

explain118.0ms (11.3%)

preprocess3.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

localize27.0ms (2.6%)

series7.0ms (0.7%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune2.0ms (0.2%)

simplify1.0ms (0.1%)

localize35.0ms (3.4%)

series5.0ms (0.5%)

simplify1.0ms (0.1%)

rewrite1.0ms (0.1%)

eval4.0ms (0.4%)

prune2.0ms (0.2%)

simplify0.0ms (0%)

localize23.0ms (2.2%)

series2.0ms (0.2%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval0.0ms (0%)

prune4.0ms (0.4%)

regimes8.0ms (0.7%)

regimes7.0ms (0.6%)

regimes2.0ms (0.2%)

regimes4.0ms (0.4%)

bsearch0.0ms (0%)

bsearch33.0ms (3.2%)

bsearch2.0ms (0.2%)

simplify6.0ms (0.6%)

end0.0ms (0%)

Profiling