Metrics for Numeric.Log:$clog1p from log-domain-0.10.2.1, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB 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 13 to 10 computations (23.1% saved)

sample669.0ms (66.8%)

Memory

19.6MiB live, 1 064.2MiB allocated

Samples

440.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 257.0ms

ival-mult: 172.0ms (66.8% of total)

ival-add: 74.0ms (28.7% of total)

ival-true: 5.0ms (1.9% of total)

exact: 4.0ms (1.6% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain97.0ms (9.7%)

Memory

-5.1MiB live, 151.9MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f64`	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`	nan-rescue	1	0
↳	`(*.f64 x #s(literal 2 binary64))`	overflow	1
↳	`(*.f64 x x)`	overflow	72

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	255

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms

512×

valid

Compiler

Compiled 105 to 36 computations (65.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 9.0ms (61.8% of total)

ival-add: 4.0ms (27.5% 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

5.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

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

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB 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
▶	99.6%	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))

Compiler

Compiled 11 to 8 computations (27.3% 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 x x)
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
cost-diff	0	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))

Calls

Call 1

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

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

localize21.0ms (2.1%)

Memory

-7.0MiB live, 31.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
accuracy	0.20312500000000003	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))

Samples

15.0ms

256×

valid

Compiler

Compiled 62 to 18 computations (71% saved)

Precisions

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

ival-mult: 5.0ms (68.4% of total)

ival-add: 2.0ms (27.4% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.4%)

Memory

7.3MiB live, 7.3MiB allocated

Counts

4 → 12

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x 2) (* x x))
1.0ms	x	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x 2) (* x x))
1.0ms	x	@	0	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x 2) (* x x))
0.0ms	y	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x 2) (* x x))
0.0ms	y	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x 2) (* x x))

simplify0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Counts

12 → 4

Calls

Call 1

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

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

rewrite0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Counts

4 → 4

Calls

Call 1

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

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

eval1.0ms (0.1%)

Memory: 1.7MiB live, 1.7MiB allocated
Compiler: Compiled 116 to 19 computations (83.6% saved)

prune1.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	5	3	8
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	5	4	9

Accuracy

100.0%

Counts

9 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
▶	82.3%	(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))
▶	59.3%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)))
▶	20.0%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x #s(literal 2 binary64)))

Compiler

Compiled 60 to 42 computations (30% saved)

simplify1.0ms (0.1%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Calls

Call 1

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

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

localize25.0ms (2.5%)

Memory

-3.5MiB live, 39.1MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))
accuracy	31.19074543542296	#s(approx (+ (* x 2) (* x x)) (*.f64 x x))
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	0.20312500000000003	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
accuracy	25.772643010544297	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)))
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	51.20171660587321	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x #s(literal 2 binary64)))

Samples

18.0ms

256×

valid

Compiler

Compiled 158 to 27 computations (82.9% saved)

Precisions

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

ival-mult: 5.0ms (68.7% of total)

ival-add: 2.0ms (27.5% 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

-32.0MiB live, 6.5MiB allocated

Counts

8 → 12

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* y y))
1.0ms	x	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* y y))
0.0ms	y	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* y y))
0.0ms	y	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* y y))
0.0ms	x	@	0	((+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* y y))

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Counts

12 → 8

Calls

Call 1

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

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

rewrite1.0ms (0.1%)

Memory

1.0MiB live, 1.0MiB allocated

Counts

8 → 8

Calls

Call 1

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

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

eval2.0ms (0.2%)

Memory: 3.4MiB live, 3.4MiB allocated
Compiler: Compiled 386 to 30 computations (92.2% saved)

prune2.0ms (0.2%)

Memory

4.6MiB live, 4.6MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	16	2	18
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	16	6	22

Accuracy

100.0%

Counts

22 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
✓	82.3%	(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))
✓	59.3%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)))
▶	50.2%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
✓	20.0%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x #s(literal 2 binary64)))
▶	42.7%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))

Compiler

Compiled 98 to 63 computations (35.7% saved)

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Calls

Call 1

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

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

localize20.0ms (2%)

Memory

-6.3MiB live, 32.1MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y y)
accuracy	31.855007116276866	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
accuracy	0.0	(*.f64 x x)
accuracy	25.772643010544297	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))
accuracy	31.19074543542296	#s(approx (+ (* x 2) (* x x)) (*.f64 x x))

Samples

15.0ms

256×

valid

Compiler

Compiled 96 to 23 computations (76% saved)

Precisions

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

ival-mult: 6.0ms (71.2% of total)

ival-add: 2.0ms (23.7% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.3%)

Memory

4.8MiB live, 4.8MiB allocated

Counts

5 → 12

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (* y y))
1.0ms	x	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (* y y))
0.0ms	y	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (* y y))
0.0ms	y	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (* y y))
0.0ms	x	@	0	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (+ (+ (* x 2) (* x x)) (* y y)) (* y y))

simplify0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Counts

12 → 5

Calls

Call 1

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

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

rewrite0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Counts

5 → 5

Calls

Call 1

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

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

eval1.0ms (0.1%)

Memory: 1.7MiB live, 1.7MiB allocated
Compiler: Compiled 207 to 19 computations (90.8% saved)

prune4.0ms (0.4%)

Memory

6.3MiB live, 6.3MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	9	0	9
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	9	6	15

Accuracy

100.0%

Counts

15 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
✓	82.3%	(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))
✓	59.3%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)))
✓	50.2%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
✓	20.0%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x #s(literal 2 binary64)))
✓	42.7%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))

Compiler

Compiled 196 to 83 computations (57.7% saved)

regimes15.0ms (1.5%)

Memory

-10.4MiB live, 28.3MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	y
3.0ms	x
3.0ms	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
2.0ms	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`y`
99.6%	1	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
99.6%	1	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`
99.6%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes12.0ms (1.2%)

Memory

28.3MiB live, 28.3MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
82.3%	1	`x`
96.4%	3	`y`
94.8%	2	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
82.3%	1	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`
96.4%	2	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes8.0ms (0.8%)

Memory

-27.4MiB live, 14.3MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	(*.f64 y y)
2.0ms	y
2.0ms	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))

Results

Accuracy	Segments	Branch
66.2%	3	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
84.3%	3	`y`
84.0%	2	`(*.f64 y y)`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes7.0ms (0.7%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
73.0%	6	`y`
75.6%	3	`x`
75.6%	2	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`
67.3%	2	`(*.f64 y y)`

Compiler

Compiled 12 to 13 computations (-8.3% saved)

regimes7.0ms (0.7%)

Memory

14.8MiB live, 14.8MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
59.3%	2	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
49.6%	5	`y`
42.7%	1	`(*.f64 y y)`
59.2%	3	`x`
59.2%	2	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes6.0ms (0.6%)

Memory

-27.5MiB live, 11.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
42.7%	1	`y`
42.7%	1	`x`
42.7%	1	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`
42.7%	1	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`

Compiler

Compiled 20 to 18 computations (10% saved)

bsearch13.0ms (1.3%)

Memory

22.6MiB live, 22.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	1.0967406561966397e-162	1.6137288478910645e-153

Samples

6.0ms

144×

valid

Compiler

Compiled 302 to 229 computations (24.2% saved)

Precisions

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

ival-mult: 2.0ms (61.2% of total)

ival-add: 1.0ms (30.6% of total)

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

exact: 0.0ms (0% of total)

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

bsearch16.0ms (1.6%)

Memory

-12.3MiB live, 26.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	6.50860090457001e-91	3.3834915044587373e-81

Samples

9.0ms

160×

valid

Compiler

Compiled 334 to 253 computations (24.3% saved)

Precisions

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

ival-mult: 2.0ms (55.5% of total)

ival-add: 1.0ms (27.7% of total)

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

exact: 0.0ms (0% of total)

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

bsearch0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.3844974443948085e+28	9.424746390907838e+41

Compiler

Compiled 14 to 13 computations (7.1% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8060493.123297569	1154677847493.5435

Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify5.0ms (0.5%)

Memory

14.2MiB live, 14.2MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
(if (<=.f64 (.f64 y y) #s(literal 7729075046034517/483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928 binary64)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))) (+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y)))
(if (<=.f64 (.f64 y y) #s(literal 2349585739513001/1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288 binary64)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y)))
(if (<=.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) #s(literal 49999999999999995716575428608 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (.f64 y y)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) #s(approx (+ (* x 2) (* x x)) (*.f64 x x))))
(if (<=.f64 (+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (.f64 y y)) #s(literal 10000000 binary64)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (.f64 x #s(literal 2 binary64))) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) #s(approx (+ (* x 2) (* x x)) (*.f64 x x))))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))

Outputs
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
(if (<=.f64 (.f64 y y) #s(literal 7729075046034517/483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928 binary64)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))) (+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y)))
(if (<=.f64 (.f64 y y) #s(literal 2349585739513001/1067993517960455041197510853084776057301352261178326384973520803911109862890320275011481043468288 binary64)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y)))
(if (<=.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) #s(literal 49999999999999995716575428608 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (.f64 y y)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) #s(approx (+ (* x 2) (* x x)) (*.f64 x x))))
(if (<=.f64 (+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (.f64 y y)) #s(literal 10000000 binary64)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (.f64 x #s(literal 2 binary64))) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) #s(approx (+ (* x 2) (* x x)) (*.f64 x x))))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))

soundness5.0ms (0.5%)

Memory

-33.1MiB live, 4.5MiB allocated

Stop Event

1×

done

Compiler

Compiled 214 to 32 computations (85% saved)

preprocess45.0ms (4.5%)

Memory: 0.0MiB live, 82.1MiB allocated
Compiler: Compiled 472 to 96 computations (79.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample669.0ms (66.8%)

explain97.0ms (9.7%)

preprocess3.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

localize21.0ms (2.1%)

series4.0ms (0.4%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

simplify1.0ms (0.1%)

localize25.0ms (2.5%)

series5.0ms (0.5%)

simplify0.0ms (0%)

rewrite1.0ms (0.1%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

simplify0.0ms (0%)

localize20.0ms (2%)

series3.0ms (0.3%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune4.0ms (0.4%)

regimes15.0ms (1.5%)

regimes12.0ms (1.2%)

regimes8.0ms (0.8%)

regimes7.0ms (0.7%)

regimes7.0ms (0.7%)

regimes6.0ms (0.6%)

bsearch13.0ms (1.3%)

bsearch16.0ms (1.6%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify5.0ms (0.5%)

soundness5.0ms (0.5%)

preprocess45.0ms (4.5%)

end0.0ms (0%)

Profiling