Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0.1%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample561.0ms (72.1%)

Memory

77.6MiB live, 699.9MiB allocated

Samples

357.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 216.0ms

ival-mult: 79.0ms (36.6% of total)

ival-div: 64.0ms (29.6% of total)

ival-add: 59.0ms (27.3% of total)

exact: 6.0ms (2.8% of total)

ival-true: 5.0ms (2.3% of total)

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

Bogosity

explain137.0ms (17.6%)

Memory

-37.5MiB live, 95.8MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	n/o	59	0
↳	`(*.f64 x x)`	overflow	59
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	59

Confusion

	Predicted +	Predicted -
+	59	0
-	0	197

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	59	0	0
-	0	0	197

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	197
1	59

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 62 to 24 computations (61.3% saved)

Precisions

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

ival-mult: 4.0ms (37% of total)

ival-div: 3.0ms (27.7% of total)

ival-add: 2.0ms (18.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess2.0ms (0.3%)

Memory

4.7MiB live, 4.7MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Outputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0.1%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.5%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Calls

Call 1

Inputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
x
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)

Outputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
x
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)

localize17.0ms (2.2%)

Memory

-9.8MiB live, 28.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	13.737126361087423	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

10.0ms

256×

valid

Compiler

Compiled 36 to 12 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (38.8% of total)

ival-mult: 2.0ms (38.8% of total)

ival-add: 1.0ms (19.4% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.3%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

3 → 15

Calls

Call 1

Inputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
1
(+ 1 (pow x 2))
(pow x 2)
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))

Calls

3 calls:

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

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Counts

15 → 3

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
1
(+ 1 (pow x 2))
(pow x 2)
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))

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

rewrite0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)

Outputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)

eval1.0ms (0.1%)

Memory: 1.4MiB live, 1.4MiB allocated
Compiler: Compiled 60 to 12 computations (80% saved)

prune1.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	5	1	6
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	5	2	7

Accuracy

78.5%

Counts

7 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	78.5%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
▶	4.3%	#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))

Calls

Call 1

Inputs
#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))
(*.f64 x x)
x

Outputs
#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))
(*.f64 x x)
x

localize14.0ms (1.8%)

Memory

23.7MiB live, 23.7MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x x)
accuracy	61.27452331654368	#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))

Samples

10.0ms

256×

valid

Compiler

Compiled 28 to 14 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (39.1% of total)

ival-mult: 2.0ms (39.1% of total)

ival-add: 1.0ms (19.5% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0.1%)

Memory

2.4MiB live, 2.4MiB allocated

Counts

2 → 12

Calls

Call 1

Inputs
#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))
(*.f64 x x)

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(pow x 2)
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))

Calls

3 calls:

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

simplify0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Counts

12 → 2

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(pow x 2)
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))

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

rewrite0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))
(*.f64 x x)

Outputs
#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))
(*.f64 x x)

eval0.0ms (0%)

Memory: 0.7MiB live, 0.7MiB allocated
Compiler: Compiled 41 to 8 computations (80.5% saved)

prune5.0ms (0.6%)

Memory

-39.1MiB live, 3.2MiB 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

78.5%

Counts

5 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	78.5%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
✓	4.3%	#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))

Compiler

Compiled 36 to 22 computations (38.9% saved)

regimes3.0ms (0.4%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Outputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Calls

2 calls:

1.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
1.0ms	x

Results

Accuracy	Segments	Branch
78.5%	1	`x`
78.5%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0.3%)

Memory

6.0MiB live, 6.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))

Outputs
#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))

Calls

2 calls:

1.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
1.0ms	x

Results

Accuracy	Segments	Branch
4.3%	1	`x`
4.3%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.5%)

Memory

10.2MiB live, 10.2MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
#s(approx (/ x (+ (* x x) 1)) (*.f64 x x))

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

soundness0.0ms (0.1%)

Memory

0.9MiB live, 0.9MiB allocated

Stop Event

1×

done

Compiler

Compiled 18 to 10 computations (44.4% saved)

preprocess24.0ms (3%)

Memory: 9.2MiB live, 47.6MiB allocated
Compiler: Compiled 64 to 40 computations (37.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0.1%)

sample561.0ms (72.1%)

explain137.0ms (17.6%)

preprocess2.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0.1%)

simplify0.0ms (0%)

localize17.0ms (2.2%)

series2.0ms (0.3%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

simplify0.0ms (0%)

localize14.0ms (1.8%)

series1.0ms (0.1%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval0.0ms (0%)

prune5.0ms (0.6%)

regimes3.0ms (0.4%)

regimes2.0ms (0.3%)

simplify4.0ms (0.5%)

soundness0.0ms (0.1%)

preprocess24.0ms (3%)

end0.0ms (0%)

Profiling