Metrics for ln(1 + x)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0.2%)

Memory

1.4MiB live, 1.4MiB 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
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
83.3%	62.5%	12.5%	0%	0%	25%	0%	4
91.7%	68.7%	6.2%	0%	0%	25%	0%	5
95.8%	71.8%	3.1%	0%	0%	25%	0%	6
97.9%	73.4%	1.6%	0%	0%	25%	0%	7
99%	74.2%	0.8%	0%	0%	25%	0%	8
99.5%	74.6%	0.4%	0%	0%	25%	0%	9
99.7%	74.8%	0.2%	0%	0%	25%	0%	10
99.9%	74.9%	0.1%	0%	0%	25%	0%	11
99.9%	74.9%	0%	0%	0%	25%	0%	12

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample413.0ms (67.9%)

Memory

-6.5MiB live, 480.8MiB allocated

Samples

227.0ms	8 256×	0	valid
0.0ms	1×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 87.0ms

ival-log1p: 79.0ms (90.6% of total)

ival-true: 6.0ms (6.9% of total)

ival-assert: 3.0ms (3.4% of total)

Bogosity

explain117.0ms (19.2%)

Memory

18.9MiB live, 73.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
171	1	(-0.0017552774230841217)	-	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
0	0	-	-	`(+.f64 #s(literal 1 binary64) x)`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) x))`	sensitivity	172	0

Confusion

	Predicted +	Predicted -
+	171	0
-	1	84

Precision

0.9941860465116279

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	171	0	0
-	1	0	84

Precision?

0.9941860465116279

Recall?

1.0

Freqs

test

number	freq
0	84
1	172

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms

512×

valid

Compiler

Compiled 35 to 20 computations (42.9% saved)

Precisions

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

ival-log1p: 5.0ms (60.6% of total)

ival-add: 3.0ms (36.3% 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

4.1MiB live, 4.1MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

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

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

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

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

prune0.0ms (0.1%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	37.4%	(log.f64 (+.f64 #s(literal 1 binary64) x))

Compiler

Compiled 4 to 4 computations (0% 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 #s(literal 1 binary64) x)
cost-diff	0	(log.f64 (+.f64 #s(literal 1 binary64) x))

Calls

Call 1

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

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

localize15.0ms (2.5%)

Memory

-20.0MiB live, 20.5MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(+.f64 #s(literal 1 binary64) x)
accuracy	40.09396669974284	(log.f64 (+.f64 #s(literal 1 binary64) x))

Samples

11.0ms

256×

valid

Compiler

Compiled 20 to 10 computations (50% saved)

Precisions

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

ival-log1p: 2.0ms (48.8% of total)

ival-add: 1.0ms (24.4% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0.2%)

Memory

2.3MiB live, 2.3MiB allocated

Counts

2 → 15

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
1
(+ 1 x)
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (/ 1 x))
(- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))
(- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))
(* x (+ 1 (/ 1 x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))

Calls

3 calls:

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

simplify0.0ms (0.1%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Counts

15 → 2

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
1
(+ 1 x)
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (/ 1 x))
(- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))
(- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))
(* x (+ 1 (/ 1 x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))

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

rewrite0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

eval0.0ms (0.1%)

Memory: 0.8MiB live, 0.8MiB allocated
Compiler: Compiled 25 to 9 computations (64% 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	3	1	4
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	3	2	5

Accuracy

37.9%

Counts

5 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	37.4%	(log.f64 (+.f64 #s(literal 1 binary64) x))
▶	4.4%	#s(approx (log (+ 1 x)) (+.f64 #s(literal 1 binary64) x))

Compiler

Compiled 12 to 11 computations (8.3% 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 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (log (+ 1 x)) (+.f64 #s(literal 1 binary64) x))

Calls

Call 1

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

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

localize14.0ms (2.4%)

Memory

-19.9MiB live, 18.2MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(+.f64 #s(literal 1 binary64) x)
accuracy	61.15939434469436	#s(approx (log (+ 1 x)) (+.f64 #s(literal 1 binary64) x))

Samples

10.0ms

256×

valid

Compiler

Compiled 24 to 13 computations (45.8% saved)

Precisions

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

ival-log1p: 4.0ms (68.3% of total)

ival-add: 1.0ms (17.1% 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

1.0MiB live, 1.0MiB allocated

Counts

2 → 15

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
1
(+ 1 x)
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (/ 1 x))
(- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))
(- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))
(* x (+ 1 (/ 1 x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))

Calls

3 calls:

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

simplify0.0ms (0.1%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Counts

15 → 2

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
1
(+ 1 x)
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (/ 1 x))
(- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))
(- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))
(* x (+ 1 (/ 1 x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))

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

rewrite0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

eval0.0ms (0.1%)

Memory: 0.8MiB live, 0.8MiB allocated
Compiler: Compiled 29 to 8 computations (72.4% saved)

prune2.0ms (0.3%)

Memory

3.1MiB live, 3.1MiB 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

37.9%

Counts

5 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	37.4%	(log.f64 (+.f64 #s(literal 1 binary64) x))
✓	4.4%	#s(approx (log (+ 1 x)) (+.f64 #s(literal 1 binary64) x))

Compiler

Compiled 24 to 19 computations (20.8% saved)

regimes4.0ms (0.7%)

Memory

8.9MiB live, 8.9MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
37.4%	1	`x`
37.4%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
37.4%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 8 to 8 computations (0% saved)

regimes3.0ms (0.6%)

Memory

7.0MiB live, 7.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
4.4%	1	`x`
4.4%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
4.4%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 8 to 8 computations (0% saved)

simplify4.0ms (0.7%)

Memory

8.5MiB live, 8.5MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

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

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

soundness0.0ms (0.1%)

Memory

0.8MiB live, 0.8MiB allocated

Stop Event

1×

done

Compiler

Compiled 12 to 8 computations (33.3% saved)

preprocess26.0ms (4.2%)

Memory: 2.4MiB live, 40.5MiB allocated
Compiler: Compiled 70 to 42 computations (40% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze1.0ms (0.2%)

sample413.0ms (67.9%)

explain117.0ms (19.2%)

preprocess2.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0.1%)

simplify0.0ms (0%)

localize15.0ms (2.5%)

series1.0ms (0.2%)

simplify0.0ms (0.1%)

rewrite0.0ms (0%)

eval0.0ms (0.1%)

prune1.0ms (0.1%)

simplify0.0ms (0%)

localize14.0ms (2.4%)

series1.0ms (0.1%)

simplify0.0ms (0.1%)

rewrite0.0ms (0%)

eval0.0ms (0.1%)

prune2.0ms (0.3%)

regimes4.0ms (0.7%)

regimes3.0ms (0.6%)

simplify4.0ms (0.7%)

soundness0.0ms (0.1%)

preprocess26.0ms (4.2%)

end0.0ms (0%)

Profiling