Metrics for Logistic function from Lakshay Garg

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample1.4s (72.9%)

Memory

50.1MiB live, 2 166.7MiB allocated; 418ms collecting garbage

Samples

528.0ms	1 776×	2	valid
361.0ms	2 415×	1	valid
251.0ms	4 065×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 908.0ms

ival-exp: 446.0ms (49.1% of total)

adjust: 123.0ms (13.5% of total)

ival-div!: 119.0ms (13.1% of total)

ival-add!: 105.0ms (11.6% of total)

ival-sub!: 61.0ms (6.7% of total)

ival-mult!: 54.0ms (5.9% of total)

Bogosity

preprocess44.0ms (2.3%)

Memory

-47.2MiB live, 53.5MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	57	30
2	186	30
3	897	30

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.5%	(-.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 1 binary64))

Compiler

Compiled 20 to 18 computations (10% saved)

series6.0ms (0.3%)

Memory

13.2MiB live, 13.2MiB allocated; 0ms collecting garbage

Counts

9 → 20

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 1 binary64))
(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x))))
#s(literal 2 binary64)
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))
#s(literal 1 binary64)
(exp.f64 (*.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) x)
#s(literal -2 binary64)
x

Outputs
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 x))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 1))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 (+ 1 x)))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 (+ 1 (* x (+ 1 (* -1/3 (pow x 2)))))))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 (+ 1 (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))))))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 2))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 (+ 2 (* -2 x))))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 (+ 2 (* x (- (* 2 x) 2)))))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 (+ 2 (* x (- (* x (+ 2 (* -4/3 x))) 2)))))
#s(approx (exp (* -2 x)) #s(hole binary64 (+ 1 (* -2 x))))
#s(approx (exp (* -2 x)) #s(hole binary64 (+ 1 (* x (- (* 2 x) 2)))))
#s(approx (exp (* -2 x)) #s(hole binary64 (+ 1 (* x (- (* x (+ 2 (* -4/3 x))) 2)))))
#s(approx (* -2 x) #s(hole binary64 (* -2 x)))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (- (* 2 (/ 1 (+ 1 (exp (* -2 x))))) 1)))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 (/ 2 (+ 1 (exp (* -2 x))))))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 (+ 1 (exp (* -2 x)))))
#s(approx (exp (* -2 x)) #s(hole binary64 (exp (* -2 x))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((- (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x)))) 2 (+ 1 (exp (* -2 x))) 1 (exp (* -2 x)) (* -2 x) -2 x)
2.0ms	x	@	inf	((- (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x)))) 2 (+ 1 (exp (* -2 x))) 1 (exp (* -2 x)) (* -2 x) -2 x)
1.0ms	x	@	0	((- (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x)))) 2 (+ 1 (exp (* -2 x))) 1 (exp (* -2 x)) (* -2 x) -2 x)

Time

Variable

Point

Expression

2.0ms

-inf

((- (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x)))) 2 (+ 1 (exp (* -2 x))) 1 (exp (* -2 x)) (* -2 x) -2 x)

2.0ms

inf

((- (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x)))) 2 (+ 1 (exp (* -2 x))) 1 (exp (* -2 x)) (* -2 x) -2 x)

1.0ms

((- (/ 2 (+ 1 (exp (* -2 x)))) 1) (/ 2 (+ 1 (exp (* -2 x)))) 2 (+ 1 (exp (* -2 x))) 1 (exp (* -2 x)) (* -2 x) -2 x)

rewrite187.0ms (9.8%)

Memory

43.2MiB live, 225.7MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	75	360
0	82	358
1	489	348
2	3128	348

Stop Event

1×	iter-limit
1×	unsound
1×	node-limit
1×	iter-limit

Counts

29 → 17

Calls

Call 1

Inputs
(-.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 1 binary64))
(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x))))
#s(literal 2 binary64)
(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))
#s(literal 1 binary64)
(exp.f64 (*.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal -2 binary64) x)
#s(literal -2 binary64)
x
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 x))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 1))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 (+ 1 x)))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 (+ 1 (* x (+ 1 (* -1/3 (pow x 2)))))))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 (+ 1 (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3)))))))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 2))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 (+ 2 (* -2 x))))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 (+ 2 (* x (- (* 2 x) 2)))))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 (+ 2 (* x (- (* x (+ 2 (* -4/3 x))) 2)))))
#s(approx (exp (* -2 x)) #s(hole binary64 (+ 1 (* -2 x))))
#s(approx (exp (* -2 x)) #s(hole binary64 (+ 1 (* x (- (* 2 x) 2)))))
#s(approx (exp (* -2 x)) #s(hole binary64 (+ 1 (* x (- (* x (+ 2 (* -4/3 x))) 2)))))
#s(approx (* -2 x) #s(hole binary64 (* -2 x)))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (- (* 2 (/ 1 (+ 1 (exp (* -2 x))))) 1)))
#s(approx (/ 2 (+ 1 (exp (* -2 x)))) #s(hole binary64 (/ 2 (+ 1 (exp (* -2 x))))))
#s(approx (+ 1 (exp (* -2 x))) #s(hole binary64 (+ 1 (exp (* -2 x)))))
#s(approx (exp (* -2 x)) #s(hole binary64 (exp (* -2 x))))

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

eval4.0ms (0.2%)

Memory: -41.6MiB live, 2.1MiB allocated; 3ms collecting garbage
Compiler: Compiled 71 to 38 computations (46.5% saved)

prune1.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

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

99.7%

Counts

9 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	55.5%	(-.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 1 binary64))
▶	51.3%	#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)

Compiler

Compiled 20 to 19 computations (5% saved)

series1.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Counts

2 → 5

Calls

Call 1

Inputs
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)
x

Outputs
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 x))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (- (* 2 (/ 1 (+ 1 (exp (* -2 x))))) 1)))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)
1.0ms	x	@	-inf	((- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)
0.0ms	x	@	0	((- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)

rewrite199.0ms (10.4%)

Memory

21.8MiB live, 157.9MiB allocated; 62ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	126
0	37	124
1	257	124
2	1585	118

Stop Event

1×	iter-limit
1×	unsound
1×	node-limit
1×	saturated

Counts

7 → 3

Calls

Call 1

Inputs
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)
x
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 x))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* -1/3 (pow x 2))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 2/15 (pow x 2)) 1/3))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/15 (* -17/315 (pow x 2)))) 1/3))))))
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) #s(hole binary64 (- (* 2 (/ 1 (+ 1 (exp (* -2 x))))) 1)))

Outputs
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)
x
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)

eval0.0ms (0%)

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

prune1.0ms (0.1%)

Memory

1.5MiB live, 1.5MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	1	1
Total	2	2

Accuracy

99.7%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	55.5%	(-.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 1 binary64))
✓	51.3%	#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)

Compiler

Compiled 39 to 37 computations (5.1% saved)

regimes6.0ms (0.3%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Counts

2 → 3

Calls

Call 1

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

Outputs

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

#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)

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

Calls

6 calls:

1.0ms	(*.f64 #s(literal -2 binary64) x)
1.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 1 binary64))
1.0ms	(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x))))
1.0ms	(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))

Results

Accuracy	Segments	Branch
99.7%	3	`(*.f64 #s(literal -2 binary64) x)`
99.7%	3	`(exp.f64 (*.f64 #s(literal -2 binary64) x))`
99.7%	3	`(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))`
99.7%	3	`(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x))))`
99.7%	3	`(-.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 1 binary64))`
99.7%	3	`x`

Compiler

Compiled 32 to 31 computations (3.1% saved)

regimes5.0ms (0.3%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)

Outputs
#s(approx (- (/ 2 (+ 1 (exp (* -2 x)))) 1) x)

Calls

6 calls:

1.0ms	(*.f64 #s(literal -2 binary64) x)
1.0ms	x
1.0ms	(-.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 1 binary64))
1.0ms	(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x))))
1.0ms	(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))

Results

Accuracy	Segments	Branch
51.3%	1	`(*.f64 #s(literal -2 binary64) x)`
51.3%	1	`(exp.f64 (*.f64 #s(literal -2 binary64) x))`
51.3%	1	`(+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))`
51.3%	1	`(/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x))))`
51.3%	1	`(-.f64 (/.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal -2 binary64) x)))) #s(literal 1 binary64))`
51.3%	1	`x`

Compiler

Compiled 32 to 31 computations (3.1% saved)

bsearch38.0ms (2%)

Memory

-12.2MiB live, 37.4MiB allocated; 5ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	1.0848852796409777e-10	32.191019889155946
16.0ms	-0.0018623716034859544	-1.0220784581390717e-6

Samples

17.0ms	176×	1	valid
5.0ms	112×	0	valid

Compiler

Compiled 373 to 391 computations (-4.8% saved)

Precisions

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

ival-exp: 6.0ms (38.9% of total)

adjust: 3.0ms (19.5% of total)

ival-div!: 2.0ms (13% of total)

ival-mult!: 2.0ms (13% of total)

ival-add!: 1.0ms (6.5% of total)

ival-sub!: 1.0ms (6.5% of total)

derivations10.0ms (0.5%)

Memory

9.3MiB live, 9.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 25 to 24 computations (4% saved)

preprocess17.0ms (0.9%)

Memory: -19.7MiB live, 26.6MiB allocated; 3ms collecting garbage
Compiler: Compiled 35 to 33 computations (5.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample1.4s (72.9%)

preprocess44.0ms (2.3%)

series6.0ms (0.3%)

rewrite187.0ms (9.8%)

eval4.0ms (0.2%)

prune1.0ms (0.1%)

series1.0ms (0.1%)

rewrite199.0ms (10.4%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes6.0ms (0.3%)

regimes5.0ms (0.3%)

bsearch38.0ms (2%)

derivations10.0ms (0.5%)

preprocess17.0ms (0.9%)

end0.0ms (0%)

Profiling