Metrics for Toniolo and Linder, Equation (3a)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze114.0ms (3.7%)

Memory

6.2MiB live, 39.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
0%	0%	99.8%	0.2%	0%	0%	0%	1
0%	0%	99.8%	0.2%	0%	0%	0%	2
50%	49.9%	49.9%	0.2%	0%	0%	0%	3
50%	49.9%	49.9%	0.2%	0%	0%	0%	4
50%	49.9%	49.9%	0.2%	0%	0%	0%	5
50%	49.9%	49.9%	0.2%	0%	0%	0%	6
75%	74.9%	25%	0.2%	0%	0%	0%	7
75%	74.9%	25%	0.2%	0%	0%	0%	8
75%	74.9%	25%	0.2%	0%	0%	0%	9
75%	74.9%	25%	0.2%	0%	0%	0%	10
87.5%	87.3%	12.5%	0.2%	0%	0%	0%	11
87.5%	87.3%	12.5%	0.2%	0%	0%	0%	12

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample51.0ms (1.6%)

Memory

-5.7MiB live, 17.0MiB allocated

Samples

39.0ms

260×

valid

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-sin: 10.0ms (30.8% of total)

ival-pow2: 7.0ms (21.5% of total)

ival-div: 5.0ms (15.4% of total)

ival-mult: 4.0ms (12.3% of total)

ival-add: 3.0ms (9.2% of total)

ival-sqrt: 3.0ms (9.2% of total)

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

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

exact: 0.0ms (0% of total)

Bogosity

explain2.7s (88.4%)

Memory

12.1MiB live, 2 005.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
38	-	0	-	`(sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))`
8	-	2	(7.999687621800781e+80 -3.662741066034915e-51 2.915686385440344e-162 1.8568855356578599e-211)	`(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`
1	-	0	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))`
0	-	0	-	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`
0	-	0	-	`Om`
0	-	0	-	`(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
0	-	0	-	`(*.f64 #s(literal 2 binary64) l)`
0	-	0	-	`(sin.f64 ky)`
0	-	0	-	`(/.f64 (*.f64 #s(literal 2 binary64) l) Om)`
0	-	0	-	`kx`
0	-	0	-	`ky`
0	-	0	-	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`
0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))))`
0	-	0	-	`(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))`
0	-	0	-	`(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64))`
0	-	0	-	`(+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
0	-	0	-	`(sin.f64 kx)`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))`
0	-	0	-	`l`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))`	oflow-rescue	38	0
↳	`(sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))`	overflow	24
↳	`(/.f64 (*.f64 #s(literal 2 binary64) l) Om)`	overflow	35
↳	`(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`	overflow	62
↳	`(+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`	overflow	62
↳	`(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64))`	overflow	67
`*.f64`	`(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`	*no**	3	0
`*.f64`	`(.f64 (pow.f64 (/.f64 (.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`	*ou**	1	0
↳	`(/.f64 (*.f64 #s(literal 2 binary64) l) Om)`	overflow	35
↳	`(pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64))`	overflow	67
↳	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`	underflow	48
↳	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`	underflow	65
↳	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`	underflow	11

Confusion

	Predicted +	Predicted -
+	2	1
-	40	213

Precision

0.047619047619047616

Recall

0.6666666666666666

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	1
-	40	0	213

Precision?

0.047619047619047616

Recall?

0.6666666666666666

2:

4:

8:

16:

32:

64:

128:

256:

512:

1024:

2048:

Freqs

test

number	freq
0	214
1	42

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Total Time

15.373291015625

Average Time

0.060051918029785156

Samples

522.0ms

3 072×

valid

Compiler

Compiled 7 716 to 1 080 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 383.0ms

ival-sin: 118.0ms (30.8% of total)

ival-pow2: 79.0ms (20.6% of total)

ival-div: 57.0ms (14.9% of total)

ival-mult: 49.0ms (12.8% of total)

ival-add: 39.0ms (10.2% of total)

ival-sqrt: 35.0ms (9.1% of total)

ival-true: 3.0ms (0.8% of total)

exact: 3.0ms (0.8% of total)

ival-assert: 1.0ms (0.3% of total)

preprocess153.0ms (4.9%)

Memory

2.8MiB live, 27.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	127	391
1	330	354
2	871	354
3	3861	354
4	7924	354
0	22	27
0	39	27
1	64	25
2	124	25
3	440	25
4	1734	25
5	3039	25
6	3563	25
7	3800	25
8	4308	25
9	5672	25
10	6664	25
0	10090	24

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Inputs

(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Outputs
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (/.f64 (*.f64 l #s(literal 2 binary64)) Om) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1/2 binary64)))

Outputs

(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

(sqrt.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 (fma.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (/.f64 (*.f64 l #s(literal 2 binary64)) Om) #s(literal 2 binary64)) #s(literal 1 binary64)))) #s(literal 1/2 binary64)))

Symmetry

(abs ky)

(abs kx)

(abs Om)

(abs l)

(sort kx ky)

Compiler

Compiled 29 to 22 computations (24.1% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 4 computations (-∞% saved)

prune1.0ms (0%)

Memory

-7.2MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.8%	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Status

Accuracy

Program

98.8%

(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Compiler

Compiled 58 to 44 computations (24.1% saved)

simplify20.0ms (0.6%)

Memory

2.3MiB live, 18.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	29
1	31	29

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Inputs

(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

Outputs
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))
(sqrt.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (/.f64 (*.f64 l #s(literal 2 binary64)) Om) #s(literal 2 binary64))) #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))))

Outputs

(sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 (*.f64 #s(literal 2 binary64) l) Om) #s(literal 2 binary64)) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))))))

(sqrt.f64 (*.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (*.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (/.f64 (*.f64 l #s(literal 2 binary64)) Om) #s(literal 2 binary64))) #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))))

soundness0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 29 to 22 computations (24.1% saved)

preprocess19.0ms (0.6%)

Memory

4.2MiB live, 13.0MiB allocated

Remove

(sort kx ky)

(abs l)

(abs Om)

(abs kx)

(abs ky)

Compiler

Compiled 696 to 528 computations (24.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze114.0ms (3.7%)

sample51.0ms (1.6%)

explain2.7s (88.4%)

preprocess153.0ms (4.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify20.0ms (0.6%)

soundness0.0ms (0%)

preprocess19.0ms (0.6%)

end0.0ms (0%)

Profiling