Metrics for Toniolo and Linder, Equation (7)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze247.0ms (10.2%)

Memory

5.8MiB live, 93.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
0%	0%	99.9%	0.1%	0%	0%	0%	7
0%	0%	74.9%	0.1%	0%	25%	0%	8
4.2%	3.1%	71.8%	0.1%	0%	25%	0%	9
6.3%	4.7%	70.2%	0.1%	0%	25%	0%	10
11.3%	7%	55.4%	0.1%	0%	37.4%	0%	11
16.9%	10.5%	51.9%	0.1%	0%	37.4%	0%	12

Compiler

Compiled 29 to 20 computations (31% saved)

sample63.0ms (2.6%)

Memory

-0.8MiB live, 22.3MiB allocated

Samples

16.0ms	95×	1	valid
14.0ms	158×	0	valid
7.0ms	81×	0	invalid
7.0ms	41×	1	invalid
2.0ms	7×	2	valid
1.0ms	4×	2	invalid

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 11.0ms (29.8% of total)

ival-div: 6.0ms (16.3% of total)

ival-sqrt: 6.0ms (16.3% of total)

ival-add: 5.0ms (13.6% of total)

ival-sub: 4.0ms (10.8% of total)

adjust: 4.0ms (10.8% of total)

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

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

exact: 0.0ms (0% of total)

Bogosity

explain1.9s (76.8%)

Memory

4.7MiB live, 1 462.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
125	0	-	36	(4.5024398014626077e+164 -2.4501047132840666e+269 -2.8705479379279573e-36)	`(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))`
109	6	(6.304051625108101e+198 -1.7743482277229006e-104 1.0896569847260764e-264)	0	-	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`
0	0	-	0	-	`(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))`
0	0	-	0	-	`(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`t`
0	0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 t t))`
0	0	-	0	-	`(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)`
0	0	-	0	-	`(+.f64 x #s(literal 1 binary64))`
0	0	-	0	-	`(*.f64 l l)`
0	0	-	0	-	`(sqrt.f64 #s(literal 2 binary64))`
0	0	-	0	-	`(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))`
0	0	-	0	-	`(*.f64 t t)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(-.f64 x #s(literal 1 binary64))`
0	0	-	0	-	`l`
0	0	-	0	-	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))`	oflow-rescue	78	0
↳	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`	overflow	78
↳	`(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))`	overflow	118
↳	`(.f64 #s(literal 2 binary64) (.f64 t t))`	overflow	81
↳	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`	overflow	118
↳	`(*.f64 t t)`	overflow	81
↳	`(*.f64 l l)`	overflow	116
`-.f64`	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`	nan-rescue	58	0
↳	`(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))`	overflow	118
↳	`(.f64 #s(literal 2 binary64) (.f64 t t))`	overflow	81
↳	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`	overflow	118
↳	`(*.f64 t t)`	overflow	81
↳	`(*.f64 l l)`	overflow	58
↳	`(*.f64 l l)`	overflow	58
`-.f64`	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`	cancellation	57	0
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))`	uflow-rescue	11	0
↳	`(-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l))`	underflow	103
↳	`(.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t))))`	underflow	19
↳	`(.f64 #s(literal 2 binary64) (.f64 t t))`	underflow	54
↳	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`	underflow	19
↳	`(*.f64 t t)`	underflow	54
↳	`(*.f64 l l)`	underflow	122
↳	`(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (*.f64 l l)))`	underflow	92

Confusion

	Predicted +	Predicted -
+	185	8
-	1	62

Precision

0.9946236559139785

Recall

0.9585492227979274

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	185	0	8
-	1	0	62

Precision?

0.9946236559139785

Recall?

0.9585492227979274

2:

4:

8:

16:

32:

64:

128:

256:

512:

1024:

2048:

Freqs

test

number	freq
0	70
1	168
2	18

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Total Time

11.0576171875

Average Time

0.043193817138671875

Samples

222.0ms	1 140×	1	valid
195.0ms	1 848×	0	valid
24.0ms	84×	2	valid

Compiler

Compiled 5 064 to 888 computations (82.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 297.0ms

ival-mult: 86.0ms (29% of total)

ival-div: 46.0ms (15.5% of total)

ival-sqrt: 46.0ms (15.5% of total)

ival-add: 40.0ms (13.5% of total)

ival-sub: 36.0ms (12.1% of total)

adjust: 36.0ms (12.1% of total)

exact: 3.0ms (1% of total)

ival-true: 2.0ms (0.7% of total)

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

preprocess214.0ms (8.9%)

Memory

13.6MiB live, 55.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	250
1	221	248
2	650	246
3	2219	246
4	7024	246
0	18	27
0	31	27
1	58	27
2	113	27
3	212	27
4	437	27
5	990	27
6	2266	27
7	5077	27
0	8183	26

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))

Inputs

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

Outputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (fma.f64 (.f64 t t) #s(literal 2 binary64) (.f64 l l)) (-.f64 x #s(literal 1 binary64))) (.f64 l l)))))

Outputs

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

(/.f64 (*.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 #s(literal -1 binary64) x) (/.f64 (fma.f64 (*.f64 t t) #s(literal 2 binary64) (*.f64 l l)) (-.f64 x #s(literal 1 binary64))) (*.f64 l l)))))

Symmetry

(abs l)

(negabs t)

Compiler

Compiled 27 to 18 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune2.0ms (0.1%)

Memory

-11.9MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	27.4%	(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))

Status

Accuracy

Program

27.4%

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

Compiler

Compiled 54 to 36 computations (33.3% saved)

simplify21.0ms (0.9%)

Memory

2.4MiB live, 18.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	33	27
2	43	27
3	52	27
4	65	27
5	82	27

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))

Inputs

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

Outputs
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (.f64 t t)))) (.f64 l l))))
(/.f64 (.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 (.f64 (+.f64 (.f64 (.f64 t t) #s(literal 2 binary64)) (.f64 l l)) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal 1 binary64)))) (.f64 l l))))

Outputs

(/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 (*.f64 l l) (*.f64 #s(literal 2 binary64) (*.f64 t t)))) (*.f64 l l))))

(/.f64 (*.f64 t (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 t t) #s(literal 2 binary64)) (*.f64 l l)) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal 1 binary64)))) (*.f64 l l))))

soundness0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 27 to 18 computations (33.3% saved)

preprocess13.0ms (0.6%)

Memory

-1.5MiB live, 6.0MiB allocated

Remove

(negabs t)

(abs l)

Compiler

Compiled 324 to 216 computations (33.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze247.0ms (10.2%)

sample63.0ms (2.6%)

explain1.9s (76.8%)

preprocess214.0ms (8.9%)

eval0.0ms (0%)

prune2.0ms (0.1%)

simplify21.0ms (0.9%)

soundness0.0ms (0%)

preprocess13.0ms (0.6%)

end0.0ms (0%)

Profiling