Metrics for Toniolo and Linder, Equation (7)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze245.0ms (2.5%)

Memory

-1.1MiB live, 93.4MiB 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)

sample61.0ms (0.6%)

Memory

-0.2MiB live, 22.0MiB allocated

Samples

16.0ms	174×	0	valid
14.0ms	83×	1	valid
7.0ms	45×	1	invalid
7.0ms	81×	0	invalid
1.0ms	3×	2	valid
0.0ms	2×	2	invalid

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 10.0ms (28.8% of total)

ival-sqrt: 6.0ms (17.3% of total)

ival-div: 5.0ms (14.4% of total)

ival-add: 5.0ms (14.4% of total)

ival-sub: 4.0ms (11.5% of total)

adjust: 4.0ms (11.5% of total)

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

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

exact: 0.0ms (0% of total)

Bogosity

explain9.2s (94.4%)

Memory

66.0MiB live, 5 531.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
138	-	-	`(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)))`
78	-	-	`(-.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	-	-	`(/.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))`
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	-	-	`#s(literal 1 binary64)`
0	-	-	`t`
0	-	-	`(.f64 #s(literal 2 binary64) (.f64 t t))`
0	-	-	`(*.f64 (sqrt.f64 #s(literal 2 binary64)) t)`
0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	-	-	`(*.f64 l l)`
0	-	-	`(sqrt.f64 #s(literal 2 binary64))`
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	-	-	`(*.f64 t t)`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(-.f64 x #s(literal 1 binary64))`
0	-	-	`l`
0	-	-	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`
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	108	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	108
↳	`(.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	119
↳	`(.f64 #s(literal 2 binary64) (.f64 t t))`	overflow	94
↳	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`	overflow	119
↳	`(*.f64 t t)`	overflow	94
↳	`(*.f64 l l)`	overflow	78
`-.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	39	0
`-.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	39	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	119
↳	`(.f64 #s(literal 2 binary64) (.f64 t t))`	overflow	94
↳	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`	overflow	119
↳	`(*.f64 t t)`	overflow	94
↳	`(*.f64 l l)`	overflow	39
↳	`(*.f64 l l)`	overflow	39
`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	30	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	30
↳	`(.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	20
↳	`(.f64 #s(literal 2 binary64) (.f64 t t))`	underflow	46
↳	`(+.f64 (.f64 l l) (.f64 #s(literal 2 binary64) (*.f64 t t)))`	underflow	20
↳	`(*.f64 t t)`	underflow	46
↳	`(*.f64 l l)`	underflow	166

Confusion

	Predicted +	Predicted -
+	188	0
-	0	68

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	188	0	0
-	0	0	68

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	68
1	160
2	28

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Total Time

37.66162109375

Average Time

0.14711570739746094

Samples

1.6s	15 210×	0	valid
1.5s	7 560×	1	valid
75.0ms	270×	2	valid

Compiler

Compiled 19 080 to 3 420 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.1s

ival-mult: 642.0ms (30.2% of total)

ival-div: 334.0ms (15.7% of total)

ival-sqrt: 333.0ms (15.7% of total)

ival-add: 278.0ms (13.1% of total)

ival-sub: 254.0ms (11.9% of total)

adjust: 231.0ms (10.9% of total)

exact: 24.0ms (1.1% of total)

ival-true: 21.0ms (1% of total)

ival-assert: 9.0ms (0.4% of total)

preprocess208.0ms (2.1%)

Memory

5.6MiB live, 55.4MiB 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)

prune1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	28.3%	(/.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

28.3%

(/.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 (0.2%)

Memory

-1.0MiB 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)

preprocess12.0ms (0.1%)

Memory

-2.0MiB live, 5.9MiB 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%)

analyze245.0ms (2.5%)

sample61.0ms (0.6%)

explain9.2s (94.4%)

preprocess208.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify21.0ms (0.2%)

soundness0.0ms (0%)

preprocess12.0ms (0.1%)

end0.0ms (0%)

Profiling