Metrics for Toniolo and Linder, Equation (2)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze316.0ms (13.4%)

Memory

4.4MiB live, 122.7MiB 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
0%	0%	99.8%	0.2%	0%	0%	0%	3
0%	0%	99.8%	0.2%	0%	0%	0%	4
0%	0%	99.8%	0.2%	0%	0%	0%	5
0%	0%	99.8%	0.2%	0%	0%	0%	6
0%	0%	99.8%	0.2%	0%	0%	0%	7
0%	0%	99.8%	0.2%	0%	0%	0%	8
19.2%	18.7%	78.8%	0.2%	0%	2.3%	0%	9
19.4%	18.7%	77.6%	0.2%	0%	3.5%	0%	10
22.8%	21.8%	73.9%	0.2%	0%	4.1%	0%	11
23.3%	21.8%	71.8%	0.2%	0%	6.1%	0%	12

Compiler

Compiled 21 to 18 computations (14.3% saved)

sample74.0ms (3.1%)

Memory

0.4MiB live, 25.1MiB allocated

Samples

28.0ms	135×	1	valid
17.0ms	191×	0	invalid
12.0ms	125×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-div: 12.0ms (27.9% of total)

ival-pow2: 10.0ms (23.3% of total)

ival-asin: 5.0ms (11.6% of total)

adjust: 4.0ms (9.3% of total)

ival-sqrt: 3.0ms (7% of total)

ival-sub: 3.0ms (7% of total)

ival-mult: 3.0ms (7% of total)

ival-add: 2.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

Bogosity

explain1.8s (76.1%)

Memory

4.9MiB live, 1 263.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
36	0	-	2	(5.430603872836379e-30 -1.7340063917571171e-189 3.722805865959954e-262 -7.50652687132508e-50)	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64))))))`
12	133	(6.294284747543222e-12 5.996509259371565e+149 -2.6105888148464896e-134 -7.571518721508329e+300)	0	-	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))`
2	0	-	0	-	`(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))`
0	0	-	0	-	`Om`
0	0	-	0	-	`t`
0	0	-	0	-	`(/.f64 t l)`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64))))`
0	0	-	0	-	`Omc`
0	114	(-1.3184255685531709e+26 -1.462301967365799e-172 3729181079881.9395 1.604013304711451e+48)	0	-	`(-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64)))`
0	0	-	0	-	`(*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))`
0	0	-	0	-	`(/.f64 Om Omc)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`l`
0	0	-	0	-	`(pow.f64 (/.f64 t l) #s(literal 2 binary64))`
0	0	-	0	-	`(pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`asin.f64`	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))`	sensitivity	145	0
`-.f64`	`(-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64)))`	cancellation	114	0
`sqrt.f64`	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64))))))`	uflow-rescue	34	0
↳	`(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))`	underflow	61
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))`	underflow	72
↳	`(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64))))))`	underflow	27
↳	`(pow.f64 (/.f64 t l) #s(literal 2 binary64))`	underflow	72
↳	`(/.f64 t l)`	underflow	27
↳	`(/.f64 Om Omc)`	underflow	57
↳	`(pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))`	underflow	139
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))`	n/o	2	0
↳	`(pow.f64 (/.f64 t l) #s(literal 2 binary64))`	overflow	63
↳	`(/.f64 t l)`	overflow	29
↳	`(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64))))`	overflow	63
↳	`(*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))`	overflow	63

Confusion

	Predicted +	Predicted -
+	48	0
-	168	40

Precision

0.2222222222222222

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	48	0	0
-	168	0	40

Precision?

0.2222222222222222

Recall?

1.0

Freqs

test

number	freq
0	40
1	137
2	79

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Total Time

8.943359375

Average Time

0.03493499755859375

Samples

362.0ms	1 608×	1	valid
147.0ms	1 464×	0	valid

Compiler

Compiled 3 816 to 792 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 355.0ms

ival-div: 88.0ms (24.8% of total)

ival-pow2: 78.0ms (22% of total)

ival-asin: 47.0ms (13.2% of total)

adjust: 43.0ms (12.1% of total)

ival-sqrt: 29.0ms (8.2% of total)

ival-mult: 24.0ms (6.8% of total)

ival-sub: 20.0ms (5.6% of total)

ival-add: 19.0ms (5.4% of total)

exact: 3.0ms (0.8% of total)

ival-true: 2.0ms (0.6% of total)

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

preprocess132.0ms (5.6%)

Memory

5.7MiB live, 27.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	278
1	192	270
2	396	270
3	1045	270
4	3020	270
5	6041	270
0	16	19
0	26	19
1	37	19
2	61	19
3	126	19
4	266	19
5	569	19
6	1183	19
7	2869	19
8	4986	19
9	7262	19
0	8090	18

Stop Event

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

Calls

Call 1

Inputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))

Inputs

(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))

Outputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal -1 binary64)))))

Outputs

(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))

(asin.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal -2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal -1 binary64)))))

Symmetry

(abs Omc)

(abs Om)

(abs l)

(abs t)

Compiler

Compiled 19 to 16 computations (15.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	86.3%	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))

Status

Accuracy

Program

86.3%

(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify29.0ms (1.2%)

Memory

-1.1MiB live, 18.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	19
1	23	19
2	27	19
3	29	19
4	30	19

Stop Event

1×

saturated

Calls

Call 1

Inputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))

Inputs

(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))

Outputs
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))
(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 (*.f64 (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)))))

Outputs

(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (pow.f64 (/.f64 t l) #s(literal 2 binary64)))))))

(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 Om Omc) #s(literal 2 binary64))) (+.f64 (*.f64 (pow.f64 (/.f64 t l) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)))))

soundness0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 19 to 16 computations (15.8% saved)

preprocess11.0ms (0.5%)

Memory

-0.1MiB live, 7.8MiB allocated

Remove

(abs t)

(abs l)

(abs Om)

(abs Omc)

Compiler

Compiled 380 to 320 computations (15.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze316.0ms (13.4%)

sample74.0ms (3.1%)

explain1.8s (76.1%)

preprocess132.0ms (5.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify29.0ms (1.2%)

soundness0.0ms (0%)

preprocess11.0ms (0.5%)

end0.0ms (0%)

Profiling