Metrics for Equirectangular approximation to distance on a great circle

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
100%	99.8%	0%	0.2%	0%	0%	0%	1

Compiler

Compiled 34 to 16 computations (52.9% saved)

sample35.0ms (0.3%)

Memory

-3.7MiB live, 11.5MiB allocated

Samples

18.0ms	216×	0	valid
8.0ms	44×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-hypot: 4.0ms (22.2% of total)

ival-mult: 3.0ms (16.6% of total)

ival-sub: 3.0ms (16.6% of total)

ival-cos: 3.0ms (16.6% of total)

ival-div: 2.0ms (11.1% of total)

ival-add: 1.0ms (5.5% of total)

adjust: 1.0ms (5.5% of total)

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

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

exact: 0.0ms (0% of total)

Bogosity

explain11.2s (98%)

Memory

-75.7MiB live, 5 286.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
173	0	-	0	-	`(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))`
75	119	(-3.264855686472017e+234 -3.115087042401687e-55 -6.169957224021614e-13 -6.205903630191249e-235 4.502356012886135e+116)	1	(-1.153014160960967e+98 1.9227767938827612e-246 -3.40661572311801e+69 -256.4840131919387 2.9560218810372394e-5)	`(cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))`
0	0	-	0	-	`(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))))`
0	0	-	0	-	`lambda2`
0	0	-	0	-	`(+.f64 phi1 phi2)`
0	0	-	0	-	`phi2`
0	0	-	0	-	`(+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))`
0	0	-	0	-	`(-.f64 lambda1 lambda2)`
0	0	-	0	-	`(*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))`
0	0	-	0	-	`R`
0	0	-	0	-	`lambda1`
0	0	-	0	-	`phi1`
0	0	-	0	-	`(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))`
0	0	-	0	-	`(-.f64 phi1 phi2)`
0	0	-	0	-	`(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`cos.f64`	`(cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))`	sensitivity	193	1
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))`	oflow-rescue	173	0
↳	`(*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))`	overflow	118
↳	`(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))))`	overflow	110
↳	`(+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))`	overflow	173

Confusion

	Predicted +	Predicted -
+	107	1
-	113	35

Precision

0.4863636363636364

Recall

0.9907407407407407

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	107	1	0
-	113	0	35

Precision?

0.48868778280542985

Recall?

1.0

Freqs

test

number	freq
0	36
1	74
2	146

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Total Time

62.606689453125

Average Time

0.24455738067626953

Samples

4.7s	16 110×	1	valid
815.0ms	6 930×	0	valid

Compiler

Compiled 22 545 to 3 240 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.1s

ival-cos: 1.0s (25.6% of total)

ival-mult: 996.0ms (24.4% of total)

ival-hypot: 562.0ms (13.8% of total)

adjust: 502.0ms (12.3% of total)

ival-sub: 352.0ms (8.6% of total)

ival-add: 337.0ms (8.3% of total)

ival-div: 248.0ms (6.1% of total)

ival-true: 20.0ms (0.5% of total)

exact: 15.0ms (0.4% of total)

ival-assert: 8.0ms (0.2% of total)

preprocess160.0ms (1.4%)

Memory

4.3MiB live, 40.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	667
1	357	661
2	923	645
3	4473	645
4	7816	645
0	17	32
0	28	32
1	43	32
2	88	32
3	302	32
4	1055	32
5	3348	32
6	6812	32
0	8149	16

Stop Event

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

Calls

Call 1

Inputs
(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Inputs

(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Outputs
(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(.f64 (hypot.f64 (-.f64 phi2 phi1) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64))) (-.f64 lambda1 lambda2))) R)

Outputs

(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

(*.f64 (hypot.f64 (-.f64 phi2 phi1) (*.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64))) (-.f64 lambda1 lambda2))) R)

Symmetry

(negabs R)

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 32 to 17 computations (46.9% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 5 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.4%	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Status

Accuracy

Program

60.4%

(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Compiler

Compiled 64 to 34 computations (46.9% saved)

simplify21.0ms (0.2%)

Memory

-7.1MiB live, 18.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	25	32
2	33	32
3	37	32
4	39	32

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Inputs

(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

Outputs
(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
(.f64 (sqrt.f64 (+.f64 (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)) (.f64 (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64))) (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64))) (-.f64 lambda1 lambda2))))) R)

Outputs

(*.f64 R (sqrt.f64 (+.f64 (*.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64)))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) #s(literal 2 binary64))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))

(*.f64 (sqrt.f64 (+.f64 (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)) (*.f64 (*.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64))) (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) #s(literal 2 binary64))) (-.f64 lambda1 lambda2))))) R)

soundness0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 32 to 17 computations (46.9% saved)

preprocess13.0ms (0.1%)

Memory

-0.0MiB live, 7.7MiB allocated

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

(negabs R)

Compiler

Compiled 512 to 272 computations (46.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample35.0ms (0.3%)

explain11.2s (98%)

preprocess160.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify21.0ms (0.2%)

soundness0.0ms (0%)

preprocess13.0ms (0.1%)

end0.0ms (0%)

Profiling