Metrics for 1/2(abs(p)+abs(r) - sqrt((p-r)^2 + 4q^2))

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%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample55.0ms (2.4%)

Memory

2.8MiB live, 19.0MiB allocated

Samples

19.0ms	102×	1	valid
16.0ms	61×	2	valid
9.0ms	97×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

adjust: 9.0ms (25.2% of total)

ival-pow2: 7.0ms (19.6% of total)

ival-mult: 5.0ms (14% of total)

ival-sub: 4.0ms (11.2% of total)

ival-add: 4.0ms (11.2% of total)

ival-sqrt: 3.0ms (8.4% of total)

ival-div: 2.0ms (5.6% of total)

ival-fabs: 2.0ms (5.6% of total)

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

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

exact: 0.0ms (0% of total)

Bogosity

explain2.0s (86.8%)

Memory

10.1MiB live, 1 415.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
148	0	-	1	(-3.425201662687631e-290 -1.2118410019842631e-161 -9.415178349086052e-239)	`(sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))`
131	31	(5.205931085885297e-220 -1.3954171667883087e-148 -1.955191305700122e-251)	0	-	`(-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64))))))`
1	0	-	0	-	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))`
0	0	-	0	-	`q`
0	0	-	0	-	`(-.f64 p r)`
0	0	-	0	-	`(pow.f64 q #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(pow.f64 (-.f64 p r) #s(literal 2 binary64))`
0	0	-	0	-	`(fabs.f64 p)`
0	0	-	0	-	`(+.f64 (fabs.f64 p) (fabs.f64 r))`
0	0	-	0	-	`(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 4 binary64)`
0	0	-	0	-	`p`
0	0	-	0	-	`(+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64))))`
0	0	-	0	-	`(fabs.f64 r)`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`r`
0	0	-	0	-	`(*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64))))))`	cancellation	162	0
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))`	oflow-rescue	143	0
↳	`(+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64))))`	overflow	144
↳	`(pow.f64 q #s(literal 2 binary64))`	overflow	74
↳	`(pow.f64 (-.f64 p r) #s(literal 2 binary64))`	overflow	102
↳	`(sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))`	overflow	1
↳	`(*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))`	overflow	74
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))`	uflow-rescue	4	0
↳	`(+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64))))`	underflow	4
↳	`(pow.f64 q #s(literal 2 binary64))`	underflow	60
↳	`(pow.f64 (-.f64 p r) #s(literal 2 binary64))`	underflow	19
↳	`(*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))`	underflow	60
`*.f64`	`(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))`	*no**	1	0

Confusion

	Predicted +	Predicted -
+	211	0
-	11	34

Precision

0.9504504504504504

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	211	0	0
-	11	0	34

Precision?

0.9504504504504504

Recall?

1.0

2:

4:

8:

16:

32:

64:

128:

256:

512:

1024:

2048:

Freqs

test

number	freq
0	34
1	134
2	88

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Total Time

11.806884765625

Average Time

0.046120643615722656

Samples

266.0ms	1 212×	1	valid
223.0ms	732×	2	valid
117.0ms	1 128×	0	valid

Compiler

Compiled 3 780 to 888 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 431.0ms

adjust: 108.0ms (25.1% of total)

ival-pow2: 83.0ms (19.3% of total)

ival-mult: 52.0ms (12.1% of total)

ival-add: 49.0ms (11.4% of total)

ival-sub: 47.0ms (10.9% of total)

ival-sqrt: 38.0ms (8.8% of total)

ival-fabs: 26.0ms (6% of total)

ival-div: 21.0ms (4.9% of total)

exact: 4.0ms (0.9% of total)

ival-true: 2.0ms (0.5% of total)

ival-assert: 1.0ms (0.2% of total)

preprocess210.0ms (9.3%)

Memory

0.5MiB live, 18.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	187
1	160	184
2	443	180
3	1440	180
4	3448	180
5	5328	180
6	7340	180
0	18	20
0	31	20
1	45	20
2	80	20
3	170	20
4	345	20
5	791	20
6	1603	20
7	3084	20
8	3825	20
9	4113	20
10	4203	20
11	4207	20
12	4207	20
13	4337	20
14	4361	20
15	4361	20
0	4361	19

Stop Event

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

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))

Inputs

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))

Outputs
(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))
(.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (fma.f64 (.f64 q q) #s(literal 4 binary64) (pow.f64 (-.f64 p r) #s(literal 2 binary64)))) (+.f64 (fabs.f64 r) (fabs.f64 p))))

Outputs

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))

(*.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (fma.f64 (*.f64 q q) #s(literal 4 binary64) (pow.f64 (-.f64 p r) #s(literal 2 binary64)))) (+.f64 (fabs.f64 r) (fabs.f64 p))))

Symmetry

(abs q)

(sort p r)

Compiler

Compiled 22 to 18 computations (18.2% 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
	22.2%	(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))

Status

Accuracy

Program

22.2%

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))

Compiler

Compiled 44 to 36 computations (18.2% saved)

simplify20.0ms (0.9%)

Memory

2.8MiB live, 18.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	22
1	29	22
2	36	22
3	40	22
4	42	22

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))

Inputs

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))

Outputs
(.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))
(.f64 (-.f64 (+.f64 (fabs.f64 r) (fabs.f64 p)) (sqrt.f64 (+.f64 (.f64 (pow.f64 q #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 (-.f64 p r) #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)))

Outputs

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (-.f64 (+.f64 (fabs.f64 p) (fabs.f64 r)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 p r) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (pow.f64 q #s(literal 2 binary64)))))))

(*.f64 (-.f64 (+.f64 (fabs.f64 r) (fabs.f64 p)) (sqrt.f64 (+.f64 (*.f64 (pow.f64 q #s(literal 2 binary64)) #s(literal 4 binary64)) (pow.f64 (-.f64 p r) #s(literal 2 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 22 to 18 computations (18.2% saved)

preprocess11.0ms (0.5%)

Memory

-5.2MiB live, 3.8MiB allocated

Remove

(sort p r)

(abs q)

Compiler

Compiled 264 to 216 computations (18.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample55.0ms (2.4%)

explain2.0s (86.8%)

preprocess210.0ms (9.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify20.0ms (0.9%)

soundness0.0ms (0%)

preprocess11.0ms (0.5%)

end0.0ms (0%)

Profiling