Metrics for atan(y/x)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze61.0ms (6.3%)

Memory

-2.7MiB live, 5.2MiB 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
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 20 to 14 computations (30% saved)

sample701.0ms (72.3%)

Memory

13.8MiB live, 246.7MiB allocated

Samples

432.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 245.0ms

ival-<=: 84.0ms (34.3% of total)

ival-div: 78.0ms (31.9% of total)

ival-atan: 47.0ms (19.2% of total)

ival-and: 23.0ms (9.4% of total)

exact: 10.0ms (4.1% of total)

ival-assert: 3.0ms (1.2% of total)

Bogosity

explain40.0ms (4.1%)

Memory

3.4MiB live, 19.1MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(atan.f64 (/.f64 y x))`
-	-	`y`
-	-	`(/.f64 y x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

20.0ms

512×

valid

Compiler

Compiled 28 to 16 computations (42.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 4.0ms (51.9% of total)

ival-atan: 3.0ms (38.9% of total)

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

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

preprocess17.0ms (1.7%)

Memory

-1.7MiB live, 5.9MiB allocated

Algorithm

1×	egg-herbie

Rules

30×	`sub-neg`
20×	`+-commutative`
14×	`div-sub`
10×	`*-commutative`
10×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	24	26
2	36	26
3	46	26
4	54	26
5	68	26
6	88	26
7	98	26
8	100	26
0	4	4
0	6	4
0	6	4

Stop Event

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

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))

Outputs
(atan.f64 (/.f64 y x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0.1%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(atan.f64 (/.f64 y x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify4.0ms (0.4%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 y x)
cost-diff	0	(atan.f64 (/.f64 y x))

Rules

2×	`lift-/.f64`
2×	`lower-atan.f32`
2×	`lift-atan.f64`
2×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
0	6	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))
(/.f64 y x)
y
x

Outputs
(atan.f64 (/.f64 y x))
(/.f64 y x)
y
x

localize19.0ms (2%)

Memory

-32.2MiB live, 5.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(/.f64 y x)
accuracy	0	(atan.f64 (/.f64 y x))

Samples

13.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (50.7% of total)

ival-atan: 1.0ms (25.4% of total)

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

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

series3.0ms (0.3%)

Memory

1.3MiB live, 1.3MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (atan.f64 (/.f64 y x))>
#<alt (/.f64 y x)>

Outputs
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (atan (/ y x))>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>
#<alt (/ y x)>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	(/ y x)
0.0ms	x	@	inf	(/ y x)
0.0ms	y	@	-inf	(/ y x)
0.0ms	y	@	0	(/ y x)
0.0ms	x	@	0	(/ y x)

simplify4.0ms (0.4%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`lower-atan.f32`
2×	`lower-/.f32`
2×	`lower-/.f64`
2×	`lower-atan.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	168
0	4	168

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(atan (/ y x))
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)
(/ y x)

Outputs
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(atan (/ y x))
(atan.f64 (/.f64 y x))
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)
(/ y x)
(/.f64 y x)

rewrite76.0ms (7.9%)

Memory

1.6MiB live, 16.7MiB allocated

Rules

522×	`lower-*.f64`
522×	`lower-*.f32`
470×	`lower-/.f32`
468×	`lower-/.f64`
136×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	14	7
2	49	7
3	224	7
0	1218	7

Stop Event

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

Counts

2 → 62

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))
(/.f64 y x)

Outputs
(-.f64 #s(literal 0 binary64) (atan.f64 (/.f64 y (neg.f64 x))))
(atan.f64 (/.f64 y x))
(neg.f64 (atan.f64 (/.f64 y (neg.f64 x))))
(*.f64 #s(literal -1 binary64) (atan.f64 (/.f64 y (neg.f64 x))))
(+.f64 #s(literal 0 binary64) (/.f64 y x))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64)) (/.f64 y x))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (/.f64 x y))))
(-.f64 #s(literal 0 binary64) (/.f64 y (neg.f64 x)))
(fma.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 0 binary64) (/.f64 y x))
(neg.f64 (/.f64 y (neg.f64 x)))
(/.f64 y x)
(/.f64 (/.f64 y x) #s(literal 1 binary64))
(/.f64 (neg.f64 y) (neg.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 x y))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal -1 binary64) (/.f64 x (neg.f64 y)))
(/.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) y))
(/.f64 (/.f64 y (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 (neg.f64 x) (.f64 y y)))
(/.f64 (neg.f64 (.f64 y y)) (.f64 (neg.f64 x) y))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 x (neg.f64 y))) (neg.f64 x)) (.f64 (neg.f64 x) (/.f64 x (neg.f64 y))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) y)) (.f64 x x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) (neg.f64 y))) (.f64 (neg.f64 x) x))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) #s(literal 1 binary64)) (.f64 (*.f64 y y) (neg.f64 x)))
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) #s(literal -1 binary64)) (.f64 (*.f64 y y) x))
(/.f64 (.f64 (neg.f64 (.f64 y y)) #s(literal 1 binary64)) (*.f64 y (neg.f64 x)))
(/.f64 (.f64 (neg.f64 (.f64 y y)) #s(literal -1 binary64)) (*.f64 y x))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 y (.f64 y y)))) (.f64 (neg.f64 x) (*.f64 y y)))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 y y))) (*.f64 (neg.f64 x) y))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (.f64 y (.f64 y y)))) (.f64 x (*.f64 y y)))
(/.f64 (.f64 #s(literal -1 binary64) (neg.f64 (.f64 y y))) (*.f64 x y))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 y (neg.f64 x)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (/.f64 y (neg.f64 x)) (/.f64 y (neg.f64 x)) (*.f64 #s(literal 0 binary64) (/.f64 y (neg.f64 x))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 y (neg.f64 x)) (/.f64 y (neg.f64 x)))) (/.f64 y (neg.f64 x)))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (.f64 y (.f64 y y)))) (.f64 y y))
(/.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (.f64 y y))) y)
(/.f64 (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal -1 binary64) x)) (.f64 y y))
(/.f64 (.f64 (neg.f64 (.f64 y y)) (/.f64 #s(literal -1 binary64) x)) y)
(pow.f64 (/.f64 y x) #s(literal 1 binary64))
(pow.f64 (/.f64 x y) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 x y) (/.f64 x y)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 x y))) #s(literal -1 binary64))
(*.f64 y (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 y x) #s(literal 1 binary64))
(*.f64 (neg.f64 y) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal 1 binary64) (/.f64 y x))
(*.f64 (/.f64 #s(literal 1 binary64) x) y)
(*.f64 #s(literal -1 binary64) (/.f64 y (neg.f64 x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 y))
(*.f64 (/.f64 #s(literal -1 binary64) x) (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)))
(*.f64 (/.f64 y (neg.f64 x)) #s(literal -1 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) y))
(*.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) (.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) (/.f64 (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) y) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) y)))
(.f64 (.f64 y (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (/.f64 y x) #s(literal 1/2 binary64))) (pow.f64 (/.f64 y x) #s(literal 1/2 binary64)))
(.f64 (/.f64 (neg.f64 y) (neg.f64 (.f64 x (.f64 x x)))) (.f64 x x))
(.f64 (/.f64 (neg.f64 y) (neg.f64 (.f64 x x))) x)

eval11.0ms (1.1%)

Memory: 1.4MiB live, 9.0MiB allocated
Compiler: Compiled 868 to 197 computations (77.3% saved)

prune10.0ms (1%)

Memory

-0.4MiB live, 8.2MiB allocated

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	1	111

Accuracy

100.0%

Counts

111 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(atan.f64 (/.f64 y x))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify7.0ms (0.7%)

Memory

-4.0MiB live, 3.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4

Stop Event

1×

saturated

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))

Outputs
(atan.f64 (/.f64 y x))

soundness0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Stop Event

1×

done

Compiler

Compiled 6 to 4 computations (33.3% saved)

preprocess16.0ms (1.7%)

Memory: 5.4MiB live, 20.8MiB allocated
Compiler: Compiled 24 to 16 computations (33.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze61.0ms (6.3%)

sample701.0ms (72.3%)

explain40.0ms (4.1%)

preprocess17.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify4.0ms (0.4%)

localize19.0ms (2%)

series3.0ms (0.3%)

simplify4.0ms (0.4%)

rewrite76.0ms (7.9%)

eval11.0ms (1.1%)

prune10.0ms (1%)

simplify7.0ms (0.7%)

soundness0.0ms (0%)

preprocess16.0ms (1.7%)

end0.0ms (0%)

Profiling