Metrics for atan(x)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	6.6%	93.4%	0%	0%	0%	0
100%	6.6%	0%	93.4%	0%	0%	0%	1

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample752.0ms (25.9%)

Memory

2.2MiB live, 263.7MiB allocated

Samples

460.0ms	8 243×	0	valid
2.0ms	3×	3	valid
1.0ms	4×	2	valid
1.0ms	6×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 273.0ms

ival-atan: 97.0ms (35.6% of total)

ival-<=: 88.0ms (32.3% of total)

ival-sub: 47.0ms (17.2% of total)

ival-and: 25.0ms (9.2% of total)

exact: 11.0ms (4% of total)

ival-assert: 3.0ms (1.1% of total)

adjust: 1.0ms (0.4% of total)

Bogosity

explain53.0ms (1.8%)

Memory

2.1MiB live, 25.7MiB allocated

FPErrors

Click to see full error table

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

21.0ms

512×

valid

Compiler

Compiled 33 to 19 computations (42.4% saved)

Precisions

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

ival-atan: 5.0ms (60% of total)

ival-sub: 2.0ms (24% of total)

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

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

preprocess27.0ms (0.9%)

Memory

-1.9MiB live, 7.1MiB allocated

Algorithm

1×	egg-herbie

Rules

84×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	29	31
2	67	29
3	121	29
4	213	29
5	329	29
6	372	29
7	392	29
0	5	5
0	8	5
1	10	5
2	15	5
3	21	5
4	29	5
5	44	5
6	77	5
7	104	5
8	148	5
9	163	5
10	171	5
0	171	5

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify9.0ms (0.3%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
32×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
0	8	11
1	10	11
2	15	11
3	21	11
4	29	11
5	44	11
6	77	11
7	104	11
8	148	11
9	163	11
10	171	11
0	171	11

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.6%)

Memory

-1.6MiB live, 6.2MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(atan.f64 y)
accuracy	0	(atan.f64 x)
accuracy	0.00390625	(-.f64 (atan.f64 x) (atan.f64 y))

Samples

10.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-atan: 3.0ms (75.2% of total)

ival-sub: 1.0ms (25.1% of total)

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

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

series1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Counts

3 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

simplify10.0ms (0.3%)

Memory

2.3MiB live, 2.3MiB allocated

Algorithm

1×	egg-herbie

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
32×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	168
1	7	168
2	12	168
3	18	168
4	26	168
5	41	168
6	74	168
7	101	168
8	145	168
9	160	168
10	168	168
0	168	168

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan y)
(atan y)
(atan y)
(atan y)
(atan y)
(atan y)
(atan y)
(atan y)
(atan y)
(atan y)
(atan y)
(atan y)

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

rewrite295.0ms (10.1%)

Memory

1.3MiB live, 119.6MiB allocated

Rules

4 624×	`lower-fma.f64`
4 624×	`lower-fma.f32`
4 504×	`lower-/.f64`
4 504×	`lower-/.f32`
3 196×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
0	8	9
1	28	9
2	173	9
3	1605	9
0	8556	9

Stop Event

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

Counts

3 → 202

Calls

Call 1

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

Outputs
(+.f64 (atan.f64 x) (neg.f64 (atan.f64 y)))
(+.f64 (neg.f64 (atan.f64 y)) (atan.f64 x))
(+.f64 #s(literal 0 binary64) (atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64))))
(+.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))))))
(+.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (neg.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64))))) #s(literal -1 binary64)))
(-.f64 (atan.f64 x) (atan.f64 y))
(-.f64 #s(literal 0 binary64) (neg.f64 (atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))))
(-.f64 #s(literal 0 binary64) (atan2.f64 (-.f64 y x) (fma.f64 x y #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (atan.f64 y) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (/.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (*.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))))) (neg.f64 (atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 9 binary64)) (+.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64))) (pow.f64 (.f64 (atan.f64 x) (atan.f64 y)) #s(literal 3 binary64)))) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (/.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 9 binary64)) (+.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64))) (pow.f64 (.f64 (atan.f64 x) (atan.f64 y)) #s(literal 3 binary64)))) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64)))) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (/.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 6 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64)))) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (.f64 (atan.f64 x) (atan.f64 y))))) (/.f64 (pow.f64 (atan.f64 y) #s(literal 3 binary64)) (+.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (.f64 (atan.f64 x) (atan.f64 y))))))
(-.f64 (/.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 9 binary64)) (+.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64))) (pow.f64 (.f64 (atan.f64 x) (atan.f64 y)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (.f64 (atan.f64 x) (atan.f64 y))))) (/.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 9 binary64)) (+.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64))) (pow.f64 (.f64 (atan.f64 x) (atan.f64 y)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (.f64 (atan.f64 x) (atan.f64 y))))))
(-.f64 (/.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64)))) (+.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (.f64 (atan.f64 x) (atan.f64 y))))) (/.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 6 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64)))) (+.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (.f64 (atan.f64 x) (atan.f64 y))))))
(-.f64 (/.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (+.f64 (pow.f64 (atan.f64 y) #s(literal 4 binary64)) (pow.f64 (.f64 (atan.f64 x) (atan.f64 y)) #s(literal 2 binary64))))) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (/.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 6 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (+.f64 (pow.f64 (atan.f64 y) #s(literal 4 binary64)) (pow.f64 (.f64 (atan.f64 x) (atan.f64 y)) #s(literal 2 binary64))))) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))))
(-.f64 (/.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 y) #s(literal 2 binary64)))) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (/.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 4 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 y) #s(literal 2 binary64)))) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (*.f64 x y))))) (neg.f64 (atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))))
(-.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (.f64 (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64))))) (/.f64 (pow.f64 (atan.f64 y) #s(literal 6 binary64)) (.f64 (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64))))))
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(.f64 (-.f64 (.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (.f64 (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (pow.f64 (atan.f64 y) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64))))
(.f64 (-.f64 (.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (.f64 (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) #s(literal 2 binary64))))
(.f64 (-.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 9 binary64)) (pow.f64 (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (pow.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (atan.f64 y) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))))))))
(.f64 (-.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) #s(literal 3 binary64))) (/.f64 (pow.f64 (atan.f64 y) #s(literal 6 binary64)) (pow.f64 (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (/.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))))))))
(.f64 (-.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))))
(.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (atan.f64 y) #s(literal 3 binary64)) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (*.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))))))
(.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (/.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (*.f64 x y)))))))
(.f64 (/.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 9 binary64)) (pow.f64 (atan.f64 y) #s(literal 9 binary64))) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64))) (pow.f64 (*.f64 (atan.f64 x) (atan.f64 y)) #s(literal 3 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64))) (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64))) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (+.f64 (pow.f64 (atan.f64 y) #s(literal 4 binary64)) (pow.f64 (*.f64 (atan.f64 x) (atan.f64 y)) #s(literal 2 binary64))))))
(.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (pow.f64 (atan.f64 y) #s(literal 4 binary64))) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 y) #s(literal 2 binary64)))))
(.f64 (/.f64 (.f64 (atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64))) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (*.f64 x y)))) (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64)))) (fma.f64 (atan.f64 y) (atan2.f64 (-.f64 y x) (fma.f64 x y #s(literal 1 binary64))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64))) (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) #s(literal 3 binary64)))) (fma.f64 (.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) (-.f64 (.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (*.f64 x y)))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (pow.f64 (atan.f64 x) #s(literal 4 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64))) (-.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (pow.f64 (.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y)))) #s(literal 2 binary64)))) (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (*.f64 x y))))))
(.f64 (pow.f64 (/.f64 (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (atan.f64 x) #s(literal 9 binary64)) (pow.f64 (atan.f64 y) #s(literal 9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64))) (pow.f64 (*.f64 (atan.f64 x) (atan.f64 y)) #s(literal 3 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (atan.f64 y) (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 y) #s(literal 3 binary64)))))
(.f64 (pow.f64 (/.f64 (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (+.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 y) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (+.f64 (pow.f64 (atan.f64 y) #s(literal 4 binary64)) (pow.f64 (*.f64 (atan.f64 x) (atan.f64 y)) #s(literal 2 binary64))))))
(.f64 (pow.f64 (/.f64 (atan2.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 x y))) (-.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (pow.f64 (atan.f64 y) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 y) #s(literal 2 binary64)))))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(+.f64 (atan.f64 x) #s(literal 0 binary64))
(exp.f64 (log.f64 (atan.f64 x)))
(exp.f64 (*.f64 (log.f64 (atan.f64 x)) #s(literal 1 binary64)))
(-.f64 (atan.f64 x) #s(literal 0 binary64))
(atan.f64 x)
(/.f64 (+.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (atan.f64 x) #s(literal 0 binary64)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 0 binary64) (*.f64 (atan.f64 x) #s(literal 0 binary64)))))
(/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x))
(pow.f64 (atan.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 0 binary64) (atan.f64 y))
(exp.f64 (log.f64 (atan.f64 y)))
(exp.f64 (*.f64 (log.f64 (atan.f64 y)) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (atan.f64 y)))
(atan.f64 y)
(neg.f64 (neg.f64 (atan.f64 y)))
(/.f64 (pow.f64 (atan.f64 y) #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64)) #s(literal 0 binary64))))
(/.f64 (neg.f64 (pow.f64 (atan.f64 y) #s(literal 2 binary64))) (neg.f64 (atan.f64 y)))
(pow.f64 (atan.f64 y) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (atan.f64 y))
(*.f64 #s(literal -1 binary64) (neg.f64 (atan.f64 y)))

eval26.0ms (0.9%)

Memory: 0.9MiB live, 22.5MiB allocated
Compiler: Compiled 9 421 to 583 computations (93.8% saved)

prune29.0ms (1%)

Memory

0.3MiB live, 25.1MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	248	2	250
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	2	251

Accuracy

100.0%

Counts

251 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
▶	86.6%	(-.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x)) (atan.f64 y))

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify172.0ms (5.9%)

Memory

-5.0MiB live, 53.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x y #s(literal 1 binary64))
cost-diff	0	(-.f64 x y)
cost-diff	0	(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
cost-diff	0	(pow.f64 (atan.f64 x) #s(literal 2 binary64))
cost-diff	0	(-.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x)) (atan.f64 y))
cost-diff	192	(-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))
cost-diff	13568	(/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x))

Rules

4 008×	`lower-*.f64`
4 008×	`lower-*.f32`
2 536×	`lower-/.f32`
2 534×	`lower-/.f64`
1 934×	`cube-div`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	57
0	24	56
1	39	56
2	62	47
3	91	41
4	145	41
5	216	41
6	363	41
7	1077	41
8	2745	41
9	4647	41
10	7371	41
0	8092	41

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x)) (atan.f64 y))
(/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x))
(-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(atan.f64 x)
x
#s(literal 2 binary64)
#s(literal 0 binary64)
(atan.f64 y)
y
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(-.f64 x y)
x
y
(fma.f64 x y #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(-.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x)) (atan.f64 y))
(-.f64 (atan.f64 x) (atan.f64 y))
(/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x))
(atan.f64 x)
(-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(atan.f64 x)
x
#s(literal 2 binary64)
#s(literal 0 binary64)
(atan.f64 y)
y
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(-.f64 x y)
x
y
(fma.f64 x y #s(literal 1 binary64))
#s(literal 1 binary64)

localize39.0ms (1.3%)

Memory

0.5MiB live, 15.8MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x y #s(literal 1 binary64))
accuracy	0	(-.f64 x y)
accuracy	0.00390625	(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
accuracy	0	(atan.f64 x)
accuracy	0.00390625	(-.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x)) (atan.f64 y))
accuracy	0.03515625	(pow.f64 (atan.f64 x) #s(literal 2 binary64))
accuracy	27.13229444664425	(/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x))

Samples

25.0ms

256×

valid

Compiler

Compiled 61 to 17 computations (72.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-atan: 3.0ms (19.8% of total)

ival-sub: 3.0ms (19.8% of total)

ival-atan2: 2.0ms (13.2% of total)

ival-pow2: 2.0ms (13.2% of total)

ival-div: 2.0ms (13.2% of total)

ival-mult: 2.0ms (13.2% of total)

ival-add: 1.0ms (6.6% of total)

exact: 0.0ms (0% of total)

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

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

series5.0ms (0.2%)

Memory

2.3MiB live, 2.3MiB allocated

Counts

8 → 144

Calls

Call 1

Inputs
#<alt (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x))>
#<alt (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))>
#<alt (-.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x)) (atan.f64 y))>
#<alt (pow.f64 (atan.f64 x) #s(literal 2 binary64))>
#<alt (atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))>
#<alt (-.f64 x y)>
#<alt (fma.f64 x y #s(literal 1 binary64))>
#<alt (atan.f64 x)>

Outputs
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (- (atan x) (atan y))>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (pow (atan x) 2)>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))>
#<alt (atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))>
#<alt (atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))>
#<alt (atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (- x y) (+ 1 (* x y)))>
#<alt (atan2 (+ x (* -1 y)) (+ 1 (* x y)))>
#<alt (atan2 (+ x (* -1 y)) (+ 1 (* x y)))>
#<alt (atan2 (+ x (* -1 y)) (+ 1 (* x y)))>
#<alt (atan2 (+ x (* -1 y)) (+ 1 (* x y)))>
#<alt (* -1 y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt x>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (* -1 y)>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt 1>
#<alt (+ 1 (* x y))>
#<alt (+ 1 (* x y))>
#<alt (+ 1 (* x y))>
#<alt (* x y)>
#<alt (* x (+ y (/ 1 x)))>
#<alt (* x (+ y (/ 1 x)))>
#<alt (* x (+ y (/ 1 x)))>
#<alt (* x y)>
#<alt (* -1 (* x (- (* -1 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 y) (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* x y))>
#<alt (+ 1 (* x y))>
#<alt (+ 1 (* x y))>
#<alt (* x y)>
#<alt (* y (+ x (/ 1 y)))>
#<alt (* y (+ x (/ 1 y)))>
#<alt (* y (+ x (/ 1 y)))>
#<alt (* x y)>
#<alt (* -1 (* y (- (* -1 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1 x) (/ 1 y))))>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>
#<alt (atan x)>

Calls

36 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(- (pow (atan x) 2) 0)
0.0ms	x	@	0	(- (pow (atan x) 2) 0)
0.0ms	x	@	-inf	(- (pow (atan x) 2) 0)
0.0ms	y	@	-inf	(+ (* x y) 1)
0.0ms	x	@	inf	(+ (* x y) 1)

simplify261.0ms (9%)

Memory

-4.3MiB live, 68.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6 496×	`lower-fma.f64`
6 496×	`lower-fma.f32`
4 208×	`lower-*.f64`
4 208×	`lower-*.f32`
2 304×	`associate-/r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	647
1	123	647
2	280	647
3	746	647
4	1586	647
5	2390	647
6	2899	647
7	3368	647
8	3654	647
9	3772	647
10	7551	647
0	8401	605

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 141

Calls

Call 1

Inputs
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(- (atan x) (atan y))
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(pow (atan x) 2)
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))
(atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))
(atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))
(atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2 (+ x (* -1 y)) (+ 1 (* x y)))
(atan2 (+ x (* -1 y)) (+ 1 (* x y)))
(atan2 (+ x (* -1 y)) (+ 1 (* x y)))
(atan2 (+ x (* -1 y)) (+ 1 (* x y)))
(* -1 y)
(- x y)
(- x y)
(- x y)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
1
(+ 1 (* x y))
(+ 1 (* x y))
(+ 1 (* x y))
(* x y)
(* x (+ y (/ 1 x)))
(* x (+ y (/ 1 x)))
(* x (+ y (/ 1 x)))
(* x y)
(* -1 (* x (- (* -1 y) (/ 1 x))))
(* -1 (* x (- (* -1 y) (/ 1 x))))
(* -1 (* x (- (* -1 y) (/ 1 x))))
1
(+ 1 (* x y))
(+ 1 (* x y))
(+ 1 (* x y))
(* x y)
(* y (+ x (/ 1 y)))
(* y (+ x (/ 1 y)))
(* y (+ x (/ 1 y)))
(* x y)
(* -1 (* y (- (* -1 x) (/ 1 y))))
(* -1 (* y (- (* -1 x) (/ 1 y))))
(* -1 (* y (- (* -1 x) (/ 1 y))))
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)
(atan x)

Outputs
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(- (atan x) (atan y))
(-.f64 (atan.f64 x) (atan.f64 y))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(pow (atan x) 2)
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (neg (+ y (* -1 x))) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (- x y) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (+ x (* -1 y)) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (+ x (* -1 y)) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (+ x (* -1 y)) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2 (+ x (* -1 y)) (+ 1 (* x y)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
x
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
1
#s(literal 1 binary64)
(+ 1 (* x y))
(fma.f64 x y #s(literal 1 binary64))
(+ 1 (* x y))
(fma.f64 x y #s(literal 1 binary64))
(+ 1 (* x y))
(fma.f64 x y #s(literal 1 binary64))
(* x y)
(*.f64 x y)
(* x (+ y (/ 1 x)))
(fma.f64 x y #s(literal 1 binary64))
(* x (+ y (/ 1 x)))
(fma.f64 x y #s(literal 1 binary64))
(* x (+ y (/ 1 x)))
(fma.f64 x y #s(literal 1 binary64))
(* x y)
(*.f64 x y)
(* -1 (* x (- (* -1 y) (/ 1 x))))
(fma.f64 x y #s(literal 1 binary64))
(* -1 (* x (- (* -1 y) (/ 1 x))))
(fma.f64 x y #s(literal 1 binary64))
(* -1 (* x (- (* -1 y) (/ 1 x))))
(fma.f64 x y #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* x y))
(fma.f64 x y #s(literal 1 binary64))
(+ 1 (* x y))
(fma.f64 x y #s(literal 1 binary64))
(+ 1 (* x y))
(fma.f64 x y #s(literal 1 binary64))
(* x y)
(*.f64 x y)
(* y (+ x (/ 1 y)))
(fma.f64 x y #s(literal 1 binary64))
(* y (+ x (/ 1 y)))
(fma.f64 x y #s(literal 1 binary64))
(* y (+ x (/ 1 y)))
(fma.f64 x y #s(literal 1 binary64))
(* x y)
(*.f64 x y)
(* -1 (* y (- (* -1 x) (/ 1 y))))
(fma.f64 x y #s(literal 1 binary64))
(* -1 (* y (- (* -1 x) (/ 1 y))))
(fma.f64 x y #s(literal 1 binary64))
(* -1 (* y (- (* -1 x) (/ 1 y))))
(fma.f64 x y #s(literal 1 binary64))
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)
(atan x)
(atan.f64 x)

rewrite310.0ms (10.6%)

Memory

-5.0MiB live, 139.6MiB allocated

Rules

9 586×	`lower-fma.f32`
9 584×	`lower-fma.f64`
3 842×	`lower-*.f64`
3 842×	`lower-*.f32`
3 116×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	48
0	24	47
1	102	47
2	782	32
0	8540	32

Stop Event

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

Counts

8 → 1 246

Calls

Call 1

Inputs
(/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x))
(-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64))
(-.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x)) (atan.f64 y))
(pow.f64 (atan.f64 x) #s(literal 2 binary64))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(-.f64 x y)
(fma.f64 x y #s(literal 1 binary64))
(atan.f64 x)

Outputs
(+.f64 (atan.f64 x) #s(literal 0 binary64))
(+.f64 (atan.f64 x) (*.f64 (/.f64 #s(literal -1 binary64) (atan.f64 x)) #s(literal 0 binary64)))
(+.f64 #s(literal 0 binary64) (atan.f64 x))
(exp.f64 (log.f64 (atan.f64 x)))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x))) #s(literal -1 binary64)))
(-.f64 (atan.f64 x) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (atan.f64 x)))
(atan.f64 x)
(fma.f64 (atan.f64 x) #s(literal 1 binary64) #s(literal 0 binary64))
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(fma.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) (pow.f64 (atan.f64 x) #s(literal 8 binary64))) (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (atan.f64 x)) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (*.f64 (/.f64 #s(literal -1 binary64) (atan.f64 x)) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))) (*.f64 (/.f64 #s(literal -1 binary64) (atan.f64 x)) #s(literal 0 binary64)))
(fma.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)))) (neg.f64 (atan.f64 x)) #s(literal 0 binary64))
(fma.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)))) (neg.f64 (atan.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (atan.f64 x)) #s(literal 0 binary64)))
(neg.f64 (neg.f64 (atan.f64 x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (atan.f64 x))))
(/.f64 (atan.f64 x) #s(literal 1 binary64))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (atan.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (atan.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 x) #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (pow.f64 (atan.f64 x) #s(literal 5 binary64))))
(/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (neg.f64 (atan.f64 x)))
(/.f64 (neg.f64 (atan.f64 x)) #s(literal -1 binary64))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 x) #s(literal 5 binary64)))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (*.f64 (neg.f64 (atan.f64 x)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)))))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (pow.f64 (atan.f64 x) #s(literal 3 binary64)))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (*.f64 (neg.f64 (atan.f64 x)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)))))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) (pow.f64 (atan.f64 x) #s(literal -2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (atan.f64 x)))
(/.f64 (pow.f64 (atan.f64 x) #s(literal -3 binary64)) (pow.f64 (atan.f64 x) #s(literal -4 binary64)))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 18 binary64)) (*.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) (pow.f64 (atan.f64 x) #s(literal 12 binary64))))
(/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64))) (*.f64 (neg.f64 (atan.f64 x)) (pow.f64 (atan.f64 x) #s(literal 4 binary64))))
(/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64))))
(/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64))) (*.f64 (atan.f64 x) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) (pow.f64 (atan.f64 x) #s(literal 4 binary64)))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 10 binary64)) (pow.f64 (atan.f64 x) #s(literal 9 binary64)))
(/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64))))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 12 binary64)) (*.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) (pow.f64 (atan.f64 x) #s(literal 6 binary64))))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 12 binary64)) (*.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 x) #s(literal 8 binary64))))
(/.f64 (pow.f64 (atan.f64 x) #s(literal 8 binary64)) (*.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 x) #s(literal 4 binary64))))
(/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))))
(/.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 x) #s(literal -2 binary64))) (pow.f64 (atan.f64 x) #s(literal 4 binary64)))
(/.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (sqrt.f64 (atan.f64 x))) (sqrt.f64 (atan.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (atan.f64 x) #s(literal -5 binary64))) (pow.f64 (atan.f64 x) #s(literal 4 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (atan.f64 x) #s(literal 5 binary64))) (pow.f64 (atan.f64 x) #s(literal 4 binary64)))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)))) (neg.f64 (atan.f64 x)))
(/.f64 (*.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) #s(literal 1 binary64)) (pow.f64 (atan.f64 x) #s(literal 4 binary64)))
(/.f64 (*.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (atan.f64 x))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))))
(/.f64 (*.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (/.f64 #s(literal -1 binary64) (atan.f64 x))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))))
(/.f64 (*.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (atan.f64 x))) (pow.f64 (atan.f64 x) #s(literal 4 binary64)))
(pow.f64 (atan.f64 x) #s(literal 1 binary64))
(pow.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (atan.f64 x)) #s(literal 2 binary64))
(*.f64 (atan.f64 x) #s(literal 1 binary64))
(.f64 (atan.f64 x) (.f64 (neg.f64 (atan.f64 x)) (/.f64 #s(literal -1 binary64) (atan.f64 x))))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (atan.f64 x)))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 x) #s(literal 3 binary64))))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (pow.f64 (atan.f64 x) #s(literal 5 binary64))))
(*.f64 #s(literal 1 binary64) (atan.f64 x))
(*.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (atan.f64 x)))
(*.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (atan.f64 x) #s(literal -2 binary64)) (/.f64 #s(literal -1 binary64) (atan.f64 x))))
(.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))) (.f64 (/.f64 #s(literal -1 binary64) (atan.f64 x)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (atan.f64 x)) #s(literal -1 binary64))
(*.f64 (neg.f64 (atan.f64 x)) (/.f64 (atan.f64 x) (neg.f64 (atan.f64 x))))
(*.f64 (neg.f64 (atan.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) (/.f64 #s(literal -1 binary64) (atan.f64 x))))
(.f64 (neg.f64 (atan.f64 x)) (.f64 (atan.f64 x) (/.f64 #s(literal -1 binary64) (atan.f64 x))))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (pow.f64 (atan.f64 x) #s(literal -5 binary64)))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (/.f64 (pow.f64 (atan.f64 x) #s(literal -4 binary64)) (atan.f64 x)))
(.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (.f64 (pow.f64 (atan.f64 x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (atan.f64 x))))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (pow.f64 (atan.f64 x) #s(literal -3 binary64)))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (/.f64 (pow.f64 (atan.f64 x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (atan.f64 x))))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 x) #s(literal 5 binary64))))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (pow.f64 (atan.f64 x) #s(literal -2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (atan.f64 x)))
(*.f64 (pow.f64 (atan.f64 x) #s(literal -3 binary64)) (pow.f64 (atan.f64 x) #s(literal 4 binary64)))
(*.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) (pow.f64 (atan.f64 x) #s(literal -4 binary64)))
(*.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) (/.f64 (pow.f64 (atan.f64 x) #s(literal -4 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))) (/.f64 (pow.f64 (atan.f64 x) #s(literal -4 binary64)) (/.f64 #s(literal -1 binary64) (atan.f64 x))))
(*.f64 (/.f64 #s(literal -1 binary64) (atan.f64 x)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))))
(*.f64 (pow.f64 (atan.f64 x) #s(literal -4 binary64)) (/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (atan.f64 x))))
(*.f64 (sqrt.f64 (atan.f64 x)) (sqrt.f64 (atan.f64 x)))
(*.f64 (sqrt.f64 (atan.f64 x)) (/.f64 (sqrt.f64 (atan.f64 x)) #s(literal 1 binary64)))
(.f64 (sqrt.f64 (atan.f64 x)) (.f64 (sqrt.f64 (atan.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (atan.f64 x) #s(literal -2 binary64)) (pow.f64 (atan.f64 x) #s(literal 3 binary64)))
(*.f64 (pow.f64 (atan.f64 x) #s(literal -2 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) (pow.f64 (atan.f64 x) #s(literal -4 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (atan.f64 x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (atan.f64 x)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (atan.f64 x) #s(literal -5 binary64)) #s(literal -1 binary64)) (pow.f64 (atan.f64 x) #s(literal -4 binary64)))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 x) #s(literal 6 binary64))) (pow.f64 (atan.f64 x) #s(literal 5 binary64)))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 x) #s(literal 3 binary64))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (atan.f64 x))) (pow.f64 (atan.f64 x) #s(literal -4 binary64)))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (sqrt.f64 (atan.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (atan.f64 x))))
(*.f64 (/.f64 (atan.f64 x) (sqrt.f64 (atan.f64 x))) (/.f64 (atan.f64 x) (sqrt.f64 (atan.f64 x))))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (sqrt.f64 (atan.f64 x))) (/.f64 (pow.f64 (atan.f64 x) #s(literal -4 binary64)) (sqrt.f64 (atan.f64 x))))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (sqrt.f64 (atan.f64 x))) (/.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) (sqrt.f64 (atan.f64 x))))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (sqrt.f64 (atan.f64 x))) (/.f64 (pow.f64 (atan.f64 x) #s(literal -2 binary64)) (sqrt.f64 (atan.f64 x))))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal -2 binary64)) (sqrt.f64 (atan.f64 x))) (/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (sqrt.f64 (atan.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (atan.f64 x))) (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (sqrt.f64 (atan.f64 x))))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)) (/.f64 #s(literal 1 binary64) (atan.f64 x))) (/.f64 (pow.f64 (atan.f64 x) #s(literal -4 binary64)) (pow.f64 (atan.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal -2 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)) (/.f64 #s(literal -1 binary64) (atan.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (atan.f64 x)) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (atan.f64 x))) (sqrt.f64 (atan.f64 x)))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) (pow.f64 (atan.f64 x) #s(literal 5 binary64))) (pow.f64 (atan.f64 x) #s(literal 4 binary64)))
(*.f64 (/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64))) (pow.f64 (atan.f64 x) #s(literal 6 binary64))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))))
(*.f64 (/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64))) (pow.f64 (atan.f64 x) #s(literal 4 binary64))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)))) (pow.f64 (atan.f64 x) #s(literal 2 binary64)))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) (pow.f64 (atan.f64 x) #s(literal 12 binary64))) (pow.f64 (atan.f64 x) #s(literal 8 binary64)))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) (pow.f64 (atan.f64 x) #s(literal 10 binary64))) (pow.f64 (atan.f64 x) #s(literal 6 binary64)))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 5 binary64)) (pow.f64 (atan.f64 x) #s(literal 8 binary64))) (pow.f64 (atan.f64 x) #s(literal 4 binary64)))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64)))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64))))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 6 binary64)))) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 4 binary64))))
(*.f64 (/.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)) (neg.f64 (pow.f64 (atan.f64 x) #s(literal 3 binary64)))) (neg.f64 (atan.f64 x)))

eval180.0ms (6.2%)

Memory: 9.4MiB live, 132.1MiB allocated
Compiler: Compiled 34 263 to 4 289 computations (87.5% saved)

prune198.0ms (6.8%)

Memory

-2.1MiB live, 179.2MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1 635	3	1 638
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	1 636	4	1 640

Accuracy

100.0%

Counts

1 640 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
	78.1%	(atan2.f64 (-.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (fma.f64 x y #s(literal 1 binary64)))
✓	100.0%	(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
	99.6%	(atan2.f64 (-.f64 x y) #s(approx (+ (* x y) 1) #s(literal 1 binary64)))
	46.8%	(atan2.f64 #s(approx (- x y) (neg.f64 y)) (fma.f64 x y #s(literal 1 binary64)))

Compiler

Compiled 111 to 53 computations (52.3% saved)

regimes10.0ms (0.4%)

Memory

1.6MiB live, 9.4MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
(atan2.f64 (-.f64 x y) #s(approx (+ (* x y) 1) #s(literal 1 binary64)))
(atan2.f64 #s(approx (- x y) (neg.f64 y)) (fma.f64 x y #s(literal 1 binary64)))
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2.f64 (-.f64 (/.f64 (.f64 x x) (+.f64 x y)) (/.f64 (.f64 y y) (+.f64 x y))) (fma.f64 x y #s(literal 1 binary64)))
(-.f64 (atan.f64 x) (atan.f64 y))
(-.f64 (/.f64 (-.f64 (pow.f64 (atan.f64 x) #s(literal 2 binary64)) #s(literal 0 binary64)) (atan.f64 x)) (atan.f64 y))

Outputs
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))

Calls

5 calls:

2.0ms	(-.f64 (atan.f64 x) (atan.f64 y))
2.0ms	(atan.f64 y)
2.0ms	(atan.f64 x)
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(-.f64 (atan.f64 x) (atan.f64 y))`
100.0%	1	`(atan.f64 x)`
100.0%	1	`(atan.f64 y)`

Compiler

Compiled 21 to 15 computations (28.6% saved)

regimes7.0ms (0.2%)

Memory

-0.2MiB live, 7.7MiB allocated

Accuracy

Total -33.9b remaining (-13278.9%)

Threshold costs -33.9b (-13278.9%)

Counts

2 → 1

Calls

Call 1

Inputs
(atan2.f64 (-.f64 x y) #s(approx (+ (* x y) 1) #s(literal 1 binary64)))
(atan2.f64 #s(approx (- x y) (neg.f64 y)) (fma.f64 x y #s(literal 1 binary64)))

Outputs
(atan2.f64 (-.f64 x y) #s(approx (+ (* x y) 1) #s(literal 1 binary64)))

Calls

5 calls:

1.0ms	(atan.f64 x)
1.0ms	(-.f64 (atan.f64 x) (atan.f64 y))
1.0ms	(atan.f64 y)
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`y`
99.6%	1	`(-.f64 (atan.f64 x) (atan.f64 y))`
99.6%	1	`(atan.f64 x)`
99.6%	1	`(atan.f64 y)`

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify8.0ms (0.3%)

Memory

-3.9MiB live, 4.0MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	15	19
2	19	19
3	21	19
4	22	19

Stop Event

1×

saturated

Calls

Call 1

Inputs
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2.f64 (-.f64 x y) #s(approx (+ (* x y) 1) #s(literal 1 binary64)))

Outputs
(atan2.f64 (-.f64 x y) (fma.f64 x y #s(literal 1 binary64)))
(atan2.f64 (-.f64 x y) #s(approx (+ (* x y) 1) #s(literal 1 binary64)))

soundness441.0ms (15.2%)

Memory

4.1MiB live, 4.1MiB allocated

Rules

6 496×	`lower-fma.f64`
6 496×	`lower-fma.f32`
4 624×	`lower-fma.f64`
4 624×	`lower-fma.f32`
4 504×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	647
1	123	647
2	280	647
3	746	647
4	1586	647
5	2390	647
6	2899	647
7	3368	647
8	3654	647
9	3772	647
10	7551	647
0	8401	605
0	5	9
0	8	9
1	28	9
2	173	9
3	1605	9
0	8556	9

Stop Event

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

Compiler

Compiled 53 to 30 computations (43.4% saved)

preprocess60.0ms (2.1%)

Memory: 0.3MiB live, 23.9MiB allocated
Compiler: Compiled 46 to 24 computations (47.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

atan(x) - atan(y)

start0.0ms (0%)

analyze1.0ms (0%)

sample752.0ms (25.9%)

explain53.0ms (1.8%)

preprocess27.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify9.0ms (0.3%)

localize17.0ms (0.6%)

series1.0ms (0%)

simplify10.0ms (0.3%)

rewrite295.0ms (10.1%)

eval26.0ms (0.9%)

prune29.0ms (1%)

simplify172.0ms (5.9%)

localize39.0ms (1.3%)

series5.0ms (0.2%)

simplify261.0ms (9%)

rewrite310.0ms (10.6%)

eval180.0ms (6.2%)

prune198.0ms (6.8%)

regimes10.0ms (0.4%)

regimes7.0ms (0.2%)

simplify8.0ms (0.3%)

soundness441.0ms (15.2%)

preprocess60.0ms (2.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	13	31
1	29	31
2	67	29
3	121	29
4	213	29
5	329	29
6	372	29
7	392	29
0	5	5
0	8	5
1	10	5
2	15	5
3	21	5
4	29	5
5	44	5
6	77	5
7	104	5
8	148	5
9	163	5
10	171	5
0	171	5

Iter	Nodes	Cost
0	5	11
0	8	11
1	10	11
2	15	11
3	21	11
4	29	11
5	44	11
6	77	11
7	104	11
8	148	11
9	163	11
10	171	11
0	171	11

Iter	Nodes	Cost
0	5	168
1	7	168
2	12	168
3	18	168
4	26	168
5	41	168
6	74	168
7	101	168
8	145	168
9	160	168
10	168	168
0	168	168

Iter	Nodes	Cost
0	13	31
1	29	31
2	67	29
3	121	29
4	213	29
5	329	29
6	372	29
7	392	29
0	5	5
0	8	5
1	10	5
2	15	5
3	21	5
4	29	5
5	44	5
6	77	5
7	104	5
8	148	5
9	163	5
10	171	5
0	171	5

Iter	Nodes	Cost
0	5	11
0	8	11
1	10	11
2	15	11
3	21	11
4	29	11
5	44	11
6	77	11
7	104	11
8	148	11
9	163	11
10	171	11
0	171	11

Iter	Nodes	Cost
0	5	168
1	7	168
2	12	168
3	18	168
4	26	168
5	41	168
6	74	168
7	101	168
8	145	168
9	160	168
10	168	168
0	168	168

Iter	Nodes	Cost
0	13	31
1	29	31
2	67	29
3	121	29
4	213	29
5	329	29
6	372	29
7	392	29
0	5	5
0	8	5
1	10	5
2	15	5
3	21	5
4	29	5
5	44	5
6	77	5
7	104	5
8	148	5
9	163	5
10	171	5
0	171	5

Iter	Nodes	Cost
0	5	11
0	8	11
1	10	11
2	15	11
3	21	11
4	29	11
5	44	11
6	77	11
7	104	11
8	148	11
9	163	11
10	171	11
0	171	11

Iter	Nodes	Cost
0	5	168
1	7	168
2	12	168
3	18	168
4	26	168
5	41	168
6	74	168
7	101	168
8	145	168
9	160	168
10	168	168
0	168	168