Metrics for 2atan (example 3.5)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	8.1%	91.9%	0%	0%	0%	0
0%	0%	8.1%	91.9%	0%	0%	0%	1
50%	4.1%	4.1%	91.9%	0%	0%	0%	2
75%	6.1%	2%	91.9%	0%	0%	0%	3
87.5%	7.1%	1%	91.9%	0%	0%	0%	4
93.8%	7.6%	0.5%	91.9%	0%	0%	0%	5
96.9%	7.9%	0.3%	91.9%	0%	0%	0%	6
98.4%	8%	0.1%	91.9%	0%	0%	0%	7
99.2%	8%	0.1%	91.9%	0%	0%	0%	8
99.6%	8.1%	0%	91.9%	0%	0%	0%	9
99.8%	8.1%	0%	91.9%	0%	0%	0%	10
99.9%	8.1%	0%	91.9%	0%	0%	0%	11
100%	8.1%	0%	91.9%	0%	0%	0%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.6s (27.4%)

Memory

37.3MiB live, 1 914.9MiB allocated

Samples

1.2s	7 475×	1	valid
75.0ms	386×	2	valid
34.0ms	395×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

ival-atan: 341.0ms (33.5% of total)

adjust: 229.0ms (22.5% of total)

const: 133.0ms (13% of total)

ival-add: 97.0ms (9.5% of total)

ival-sub: 88.0ms (8.6% of total)

ival->: 61.0ms (6% of total)

ival-<: 46.0ms (4.5% of total)

ival-and: 13.0ms (1.3% of total)

exact: 8.0ms (0.8% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain145.0ms (2.4%)

Memory

19.7MiB live, 141.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
254	-	-	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
0	-	-	`N`
0	-	-	`(+.f64 N #s(literal 1 binary64))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(atan.f64 N)`
0	-	-	`(atan.f64 (+.f64 N #s(literal 1 binary64)))`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`	cancellation	254	0

Confusion

	Predicted +	Predicted -
+	254	0
-	0	2

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	254	0	0
-	0	0	2

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	2
1	254

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

64.0ms	456×	1	valid
35.0ms	32×	2	valid
1.0ms	24×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-add: 34.0ms (46% of total)

ival-atan: 21.0ms (28.4% of total)

adjust: 12.0ms (16.2% of total)

ival-sub: 5.0ms (6.8% of total)

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

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

exact: 0.0ms (0% of total)

preprocess19.0ms (0.3%)

Memory

-13.8MiB live, 22.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Outputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) (atan.f64 N))

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.0%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(atan.f64 N)
cost-diff	0	(+.f64 N #s(literal 1 binary64))
cost-diff	0	(atan.f64 (+.f64 N #s(literal 1 binary64)))
cost-diff	0	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(+.f64 N #s(literal 1 binary64))
N
#s(literal 1 binary64)
(atan.f64 N)

Outputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(atan.f64 (+.f64 #s(literal 1 binary64) N))
(+.f64 N #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) N)
N
#s(literal 1 binary64)
(atan.f64 N)

localize56.0ms (0.9%)

Memory

-12.5MiB live, 32.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 N #s(literal 1 binary64))
accuracy	0	(atan.f64 (+.f64 N #s(literal 1 binary64)))
accuracy	0	(atan.f64 N)
accuracy	58.20863744250333	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Samples

44.0ms	228×	1	valid
3.0ms	16×	2	valid
1.0ms	12×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

adjust: 23.0ms (59.8% of total)

ival-atan: 10.0ms (26% of total)

ival-add: 3.0ms (7.8% of total)

ival-sub: 2.0ms (5.2% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())
#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())

Outputs
#s(alt (- (atan (+ 1 N)) (atan N)) (taylor 0 N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (- (atan (+ 1 N)) (atan N)) (taylor 0 N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (- (atan (+ 1 N)) (atan N)) (taylor 0 N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (- (atan (+ 1 N)) (atan N)) (taylor 0 N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (atan (+ 1 N)) (taylor 0 N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan (+ 1 N)) (taylor 0 N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan (+ 1 N)) (taylor 0 N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan (+ 1 N)) (taylor 0 N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor 0 N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor 0 N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor 0 N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor 0 N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (- (atan (+ 1 N)) (atan N)) (taylor inf N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (- (atan (+ 1 N)) (atan N)) (taylor inf N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (- (atan (+ 1 N)) (atan N)) (taylor inf N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (- (atan (+ 1 N)) (atan N)) (taylor inf N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (atan (+ 1 N)) (taylor inf N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan (+ 1 N)) (taylor inf N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan (+ 1 N)) (taylor inf N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan (+ 1 N)) (taylor inf N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt N (taylor inf N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor inf N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor inf N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor inf N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor inf N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor inf N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor inf N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor inf N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (- (atan (- 1 (* -1 N))) (atan N)) (taylor -inf N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (- (atan (- 1 (* -1 N))) (atan N)) (taylor -inf N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (- (atan (- 1 (* -1 N))) (atan N)) (taylor -inf N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (- (atan (- 1 (* -1 N))) (atan N)) (taylor -inf N) (#s(alt (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) (patch (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N)) #<representation binary64>) () ())) ())
#s(alt (atan (- 1 (* -1 N))) (taylor -inf N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan (- 1 (* -1 N))) (taylor -inf N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan (- 1 (* -1 N))) (taylor -inf N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan (- 1 (* -1 N))) (taylor -inf N) (#s(alt (atan.f64 (+.f64 N #s(literal 1 binary64))) (patch (atan.f64 (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt N (taylor -inf N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor -inf N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor -inf N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor -inf N) (#s(alt (+.f64 N #s(literal 1 binary64)) (patch (+.f64 N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor -inf N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor -inf N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor -inf N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())
#s(alt (atan N) (taylor -inf N) (#s(alt (atan.f64 N) (patch (atan.f64 N) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	N	@	-inf	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) (atan N))
0.0ms	N	@	inf	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) (atan N))
0.0ms	N	@	0	((- (atan (+ N 1)) (atan N)) (atan (+ N 1)) (+ N 1) (atan N))

simplify13.0ms (0.2%)

Memory

8.6MiB live, 8.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	186
1	34	186
2	44	186
3	89	186
4	189	186
5	335	186
6	383	186
7	420	186
8	474	186
9	489	186
10	497	186
0	497	186

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 46

Calls

Call 1

Inputs
(- (atan (+ 1 N)) (atan N))
(- (atan (+ 1 N)) (atan N))
(- (atan (+ 1 N)) (atan N))
(- (atan (+ 1 N)) (atan N))
(atan (+ 1 N))
(atan (+ 1 N))
(atan (+ 1 N))
(atan (+ 1 N))
1
(+ 1 N)
(+ 1 N)
(+ 1 N)
(atan N)
(atan N)
(atan N)
(atan N)
(- (atan (+ 1 N)) (atan N))
(- (atan (+ 1 N)) (atan N))
(- (atan (+ 1 N)) (atan N))
(- (atan (+ 1 N)) (atan N))
(atan (+ 1 N))
(atan (+ 1 N))
(atan (+ 1 N))
(atan (+ 1 N))
N
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (/ 1 N)))
(atan N)
(atan N)
(atan N)
(atan N)
(- (atan (- 1 (* -1 N))) (atan N))
(- (atan (- 1 (* -1 N))) (atan N))
(- (atan (- 1 (* -1 N))) (atan N))
(- (atan (- 1 (* -1 N))) (atan N))
(atan (- 1 (* -1 N)))
(atan (- 1 (* -1 N)))
(atan (- 1 (* -1 N)))
(atan (- 1 (* -1 N)))
N
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (/ 1 N)))
(atan N)
(atan N)
(atan N)
(atan N)

Outputs
(- (atan (+ 1 N)) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(- (atan (+ 1 N)) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(- (atan (+ 1 N)) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(- (atan (+ 1 N)) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(atan (+ 1 N))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
(atan (+ 1 N))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
(atan (+ 1 N))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
(atan (+ 1 N))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(atan N)
(atan.f64 N)
(atan N)
(atan.f64 N)
(atan N)
(atan.f64 N)
(atan N)
(atan.f64 N)
(- (atan (+ 1 N)) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(- (atan (+ 1 N)) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(- (atan (+ 1 N)) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(- (atan (+ 1 N)) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(atan (+ 1 N))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
(atan (+ 1 N))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
(atan (+ 1 N))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
(atan (+ 1 N))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
N
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(atan N)
(atan.f64 N)
(atan N)
(atan.f64 N)
(atan N)
(atan.f64 N)
(atan N)
(atan.f64 N)
(- (atan (- 1 (* -1 N))) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(- (atan (- 1 (* -1 N))) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(- (atan (- 1 (* -1 N))) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(- (atan (- 1 (* -1 N))) (atan N))
(-.f64 (atan.f64 (-.f64 N #s(literal -1 binary64))) (atan.f64 N))
(atan (- 1 (* -1 N)))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
(atan (- 1 (* -1 N)))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
(atan (- 1 (* -1 N)))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
(atan (- 1 (* -1 N)))
(atan.f64 (-.f64 N #s(literal -1 binary64)))
N
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(atan N)
(atan.f64 N)
(atan N)
(atan.f64 N)
(atan N)
(atan.f64 N)
(atan N)
(atan.f64 N)

rewrite141.0ms (2.4%)

Memory

12.1MiB live, 164.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	44	16
2	284	16
3	2885	16
0	8353	16

Stop Event

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

Counts

4 → 239

Calls

Call 1

Inputs
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan.f64 (+.f64 N #s(literal 1 binary64)))
(+.f64 N #s(literal 1 binary64))
(atan.f64 N)

Outputs
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eval37.0ms (0.6%)

Memory: 10.2MiB live, 85.8MiB allocated
Compiler: Compiled 7 832 to 922 computations (88.2% saved)

prune10.0ms (0.2%)

Memory

-15.6MiB live, 22.3MiB allocated

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	285	1	286

Accuracy

99.5%

Counts

286 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify4.0ms (0.1%)

Memory

2.6MiB live, 2.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 #s(literal 1 binary64) N)
cost-diff	0	(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

New

Metric

Score

Program

cost-diff

(+.f64 #s(literal 1 binary64) N)

cost-diff

(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))

cost-diff

(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	19
0	9	19
1	14	19
2	21	19
3	29	19
4	39	19
5	42	19
6	45	19
0	45	19

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) N)
N

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
(fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) N)
(+.f64 N #s(literal 1 binary64))
N

localize45.0ms (0.8%)

Memory

-21.8MiB live, 30.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
accuracy	0	(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))
accuracy	0	(+.f64 #s(literal 1 binary64) N)
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

New

Metric

Score

Program

accuracy

(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))

accuracy

(+.f64 #s(literal 1 binary64) N)

accuracy

0.30859375

(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

Samples

12.0ms

256×

valid

Compiler

Compiled 23 to 8 computations (65.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 3.0ms (46.6% of total)

ival-atan2: 2.0ms (31% of total)

ival-mult: 2.0ms (31% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())

Inputs

#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())

#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())

#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())

Outputs
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor inf N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor inf N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor inf N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor inf N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor inf N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (+ 1 (/ 1 N))) (taylor inf N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2))))) (taylor inf N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2))))) (taylor inf N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt N (taylor inf N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor inf N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor inf N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor inf N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (taylor -inf N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (taylor -inf N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (taylor -inf N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (taylor -inf N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor -inf N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (+ 1 (/ 1 N))) (taylor -inf N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2))))) (taylor -inf N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2))))) (taylor -inf N) (#s(alt (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) (patch (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt N (taylor -inf N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor -inf N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor -inf N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (/ 1 N))) (taylor -inf N) (#s(alt (+.f64 #s(literal 1 binary64) N) (patch (+.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	N	@	inf	((atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ 1 N))
0.0ms	N	@	-inf	((atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ 1 N))
0.0ms	N	@	0	((atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ 1 N))

simplify116.0ms (2%)

Memory

29.8MiB live, 137.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	208
1	67	200
2	117	200
3	451	200
4	2326	200
5	5354	200
0	8132	180

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 34

Calls

Call 1

Inputs
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 N))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
1
(+ 1 N)
(+ 1 N)
(+ 1 N)
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
N
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (/ 1 N)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
N
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (/ 1 N)))
(* N (+ 1 (/ 1 N)))

Outputs
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
N
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
N
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))
(* N (+ 1 (/ 1 N)))
(-.f64 N #s(literal -1 binary64))

rewrite190.0ms (3.2%)

Memory

-14.9MiB live, 187.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	9	17
1	37	17
2	262	17
3	2791	17
0	8379	17

Stop Event

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

Counts

3 → 289

Calls

Call 1

Inputs

(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))

(fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64))

(+.f64 #s(literal 1 binary64) N)

Outputs
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eval48.0ms (0.8%)

Memory: -2.3MiB live, 70.7MiB allocated
Compiler: Compiled 7 546 to 1 145 computations (84.8% saved)

prune21.0ms (0.4%)

Memory

14.8MiB live, 52.8MiB allocated

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	306	17	323
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	307	17	324

Accuracy

99.7%

Counts

324 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	73.8%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 4 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) N) (fma.f64 N N #s(literal 1 binary64)))) N #s(literal 1 binary64)))
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) N #s(literal 1 binary64)))
	99.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) (*.f64 N N))) (+.f64 N #s(literal 1 binary64)) #s(literal 1 binary64)))
▶	99.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) N) #s(literal 1 binary64)))
	73.8%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (pow.f64 (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
▶	99.2%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
	99.1%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)) #s(literal -1 binary64)) N) #s(literal 1 binary64)))
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) #s(literal 1 binary64)))
	46.6%	(atan2.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 N N N) (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal -1 binary64)) #s(literal 1 binary64))))
▶	73.9%	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))))
▶	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
	99.4%	(atan2.f64 #s(literal 1 binary64) (.f64 (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)) (.f64 (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal -1 binary64)) (pow.f64 (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal -1 binary64)) #s(literal -1 binary64)))))
	96.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
	7.8%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
	92.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
▶	6.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 504 to 296 computations (41.3% saved)

simplify165.0ms (2.8%)

Memory

33.3MiB live, 144.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 #s(literal 1 binary64) (fma.f64 N N N))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))))
cost-diff	0	(pow.f64 N #s(literal 3 binary64))
cost-diff	0	(+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
cost-diff	192	(fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64))
cost-diff	0	(*.f64 N N)
cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 N N))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
cost-diff	128	(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
cost-diff	0	#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 N N #s(literal 1 binary64))
cost-diff	0	(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	223
0	59	221
1	104	221
2	197	217
3	540	215
4	1512	213
5	4908	213
0	8166	213

Stop Event

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

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
#s(literal 1 binary64)
(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(fma.f64 N N #s(literal 1 binary64))
N
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 N N))
(*.f64 N N)
N
(/.f64 N (-.f64 #s(literal 1 binary64) N))
(-.f64 #s(literal 1 binary64) N)
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64))
(+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64))
(pow.f64 N #s(literal 3 binary64))
N
#s(literal 3 binary64)
(/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
(fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))
(-.f64 N #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))
(-.f64 #s(literal 1 binary64) (fma.f64 N N N))
(fma.f64 N N N)
N
(-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))
(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
#s(literal 1 binary64)
(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(fma.f64 N N #s(literal 1 binary64))
N
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
#s(literal 1 binary64)
#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 N (-.f64 N #s(literal 1 binary64))) (fma.f64 N N #s(literal -1 binary64)) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(fma.f64 (/.f64 N (-.f64 N #s(literal 1 binary64))) (fma.f64 N N #s(literal -1 binary64)) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 N N))
(*.f64 N N)
N
(/.f64 N (-.f64 #s(literal 1 binary64) N))
(-.f64 #s(literal 1 binary64) N)
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64))
(+.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64))
(+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64))
(pow.f64 N #s(literal 3 binary64))
N
#s(literal 3 binary64)
(/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
(fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))
(-.f64 N #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal -1 binary64))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))
(/.f64 (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal -1 binary64)) (-.f64 (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (fma.f64 N N N))
(fma.f64 N N N)
N
(-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))
(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))
#s(literal 2 binary64)

localize167.0ms (2.8%)

Memory

-6.5MiB live, 188.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))))
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))))
accuracy	0.43263627930532605	(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))
accuracy	16.642985602158923	(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))
accuracy	0.0078125	(+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64))
accuracy	0.265625	(/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
accuracy	0.3427925293053261	(fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64))
accuracy	0	(-.f64 #s(literal 1 binary64) N)
accuracy	0	(*.f64 N N)
accuracy	0.0703125	(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
accuracy	59.97969978960472	#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
accuracy	0	(fma.f64 N N #s(literal 1 binary64))
accuracy	0.046875	(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))

Samples

134.0ms

256×

valid

Compiler

Compiled 242 to 36 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-mult: 25.0ms (31.4% of total)

ival-div: 21.0ms (26.3% of total)

ival-add: 10.0ms (12.5% of total)

ival-atan2: 8.0ms (10% of total)

ival-pow2: 7.0ms (8.8% of total)

ival-sub: 6.0ms (7.5% of total)

ival-pow: 3.0ms (3.8% of total)

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

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

exact: 0.0ms (0% of total)

series22.0ms (0.4%)

Memory

-14.6MiB live, 36.5MiB allocated

Counts

20 → 240

Calls

Call 1

Inputs
#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #<representation binary64>) () ())
#s(alt (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) (patch (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) #<representation binary64>) () ())
#s(alt (fma.f64 N N #s(literal 1 binary64)) (patch (fma.f64 N N #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())
#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())
#s(alt (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)) (patch (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (patch (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 N #s(literal 3 binary64)) (patch (pow.f64 N #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))))) (patch (atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) N) (patch (-.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())
#s(alt (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) (patch (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (patch (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) (patch (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) (patch (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) (patch (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) (patch (+.f64 (fma.f64 N N #s(literal 1 binary64)) N) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt (fma.f64 N N #s(literal 1 binary64)) (patch (fma.f64 N N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow N 2)) (taylor 0 N) (#s(alt (fma.f64 N N #s(literal 1 binary64)) (patch (fma.f64 N N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow N 2)) (taylor 0 N) (#s(alt (fma.f64 N N #s(literal 1 binary64)) (patch (fma.f64 N N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow N 2)) (taylor 0 N) (#s(alt (fma.f64 N N #s(literal 1 binary64)) (patch (fma.f64 N N #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow N 2))) (taylor 0 N) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow N 2))) (taylor 0 N) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow N 2))) (taylor 0 N) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor 0 N) (#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor 0 N) (#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor 0 N) (#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor 0 N) (#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())) ())
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#s(alt (/ (+ 1 (* -1 (/ (- 1 (/ 1 (pow N 2))) N))) (pow N 2)) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 (pow N 2))) N))) (pow N 2)) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow N 2)) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow N 2) (+ 1 (/ 1 N)))) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1)) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1)) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* -1 N) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) N) (patch (-.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (* -1 (* N (- 1 (/ 1 N)))) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) N) (patch (-.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (* -1 (* N (- 1 (/ 1 N)))) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) N) (patch (-.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (* -1 (* N (- 1 (/ 1 N)))) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) N) (patch (-.f64 #s(literal 1 binary64) N) #<representation binary64>) () ())) ())
#s(alt (/ 1 N) (taylor -inf N) (#s(alt (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) (patch (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (/ 1 N)) N) (taylor -inf N) (#s(alt (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) (patch (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (- 1 (/ 1 (pow N 2))) N)) 1) N)) (taylor -inf N) (#s(alt (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) (patch (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1 (* -1 (/ (+ 1 (/ 1 N)) (pow N 2)))) N)) 1) N)) (taylor -inf N) (#s(alt (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) (patch (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow N 4) (taylor -inf N) (#s(alt (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (patch (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 4) (+ 1 (* 2 (/ 1 N)))) (taylor -inf N) (#s(alt (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (patch (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2))))) (taylor -inf N) (#s(alt (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (patch (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2))))) (taylor -inf N) (#s(alt (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) (patch (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

10.0ms

inf

((atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ (* (- 1 (* N N)) (/ N (- 1 N))) 1) (atan2 1 (+ (* (- 1 (* N N)) (/ N (- 1 N))) 1)) (- 1 (* N N)) (* N N) (+ (* (+ (pow N 3) 1) (/ N (+ (* (- N 1) N) 1))) 1) (atan2 1 (+ (* (+ (pow N 3) 1) (/ N (+ (* (- N 1) N) 1))) 1)) (+ (pow N 3) 1) (pow N 3) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))))) (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (- 1 (+ (* N N) N)) (- 1 N) (/ N (+ (* (- N 1) N) 1)) (pow (+ (* N N) N) 2))

3.0ms

-inf

((atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ (* (- 1 (* N N)) (/ N (- 1 N))) 1) (atan2 1 (+ (* (- 1 (* N N)) (/ N (- 1 N))) 1)) (- 1 (* N N)) (* N N) (+ (* (+ (pow N 3) 1) (/ N (+ (* (- N 1) N) 1))) 1) (atan2 1 (+ (* (+ (pow N 3) 1) (/ N (+ (* (- N 1) N) 1))) 1)) (+ (pow N 3) 1) (pow N 3) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))))) (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (- 1 (+ (* N N) N)) (- 1 N) (/ N (+ (* (- N 1) N) 1)) (pow (+ (* N N) N) 2))

2.0ms

((atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 1 (+ (* (+ 1 N) N) 1)) (+ (* (+ 1 N) N) 1) (+ (* (- 1 (* N N)) (/ N (- 1 N))) 1) (atan2 1 (+ (* (- 1 (* N N)) (/ N (- 1 N))) 1)) (- 1 (* N N)) (* N N) (+ (* (+ (pow N 3) 1) (/ N (+ (* (- N 1) N) 1))) 1) (atan2 1 (+ (* (+ (pow N 3) 1) (/ N (+ (* (- N 1) N) 1))) 1)) (+ (pow N 3) 1) (pow N 3) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))))) (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (- 1 (+ (* N N) N)) (- 1 N) (/ N (+ (* (- N 1) N) 1)) (pow (+ (* N N) N) 2))

simplify150.0ms (2.5%)

Memory

23.4MiB live, 249.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	167	1848
1	470	1797
2	1087	1766
3	3863	1757
0	8334	1632

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 239

Calls

Call 1

Inputs
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
1
(+ 1 (pow N 2))
(+ 1 (pow N 2))
(+ 1 (pow N 2))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 N))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N))))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N))))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N))))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N))))
1
(+ 1 (* -1 (pow N 2)))
(+ 1 (* -1 (pow N 2)))
(+ 1 (* -1 (pow N 2)))
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 2)
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
(atan2 1 (+ 1 (/ (* N (+ 1 (pow N 3))) (+ 1 (* N (- N 1))))))
(atan2 1 (+ 1 (/ (* N (+ 1 (pow N 3))) (+ 1 (* N (- N 1))))))
(atan2 1 (+ 1 (/ (* N (+ 1 (pow N 3))) (+ 1 (* N (- N 1))))))
(atan2 1 (+ 1 (/ (* N (+ 1 (pow N 3))) (+ 1 (* N (- N 1))))))
1
(+ 1 (pow N 3))
(+ 1 (pow N 3))
(+ 1 (pow N 3))
(pow N 3)
(pow N 3)
(pow N 3)
(pow N 3)
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
1
(+ 1 (* -1 N))
(+ 1 (* N (- (pow N 2) 1)))
(+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1)))
1
(+ 1 (* -1 N))
(+ 1 (* N (- (* -1 N) 1)))
(+ 1 (* N (- (* -1 N) 1)))
1
(+ 1 (* -1 N))
(+ 1 (* -1 N))
(+ 1 (* -1 N))
N
(* N (+ 1 N))
(* N (+ 1 (* N (+ 1 (* -1 (pow N 2))))))
(* N (+ 1 (* N (+ 1 (* (pow N 2) (- (* -1 N) 1))))))
(pow N 2)
(* (pow N 2) (+ 1 (* 2 N)))
(* (pow N 2) (+ 1 (* N (+ 2 N))))
(* (pow N 2) (+ 1 (* N (+ 2 N))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(atan2 1 (- (+ 1 (/ N (- 1 N))) (/ (pow N 3) (- 1 N))))
(atan2 1 (- (+ 1 (/ N (- 1 N))) (/ (pow N 3) (- 1 N))))
(atan2 1 (- (+ 1 (/ N (- 1 N))) (/ (pow N 3) (- 1 N))))
(atan2 1 (- (+ 1 (/ N (- 1 N))) (/ (pow N 3) (- 1 N))))
(* -1 (pow N 2))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(atan2 1 (+ 1 (+ (/ N (- (+ 1 (pow N 2)) N)) (/ (pow N 4) (- (+ 1 (pow N 2)) N)))))
(atan2 1 (+ 1 (+ (/ N (- (+ 1 (pow N 2)) N)) (/ (pow N 4) (- (+ 1 (pow N 2)) N)))))
(atan2 1 (+ 1 (+ (/ N (- (+ 1 (pow N 2)) N)) (/ (pow N 4) (- (+ 1 (pow N 2)) N)))))
(atan2 1 (+ 1 (+ (/ N (- (+ 1 (pow N 2)) N)) (/ (pow N 4) (- (+ 1 (pow N 2)) N)))))
(pow N 3)
(* (pow N 3) (+ 1 (/ 1 (pow N 3))))
(* (pow N 3) (+ 1 (/ 1 (pow N 3))))
(* (pow N 3) (+ 1 (/ 1 (pow N 3))))
(pow N 3)
(pow N 3)
(pow N 3)
(pow N 3)
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(/ 1 (pow N 2))
(/ (- 1 (/ 1 N)) (pow N 2))
(/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 N)) (pow N 2))
(/ (- (+ 1 (/ 1 (pow N 3))) (+ (/ 1 N) (/ 1 (pow N 4)))) (pow N 2))
(* -1 (pow N 2))
(* -1 (* (pow N 2) (+ 1 (/ 1 N))))
(* (pow N 2) (- (/ 1 (pow N 2)) (+ 1 (/ 1 N))))
(* (pow N 2) (- (/ 1 (pow N 2)) (+ 1 (/ 1 N))))
(* -1 N)
(* N (- (/ 1 N) 1))
(* N (- (/ 1 N) 1))
(* N (- (/ 1 N) 1))
(/ 1 N)
(/ (+ 1 (/ 1 N)) N)
(/ (- (+ 1 (/ 1 N)) (/ 1 (pow N 3))) N)
(/ (+ 1 (+ (* -1 (/ (+ 1 (/ 1 N)) (pow N 3))) (/ 1 N))) N)
(pow N 4)
(* (pow N 4) (+ 1 (* 2 (/ 1 N))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (+ 1 (* -1 N)))))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (+ 1 (* -1 N)))))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (+ 1 (* -1 N)))))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (+ 1 (* -1 N)))))
(* -1 (pow N 2))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))
(atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))
(atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))
(atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))
(pow N 3)
(* (pow N 3) (+ 1 (/ 1 (pow N 3))))
(* (pow N 3) (+ 1 (/ 1 (pow N 3))))
(* (pow N 3) (+ 1 (/ 1 (pow N 3))))
(pow N 3)
(pow N 3)
(pow N 3)
(pow N 3)
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(/ 1 (pow N 2))
(/ (- 1 (/ 1 N)) (pow N 2))
(/ (+ 1 (* -1 (/ (- 1 (/ 1 (pow N 2))) N))) (pow N 2))
(/ (+ 1 (* -1 (/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 (pow N 2))) N))) (pow N 2))
(* -1 (pow N 2))
(* -1 (* (pow N 2) (+ 1 (/ 1 N))))
(* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1))
(* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1))
(* -1 N)
(* -1 (* N (- 1 (/ 1 N))))
(* -1 (* N (- 1 (/ 1 N))))
(* -1 (* N (- 1 (/ 1 N))))
(/ 1 N)
(/ (+ 1 (/ 1 N)) N)
(* -1 (/ (- (* -1 (/ (- 1 (/ 1 (pow N 2))) N)) 1) N))
(* -1 (/ (- (* -1 (/ (+ 1 (* -1 (/ (+ 1 (/ 1 N)) (pow N 2)))) N)) 1) N))
(pow N 4)
(* (pow N 4) (+ 1 (* 2 (/ 1 N))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))

Outputs
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(+ 1 (* N (+ 1 N)))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (pow N 2))
(fma.f64 N N #s(literal 1 binary64))
(+ 1 (pow N 2))
(fma.f64 N N #s(literal 1 binary64))
(+ 1 (pow N 2))
(fma.f64 N N #s(literal 1 binary64))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N N) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(+ 1 (* N (+ 1 N)))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(+ 1 (* N (+ 1 N)))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 N (pow.f64 N #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 N (pow.f64 N #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 N (pow.f64 N #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
(atan2 1 (+ 1 (/ (* N (- 1 (pow N 2))) (- 1 N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (-.f64 N (pow.f64 N #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow N 2)))
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(atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
(atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
(pow N 3)
(pow.f64 N #s(literal 3 binary64))
(* (pow N 3) (+ 1 (/ 1 (pow N 3))))
(-.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))
(* (pow N 3) (+ 1 (/ 1 (pow N 3))))
(-.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))
(* (pow N 3) (+ 1 (/ 1 (pow N 3))))
(-.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal -1 binary64))
(pow N 3)
(pow.f64 N #s(literal 3 binary64))
(pow N 3)
(pow.f64 N #s(literal 3 binary64))
(pow N 3)
(pow.f64 N #s(literal 3 binary64))
(pow N 3)
(pow.f64 N #s(literal 3 binary64))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(+.f64 (fma.f64 N N N) #s(literal 1 binary64))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(/ 1 (pow N 2))
(/.f64 (/.f64 #s(literal 1 binary64) N) N)
(/ (- 1 (/ 1 N)) (pow N 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) N) N)
(/ (+ 1 (* -1 (/ (- 1 (/ 1 (pow N 2))) N))) (pow N 2))
(/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 3 binary64)))) (*.f64 N N))
(/ (+ 1 (* -1 (/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 (pow N 2))) N))) (pow N 2))
(/.f64 (/.f64 (+.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (-.f64 N #s(literal 1 binary64)) #s(literal -1 binary64)) N) #s(literal 1 binary64)) N) N)
(* -1 (pow N 2))
(*.f64 (neg.f64 N) N)
(* -1 (* (pow N 2) (+ 1 (/ 1 N))))
(*.f64 (-.f64 #s(literal -1 binary64) N) N)
(* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1))
(fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))
(* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1))
(fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))
(* -1 N)
(neg.f64 N)
(* -1 (* N (- 1 (/ 1 N))))
(-.f64 #s(literal 1 binary64) N)
(* -1 (* N (- 1 (/ 1 N))))
(-.f64 #s(literal 1 binary64) N)
(* -1 (* N (- 1 (/ 1 N))))
(-.f64 #s(literal 1 binary64) N)
(/ 1 N)
(/.f64 #s(literal 1 binary64) N)
(/ (+ 1 (/ 1 N)) N)
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) N)
(* -1 (/ (- (* -1 (/ (- 1 (/ 1 (pow N 2))) N)) 1) N))
(/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) (fma.f64 N N #s(literal -1 binary64)) #s(literal 1 binary64)) N)
(* -1 (/ (- (* -1 (/ (+ 1 (* -1 (/ (+ 1 (/ 1 N)) (pow N 2)))) N)) 1) N))
(/.f64 (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))))) N)
(pow N 4)
(pow.f64 N #s(literal 4 binary64))
(* (pow N 4) (+ 1 (* 2 (/ 1 N))))
(*.f64 (+.f64 #s(literal 2 binary64) N) (pow.f64 N #s(literal 3 binary64)))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)

rewrite234.0ms (3.9%)

Memory

-13.6MiB live, 307.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	186
0	59	132
1	269	125
2	2292	125
0	8423	125

Stop Event

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

Counts

20 → 1 143

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(+.f64 (fma.f64 N N #s(literal 1 binary64)) N)
(fma.f64 N N #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
#s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64))
(fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 N N))
(*.f64 N N)
(fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
(+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64))
(pow.f64 N #s(literal 3 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))
(-.f64 #s(literal 1 binary64) (fma.f64 N N N))
(-.f64 #s(literal 1 binary64) N)
(/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)))
(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))

Outputs
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eval222.0ms (3.7%)

Memory: 4.8MiB live, 432.6MiB allocated
Compiler: Compiled 33 733 to 3 016 computations (91.1% saved)

prune59.0ms (1%)

Memory

-42.4MiB live, 121.2MiB allocated

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	1 372	10	1 382
Fresh	12	0	12
Picked	2	3	5
Done	0	0	0
Total	1 386	13	1 399

Accuracy

99.7%

Counts

1 399 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (*.f64 N N) N #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
▶	99.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
✓	99.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
	92.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) #s(approx (/ N (+ (* (- N 1) N) 1)) (/.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
▶	73.9%	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))))
	73.8%	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) #s(approx (pow (+ (* N N) N) 2) (.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N))))))
▶	92.5%	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
✓	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
	96.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) (*.f64 N N)) N))
▶	7.8%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
▶	96.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)))
	92.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (*.f64 N N)))
✓	6.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 294 to 173 computations (41.2% saved)

simplify174.0ms (2.9%)

Memory

-6.2MiB live, 190.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 #s(literal 1 binary64) (fma.f64 N N N))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N)))))
cost-diff	0	(/.f64 (/.f64 #s(literal 1 binary64) N) N)
cost-diff	0	#s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N)))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
cost-diff	0	(fma.f64 N N N)
cost-diff	0	#s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)))
cost-diff	0	#s(approx (+ (* N N) 1) #s(literal 1 binary64))
cost-diff	0	(+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 N N))
cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
cost-diff	512	(/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (+.f64 N #s(literal 1 binary64))))
cost-diff	1920	(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	323
0	59	308
1	106	305
2	223	297
3	709	275
4	2352	275
5	7196	275
0	8045	272

Stop Event

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

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 N N))
(*.f64 N N)
N
(/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (+.f64 N #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (+.f64 N #s(literal 1 binary64)))
(+.f64 N #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
#s(literal 1 binary64)
(+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)
#s(approx (+ (* N N) 1) #s(literal 1 binary64))
N
(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)))
#s(literal 1 binary64)
#s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))
(fma.f64 N N N)
N
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N)))
#s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))
(/.f64 (/.f64 #s(literal 1 binary64) N) N)
(/.f64 #s(literal 1 binary64) N)
N
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N)))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))
(-.f64 #s(literal 1 binary64) (fma.f64 N N N))
(fma.f64 N N N)
N
(-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N)))
(*.f64 (fma.f64 N N N) (fma.f64 N N N))

Outputs
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 N N))
(*.f64 N N)
N
(/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (+.f64 N #s(literal 1 binary64))))
(/.f64 (fma.f64 N N N) (-.f64 #s(literal 1 binary64) (*.f64 N N)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (+.f64 N #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (-.f64 N #s(literal -1 binary64)))
(+.f64 N #s(literal 1 binary64))
(-.f64 N #s(literal -1 binary64))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
#s(literal 1 binary64)
(+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)
#s(approx (+ (* N N) 1) #s(literal 1 binary64))
N
(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)))
#s(literal 1 binary64)
#s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))
(fma.f64 N N N)
N
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N)))
#s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))
(/.f64 (/.f64 #s(literal 1 binary64) N) N)
(/.f64 #s(literal 1 binary64) N)
N
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 N N N))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N)))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 N N N)))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))
(-.f64 #s(literal 1 binary64) (fma.f64 N N N))
(fma.f64 N N N)
N
(-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N)))
(-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64)))
(*.f64 (fma.f64 N N N) (fma.f64 N N N))
(pow.f64 (fma.f64 N N N) #s(literal 2 binary64))

localize75.0ms (1.3%)

Memory

38.0MiB live, 76.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N)))))
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))))
accuracy	0.43263627930532605	(*.f64 (fma.f64 N N N) (fma.f64 N N N))
accuracy	16.642985602158923	(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))
accuracy	0.2265625	(/.f64 (/.f64 #s(literal 1 binary64) N) N)
accuracy	0.2578125	(/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N)))
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
accuracy	4.5265259367866255	#s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))
accuracy	0	(fma.f64 N N N)
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)))
accuracy	2.083307195495552	#s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))
accuracy	0.046875	(+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
accuracy	59.97838909311519	#s(approx (+ (* N N) 1) #s(literal 1 binary64))
accuracy	0	(*.f64 N N)
accuracy	0.0625	(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (+.f64 N #s(literal 1 binary64)))
accuracy	0.0703125	(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))
accuracy	0.30859375	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))

Samples

56.0ms

256×

valid

Compiler

Compiled 319 to 29 computations (90.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-div: 12.0ms (28.9% of total)

ival-mult: 10.0ms (24.1% of total)

ival-add: 6.0ms (14.5% of total)

ival-atan2: 6.0ms (14.5% of total)

ival-sub: 5.0ms (12% of total)

ival-pow2: 3.0ms (7.2% of total)

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

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

exact: 0.0ms (0% of total)

series43.0ms (0.7%)

Memory

-28.0MiB live, 10.5MiB allocated

Counts

21 → 252

Calls

Call 1

Inputs
#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) (patch (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())
#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) #<representation binary64>) () ())
#s(alt (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) (patch (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) #<representation binary64>) () ())
#s(alt #s(approx (+ (* N N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* N N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) #<representation binary64>) () ())
#s(alt #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) (patch #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) #<representation binary64>) () ())
#s(alt (fma.f64 N N N) (patch (fma.f64 N N N) #<representation binary64>) () ())
#s(alt (atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N)))) (patch (atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))) #<representation binary64>) () ())
#s(alt #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N)) (patch #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal 1 binary64) N) N) (patch (/.f64 (/.f64 #s(literal 1 binary64) N) N) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N))))) #<representation binary64>) () ())
#s(alt (atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))))) (patch (atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 N N N) (fma.f64 N N N)) (patch (.f64 (fma.f64 N N N) (fma.f64 N N N)) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 N) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt N (taylor 0 N) (#s(alt (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) (patch (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 N)) (taylor 0 N) (#s(alt (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) (patch (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) (patch (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* N (+ 1 (* N (+ 1 (* N (+ 1 N)))))) (taylor 0 N) (#s(alt (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) (patch (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (* N (+ 1 N)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) (patch (atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow N 2))) (taylor 0 N) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow N 2))) (taylor 0 N) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow N 2))) (taylor 0 N) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 N N)) (patch (-.f64 #s(literal 1 binary64) (.f64 N N)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (+ 1 (+ N (pow N 2)))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) (patch (atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) (patch (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) (patch (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) (patch (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) (patch (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt #s(approx (+ (* N N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* N N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow N 2)) (taylor 0 N) (#s(alt #s(approx (+ (* N N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* N N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow N 2)) (taylor 0 N) (#s(alt #s(approx (+ (* N N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* N N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow N 2)) (taylor 0 N) (#s(alt #s(approx (+ (* N N) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* N N) 1) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2))))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2))))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2))))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) #<representation binary64>) () ())) ())
#s(alt (atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2))))) (taylor 0 N) (#s(alt (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) (patch (atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 N) (#s(alt #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) (patch #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (+ 1 N) (taylor 0 N) (#s(alt #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) (patch #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) (patch #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* N (+ 1 N))) (taylor 0 N) (#s(alt #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) (patch #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt N (taylor 0 N) (#s(alt (fma.f64 N N N) (patch (fma.f64 N N N) #<representation binary64>) () ())) ())
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#s(alt (/ 1 (pow N 2)) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 N)) (pow N 2)) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (- 1 (/ 1 (pow N 2))) N))) (pow N 2)) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 1 (* -1 (/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 (pow N 2))) N))) (pow N 2)) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 N N N) (fma.f64 N N N)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow N 2)) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow N 2) (+ 1 (/ 1 N)))) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1)) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1)) (taylor -inf N) (#s(alt (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (patch (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* -1 N) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* N (- 1 (/ 1 N)))) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* N (- 1 (/ 1 N)))) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* N (- 1 (/ 1 N)))) (taylor -inf N) (#s(alt (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) (patch (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor -inf N) (#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor -inf N) (#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor -inf N) (#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())) ())
#s(alt (pow N 2) (taylor -inf N) (#s(alt (.f64 N N) (patch (.f64 N N) #<representation binary64>) () ())) ())
#s(alt (pow N 4) (taylor -inf N) (#s(alt (.f64 (fma.f64 N N N) (fma.f64 N N N)) (patch (.f64 (fma.f64 N N N) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 4) (+ 1 (* 2 (/ 1 N)))) (taylor -inf N) (#s(alt (.f64 (fma.f64 N N N) (fma.f64 N N N)) (patch (.f64 (fma.f64 N N N) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2))))) (taylor -inf N) (#s(alt (.f64 (fma.f64 N N N) (fma.f64 N N N)) (patch (.f64 (fma.f64 N N N) (fma.f64 N N N)) #<representation binary64>) () ())) ())
#s(alt (* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2))))) (taylor -inf N) (#s(alt (.f64 (fma.f64 N N N) (fma.f64 N N N)) (patch (.f64 (fma.f64 N N N) (fma.f64 N N N)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

((+ (* (- 1 (* N N)) (/ N (/ (- 1 (* N N)) (+ N 1)))) 1) (/ N (/ (- 1 (* N N)) (+ N 1))) (atan2 1 (+ (* (- 1 (* N N)) (/ N (/ (- 1 (* N N)) (+ N 1)))) 1)) (- 1 (* N N)) (atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))))) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (+ (* N N) N) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))))) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/ (/ 1 N) N) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (* (+ (* N N) N) (+ (* N N) N))))) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (* (+ (* N N) N) (+ (* N N) N)))))) (/ (- 1 (+ (* N N) N)) (- 1 (* (+ (* N N) N) (+ (* N N) N)))) (- 1 (+ (* N N) N)) (/ (- 1 (* N N)) (+ N 1)) (* N N) (* (+ (* N N) N) (+ (* N N) N)))

1.0ms

-inf

((+ (* (- 1 (* N N)) (/ N (/ (- 1 (* N N)) (+ N 1)))) 1) (/ N (/ (- 1 (* N N)) (+ N 1))) (atan2 1 (+ (* (- 1 (* N N)) (/ N (/ (- 1 (* N N)) (+ N 1)))) 1)) (- 1 (* N N)) (atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))))) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (+ (* N N) N) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))))) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/ (/ 1 N) N) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (* (+ (* N N) N) (+ (* N N) N))))) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (* (+ (* N N) N) (+ (* N N) N)))))) (/ (- 1 (+ (* N N) N)) (- 1 (* (+ (* N N) N) (+ (* N N) N)))) (- 1 (+ (* N N) N)) (/ (- 1 (* N N)) (+ N 1)) (* N N) (* (+ (* N N) N) (+ (* N N) N)))

1.0ms

inf

((+ (* (- 1 (* N N)) (/ N (/ (- 1 (* N N)) (+ N 1)))) 1) (/ N (/ (- 1 (* N N)) (+ N 1))) (atan2 1 (+ (* (- 1 (* N N)) (/ N (/ (- 1 (* N N)) (+ N 1)))) 1)) (- 1 (* N N)) (atan2 1 (+ (+ (* N N) 1) N)) (+ (+ (* N N) 1) N) (+ (* N N) 1) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))))) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (+ (* N N) N) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))))) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/ (/ 1 N) N) (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (* (+ (* N N) N) (+ (* N N) N))))) (atan2 1 (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (* (+ (* N N) N) (+ (* N N) N)))))) (/ (- 1 (+ (* N N) N)) (- 1 (* (+ (* N N) N) (+ (* N N) N)))) (- 1 (+ (* N N) N)) (/ (- 1 (* N N)) (+ N 1)) (* N N) (* (+ (* N N) N) (+ (* N N) N)))

simplify136.0ms (2.3%)

Memory

22.7MiB live, 99.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	2049
1	335	2008
2	819	1984
3	2721	1974
0	8365	1804

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 250

Calls

Call 1

Inputs
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
N
(* N (+ 1 N))
(* N (+ 1 (* N (+ 1 N))))
(* N (+ 1 (* N (+ 1 (* N (+ 1 N))))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2 1 (+ 1 (* N (+ 1 N))))
1
(+ 1 (* -1 (pow N 2)))
(+ 1 (* -1 (pow N 2)))
(+ 1 (* -1 (pow N 2)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
1
(+ 1 (pow N 2))
(+ 1 (pow N 2))
(+ 1 (pow N 2))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
N
(* N (+ 1 N))
(* N (+ 1 N))
(* N (+ 1 N))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
1
(+ 1 (* -1 N))
(+ 1 (* N (- (pow N 2) 1)))
(+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1)))
(/ 1 (pow N 2))
(/ 1 (pow N 2))
(/ 1 (pow N 2))
(/ 1 (pow N 2))
1
(+ 1 N)
(+ 1 (* N (+ 1 N)))
(+ 1 (* N (+ 1 N)))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
1
(+ 1 (* -1 N))
(+ 1 (* N (- (pow N 2) 1)))
(+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1)))
1
(+ 1 (* -1 N))
(+ 1 (* N (- (* -1 N) 1)))
(+ 1 (* N (- (* -1 N) 1)))
1
(+ 1 (* -1 N))
(+ 1 (* -1 N))
(+ 1 (* -1 N))
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 2)
(* (pow N 2) (+ 1 (* 2 N)))
(* (pow N 2) (+ 1 (* N (+ 2 N))))
(* (pow N 2) (+ 1 (* N (+ 2 N))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
-1
(* -1 (+ 1 (/ 1 N)))
(- (* -1 (/ (+ 1 (/ 1 N)) N)) 1)
(- (* -1 (/ (+ 1 (/ 1 N)) (pow N 2))) (+ 1 (/ 1 N)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(* -1 (pow N 2))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2 1 (+ 1 (+ N (pow N 2))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (/ 1 N)))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(/ 1 (pow N 2))
(/ (- 1 (/ 1 N)) (pow N 2))
(/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 N)) (pow N 2))
(/ (- (+ 1 (/ 1 (pow N 3))) (+ (/ 1 N) (/ 1 (pow N 4)))) (pow N 2))
(/ 1 (pow N 2))
(/ 1 (pow N 2))
(/ 1 (pow N 2))
(/ 1 (pow N 2))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(/ 1 (pow N 2))
(/ (- 1 (/ 1 N)) (pow N 2))
(/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 N)) (pow N 2))
(/ (- (+ 1 (/ 1 (pow N 3))) (+ (/ 1 N) (/ 1 (pow N 4)))) (pow N 2))
(* -1 (pow N 2))
(* -1 (* (pow N 2) (+ 1 (/ 1 N))))
(* (pow N 2) (- (/ 1 (pow N 2)) (+ 1 (/ 1 N))))
(* (pow N 2) (- (/ 1 (pow N 2)) (+ 1 (/ 1 N))))
(* -1 N)
(* N (- (/ 1 N) 1))
(* N (- (/ 1 N) 1))
(* N (- (/ 1 N) 1))
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 4)
(* (pow N 4) (+ 1 (* 2 (/ 1 N))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
-1
(* -1 (+ 1 (/ 1 N)))
(- (* -1 (/ (+ 1 (/ 1 N)) N)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))) N)) 1)
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(* -1 (pow N 2))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (/ 1 N)))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(/ 1 (pow N 2))
(/ (- 1 (/ 1 N)) (pow N 2))
(/ (+ 1 (* -1 (/ (- 1 (/ 1 (pow N 2))) N))) (pow N 2))
(/ (+ 1 (* -1 (/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 (pow N 2))) N))) (pow N 2))
(/ 1 (pow N 2))
(/ 1 (pow N 2))
(/ 1 (pow N 2))
(/ 1 (pow N 2))
(pow N 2)
(* (pow N 2) (+ 1 (/ 1 N)))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(/ 1 (pow N 2))
(/ (- 1 (/ 1 N)) (pow N 2))
(/ (+ 1 (* -1 (/ (- 1 (/ 1 (pow N 2))) N))) (pow N 2))
(/ (+ 1 (* -1 (/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 (pow N 2))) N))) (pow N 2))
(* -1 (pow N 2))
(* -1 (* (pow N 2) (+ 1 (/ 1 N))))
(* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1))
(* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1))
(* -1 N)
(* -1 (* N (- 1 (/ 1 N))))
(* -1 (* N (- 1 (/ 1 N))))
(* -1 (* N (- 1 (/ 1 N))))
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 2)
(pow N 4)
(* (pow N 4) (+ 1 (* 2 (/ 1 N))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))

Outputs
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
N
(* N (+ 1 N))
(fma.f64 N N N)
(* N (+ 1 (* N (+ 1 N))))
(fma.f64 (fma.f64 N N N) N N)
(* N (+ 1 (* N (+ 1 (* N (+ 1 N))))))
(*.f64 (fma.f64 N N #s(literal 1 binary64)) (fma.f64 N N N))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow N 2)))
(fma.f64 (neg.f64 N) N #s(literal 1 binary64))
(+ 1 (* -1 (pow N 2)))
(fma.f64 (neg.f64 N) N #s(literal 1 binary64))
(+ 1 (* -1 (pow N 2)))
(fma.f64 (neg.f64 N) N #s(literal 1 binary64))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (pow N 2))
(fma.f64 N N #s(literal 1 binary64))
(+ 1 (pow N 2))
(fma.f64 N N #s(literal 1 binary64))
(+ 1 (pow N 2))
(fma.f64 N N #s(literal 1 binary64))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
N
(* N (+ 1 N))
(fma.f64 N N N)
(* N (+ 1 N))
(fma.f64 N N N)
(* N (+ 1 N))
(fma.f64 N N N)
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 N))
(-.f64 #s(literal 1 binary64) N)
(+ 1 (* N (- (pow N 2) 1)))
(fma.f64 (fma.f64 N N #s(literal -1 binary64)) N #s(literal 1 binary64))
(+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1)))
(*.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
1
#s(literal 1 binary64)
(+ 1 N)
(-.f64 N #s(literal -1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(+ 1 (* N (+ 1 N)))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1 N))
(-.f64 #s(literal 1 binary64) N)
(+ 1 (* N (- (pow N 2) 1)))
(fma.f64 (fma.f64 N N #s(literal -1 binary64)) N #s(literal 1 binary64))
(+ 1 (* N (- (* (pow N 2) (+ 1 (* -1 N))) 1)))
(*.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) N))
1
#s(literal 1 binary64)
(+ 1 (* -1 N))
(-.f64 #s(literal 1 binary64) N)
(+ 1 (* N (- (* -1 N) 1)))
(fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))
(+ 1 (* N (- (* -1 N) 1)))
(fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 N))
(-.f64 #s(literal 1 binary64) N)
(+ 1 (* -1 N))
(-.f64 #s(literal 1 binary64) N)
(+ 1 (* -1 N))
(-.f64 #s(literal 1 binary64) N)
(pow N 2)
(*.f64 N N)
(pow N 2)
(*.f64 N N)
(pow N 2)
(*.f64 N N)
(pow N 2)
(*.f64 N N)
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (* 2 N)))
(.f64 (.f64 (fma.f64 #s(literal 2 binary64) N #s(literal 1 binary64)) N) N)
(* (pow N 2) (+ 1 (* N (+ 2 N))))
(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)
(* (pow N 2) (+ 1 (* N (+ 2 N))))
(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 N)))
(/.f64 (-.f64 #s(literal -1 binary64) N) N)
(- (* -1 (/ (+ 1 (/ 1 N)) N)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 N #s(literal -1 binary64)) N) N))
(- (* -1 (/ (+ 1 (/ 1 N)) (pow N 2))) (+ 1 (/ 1 N)))
(*.f64 (/.f64 (-.f64 N #s(literal -1 binary64)) N) (-.f64 (/.f64 (/.f64 #s(literal -1 binary64) N) N) #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(* -1 (pow N 2))
(*.f64 (neg.f64 N) N)
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(fma.f64 (neg.f64 N) N #s(literal 1 binary64))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(fma.f64 (neg.f64 N) N #s(literal 1 binary64))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(fma.f64 (neg.f64 N) N #s(literal 1 binary64))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (+ N (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(fma.f64 N N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(fma.f64 N N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(fma.f64 N N #s(literal 1 binary64))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ (- 1 (/ 1 N)) (pow N 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) N) N)
(/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 N)) (pow N 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) N)) (*.f64 N N))
(/ (- (+ 1 (/ 1 (pow N 3))) (+ (/ 1 N) (/ 1 (pow N 4)))) (pow N 2))
(/.f64 (/.f64 (-.f64 (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 N N))) N)) N) N)
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (+ N (pow N 2)) 2)) (- 1 (+ N (pow N 2)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ (- 1 (/ 1 N)) (pow N 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) N) N)
(/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 N)) (pow N 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) N)) (*.f64 N N))
(/ (- (+ 1 (/ 1 (pow N 3))) (+ (/ 1 N) (/ 1 (pow N 4)))) (pow N 2))
(/.f64 (/.f64 (-.f64 (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 N #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 N N))) N)) N) N)
(* -1 (pow N 2))
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(fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))
(* (pow N 2) (- (/ 1 (pow N 2)) (+ 1 (/ 1 N))))
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(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)
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(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)
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(fma.f64 N N N)
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(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (/ 1 N)))
(/.f64 (-.f64 #s(literal -1 binary64) N) N)
(- (* -1 (/ (+ 1 (/ 1 N)) N)) 1)
(-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (-.f64 N #s(literal -1 binary64)) N) N))
(- (* -1 (/ (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))) N)) 1)
(*.f64 (/.f64 (-.f64 N #s(literal -1 binary64)) N) (-.f64 (/.f64 (/.f64 #s(literal -1 binary64) N) N) #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (+ 1 (* N (- 1 (* -1 N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(* -1 (pow N 2))
(*.f64 (neg.f64 N) N)
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(fma.f64 (neg.f64 N) N #s(literal 1 binary64))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(fma.f64 (neg.f64 N) N #s(literal 1 binary64))
(* (pow N 2) (- (/ 1 (pow N 2)) 1))
(fma.f64 (neg.f64 N) N #s(literal 1 binary64))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64)))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(fma.f64 N N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(fma.f64 N N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (/ 1 (pow N 2))))
(fma.f64 N N #s(literal 1 binary64))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ (- 1 (/ 1 N)) (pow N 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) N) N)
(/ (+ 1 (* -1 (/ (- 1 (/ 1 (pow N 2))) N))) (pow N 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) N)) (*.f64 N N))
(/ (+ 1 (* -1 (/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 (pow N 2))) N))) (pow N 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) N) N)) N)) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(pow N 2)
(*.f64 N N)
(* (pow N 2) (+ 1 (/ 1 N)))
(fma.f64 N N N)
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))
(fma.f64 (-.f64 N #s(literal -1 binary64)) N #s(literal 1 binary64))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(atan2 1 (/ (- 1 (pow (- (pow N 2) (* -1 N)) 2)) (- (+ 1 (* -1 N)) (pow N 2))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))) (fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))))
(/ 1 (pow N 2))
(/.f64 #s(literal 1 binary64) (*.f64 N N))
(/ (- 1 (/ 1 N)) (pow N 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) N) N)
(/ (+ 1 (* -1 (/ (- 1 (/ 1 (pow N 2))) N))) (pow N 2))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) N)) (*.f64 N N))
(/ (+ 1 (* -1 (/ (- (+ 1 (/ 1 (pow N 3))) (/ 1 (pow N 2))) N))) (pow N 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) N)) N) N)) N)) (*.f64 N N))
(* -1 (pow N 2))
(*.f64 (neg.f64 N) N)
(* -1 (* (pow N 2) (+ 1 (/ 1 N))))
(*.f64 (-.f64 #s(literal -1 binary64) N) N)
(* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1))
(fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))
(* (pow N 2) (- (* -1 (/ (- 1 (/ 1 N)) N)) 1))
(fma.f64 (-.f64 #s(literal -1 binary64) N) N #s(literal 1 binary64))
(* -1 N)
(neg.f64 N)
(* -1 (* N (- 1 (/ 1 N))))
(-.f64 #s(literal 1 binary64) N)
(* -1 (* N (- 1 (/ 1 N))))
(-.f64 #s(literal 1 binary64) N)
(* -1 (* N (- 1 (/ 1 N))))
(-.f64 #s(literal 1 binary64) N)
(pow N 2)
(*.f64 N N)
(pow N 2)
(*.f64 N N)
(pow N 2)
(*.f64 N N)
(pow N 2)
(*.f64 N N)
(pow N 4)
(pow.f64 N #s(literal 4 binary64))
(* (pow N 4) (+ 1 (* 2 (/ 1 N))))
(*.f64 (pow.f64 N #s(literal 3 binary64)) (+.f64 #s(literal 2 binary64) N))
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)
(* (pow N 4) (+ 1 (+ (* 2 (/ 1 N)) (/ 1 (pow N 2)))))
(.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N)

rewrite292.0ms (4.9%)

Memory

-20.2MiB live, 174.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	292
0	59	280
1	241	176
2	1785	176
0	8241	173

Stop Event

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

Counts

21 → 786

Calls

Call 1

Inputs
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64))
(/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (+.f64 N #s(literal 1 binary64))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 N N))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
(+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N)
#s(approx (+ (* N N) 1) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)))
#s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N))
(fma.f64 N N N)
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N)))
#s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))
(/.f64 (/.f64 #s(literal 1 binary64) N) N)
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))))
(/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))
(-.f64 #s(literal 1 binary64) (fma.f64 N N N))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (+.f64 N #s(literal 1 binary64)))
(*.f64 N N)
(*.f64 (fma.f64 N N N) (fma.f64 N N N))

Outputs
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eval649.0ms (10.9%)

Memory: 18.8MiB live, 412.8MiB allocated
Compiler: Compiled 36 742 to 5 243 computations (85.7% saved)

prune138.0ms (2.3%)

Memory

12.7MiB live, 128.1MiB allocated

Pruning

16 alts after pruning (10 fresh and 6 done)

	Pruned	Kept	Total
New	1 354	7	1 361
Fresh	2	3	5
Picked	2	3	5
Done	0	3	3
Total	1 358	16	1 374

Accuracy

99.7%

Counts

1 374 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (*.f64 N N) N #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 N (-.f64 #s(literal 1 binary64) (.f64 N N))) (.f64 (+.f64 N #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 N N))) #s(literal 1 binary64)))
	96.2%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 #s(approx (- 1 ( N N)) (*.f64 (neg.f64 N) N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
✓	99.5%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
	99.4%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) N) N)) #s(literal 1 binary64)))
	99.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (neg.f64 N) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) N))) #s(literal 1 binary64)))
	92.7%	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (pow.f64 N #s(literal -2 binary64)))))
✓	92.5%	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
	92.2%	(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (*.f64 (/.f64 #s(literal -1 binary64) N) (/.f64 #s(literal -1 binary64) N)))))
✓	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
	96.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) (*.f64 N N)) N))
✓	7.8%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
✓	96.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)))
	96.2%	(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (/.f64 (*.f64 (fma.f64 N N #s(literal -1 binary64)) N) (-.f64 N #s(literal 1 binary64)))))
	92.5%	(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (*.f64 N N)))
✓	6.3%	(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Compiler

Compiled 694 to 274 computations (60.5% saved)

regimes52.0ms (0.9%)

Memory

-28.2MiB live, 19.5MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) (*.f64 N N)) N))
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) N) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (/.f64 (*.f64 (fma.f64 N N #s(literal -1 binary64)) N) (-.f64 N #s(literal 1 binary64)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 N (-.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (neg.f64 N) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) N))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (*.f64 N N) N #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (*.f64 (/.f64 #s(literal -1 binary64) N) (/.f64 #s(literal -1 binary64) N)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (*.f64 N N)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) N) N)) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 N (-.f64 #s(literal 1 binary64) (.f64 N N))) (.f64 (+.f64 N #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 N N))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) (*.f64 N N))) (+.f64 N #s(literal 1 binary64)) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 #s(approx (- 1 ( N N)) (*.f64 (neg.f64 N) N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 N (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 N #s(literal 1 binary64)))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 N N N) (fma.f64 N N N))))))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) #s(approx (pow (+ (* N N) N) 2) (.f64 (.f64 (fma.f64 (+.f64 #s(literal 2 binary64) N) N #s(literal 1 binary64)) N) N))))))
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2))) (pow.f64 N #s(literal -2 binary64)))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) #s(approx (/ N (+ (* (- N 1) N) 1)) (/.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)) N) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 N (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64))) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 N #s(literal 4 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) N) (fma.f64 N N #s(literal 1 binary64)))) N #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (.f64 (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)) (.f64 (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal -1 binary64)) (pow.f64 (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal -1 binary64)) #s(literal -1 binary64)))))
(atan2.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (fma.f64 N N N)) (-.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 N N N) #s(literal 2 binary64))))))
(atan2.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (fma.f64 N N N) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 N N N) (fma.f64 (+.f64 N #s(literal 1 binary64)) N #s(literal -1 binary64)) #s(literal 1 binary64))))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 4 binary64)) N) (pow.f64 (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) (fma.f64 (+.f64 (pow.f64 N #s(literal 3 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (fma.f64 (-.f64 N #s(literal 1 binary64)) N #s(literal 1 binary64)) #s(literal -1 binary64)) N) #s(literal 1 binary64)))

Outputs
(atan2.f64 #s(literal 1 binary64) (+.f64 (fma.f64 N N #s(literal 1 binary64)) N))

Calls

2 calls:

43.0ms	N
8.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
99.5%	1	`N`
99.5%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes6.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (fma.f64 N N N)))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) (*.f64 N N)) N))

Outputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (fma.f64 N N N)))

Calls

2 calls:

3.0ms	N
2.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
96.3%	1	`N`
96.3%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes5.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))
(atan2.f64 #s(literal 1 binary64) #s(approx (/ 1 (/ (- 1 (+ (* N N) N)) (- 1 (pow (+ (* N N) N) 2)))) (*.f64 N N)))

Outputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (*.f64 N N)))

Calls

2 calls:

2.0ms	N
2.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
92.5%	1	`N`
92.5%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes4.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) (-.f64 N #s(literal -1 binary64))))

(atan2.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ (* N N) 1) #s(literal 1 binary64)) N))

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

Calls

2 calls:

2.0ms	N
1.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
7.8%	1	`N`
7.8%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Outputs
(atan2.f64 #s(literal 1 binary64) #s(approx (+ (* (+ 1 N) N) 1) #s(literal 1 binary64)))

Calls

2 calls:

1.0ms	N
1.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
6.3%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
6.3%	1	`N`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify27.0ms (0.5%)

Memory

-2.1MiB live, 36.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	59
1	26	59
2	29	59
3	30	59
4	31	59

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness790.0ms (13.3%)

Memory

-13.6MiB live, 275.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	44	16
2	284	16
3	2885	16
0	8353	16
0	5	17
0	9	17
1	37	17
2	262	17
3	2791	17
0	8379	17
0	25	208
1	67	200
2	117	200
3	451	200
4	2326	200
5	5354	200
0	8132	180

Stop Event

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

Compiler

Compiled 141 to 81 computations (42.6% saved)

preprocess51.0ms (0.9%)

Memory: 3.7MiB live, 80.8MiB allocated
Compiler: Compiled 92 to 56 computations (39.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Iter	Nodes	Cost
0	14	186
1	34	186
2	44	186
3	89	186
4	189	186
5	335	186
6	383	186
7	420	186
8	474	186
9	489	186
10	497	186
0	497	186

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Iter	Nodes	Cost
0	14	186
1	34	186
2	44	186
3	89	186
4	189	186
5	335	186
6	383	186
7	420	186
8	474	186
9	489	186
10	497	186
0	497	186

start0.0ms (0%)

analyze2.0ms (0%)

sample1.6s (27.4%)

explain145.0ms (2.4%)

preprocess19.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize56.0ms (0.9%)

series2.0ms (0%)

simplify13.0ms (0.2%)

rewrite141.0ms (2.4%)

eval37.0ms (0.6%)

prune10.0ms (0.2%)

simplify4.0ms (0.1%)

localize45.0ms (0.8%)

series2.0ms (0%)

simplify116.0ms (2%)

rewrite190.0ms (3.2%)

eval48.0ms (0.8%)

prune21.0ms (0.4%)

simplify165.0ms (2.8%)

localize167.0ms (2.8%)

series22.0ms (0.4%)

simplify150.0ms (2.5%)

rewrite234.0ms (3.9%)

eval222.0ms (3.7%)

prune59.0ms (1%)

simplify174.0ms (2.9%)

localize75.0ms (1.3%)

series43.0ms (0.7%)

simplify136.0ms (2.3%)

rewrite292.0ms (4.9%)

eval649.0ms (10.9%)

prune138.0ms (2.3%)

regimes52.0ms (0.9%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

simplify27.0ms (0.5%)

soundness790.0ms (13.3%)

preprocess51.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Iter	Nodes	Cost
0	14	186
1	34	186
2	44	186
3	89	186
4	189	186
5	335	186
6	383	186
7	420	186
8	474	186
9	489	186
10	497	186
0	497	186