Metrics for 2atan (example 3.5)

analyze3.0ms (0%)

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 10 computations (33.3% saved)

Precisions

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

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

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

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

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

...c/correct-round.rkt:119:19: 0.0ms (0% of total)

const: 0.0ms (0% of total)

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

backward-pass: 0.0ms (0% of total)

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

sample2.0s (23.7%)

Results

1.5s	7311×	1	valid
170.0ms	657×	2	valid
24.0ms	288×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-atan: 514.0ms (42.5% of total)

backward-pass: 178.0ms (14.7% of total)

...c/correct-round.rkt:119:19: 143.0ms (11.8% of total)

ival-add: 118.0ms (9.7% of total)

ival->: 92.0ms (7.6% of total)

ival-sub: 91.0ms (7.5% of total)

ival-and: 30.0ms (2.5% of total)

ival-<: 27.0ms (2.2% of total)

const: 18.0ms (1.5% of total)

Bogosity

preprocess43.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

270×	`sum3-define`
244×	`fnmadd-define`
184×	`fmsub-define`
168×	`fnmsub-define`
168×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	29	24
2	56	23
3	103	23
4	194	23
5	392	23
6	584	23
7	760	23
8	852	23
9	958	23
10	1036	23
11	1042	23
0	6	7
1	13	7
2	17	7
3	24	7
4	34	7
5	66	7
6	124	7
7	212	7
8	297	7
9	403	7
10	481	7
11	487	7
0	487	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

Inputs
(- (atan (+ N 1)) (atan N))
(- (atan (+ (neg N) 1)) (atan (neg N)))
(neg (- (atan (+ (neg N) 1)) (atan (neg N))))

Outputs
(- (atan (+ N 1)) (atan N))
(- (atan (+ (neg N) 1)) (atan (neg N)))
(- (atan (- 1 N)) (atan (neg N)))
(neg (- (atan (+ (neg N) 1)) (atan (neg N))))
(- (atan (neg N)) (atan (- 1 N)))

explain145.0ms (1.7%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
255	-	2	(7.7191469237214365)	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`
0	-	0	-	`(atan.f64 (+.f64 N #s(literal 1 binary64)))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(atan.f64 N)`
0	-	0	-	`(+.f64 N #s(literal 1 binary64))`
0	-	0	-	`N`

Results

95.0ms	450×	1	valid
16.0ms	42×	2	valid
2.0ms	20×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-atan: 25.0ms (41.6% of total)

backward-pass: 17.0ms (28.3% of total)

ival-add: 11.0ms (18.3% of total)

ival-sub: 6.0ms (10% of total)

const: 1.0ms (1.7% of total)

eval0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	10.0%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

124×	`fnmadd-define`
122×	`sum3-define`
80×	`fma-lowering-fma.f32`
80×	`fnmsub-define`
80×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	13	18
2	17	18
3	24	18
4	34	18
5	66	18
6	124	18
7	212	18
8	297	18
9	403	18
10	481	18
11	487	18
0	487	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize74.0ms (0.9%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 N #s(literal 1 binary64))
✓	accuracy	100.0%	(atan.f64 (+.f64 N #s(literal 1 binary64)))
✓	accuracy	100.0%	(atan.f64 N)
✓	accuracy	10.0%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

54.0ms	225×	1	valid
9.0ms	21×	2	valid
1.0ms	10×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

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

ival-atan: 14.0ms (36.9% of total)

ival-sub: 13.0ms (34.2% of total)

backward-pass: 6.0ms (15.8% of total)

ival-add: 4.0ms (10.5% of total)

const: 1.0ms (2.6% of total)

series1.0ms (0%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (- (atan (+ N 1)) (atan N))>
#<alt (atan (+ N 1))>
#<alt (+ N 1)>
#<alt (atan N)>

Outputs
#<alt (- (atan (+ 1 N)) (atan N))>
#<alt (- (atan (+ 1 N)) (atan N))>
#<alt (- (atan (+ 1 N)) (atan N))>
#<alt (- (atan (+ 1 N)) (atan N))>
#<alt (- (atan (+ 1 N)) (atan N))>
#<alt (- (atan (+ 1 N)) (atan N))>
#<alt (- (atan (+ 1 N)) (atan N))>
#<alt (- (atan (+ 1 N)) (atan N))>
#<alt (- (atan (- 1 (* -1 N))) (atan N))>
#<alt (- (atan (- 1 (* -1 N))) (atan N))>
#<alt (- (atan (- 1 (* -1 N))) (atan N))>
#<alt (- (atan (- 1 (* -1 N))) (atan N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (- 1 (* -1 N)))>
#<alt (atan (- 1 (* -1 N)))>
#<alt (atan (- 1 (* -1 N)))>
#<alt (atan (- 1 (* -1 N)))>
#<alt 1>
#<alt (+ 1 N)>
#<alt (+ 1 N)>
#<alt (+ 1 N)>
#<alt N>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt N>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>
#<alt (atan N)>

Calls

12 calls:

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

rewrite329.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2864×	`-lowering-.f32`
2864×	`-lowering-.f64`
2066×	`pow-lowering-pow.f64`
2066×	`pow-lowering-pow.f32`
2038×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	42	16
2	295	16
3	3184	16
0	8281	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 166

Calls

Call 1

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

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

simplify36.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

270×	`fnmadd-define`
228×	`fma-lowering-fma.f32`
228×	`fma-lowering-fma.f64`
226×	`sum3-define`
218×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	186
1	39	186
2	53	186
3	103	186
4	220	186
5	443	186
6	643	186
7	778	186
8	939	186
9	1061	186
10	1139	186
11	1145	186
0	1145	186

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

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

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

eval26.0ms (0.3%)

Compiler: Compiled 5971 to 614 computations (89.7% saved)

prune30.0ms (0.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	204	10	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	10	215

Accuracy

99.7%

Counts

215 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
▶	99.4%	(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))
	99.5%	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))
▶	99.4%	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
	99.2%	(.f64 (/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (atan.f64 N) #s(literal 3 binary64)))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (-.f64 N (+.f64 N #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))))
	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))) #s(literal -1 binary64)))
	99.4%	(.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))))
▶	99.5%	(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
	99.4%	(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))))
▶	92.4%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) #s(literal -1 binary64)))

Compiler

Compiled 808 to 274 computations (66.1% saved)

simplify228.0ms (2.7%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(atan.f64 (+.f64 N #s(literal 1 binary64)))
✓	cost-diff	0	(pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))
✓	cost-diff	53760	(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
✓	cost-diff	0	(+.f64 N (+.f64 N #s(literal 1 binary64)))
✓	cost-diff	0	(atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
✓	cost-diff	128	(.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))))
✓	cost-diff	14464	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
✓	cost-diff	0	(.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))
✓	cost-diff	14464	(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))
✓	cost-diff	0	(log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))))
✓	cost-diff	256	(.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) #s(literal -1 binary64))
✓	cost-diff	12800	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) #s(literal -1 binary64)))
✓	cost-diff	0	(+.f64 N #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 N (+.f64 N #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))

Rules

2966×	`-lowering-.f32`
2966×	`-lowering-.f64`
1912×	`/-lowering-/.f32`
1912×	`/-lowering-/.f64`
1836×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	422
1	75	346
2	159	344
3	395	344
4	1296	344
5	4607	344
6	5463	344
7	6800	344
8	7900	344
0	8098	344

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize235.0ms (2.8%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
✓	accuracy	99.4%	(/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
✓	accuracy	99.3%	(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
✓	accuracy	98.7%	(+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))
✓	accuracy	99.6%	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
✓	accuracy	99.4%	(.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))))
✓	accuracy	100.0%	(*.f64 N (+.f64 N #s(literal 1 binary64)))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
✓	accuracy	99.4%	(.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))
✓	accuracy	99.4%	(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))
✓	accuracy	100.0%	(log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
✓	accuracy	92.4%	(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) #s(literal -1 binary64)))
✓	accuracy	100.0%	(+.f64 N #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))
✓	accuracy	100.0%	(*.f64 N (+.f64 N #s(literal 1 binary64)))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))

Results

124.0ms

256×

valid

Compiler

Compiled 541 to 28 computations (94.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-mult: 12.0ms (27.6% of total)

ival-div: 6.0ms (13.8% of total)

ival-add: 6.0ms (13.8% of total)

ival-atan2: 4.0ms (9.2% of total)

ival-log: 4.0ms (9.2% of total)

ival-exp: 3.0ms (6.9% of total)

ival-atan: 3.0ms (6.9% of total)

ival-pow: 3.0ms (6.9% of total)

ival-sub: 1.0ms (2.3% of total)

const: 1.0ms (2.3% of total)

backward-pass: 0.0ms (0% of total)

series108.0ms (1.3%)

Counts

20 → 240

Calls

Call 1

Inputs
#<alt (atan2 1 (+ 1 (* N (+ N 1))))>
#<alt (+ 1 (* N (+ N 1)))>
#<alt (* N (+ N 1))>
#<alt (+ N 1)>
#<alt (exp (* (log (/ 1 (atan2 1 (+ 1 (* N (+ N 1)))))) -1))>
#<alt (* (log (/ 1 (atan2 1 (+ 1 (* N (+ N 1)))))) -1)>
#<alt (log (/ 1 (atan2 1 (+ 1 (* N (+ N 1))))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ N 1)))))>
#<alt (/ (* (atan2 1 (+ 1 (* N (+ N 1)))) (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1))))) (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))))>
#<alt (* (atan2 1 (+ 1 (* N (+ N 1)))) (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))))>
#<alt (* (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))) (* (atan2 1 (+ 1 (* N (+ N 1)))) (/ 1 (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))))))>
#<alt (* (atan2 1 (+ 1 (* N (+ N 1)))) (/ 1 (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1))))))>
#<alt (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1))))>
#<alt (+ N (+ N 1))>
#<alt (* (+ (pow (atan (+ N 1)) 2) (* (atan N) (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))))) (/ (atan2 1 (+ 1 (* N (+ N 1)))) (+ (pow (atan (+ N 1)) 2) (* (atan N) (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1))))))))>
#<alt (+ (pow (atan (+ N 1)) 2) (* (atan N) (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1))))))>
#<alt (pow (atan (+ N 1)) 2)>
#<alt (atan (+ N 1))>
#<alt (/ 1 (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))))>
#<alt (/ (atan2 1 (+ 1 (* N (+ N 1)))) (+ (pow (atan (+ N 1)) 2) (* (atan N) (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))))))>

Outputs
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt 1>
#<alt (+ 1 N)>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt N>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt 1>
#<alt (+ 1 N)>
#<alt (+ 1 N)>
#<alt (+ 1 N)>
#<alt N>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt N>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))))>
#<alt (* -1 (log (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (+ N (pow N 2))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (+ N (pow N 2))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (+ N (pow N 2))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (+ N (pow N 2))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))))>
#<alt (log (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (* (atan2 1 (+ 1 (* N (+ 1 N)))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (* (atan2 1 (+ 1 (* N (+ 1 N)))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (* (atan2 1 (+ 1 (* N (+ 1 N)))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (* (atan2 1 (+ 1 (* N (+ 1 N)))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (* (atan2 1 (+ 1 (+ N (pow N 2)))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (* (atan2 1 (+ 1 (+ N (pow N 2)))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (* (atan2 1 (+ 1 (+ N (pow N 2)))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (* (atan2 1 (+ 1 (+ N (pow N 2)))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (* (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (* (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (* (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (* (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (/ (atan2 1 (+ 1 (* N (+ 1 N)))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (/ (atan2 1 (+ 1 (* N (+ 1 N)))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (/ (atan2 1 (+ 1 (* N (+ 1 N)))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (/ (atan2 1 (+ 1 (* N (+ 1 N)))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (/ (atan2 1 (+ 1 (+ N (pow N 2)))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (/ (atan2 1 (+ 1 (+ N (pow N 2)))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (/ (atan2 1 (+ 1 (+ N (pow N 2)))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (/ (atan2 1 (+ 1 (+ N (pow N 2)))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (/ (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (/ (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (/ (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (/ (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))>
#<alt (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))>
#<alt 1>
#<alt (+ 1 (* 2 N))>
#<alt (+ 1 (* 2 N))>
#<alt (+ 1 (* 2 N))>
#<alt (* 2 N)>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* 2 N)>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (pow (atan (+ 1 N)) 2))>
#<alt (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (pow (atan (+ 1 N)) 2))>
#<alt (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (pow (atan (+ 1 N)) 2))>
#<alt (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (pow (atan (+ 1 N)) 2))>
#<alt (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (pow (atan (+ 1 N)) 2))>
#<alt (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (pow (atan (+ 1 N)) 2))>
#<alt (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (pow (atan (+ 1 N)) 2))>
#<alt (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (pow (atan (+ 1 N)) 2))>
#<alt (+ (* (atan N) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (pow (atan (- 1 (* -1 N))) 2))>
#<alt (+ (* (atan N) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (pow (atan (- 1 (* -1 N))) 2))>
#<alt (+ (* (atan N) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (pow (atan (- 1 (* -1 N))) 2))>
#<alt (+ (* (atan N) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (pow (atan (- 1 (* -1 N))) 2))>
#<alt (pow (atan (+ 1 N)) 2)>
#<alt (pow (atan (+ 1 N)) 2)>
#<alt (pow (atan (+ 1 N)) 2)>
#<alt (pow (atan (+ 1 N)) 2)>
#<alt (pow (atan (+ 1 N)) 2)>
#<alt (pow (atan (+ 1 N)) 2)>
#<alt (pow (atan (+ 1 N)) 2)>
#<alt (pow (atan (+ 1 N)) 2)>
#<alt (pow (atan (- 1 (* -1 N))) 2)>
#<alt (pow (atan (- 1 (* -1 N))) 2)>
#<alt (pow (atan (- 1 (* -1 N))) 2)>
#<alt (pow (atan (- 1 (* -1 N))) 2)>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (+ 1 N))>
#<alt (atan (- 1 (* -1 N)))>
#<alt (atan (- 1 (* -1 N)))>
#<alt (atan (- 1 (* -1 N)))>
#<alt (atan (- 1 (* -1 N)))>
#<alt (/ 1 (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (/ 1 (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (/ 1 (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (/ 1 (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N))))))>
#<alt (/ (atan2 1 (+ 1 (* N (+ 1 N)))) (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (pow (atan (+ 1 N)) 2)))>
#<alt (/ (atan2 1 (+ 1 (* N (+ 1 N)))) (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (pow (atan (+ 1 N)) 2)))>
#<alt (/ (atan2 1 (+ 1 (* N (+ 1 N)))) (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (pow (atan (+ 1 N)) 2)))>
#<alt (/ (atan2 1 (+ 1 (* N (+ 1 N)))) (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (pow (atan (+ 1 N)) 2)))>
#<alt (/ (atan2 1 (+ 1 (+ N (pow N 2)))) (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (pow (atan (+ 1 N)) 2)))>
#<alt (/ (atan2 1 (+ 1 (+ N (pow N 2)))) (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (pow (atan (+ 1 N)) 2)))>
#<alt (/ (atan2 1 (+ 1 (+ N (pow N 2)))) (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (pow (atan (+ 1 N)) 2)))>
#<alt (/ (atan2 1 (+ 1 (+ N (pow N 2)))) (+ (* (atan N) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (pow (atan (+ 1 N)) 2)))>
#<alt (/ (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (+ (* (atan N) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (pow (atan (- 1 (* -1 N))) 2)))>
#<alt (/ (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (+ (* (atan N) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (pow (atan (- 1 (* -1 N))) 2)))>
#<alt (/ (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (+ (* (atan N) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (pow (atan (- 1 (* -1 N))) 2)))>
#<alt (/ (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) (+ (* (atan N) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (pow (atan (- 1 (* -1 N))) 2)))>

Calls

60 calls:

Time	Variable		Point	Expression
34.0ms	N	@	0	(* (log (/ 1 (atan2 1 (+ 1 (* N (+ N 1)))))) -1)
28.0ms	N	@	inf	(* (log (/ 1 (atan2 1 (+ 1 (* N (+ N 1)))))) -1)
18.0ms	N	@	-inf	(* (log (/ 1 (atan2 1 (+ 1 (* N (+ N 1)))))) -1)
13.0ms	N	@	inf	(* (atan2 1 (+ 1 (* N (+ N 1)))) (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))))
1.0ms	N	@	inf	(/ (atan2 1 (+ 1 (* N (+ N 1)))) (+ (pow (atan (+ N 1)) 2) (* (atan N) (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))))))

rewrite519.0ms (6.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3568×	`/-lowering-/.f32`
3568×	`/-lowering-/.f64`
3254×	`-lowering-.f32`
3254×	`-lowering-.f64`
2080×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	238
1	153	194
2	1156	192
0	8793	192

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 1232

Calls

Call 1

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

Outputs
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(.f64 (/.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/2 binary64)) (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 4 binary64)) (pow.f64 (.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) (atan.f64 N)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) (atan.f64 N))))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) (atan.f64 N))) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N)) #s(literal 2 binary64)) (.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) (atan.f64 N))) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))) #s(literal -1/2 binary64)))

simplify224.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1508×	`/-lowering-/.f32`
1508×	`/-lowering-/.f64`
1422×	`-lowering-.f32`
1422×	`-lowering-.f64`
1404×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	70	2809
1	187	2272
2	358	2272
3	947	2272
4	4592	2272
0	8044	2272

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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

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

eval668.0ms (7.9%)

Compiler: Compiled 276069 to 7546 computations (97.3% saved)

prune454.0ms (5.3%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	4300	22	4322
Fresh	4	1	5
Picked	4	1	5
Done	0	0	0
Total	4308	24	4332

Accuracy

100.0%

Counts

4332 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
	78.9%	(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))) #s(literal -1/2 binary64))
▶	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) N))
	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N) (+.f64 N #s(literal -1 binary64)))))
	78.7%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))
	99.4%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 N (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)))))
	78.8%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 N N) N) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (-.f64 (.f64 N N) N))))))
▶	99.4%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N)))))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
	99.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) (-.f64 #s(literal 1 binary64) N)))))))
	95.5%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
	92.0%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
▶	6.5%	(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))
	78.5%	(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))
	92.0%	(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))
	99.2%	(.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
▶	99.5%	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
	92.1%	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
	95.7%	(.f64 (atan2.f64 (+.f64 N N) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
	99.2%	(.f64 (/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (atan.f64 N) #s(literal 3 binary64)))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (-.f64 N (+.f64 N #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))))
	98.8%	(.f64 (+.f64 (pow.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
	98.8%	(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
	92.3%	(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
	92.4%	(exp.f64 (log.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))

Compiler

Compiled 1326 to 580 computations (56.3% saved)

simplify198.0ms (2.3%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 N #s(literal 1 binary64))
✓	cost-diff	0	(+.f64 N (+.f64 N #s(literal 1 binary64)))
✓	cost-diff	0	(atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
✓	cost-diff	14464	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
✓	cost-diff	64	(pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/2 binary64))
✓	cost-diff	12864	(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N))))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N)))))
✓	cost-diff	256	(/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N)))
✓	cost-diff	0	(atan2.f64 #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	(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) N)
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) N))

Rules

1812×	`sum4-define`
1780×	`fma-lowering-fma.f32`
1780×	`fma-lowering-fma.f64`
1508×	`-lowering-.f32`
1508×	`-lowering-.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	39	243
1	95	231
2	207	221
3	557	202
4	2178	201
0	8717	201

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize264.0ms (3.1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 N (+.f64 N #s(literal 1 binary64)))
✓	accuracy	99.6%	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))
✓	accuracy	99.5%	(/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N)))))
✓	accuracy	100.0%	(*.f64 N (+.f64 #s(literal 1 binary64) N))
✓	accuracy	99.8%	(pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/2 binary64))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
✓	accuracy	99.3%	(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
✓	accuracy	99.7%	(/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N)))
✓	accuracy	99.6%	(.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N)
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N)))))
✓	accuracy	100.0%	(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 N N)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 N N))
✓	accuracy	99.9%	(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) N)
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) N))

Results

170.0ms

256×

valid

Compiler

Compiled 310 to 40 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 56.0ms

ival-atan2: 12.0ms (21.5% of total)

ival-add: 12.0ms (21.5% of total)

ival-mult: 12.0ms (21.5% of total)

ival-pow: 8.0ms (14.4% of total)

ival-sub: 5.0ms (9% of total)

ival-div: 5.0ms (9% of total)

const: 1.0ms (1.8% of total)

backward-pass: 0.0ms (0% of total)

series28.0ms (0.3%)

Counts

22 → 252

Calls

Call 1

Inputs
#<alt (atan2 1 (+ (+ 1 (* N N)) N))>
#<alt (+ (+ 1 (* N N)) N)>
#<alt (+ 1 (* N N))>
#<alt (* N N)>
#<alt (atan2 1 1)>
#<alt (/ 1 (/ (+ N -1) (* (+ (* N N) -1) N)))>
#<alt (/ (+ N -1) (* (+ (* N N) -1) N))>
#<alt (atan2 1 (+ 1 (/ 1 (/ (+ N -1) (* (+ (* N N) -1) N)))))>
#<alt (+ 1 (/ 1 (/ (+ N -1) (* (+ (* N N) -1) N))))>
#<alt (pow (pow (atan2 1 (+ 1 (* N (+ 1 N)))) 1/2) 2)>
#<alt (pow (atan2 1 (+ 1 (* N (+ 1 N)))) 1/2)>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (* (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))) (/ (atan2 1 (- 1 (* N (- -1 N)))) (atan2 (- 1 (* N -2)) (+ 1 (* N (- -1 N))))))>
#<alt (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1))))>
#<alt (+ N (+ N 1))>
#<alt (+ N 1)>
#<alt (* (+ (* N N) -1) N)>
#<alt (* N (+ 1 N))>
#<alt (/ (atan2 1 (- 1 (* N (- -1 N)))) (atan2 (- 1 (* N -2)) (+ 1 (* N (- -1 N)))))>
#<alt (atan2 1 (- 1 (* N (- -1 N))))>
#<alt (* N (+ N 1))>

Outputs
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))>
#<alt (atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))>
#<alt (atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))>
#<alt (atan2 1 (- (+ 1 (pow N 2)) (* -1 N)))>
#<alt 1>
#<alt (+ 1 N)>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt 1>
#<alt (+ 1 (pow N 2))>
#<alt (+ 1 (pow N 2))>
#<alt (+ 1 (pow N 2))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 (pow N 2))))>
#<alt (* (pow N 2) (+ 1 (/ 1 (pow N 2))))>
#<alt (* (pow N 2) (+ 1 (/ 1 (pow N 2))))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 (pow N 2))))>
#<alt (* (pow N 2) (+ 1 (/ 1 (pow N 2))))>
#<alt (* (pow N 2) (+ 1 (/ 1 (pow N 2))))>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt N>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (/ 1 N)>
#<alt (/ (+ 1 (* -1 N)) N)>
#<alt (/ (+ 1 (* N (- N 1))) N)>
#<alt (/ (+ 1 (* N (- (* N (+ 1 (* -1 N))) 1))) N)>
#<alt (/ 1 (pow N 2))>
#<alt (/ (- 1 (/ 1 N)) (pow N 2))>
#<alt (/ (- (+ 1 (/ 1 (pow N 2))) (/ 1 N)) (pow N 2))>
#<alt (/ (- (+ 1 (/ 1 (pow N 2))) (+ (/ 1 N) (/ 1 (pow N 3)))) (pow N 2))>
#<alt (/ 1 (pow N 2))>
#<alt (/ (- 1 (/ 1 N)) (pow N 2))>
#<alt (/ (+ 1 (* -1 (/ (- 1 (/ 1 N)) N))) (pow N 2))>
#<alt (/ (+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 N)) N))) N))) (pow N 2))>
#<alt (atan2 1 (+ 1 (/ (* N (- (pow N 2) 1)) (- N 1))))>
#<alt (atan2 1 (+ 1 (/ (* N (- (pow N 2) 1)) (- N 1))))>
#<alt (atan2 1 (+ 1 (/ (* N (- (pow N 2) 1)) (- N 1))))>
#<alt (atan2 1 (+ 1 (/ (* N (- (pow N 2) 1)) (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (* -1 (/ (pow N 3) (+ 1 (* -1 N))))) (* -1 (/ N (+ 1 (* -1 N))))))>
#<alt (atan2 1 (- (+ 1 (* -1 (/ (pow N 3) (+ 1 (* -1 N))))) (* -1 (/ N (+ 1 (* -1 N))))))>
#<alt (atan2 1 (- (+ 1 (* -1 (/ (pow N 3) (+ 1 (* -1 N))))) (* -1 (/ N (+ 1 (* -1 N))))))>
#<alt (atan2 1 (- (+ 1 (* -1 (/ (pow N 3) (+ 1 (* -1 N))))) (* -1 (/ N (+ 1 (* -1 N))))))>
#<alt 1>
#<alt (+ 1 N)>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (sqrt (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (sqrt (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (sqrt (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (sqrt (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (sqrt (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (sqrt (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (sqrt (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (sqrt (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (sqrt (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (sqrt (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (sqrt (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (sqrt (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt 1>
#<alt (+ 1 N)>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (/ (* (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (atan2 (- 1 (* -2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (* (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (atan2 (- 1 (* -2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (* (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (atan2 (- 1 (* -2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (* (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))) (atan2 (- 1 (* -2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (* (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (atan2 (+ 1 (* 2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (* (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (atan2 (+ 1 (* 2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (* (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (atan2 (+ 1 (* 2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (* (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))) (atan2 (+ 1 (* 2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (* (atan2 1 (- 1 (* N (- (* -1 N) 1)))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (atan2 (- 1 (* -2 N)) (+ 1 (* N (- (* -1 N) 1)))))>
#<alt (/ (* (atan2 1 (- 1 (* N (- (* -1 N) 1)))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (atan2 (- 1 (* -2 N)) (+ 1 (* N (- (* -1 N) 1)))))>
#<alt (/ (* (atan2 1 (- 1 (* N (- (* -1 N) 1)))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (atan2 (- 1 (* -2 N)) (+ 1 (* N (- (* -1 N) 1)))))>
#<alt (/ (* (atan2 1 (- 1 (* N (- (* -1 N) 1)))) (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))) (atan2 (- 1 (* -2 N)) (+ 1 (* N (- (* -1 N) 1)))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (* N (+ 1 N))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))>
#<alt (atan2 (+ 1 (* 2 N)) (- 1 (+ N (pow N 2))))>
#<alt (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 (- 1 (* -2 N)) (- 1 (* N (- 1 (* -1 N)))))>
#<alt 1>
#<alt (+ 1 (* 2 N))>
#<alt (+ 1 (* 2 N))>
#<alt (+ 1 (* 2 N))>
#<alt (* 2 N)>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* 2 N)>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt (* N (+ 2 (/ 1 N)))>
#<alt 1>
#<alt (+ 1 N)>
#<alt (+ 1 N)>
#<alt (+ 1 N)>
#<alt N>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt N>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* N (+ 1 (/ 1 N)))>
#<alt (* -1 N)>
#<alt (* N (- (pow N 2) 1))>
#<alt (* N (- (pow N 2) 1))>
#<alt (* N (- (pow N 2) 1))>
#<alt (pow N 3)>
#<alt (* (pow N 3) (- 1 (/ 1 (pow N 2))))>
#<alt (* (pow N 3) (- 1 (/ 1 (pow N 2))))>
#<alt (* (pow N 3) (- 1 (/ 1 (pow N 2))))>
#<alt (pow N 3)>
#<alt (* -1 (* (pow N 3) (- (/ 1 (pow N 2)) 1)))>
#<alt (* -1 (* (pow N 3) (- (/ 1 (pow N 2)) 1)))>
#<alt (* -1 (* (pow N 3) (- (/ 1 (pow N 2)) 1)))>
#<alt N>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (/ (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (- 1 (* -2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (- 1 (* -2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (- 1 (* -2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (- 1 (* -2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (atan2 1 (- 1 (* -1 (* N (+ 1 N))))) (atan2 (+ 1 (* 2 N)) (+ 1 (* -1 (* N (+ 1 N))))))>
#<alt (/ (atan2 1 (- 1 (* N (- (* -1 N) 1)))) (atan2 (- 1 (* -2 N)) (+ 1 (* N (- (* -1 N) 1)))))>
#<alt (/ (atan2 1 (- 1 (* N (- (* -1 N) 1)))) (atan2 (- 1 (* -2 N)) (+ 1 (* N (- (* -1 N) 1)))))>
#<alt (/ (atan2 1 (- 1 (* N (- (* -1 N) 1)))) (atan2 (- 1 (* -2 N)) (+ 1 (* N (- (* -1 N) 1)))))>
#<alt (/ (atan2 1 (- 1 (* N (- (* -1 N) 1)))) (atan2 (- 1 (* -2 N)) (+ 1 (* N (- (* -1 N) 1)))))>
#<alt (atan2 1 (- 1 (* -1 (* N (+ 1 N)))))>
#<alt (atan2 1 (- 1 (* -1 (* N (+ 1 N)))))>
#<alt (atan2 1 (- 1 (* -1 (* N (+ 1 N)))))>
#<alt (atan2 1 (- 1 (* -1 (* N (+ 1 N)))))>
#<alt (atan2 1 (- 1 (* -1 (* N (+ 1 N)))))>
#<alt (atan2 1 (- 1 (* -1 (* N (+ 1 N)))))>
#<alt (atan2 1 (- 1 (* -1 (* N (+ 1 N)))))>
#<alt (atan2 1 (- 1 (* -1 (* N (+ 1 N)))))>
#<alt (atan2 1 (- 1 (* N (- (* -1 N) 1))))>
#<alt (atan2 1 (- 1 (* N (- (* -1 N) 1))))>
#<alt (atan2 1 (- 1 (* N (- (* -1 N) 1))))>
#<alt (atan2 1 (- 1 (* N (- (* -1 N) 1))))>
#<alt N>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>

Calls

63 calls:

Time	Variable		Point	Expression
14.0ms	N	@	inf	(* (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))) (/ (atan2 1 (- 1 (* N (- -1 N)))) (atan2 (- 1 (* N -2)) (+ 1 (* N (- -1 N))))))
1.0ms	N	@	-inf	(* (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))) (/ (atan2 1 (- 1 (* N (- -1 N)))) (atan2 (- 1 (* N -2)) (+ 1 (* N (- -1 N))))))
1.0ms	N	@	0	(* (atan2 (+ N (+ N 1)) (- 1 (* N (+ N 1)))) (/ (atan2 1 (- 1 (* N (- -1 N)))) (atan2 (- 1 (* N -2)) (+ 1 (* N (- -1 N))))))
1.0ms	N	@	inf	(/ (atan2 1 (- 1 (* N (- -1 N)))) (atan2 (- 1 (* N -2)) (+ 1 (* N (- -1 N)))))
1.0ms	N	@	-inf	(/ (atan2 1 (- 1 (* N (- -1 N)))) (atan2 (- 1 (* N -2)) (+ 1 (* N (- -1 N)))))

rewrite460.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3568×	`-lowering-.f32`
3568×	`-lowering-.f64`
2416×	`+-lowering-+.f64`
2416×	`+-lowering-+.f32`
2342×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	201
1	260	164
2	2349	161
0	9426	161

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 617

Calls

Call 1

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

Outputs
(exp.f64 (log.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))))
(exp.f64 (.f64 (log.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(fabs.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))
(sqrt.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 2 binary64)))
(pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 2 binary64)) (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 2 binary64))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))))))
(.f64 (sqrt.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (sqrt.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))))
(.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)) (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 3/4 binary64)))
(.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 3/4 binary64)) (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
(+.f64 N (+.f64 #s(literal 1 binary64) (*.f64 N N)))
(+.f64 (*.f64 N N) (+.f64 #s(literal 1 binary64) N))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) N)
(+.f64 (+.f64 #s(literal 1 binary64) N) (*.f64 N N))
(+.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))) (-.f64 N N))
(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))) (fma.f64 (-.f64 #s(literal 0 binary64) N) #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) N)))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) (-.f64 #s(literal 0 binary64) N))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N)))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))
(-.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) (/.f64 (.f64 N N) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))))
(fma.f64 #s(literal 1 binary64) N (+.f64 #s(literal 1 binary64) (*.f64 N N)))
(fma.f64 #s(literal 1 binary64) (*.f64 N N) (+.f64 #s(literal 1 binary64) N))
(fma.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(fma.f64 N #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N N)))
(fma.f64 N N (+.f64 #s(literal 1 binary64) N))
(fma.f64 N (+.f64 #s(literal 1 binary64) N) #s(literal 1 binary64))
(fma.f64 (*.f64 N N) #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1 binary64))
(fma.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (.f64 N N))
(fma.f64 (+.f64 (*.f64 N N) #s(literal -1 binary64)) (/.f64 N (+.f64 N #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 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 (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 N N) (+.f64 (.f64 N N) #s(literal -1 binary64))))) N)
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 N N) (+.f64 (.f64 N N) #s(literal -1 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) N)))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) (.f64 N N))
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 N N) (.f64 N N))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N N))) N)
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 N N) (.f64 N N))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N N))) (neg.f64 (-.f64 #s(literal 0 binary64) N)))
(fma.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (.f64 N N))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))))) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (-.f64 #s(literal 0 binary64) (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64)))) #s(literal 1 binary64))
(fma.f64 (pow.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64)) (pow.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N #s(literal 1 binary64))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) N) (+.f64 (.f64 N N) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (+.f64 (.f64 N N) #s(literal -1 binary64))) N #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (.f64 N (.f64 N N)))) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))) #s(literal 1 binary64))
(fma.f64 (/.f64 (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 (*.f64 N N) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) N) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (-.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))) (.f64 N (-.f64 N (+.f64 #s(literal 1 binary64) (.f64 N N))))) (+.f64 (.f64 N (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))))
(/.f64 (+.f64 (.f64 N (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))))) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))) (.f64 N (-.f64 N (+.f64 #s(literal 1 binary64) (.f64 N N))))))
(/.f64 (+.f64 (.f64 N (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))))) (+.f64 (.f64 N N) (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))) (.f64 N (+.f64 #s(literal 1 binary64) (*.f64 N N))))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (-.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N)))))) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N)))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N))))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N)))))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N))))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (-.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (+.f64 (.f64 N (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N)))))) (neg.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))) (.f64 N (-.f64 N (+.f64 #s(literal 1 binary64) (.f64 N N)))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N))) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 (+.f64 #s(literal 1 binary64) N) (+.f64 #s(literal 1 binary64) N)))) (+.f64 (.f64 (.f64 N N) (.f64 N N)) (-.f64 (.f64 (+.f64 #s(literal 1 binary64) N) (+.f64 #s(literal 1 binary64) N)) (.f64 (*.f64 N N) (+.f64 #s(literal 1 binary64) N)))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1 binary64)) (-.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 N N) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N)))) (-.f64 N (+.f64 #s(literal 1 binary64) (*.f64 N N))))
(/.f64 (-.f64 (.f64 (.f64 N N) (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) N) (+.f64 #s(literal 1 binary64) N))) (-.f64 (*.f64 N N) (+.f64 #s(literal 1 binary64) N)))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (-.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N))))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))) (-.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))) (.f64 N (-.f64 N (+.f64 #s(literal 1 binary64) (.f64 N N))))) (+.f64 (.f64 N (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N)))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 N (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N N)) (+.f64 #s(literal 1 binary64) (.f64 N N))) (.f64 N (-.f64 N (+.f64 #s(literal 1 binary64) (*.f64 N N)))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (.f64 (+.f64 #s(literal 1 binary64) N) (.f64 N (.f64 N (+.f64 #s(literal 1 binary64) N)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (-.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))))))
(.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64))))))
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(+.f64 (-.f64 #s(literal 0 binary64) N) (.f64 N (.f64 N N)))
(fma.f64 N (*.f64 N N) (-.f64 #s(literal 0 binary64) N))
(fma.f64 N #s(literal -1 binary64) (.f64 N (.f64 N N)))
(fma.f64 (*.f64 N N) N (-.f64 #s(literal 0 binary64) N))
(fma.f64 #s(literal -1 binary64) N (.f64 N (.f64 N N)))
(fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N))
(/.f64 (.f64 N (+.f64 #s(literal -1 binary64) (.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N))))) (+.f64 (.f64 (.f64 N N) (.f64 N N)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 N N) #s(literal -1 binary64)))))
(/.f64 (.f64 N (+.f64 (.f64 (.f64 N N) (.f64 N N)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N N)))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N)))) N) (+.f64 (.f64 (.f64 N N) (.f64 N N)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 N N) #s(literal -1 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 N N) (.f64 N N)) #s(literal -1 binary64)) N) (+.f64 #s(literal 1 binary64) (*.f64 N N)))
(.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64)))
(.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N)
(.f64 (+.f64 #s(literal 1 binary64) N) (.f64 (+.f64 N #s(literal -1 binary64)) N))
(.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (+.f64 N #s(literal -1 binary64)))
(+.f64 N (*.f64 N N))
(+.f64 (*.f64 N N) N)
(exp.f64 (log.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N))))
(fma.f64 #s(literal 1 binary64) N (*.f64 N N))
(fma.f64 #s(literal 1 binary64) (*.f64 N N) N)
(fma.f64 N #s(literal 1 binary64) (*.f64 N N))
(fma.f64 N N N)
(fma.f64 (*.f64 N N) #s(literal 1 binary64) N)
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
(/.f64 (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 N #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) N))
(/.f64 (.f64 (.f64 N N) (+.f64 (.f64 N N) #s(literal -1 binary64))) (.f64 N (+.f64 N #s(literal -1 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64)))))
(/.f64 (+.f64 (.f64 N (.f64 N N)) (.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N)))) (+.f64 (.f64 N N) (-.f64 (.f64 (.f64 N N) (.f64 N N)) (.f64 N (*.f64 N N)))))
(/.f64 (+.f64 (.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N))) (.f64 N (.f64 N N))) (+.f64 (.f64 (.f64 N N) (.f64 N N)) (-.f64 (.f64 N N) (.f64 N (*.f64 N N)))))
(/.f64 (.f64 N (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N)))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))
(/.f64 (.f64 N (-.f64 #s(literal 1 binary64) (.f64 N N))) (-.f64 #s(literal 1 binary64) N))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64)))) (+.f64 N #s(literal -1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) N))
(/.f64 (-.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N))) (-.f64 N (*.f64 N N)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))) #s(literal -1 binary64))
(pow.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))) (/.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))
(*.f64 N (+.f64 #s(literal 1 binary64) N))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))))
(.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) (/.f64 N (+.f64 N #s(literal -1 binary64))))
(.f64 (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) N) N)
(*.f64 (+.f64 #s(literal 1 binary64) N) (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)))
(.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (-.f64 #s(literal 0 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))))) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N)
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) N) (+.f64 (*.f64 N N) #s(literal -1 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (+.f64 (*.f64 N N) #s(literal -1 binary64))) N)
(.f64 (/.f64 (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (.f64 N (.f64 N N)))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))
(.f64 (/.f64 (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) N))
(exp.f64 (.f64 (log.f64 (/.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (-.f64 #s(literal 0 binary64) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N)))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N))))) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
(/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N)))))))
(/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N)))))
(/.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N))))) (-.f64 #s(literal 0 binary64) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N)))))))
(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) #s(literal 1 binary64)) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))))
(pow.f64 (/.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N))))))
(.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N))))))
(.f64 (-.f64 #s(literal 0 binary64) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))))))
(.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N))))) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))))
(.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 #s(literal 1 binary64) (.f64 N #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N))))) (pow.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N))))) #s(literal -1 binary64)))
(atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))
(+.f64 N (*.f64 N N))
(+.f64 (*.f64 N N) N)
(exp.f64 (log.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N))))
(fma.f64 #s(literal 1 binary64) N (*.f64 N N))
(fma.f64 #s(literal 1 binary64) (*.f64 N N) N)
(fma.f64 N #s(literal 1 binary64) (*.f64 N N))
(fma.f64 N N N)
(fma.f64 (*.f64 N N) #s(literal 1 binary64) N)
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
(/.f64 (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 N #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) N))
(/.f64 (.f64 (.f64 N N) (+.f64 (.f64 N N) #s(literal -1 binary64))) (.f64 N (+.f64 N #s(literal -1 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64)))))
(/.f64 (+.f64 (.f64 N (.f64 N N)) (.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N)))) (+.f64 (.f64 N N) (-.f64 (.f64 (.f64 N N) (.f64 N N)) (.f64 N (*.f64 N N)))))
(/.f64 (+.f64 (.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N))) (.f64 N (.f64 N N))) (+.f64 (.f64 (.f64 N N) (.f64 N N)) (-.f64 (.f64 N N) (.f64 N (*.f64 N N)))))
(/.f64 (.f64 N (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N)))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))
(/.f64 (.f64 N (-.f64 #s(literal 1 binary64) (.f64 N N))) (-.f64 #s(literal 1 binary64) N))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64)))) (+.f64 N #s(literal -1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) N) (-.f64 #s(literal 1 binary64) N))
(/.f64 (-.f64 (.f64 N N) (.f64 (.f64 N N) (.f64 N N))) (-.f64 N (*.f64 N N)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))) #s(literal -1 binary64))
(pow.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))) (/.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))
(*.f64 N (+.f64 #s(literal 1 binary64) N))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))))
(.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) (/.f64 N (+.f64 N #s(literal -1 binary64))))
(.f64 (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))))
(*.f64 (+.f64 #s(literal 1 binary64) N) N)
(*.f64 (+.f64 #s(literal 1 binary64) N) (pow.f64 (/.f64 #s(literal 1 binary64) N) #s(literal -1 binary64)))
(.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (-.f64 #s(literal 0 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) N)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 N (+.f64 (*.f64 N N) #s(literal -1 binary64))))) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 N (+.f64 #s(literal 1 binary64) N)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N)
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) N) (+.f64 (*.f64 N N) #s(literal -1 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) (+.f64 (*.f64 N N) #s(literal -1 binary64))) N)
(.f64 (/.f64 (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 #s(literal -1 binary64) (.f64 N (.f64 N N)))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))
(.f64 (/.f64 (.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 (.f64 N N) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) N))

simplify211.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2554×	`-lowering-.f32`
2554×	`-lowering-.f64`
1464×	`fmsub-define`
1380×	`+-lowering-+.f64`
1380×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	2010
1	308	1519
2	755	1509
3	2713	1507
0	8435	1507

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

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

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

eval176.0ms (2.1%)

Compiler: Compiled 23151 to 1879 computations (91.9% saved)

prune97.0ms (1.1%)

Pruning

29 alts after pruning (26 fresh and 3 done)

	Pruned	Kept	Total
New	916	13	929
Fresh	5	13	18
Picked	3	2	5
Done	0	1	1
Total	924	29	953

Accuracy

100.0%

Counts

953 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(pow.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
	98.6%	(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)) #s(literal 4 binary64))
	91.6%	(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (*.f64 N N)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
▶	78.9%	(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))) #s(literal -1/2 binary64))
	99.1%	(pow.f64 (sqrt.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))) #s(literal 2 binary64))
	78.7%	(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 N N) (.f64 N N))))) N))
✓	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) N))
	95.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) N))
▶	78.7%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))
	99.4%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 N (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)))))
▶	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N))))
▶	99.0%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N))))))
	95.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 N (.f64 N N))))))
	99.4%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) N) (+.f64 (*.f64 N N) #s(literal -1 binary64)))))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
	95.5%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
▶	92.0%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
✓	6.5%	(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))
	78.5%	(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))
	99.2%	(.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
	99.4%	(.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 3/4 binary64)) (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)))
	92.1%	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
	95.7%	(.f64 (atan2.f64 (+.f64 N N) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
	92.1%	(.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
	99.2%	(.f64 (/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (atan.f64 N) #s(literal 3 binary64)))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (-.f64 N (+.f64 N #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))))
	98.8%	(.f64 (+.f64 (pow.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
	98.8%	(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
	92.3%	(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
	92.4%	(exp.f64 (log.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))

Compiler

Compiled 1392 to 659 computations (52.7% saved)

simplify164.0ms (1.9%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N))))))
✓	cost-diff	256	(/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N)))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N))))
✓	cost-diff	19200	(fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))
✓	cost-diff	0	(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))) #s(literal -1/2 binary64))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1 binary64) (.f64 N (*.f64 N N))) N)
✓	cost-diff	0	(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N))))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))
✓	cost-diff	0	(*.f64 N N)
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N)))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N))))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N))

Rules

2800×	`sum5-define`
2488×	`sum3-define`
1656×	`sum4-define`
1578×	`-lowering-.f32`
1578×	`-lowering-.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	245
1	92	201
2	169	195
3	440	195
4	1273	195
5	2637	195
6	7069	195
0	8240	195

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(atan2 1 (+ 1 (/ 1 (/ (/ 1 (+ 1 N)) N))))
1
(+ 1 (/ 1 (/ (/ 1 (+ 1 N)) N)))
(/ 1 (/ (/ 1 (+ 1 N)) N))
(/ (/ 1 (+ 1 N)) N)
(/ 1 (+ 1 N))
(+ 1 N)
N
(atan2 1 (* N N))
1
(* N N)
N
(atan2 1 (+ 1 (/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N)))))
1
(+ 1 (/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N))))
(/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N)))
(* (+ 1 (* N (* N N))) N)
(+ 1 (* N (* N N)))
(* N (* N N))
N
(* N N)
(+ (* N N) (- 1 N))
(- 1 N)
(pow (* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))) -1/2)
(* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))
(/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))
1
(atan2 1 (+ 1 (* N (+ 1 N))))
(+ 1 (* N (+ 1 N)))
(* N (+ 1 N))
N
(+ 1 N)
-1/2
(atan2 1 (+ 1 (/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))))))
1
(+ 1 (/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N)))))
(/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))))
(/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N)))
(+ N -1)
N
-1
(+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))
(pow N 3/2)
3/2
(- 0 N)
0

Outputs
(atan2 1 (+ 1 (/ 1 (/ (/ 1 (+ 1 N)) N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
1
#s(literal 1 binary64)
(+ 1 (/ 1 (/ (/ 1 (+ 1 N)) N)))
(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
(/ 1 (/ (/ 1 (+ 1 N)) N))
(*.f64 N (+.f64 #s(literal 1 binary64) N))
(/ (/ 1 (+ 1 N)) N)
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N)
(/ 1 (+ 1 N))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N))
(+ 1 N)
(+.f64 #s(literal 1 binary64) N)
N
(atan2 1 (* N N))
(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
1
#s(literal 1 binary64)
(* N N)
(*.f64 N N)
N
(atan2 1 (+ 1 (/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64)))) N))))
1
#s(literal 1 binary64)
(+ 1 (/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N))))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64)))) N)))
(/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N)))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64)))) N))
(* (+ 1 (* N (* N N))) N)
(.f64 N (+.f64 #s(literal 1 binary64) (.f64 N (*.f64 N N))))
(+ 1 (* N (* N N)))
(+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N)))
(* N (* N N))
(.f64 N (.f64 N N))
N
(* N N)
(*.f64 N N)
(+ (* N N) (- 1 N))
(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64))))
(- 1 N)
(-.f64 #s(literal 1 binary64) N)
(pow (* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))) -1/2)
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))) #s(literal -1/2 binary64))
(* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))
(/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))))
(/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))
(/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))
1
#s(literal 1 binary64)
(atan2 1 (+ 1 (* N (+ 1 N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
(+ 1 (* N (+ 1 N)))
(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
(* N (+ 1 N))
(*.f64 N (+.f64 #s(literal 1 binary64) N))
N
(+ 1 N)
(+.f64 #s(literal 1 binary64) N)
-1/2
#s(literal -1/2 binary64)
(atan2 1 (+ 1 (/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
1
#s(literal 1 binary64)
(+ 1 (/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N)))))
(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
(/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))))
(*.f64 N (+.f64 #s(literal 1 binary64) N))
(/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N)))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N)
(+ N -1)
(+.f64 N #s(literal -1 binary64))
N
-1
#s(literal -1 binary64)
(+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))
(.f64 N (+.f64 (.f64 N N) #s(literal -1 binary64)))
(pow N 3/2)
(pow.f64 N #s(literal 3/2 binary64))
3/2
#s(literal 3/2 binary64)
(- 0 N)
(-.f64 #s(literal 0 binary64) N)
0
#s(literal 0 binary64)

localize281.0ms (3.3%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N))))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N))))))
✓	accuracy	99.2%	(fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))
✓	accuracy	99.3%	(.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))))
✓	accuracy	79.0%	(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))) #s(literal -1/2 binary64))
✓	accuracy	99.8%	(.f64 (+.f64 #s(literal 1 binary64) (.f64 N (*.f64 N N))) N)
✓	accuracy	99.6%	(.f64 N (.f64 N N))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))
✓	accuracy	78.6%	(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))
✓	accuracy	100.0%	(*.f64 N N)
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N))
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N))))

Results

155.0ms

256×

valid

Compiler

Compiled 333 to 37 computations (88.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-pow: 21.0ms (29.1% of total)

ival-div: 12.0ms (16.6% of total)

ival-add: 12.0ms (16.6% of total)

ival-mult: 11.0ms (15.2% of total)

ival-atan2: 9.0ms (12.5% of total)

compiled-spec: 4.0ms (5.5% of total)

ival-sub: 3.0ms (4.2% of total)

const: 1.0ms (1.4% of total)

backward-pass: 0.0ms (0% of total)

series16.0ms (0.2%)

Counts

20 → 240

Calls

Call 1

Inputs
#<alt (/ 1 (/ (/ 1 (+ 1 N)) N))>
#<alt (atan2 1 (+ 1 (/ 1 (/ (/ 1 (+ 1 N)) N))))>
#<alt (+ 1 (/ 1 (/ (/ 1 (+ 1 N)) N)))>
#<alt (/ (/ 1 (+ 1 N)) N)>
#<alt (atan2 1 (* N N))>
#<alt (* N N)>
#<alt (atan2 1 (+ 1 (/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N)))))>
#<alt (+ 1 (/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N))))>
#<alt (/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N)))>
#<alt (* (+ 1 (* N (* N N))) N)>
#<alt (* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))>
#<alt (pow (* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))) -1/2)>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))>
#<alt (/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))))>
#<alt (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N)))>
#<alt (atan2 1 (+ 1 (/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))))))>
#<alt (/ 1 (+ 1 N))>
#<alt (* N (* N N))>

Outputs
#<alt N>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt 1>
#<alt (+ 1 N)>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (/ 1 N)>
#<alt (/ (+ 1 (* -1 N)) N)>
#<alt (/ (+ 1 (* N (- N 1))) N)>
#<alt (/ (+ 1 (* N (- (* N (+ 1 (* -1 N))) 1))) N)>
#<alt (/ 1 (pow N 2))>
#<alt (/ (- 1 (/ 1 N)) (pow N 2))>
#<alt (/ (- (+ 1 (/ 1 (pow N 2))) (/ 1 N)) (pow N 2))>
#<alt (/ (- (+ 1 (/ 1 (pow N 2))) (+ (/ 1 N) (/ 1 (pow N 3)))) (pow N 2))>
#<alt (/ 1 (pow N 2))>
#<alt (/ (- 1 (/ 1 N)) (pow N 2))>
#<alt (/ (+ 1 (* -1 (/ (- 1 (/ 1 N)) N))) (pow N 2))>
#<alt (/ (+ 1 (* -1 (/ (+ 1 (* -1 (/ (- 1 (/ 1 N)) N))) N))) (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (atan2 1 (pow N 2))>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (pow N 2)>
#<alt (atan2 1 (+ 1 (/ (* N (+ 1 (pow N 3))) (- (+ 1 (pow N 2)) N))))>
#<alt (atan2 1 (+ 1 (/ (* N (+ 1 (pow N 3))) (- (+ 1 (pow N 2)) N))))>
#<alt (atan2 1 (+ 1 (/ (* N (+ 1 (pow N 3))) (- (+ 1 (pow N 2)) N))))>
#<alt (atan2 1 (+ 1 (/ (* N (+ 1 (pow N 3))) (- (+ 1 (pow N 2)) N))))>
#<alt (atan2 1 (+ 1 (+ (/ N (- (+ 1 (pow N 2)) N)) (/ (pow N 4) (- (+ 1 (pow N 2)) N)))))>
#<alt (atan2 1 (+ 1 (+ (/ N (- (+ 1 (pow N 2)) N)) (/ (pow N 4) (- (+ 1 (pow N 2)) N)))))>
#<alt (atan2 1 (+ 1 (+ (/ N (- (+ 1 (pow N 2)) N)) (/ (pow N 4) (- (+ 1 (pow N 2)) N)))))>
#<alt (atan2 1 (+ 1 (+ (/ N (- (+ 1 (pow N 2)) N)) (/ (pow N 4) (- (+ 1 (pow N 2)) N)))))>
#<alt (atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))>
#<alt (atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))>
#<alt (atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))>
#<alt (atan2 1 (+ 1 (/ (* N (- 1 (* -1 (pow N 3)))) (+ 1 (+ (* -1 N) (pow N 2))))))>
#<alt 1>
#<alt (+ 1 N)>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (+ 1 (* N (+ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt (* (pow N 2) (+ 1 (+ (/ 1 N) (/ 1 (pow N 2)))))>
#<alt N>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt N>
#<alt (* N (+ 1 (pow N 3)))>
#<alt (* N (+ 1 (pow N 3)))>
#<alt (* N (+ 1 (pow N 3)))>
#<alt (pow N 4)>
#<alt (* (pow N 4) (+ 1 (/ 1 (pow N 3))))>
#<alt (* (pow N 4) (+ 1 (/ 1 (pow N 3))))>
#<alt (* (pow N 4) (+ 1 (/ 1 (pow N 3))))>
#<alt (pow N 4)>
#<alt (* (pow N 4) (+ 1 (/ 1 (pow N 3))))>
#<alt (* (pow N 4) (+ 1 (/ 1 (pow N 3))))>
#<alt (* (pow N 4) (+ 1 (/ 1 (pow N 3))))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (* N (+ 1 N)))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (* N (+ 1 N)))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (* N (+ 1 N)))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (* N (+ 1 N)))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (+ N (pow N 2)))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (+ N (pow N 2)))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (+ N (pow N 2)))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (+ N (pow N 2)))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) 2))>
#<alt (/ 1 (pow (atan2 1 (+ 1 (* N (- 1 (* -1 N))))) 2))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))>
#<alt (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 1 (+ 1 (+ N (pow N 2)))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (/ 1 (atan2 1 (+ 1 (* N (- 1 (* -1 N))))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (* N (+ 1 N))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (+ N (pow N 2))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (atan2 1 (+ 1 (* N (- 1 (* -1 N)))))>
#<alt (* -1 N)>
#<alt (* N (- (pow N 2) 1))>
#<alt (* N (- (pow N 2) 1))>
#<alt (* N (- (pow N 2) 1))>
#<alt (pow N 3)>
#<alt (* (pow N 3) (- 1 (/ 1 (pow N 2))))>
#<alt (* (pow N 3) (- 1 (/ 1 (pow N 2))))>
#<alt (* (pow N 3) (- 1 (/ 1 (pow N 2))))>
#<alt (* -1 (* (pow N 3) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (pow N 3) (+ (/ 1 (pow N 2)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* (pow N 3) (+ (/ 1 (pow N 2)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* (pow N 3) (+ (/ 1 (pow N 2)) (pow (sqrt -1) 2))))>
#<alt N>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (* N (+ 1 N))>
#<alt (pow N 2)>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* (pow N 2) (+ 1 (/ 1 N)))>
#<alt (* -1 (* (pow N 2) (pow (sqrt -1) 2)))>
#<alt (* (pow N 2) (+ (* -1 (/ (pow (sqrt -1) 2) N)) (* -1 (pow (sqrt -1) 2))))>
#<alt (* (pow N 2) (+ (* -1 (/ (- (+ (/ 1 N) (pow (sqrt -1) 2)) (* -1 (/ (pow (sqrt -1) 2) N))) N)) (* -1 (pow (sqrt -1) 2))))>
#<alt (* (pow N 2) (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (- 1 (* -1 (pow (sqrt -1) 2)))) (* -1 (/ (pow (sqrt -1) 2) N))) (/ 1 N)) N)) (pow (sqrt -1) 2)) N)) (* -1 (pow (sqrt -1) 2))))>
#<alt (/ 1 N)>
#<alt (/ (+ 1 (* -1 N)) N)>
#<alt (/ (+ 1 (* N (- N 1))) N)>
#<alt (/ (+ 1 (* N (- (* N (+ 1 (* -1 N))) 1))) N)>
#<alt (/ 1 (pow N 2))>
#<alt (/ (- 1 (/ 1 N)) (pow N 2))>
#<alt (/ (- (+ 1 (/ 1 (pow N 2))) (/ 1 N)) (pow N 2))>
#<alt (/ (- (+ 1 (/ 1 (pow N 2))) (+ (/ 1 N) (/ 1 (pow N 3)))) (pow N 2))>
#<alt (/ -1 (* (pow N 2) (pow (sqrt -1) 2)))>
#<alt (/ (- (/ 1 (* N (pow (sqrt -1) 2))) (/ 1 (pow (sqrt -1) 2))) (pow N 2))>
#<alt (/ (- (+ (/ 1 (* N (pow (sqrt -1) 2))) (/ 1 (* (pow N 2) (pow (sqrt -1) 4)))) (/ 1 (pow (sqrt -1) 2))) (pow N 2))>
#<alt (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 (pow (sqrt -1) 4)) (/ 1 (* N (pow (sqrt -1) 4)))) N)) (/ 1 (pow (sqrt -1) 2))) N)) (/ 1 (pow (sqrt -1) 2))) (pow N 2))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (- (+ 1 (/ (pow N 3) (- N 1))) (/ N (- N 1))))>
#<alt (atan2 1 (+ 1 (* -1 (/ (+ (* -1 N) (* -1 (* (pow N 3) (pow (sqrt -1) 2)))) (+ 1 (* -1 N))))))>
#<alt (atan2 1 (+ 1 (* -1 (/ (+ (* -1 N) (* -1 (* (pow N 3) (pow (sqrt -1) 2)))) (+ 1 (* -1 N))))))>
#<alt (atan2 1 (+ 1 (* -1 (/ (+ (* -1 N) (* -1 (* (pow N 3) (pow (sqrt -1) 2)))) (+ 1 (* -1 N))))))>
#<alt (atan2 1 (+ 1 (* -1 (/ (+ (* -1 N) (* -1 (* (pow N 3) (pow (sqrt -1) 2)))) (+ 1 (* -1 N))))))>
#<alt 1>
#<alt (+ 1 (* -1 N))>
#<alt (+ 1 (* N (- N 1)))>
#<alt (+ 1 (* N (- (* N (+ 1 (* -1 N))) 1)))>
#<alt (/ 1 N)>
#<alt (/ (- 1 (/ 1 N)) N)>
#<alt (/ (- (+ 1 (/ 1 (pow N 2))) (/ 1 N)) N)>
#<alt (/ (- (+ 1 (/ 1 (pow N 2))) (+ (/ 1 N) (/ 1 (pow N 3)))) N)>
#<alt (/ 1 N)>
#<alt (* -1 (/ (- (/ 1 N) 1) N))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ 1 N) 1) N)) 1) N))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 N) 1) N)) 1) N)) 1) N))>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>
#<alt (pow N 3)>

Calls

60 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))
1.0ms	N	@	inf	(* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))
1.0ms	N	@	0	(* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))
1.0ms	N	@	-inf	(+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))
0.0ms	N	@	-inf	(/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))))

rewrite230.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1852×	`prod-diff`
1758×	`-lowering-.f32`
1758×	`-lowering-.f64`
1722×	`fma-lowering-fma.f32`
1722×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	165
1	263	122
2	2471	122
0	9391	122

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 769

Calls

Call 1

Inputs
(/ 1 (/ (/ 1 (+ 1 N)) N))
(atan2 1 (+ 1 (/ 1 (/ (/ 1 (+ 1 N)) N))))
(+ 1 (/ 1 (/ (/ 1 (+ 1 N)) N)))
(/ (/ 1 (+ 1 N)) N)
(atan2 1 (* N N))
(* N N)
(atan2 1 (+ 1 (/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N)))))
(+ 1 (/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N))))
(/ (* (+ 1 (* N (* N N))) N) (+ (* N N) (- 1 N)))
(* (+ 1 (* N (* N N))) N)
(* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))))
(pow (* (/ 1 (atan2 1 (+ 1 (* N (+ 1 N))))) (/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))) -1/2)
(/ 1 (atan2 1 (+ 1 (* N (+ 1 N)))))
(atan2 1 (+ 1 (* N (+ 1 N))))
(+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))
(/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))))
(/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N)))
(atan2 1 (+ 1 (/ 1 (/ (+ N -1) (+ (* (pow N 3/2) (pow N 3/2)) (- 0 N))))))
(/ 1 (+ 1 N))
(* N (* N N))

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

simplify219.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

2840×	`-lowering-.f32`
2840×	`-lowering-.f64`
1816×	`sum3-define`
1472×	`/-lowering-/.f32`
1472×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1953
1	505	1599
2	1617	1547
3	6781	1547
0	8227	1547

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

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

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

eval153.0ms (1.8%)

Compiler: Compiled 25018 to 2758 computations (89% saved)

prune167.0ms (2%)

Pruning

31 alts after pruning (26 fresh and 5 done)

	Pruned	Kept	Total
New	1152	9	1161
Fresh	4	17	21
Picked	3	2	5
Done	0	3	3
Total	1159	31	1190

Accuracy

100.0%

Counts

1190 → 31

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(pow.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
	98.6%	(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)) #s(literal 4 binary64))
	91.6%	(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (*.f64 N N)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
	71.0%	(pow.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64)))))) #s(literal 2 binary64)) #s(literal -1/2 binary64))
	71.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))))) #s(literal -1/2 binary64))
	71.2%	(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64))))) #s(literal -1/2 binary64)) #s(literal -1 binary64))))) #s(literal -1/2 binary64))
	99.1%	(pow.f64 (sqrt.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))) #s(literal 2 binary64))
	91.9%	(atan2.f64 #s(literal 1 binary64) (/.f64 (.f64 N (.f64 N N)) N))
	78.7%	(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 N N) (.f64 N N))))) N))
✓	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) N))
	95.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) N))
	75.9%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 N (.f64 N (.f64 N N))) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))
	99.4%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 N (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)))))
✓	99.5%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N))))
	91.9%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
	95.0%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 9/4 binary64)) (pow.f64 N #s(literal 3/4 binary64)) N)))))
	95.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 N (.f64 N N))))))
	99.4%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) N) (+.f64 (*.f64 N N) #s(literal -1 binary64)))))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
	95.5%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))
✓	92.0%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
✓	6.5%	(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))
	91.4%	(.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64))))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
	99.4%	(.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 3/4 binary64)) (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)))
	92.1%	(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
	95.7%	(.f64 (atan2.f64 (+.f64 N N) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
	92.1%	(.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
	99.2%	(.f64 (/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (atan.f64 N) #s(literal 3 binary64)))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (-.f64 N (+.f64 N #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))))
	98.8%	(.f64 (+.f64 (pow.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
	92.3%	(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
	92.4%	(exp.f64 (log.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))

Compiler

Compiled 2058 to 560 computations (72.8% saved)

regimes32.0ms (0.4%)

Counts

55 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) N))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 N N)) N))
(atan2.f64 #s(literal 1 binary64) (/.f64 (.f64 N (.f64 N N)) N))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) N) N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 N (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) N)) N))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 N (.f64 N N))))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N) (+.f64 N #s(literal -1 binary64)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 N #s(literal -1 binary64))) N) (+.f64 (*.f64 N N) #s(literal -1 binary64)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (.f64 (+.f64 (.f64 N N) #s(literal -1 binary64)) N)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 N (.f64 N (.f64 N N))) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 N N)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 N N) (.f64 N N))))) N))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) (-.f64 #s(literal 1 binary64) N)))))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 N N) N) (.f64 (.f64 N (+.f64 #s(literal 1 binary64) N)) (-.f64 (.f64 N N) N))))))
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (*.f64 N N)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(exp.f64 (log.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
(pow.f64 (sqrt.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N))))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64)))))) #s(literal 2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64)))))))) #s(literal -1/2 binary64))
(.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))
(.f64 (atan2.f64 (+.f64 N N) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
(.f64 (atan2.f64 (+.f64 N N) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))
(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (-.f64 #s(literal -1 binary64) N)))) (atan2.f64 (-.f64 #s(literal 1 binary64) (.f64 N #s(literal -2 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 N (-.f64 #s(literal -1 binary64) N))))))
(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))))
(.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))
(/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 N (.f64 N N))) N) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 N N) (-.f64 #s(literal 1 binary64) N)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))
(pow.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 9/4 binary64)) (pow.f64 N #s(literal 3/4 binary64)) N)))))
(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 N #s(literal -1 binary64)) (fma.f64 (pow.f64 N #s(literal 3/2 binary64)) (pow.f64 N #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) N))))))
(.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 3/4 binary64)) (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal 1/4 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64))))) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N))))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal -1 binary64))))) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal -1 binary64))))) #s(literal -1/2 binary64)) #s(literal -1 binary64))))) #s(literal -1/2 binary64))
(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))))))
(.f64 (/.f64 (.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (atan.f64 N) #s(literal 3 binary64)))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (-.f64 N (+.f64 N #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))))
(.f64 (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))
(.f64 (+.f64 (pow.f64 (pow.f64 (sqrt.f64 (atan.f64 (+.f64 #s(literal 1 binary64) N))) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))))) (/.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (+.f64 (pow.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (atan.f64 N) (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64)))))))))

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

Calls

2 calls:

15.0ms	N
14.0ms	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

Accuracy	Segments	Branch
99.6%	1	`N`
99.6%	1	`(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
95.5%	1	`N`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
92.0%	1	`N`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Outputs
(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
6.5%	1	`N`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	18	24

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness599.0ms (7%)

Rules

2864×	`-lowering-.f32`
2864×	`-lowering-.f64`
2066×	`pow-lowering-pow.f64`
2066×	`pow-lowering-pow.f32`
2038×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	2809
1	187	2272
2	358	2272
3	947	2272
4	4592	2272
0	8044	2272
0	6	16
1	42	16
2	295	16
3	3184	16
0	8281	16

Stop Event

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

Compiler

Compiled 83 to 46 computations (44.6% saved)

preprocess39.0ms (0.5%)

Compiler: Compiled 88 to 46 computations (47.7% saved)

Iter	Nodes	Cost
0	6	18
1	13	18
2	17	18
3	24	18
4	34	18
5	66	18
6	124	18
7	212	18
8	297	18
9	403	18
10	481	18
11	487	18
0	487	18

Iter	Nodes	Cost
0	6	18
1	13	18
2	17	18
3	24	18
4	34	18
5	66	18
6	124	18
7	212	18
8	297	18
9	403	18
10	481	18
11	487	18
0	487	18

analyze3.0ms (0%)

sample2.0s (23.7%)

preprocess43.0ms (0.5%)

explain145.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify19.0ms (0.2%)

localize74.0ms (0.9%)

series1.0ms (0%)

rewrite329.0ms (3.9%)

simplify36.0ms (0.4%)

eval26.0ms (0.3%)

prune30.0ms (0.4%)

simplify228.0ms (2.7%)

localize235.0ms (2.8%)

series108.0ms (1.3%)

rewrite519.0ms (6.1%)

simplify224.0ms (2.6%)

eval668.0ms (7.9%)

prune454.0ms (5.3%)

simplify198.0ms (2.3%)

localize264.0ms (3.1%)

series28.0ms (0.3%)

rewrite460.0ms (5.4%)

simplify211.0ms (2.5%)

eval176.0ms (2.1%)

prune97.0ms (1.1%)

simplify164.0ms (1.9%)

localize281.0ms (3.3%)

series16.0ms (0.2%)

rewrite230.0ms (2.7%)

simplify219.0ms (2.6%)

eval153.0ms (1.8%)

prune167.0ms (2%)

regimes32.0ms (0.4%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

simplify7.0ms (0.1%)

soundness599.0ms (7%)

preprocess39.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	18
1	13	18
2	17	18
3	24	18
4	34	18
5	66	18
6	124	18
7	212	18
8	297	18
9	403	18
10	481	18
11	487	18
0	487	18