Metrics for 2atan (example 3.5)

analyze3.0ms (0.1%)

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)

sample1.8s (41%)

Results

1.3s	7355×	1	valid
161.0ms	641×	2	valid
22.0ms	260×	0	valid

Precisions

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

ival-atan: 347.0ms (34% of total)

backward-pass: 173.0ms (16.9% of total)

...c/correct-round.rkt:119:19: 123.0ms (12% of total)

ival-add: 123.0ms (12% of total)

ival-sub: 92.0ms (9% of total)

ival->: 82.0ms (8% of total)

ival-and: 34.0ms (3.3% of total)

ival-<: 32.0ms (3.1% of total)

const: 16.0ms (1.6% of total)

Bogosity

preprocess40.0ms (0.9%)

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	25	24
2	52	23
3	99	23
4	190	23
5	387	23
6	579	23
7	755	23
8	849	23
9	955	23
10	1033	23
11	1039	23
0	6	7
1	11	7
2	15	7
3	22	7
4	32	7
5	64	7
6	122	7
7	210	7
8	295	7
9	401	7
10	479	7
11	485	7
0	485	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)))

explain177.0ms (4.1%)

FPErrors

Click to see full error table

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

Results

130.0ms	452×	1	valid
15.0ms	48×	2	valid
1.0ms	12×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-add: 27.0ms (38.4% of total)

ival-atan: 23.0ms (32.7% of total)

backward-pass: 13.0ms (18.5% of total)

ival-sub: 6.0ms (8.5% of total)

const: 1.0ms (1.4% 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
▶	7.5%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify14.0ms (0.3%)

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	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	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)

localize67.0ms (1.5%)

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	7.5%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

49.0ms	226×	1	valid
7.0ms	24×	2	valid
1.0ms	6×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-atan: 11.0ms (44.7% of total)

backward-pass: 6.0ms (24.4% of total)

ival-add: 4.0ms (16.3% of total)

ival-sub: 3.0ms (12.2% of total)

const: 1.0ms (4.1% 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)

rewrite179.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1896×	`sum5-define`
1840×	`fnmadd-define`
1836×	`fma-lowering-fma.f32`
1836×	`fma-lowering-fma.f64`
1790×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	15	16
2	27	16
3	54	16
4	91	16
5	171	16
6	288	16
7	477	16
8	2204	16
9	3650	16
10	6570	16
0	8423	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 278

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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))
(+.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))) #s(literal 0 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))))))
(+.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(+.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (-.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 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (.f64 (-.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)))))) #s(literal 1 binary64)))
(+.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 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))))) #s(literal -1 binary64)))
(+.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))))
(+.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (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)))))))
(+.f64 (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)))
(+.f64 (-.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 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(+.f64 (+.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)))
(+.f64 (-.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))) (atan.f64 N)) (atan.f64 N))
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.f64 (atan.f64 N) (*.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))))) #s(literal 0 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))))))
(-.f64 (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)) (atan.f64 (+.f64 N #s(literal 1 binary64))))
(-.f64 (.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 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (+.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))))
(-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 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)))))))
(-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.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 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(-.f64 (-.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 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)))
(-.f64 (+.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(-.f64 (-.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))) (atan.f64 N)) (-.f64 #s(literal 0 binary64) (atan.f64 N)))
(fma.f64 #s(literal 1 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (atan.f64 N)))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 N)) (atan.f64 (+.f64 N #s(literal 1 binary64))))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))
(fma.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 0 binary64))
(fma.f64 #s(literal 1 binary64) (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (-.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)))))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (neg.f64 (+.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))))))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (neg.f64 (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.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)))))))))
(fma.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)))
(fma.f64 #s(literal 1 binary64) (-.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 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 N)))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -1 binary64) (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64) (-.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)))))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64) (neg.f64 (+.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))))))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64) (neg.f64 (-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.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)))))))))
(fma.f64 (atan.f64 N) #s(literal -1 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) #s(literal 1 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))
(fma.f64 #s(literal -1 binary64) (atan.f64 N) (atan.f64 (+.f64 N #s(literal 1 binary64))))
(fma.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 0 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) (atan.f64 N)))
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(atan.f64 (+.f64 N #s(literal 1 binary64)))
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(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 1 binary64) #s(literal 0 binary64))
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(fma.f64 (atan.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))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.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))))))
(fma.f64 #s(literal -1 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 N)) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))
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(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #s(literal 0 binary64))
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(+.f64 (-.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
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(+.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(+.f64 (+.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)))
(+.f64 (.f64 (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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(+.f64 (.f64 (-.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)))))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(+.f64 (+.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)))
(+.f64 (+.f64 (atan2.f64 (+.f64 N (+.f64 N #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (.f64 N (+.f64 N #s(literal 1 binary64))))) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)))
(+.f64 (+.f64 (atan.f64 N) (atan.f64 N)) (-.f64 #s(literal 0 binary64) (atan.f64 N)))
(+.f64 (-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)))
(-.f64 (atan.f64 (+.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 (atan.f64 N) #s(literal 0 binary64))
(-.f64 (atan2.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.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 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 N)))
(-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))
(-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (+.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.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 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (+.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))))))
(-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (-.f64 (-.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)))))) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (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)))))))
(-.f64 (-.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)))
(-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))))
(-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (+.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 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))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))
(-.f64 (+.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64)))
(-.f64 (+.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(-.f64 (+.f64 (atan.f64 N) (atan.f64 N)) (atan.f64 N))
(-.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(-.f64 (-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (atan.f64 N))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(atan.f64 N)
(fma.f64 #s(literal 1 binary64) (atan.f64 (+.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))))))
(fma.f64 #s(literal 1 binary64) (atan.f64 N) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (atan2.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))
(fma.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (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))))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.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)))))))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (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))))))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (neg.f64 (+.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (neg.f64 (-.f64 (-.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)))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))))
(fma.f64 #s(literal 1 binary64) (-.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)) (neg.f64 (+.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))))
(fma.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) (+.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 1 binary64) (atan2.f64 #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))) #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))))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64) (-.f64 (atan.f64 N) (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64) (neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.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)))))))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (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))))))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64) (neg.f64 (+.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64) (neg.f64 (-.f64 (-.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)))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64)))))
(fma.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64) (neg.f64 (+.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))))
(fma.f64 (atan.f64 N) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (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))))))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 N)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 (+.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))))))
(fma.f64 #s(literal -1 binary64) (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))
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(fma.f64 #s(literal -1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (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))))))))
(fma.f64 #s(literal -1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (neg.f64 (+.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))))
(fma.f64 #s(literal -1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (neg.f64 (-.f64 (-.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)))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))))
(fma.f64 #s(literal -1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) (-.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))))
(fma.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64))) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 3 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64)) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64)))))
(fma.f64 #s(literal -1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64)) (neg.f64 (+.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))))
(fma.f64 #s(literal -1 binary64) (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))
(fma.f64 (atan2.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))) #s(literal 1 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))))
(fma.f64 #s(literal 2 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (atan.f64 N) (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))))
(fma.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.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)))))))))
(fma.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (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))))))))
(fma.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (neg.f64 (+.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))))
(fma.f64 #s(literal 2 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (neg.f64 (-.f64 (-.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)))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #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))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #s(literal -1 binary64) (atan2.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #s(literal 2 binary64) (neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.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)))))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #s(literal 2 binary64) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (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))))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #s(literal 2 binary64) (neg.f64 (+.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #s(literal 2 binary64) (neg.f64 (-.f64 (-.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)))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #s(literal -2 binary64) (-.f64 (atan.f64 N) (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #s(literal -3 binary64) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) #s(literal -3 binary64) (neg.f64 (+.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))))
(fma.f64 (atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))) #s(literal -1 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))))
(fma.f64 (-.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)) #s(literal -1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal 1 binary64) (-.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal -1 binary64) (neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.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)))))))))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal -1 binary64) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (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))))))))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal -1 binary64) (neg.f64 (+.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) #s(literal -1 binary64) (neg.f64 (-.f64 (-.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)))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) #s(literal 1 binary64) (neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.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)))))))))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) #s(literal 1 binary64) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (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))))))))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) #s(literal 1 binary64) (neg.f64 (+.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) #s(literal 1 binary64) (neg.f64 (-.f64 (-.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)))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))))
(fma.f64 (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -2 binary64)) #s(literal -1 binary64) (-.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))))
(fma.f64 (-.f64 (atan.f64 N) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))) #s(literal 1 binary64) (.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)))
(fma.f64 #s(literal -2 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.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)))))))))
(fma.f64 #s(literal -2 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (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))))))))
(fma.f64 #s(literal -2 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (neg.f64 (+.f64 (-.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 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))))))
(fma.f64 #s(literal -2 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (neg.f64 (-.f64 (-.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)))))) (atan.f64 (+.f64 N #s(literal 1 binary64))))))
(fma.f64 #s(literal -2 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64)))) (-.f64 (atan.f64 N) (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64))))
(fma.f64 #s(literal 3 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (neg.f64 (-.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal -3 binary64)))))
(fma.f64 #s(literal 3 binary64) (atan.f64 (+.f64 N #s(literal 1 binary64))) (neg.f64 (+.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (-.f64 (*.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) #s(literal 2 binary64)) (atan.f64 N)))))
(neg.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)))
(*.f64 #s(literal 1 binary64) (atan.f64 N))
(*.f64 (atan.f64 N) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (atan.f64 N)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (atan.f64 N)))

simplify34.0ms (0.8%)

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	35	186
2	49	186
3	99	186
4	218	186
5	441	186
6	641	186
7	776	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)

eval39.0ms (0.9%)

Compiler: Compiled 5855 to 532 computations (90.9% saved)

prune32.0ms (0.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	325	1	326
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	326	1	327

Accuracy

99.6%

Counts

327 → 1

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)))))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 N #s(literal 1 binary64))
✓	cost-diff	(*.f64 N (+.f64 N #s(literal 1 binary64)))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64))))
✓	cost-diff	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))

Rules

50×	`fma-define`
46×	`fma-lowering-fma.f32`
46×	`fma-lowering-fma.f64`
30×	`-lowering-.f32`
30×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	26
1	16	21
2	30	21
3	49	21
4	68	21
5	73	21
6	74	21
0	74	21

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(atan2 1 (+ 1 (* N (+ N 1))))
1
(+ 1 (* N (+ N 1)))
(* N (+ N 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)

localize38.0ms (0.9%)

Localize:

Found 4 expressions of interest:

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

24.0ms

256×

valid

Compiler

Compiled 28 to 7 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-add: 3.0ms (41.7% of total)

ival-atan2: 2.0ms (27.8% of total)

ival-mult: 2.0ms (27.8% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (atan2 1 (+ 1 (* N (+ N 1))))>
#<alt (+ 1 (* N (+ N 1)))>
#<alt (* N (+ N 1))>
#<alt (+ 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)))>

Calls

12 calls:

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

rewrite20.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

60×	`fma-define`
50×	`fma-lowering-fma.f32`
50×	`fma-lowering-fma.f64`
34×	`+-lowering-+.f64`
34×	`+-lowering-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	24
1	16	19
2	32	19
3	55	19
4	81	19
5	106	19
6	122	19
7	130	19
0	130	19

Stop Event

1×	iter limit
1×	saturated

Counts

4 → 39

Calls

Call 1

Inputs
(atan2 1 (+ 1 (* N (+ N 1))))
(+ 1 (* N (+ N 1)))
(* N (+ N 1))
(+ N 1)

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

simplify120.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1682×	`-lowering-.f32`
1682×	`-lowering-.f64`
1378×	`fmsub-define`
1218×	`/-lowering-/.f32`
1218×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	285
1	69	201
2	148	201
3	548	201
4	3615	201
0	8278	201

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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)))

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))
(*.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
#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)

eval10.0ms (0.2%)

Compiler: Compiled 772 to 106 computations (86.3% saved)

prune6.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	5	88

Accuracy

99.6%

Counts

88 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 N N (+.f64 #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)))))
▶	97.3%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
▶	94.9%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
▶	6.2%	(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Compiler

Compiled 37 to 23 computations (37.8% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) N)
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 N N (+.f64 #s(literal 1 binary64) N)))
✓	cost-diff	6272	(fma.f64 N N (+.f64 #s(literal 1 binary64) N))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) N)
✓	cost-diff	0	(*.f64 N (+.f64 #s(literal 1 binary64) N))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (*.f64 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	(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Rules

48×	`fma-define`
46×	`fma-lowering-fma.f32`
46×	`fma-lowering-fma.f64`
30×	`-lowering-.f32`
30×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	23	44
2	36	44
3	54	44
4	67	44
5	72	44
6	73	44
0	73	44

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(atan2 1 1)
1
(atan2 1 (* N N))
1
(* N N)
N
(atan2 1 (* N (+ 1 N)))
1
(* N (+ 1 N))
N
(+ 1 N)
(atan2 1 (+ (* N N) (+ 1 N)))
1
(+ (* N N) (+ 1 N))
N
(+ 1 N)

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

localize64.0ms (1.5%)

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 N N (+.f64 #s(literal 1 binary64) N))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) N)
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 N N (+.f64 #s(literal 1 binary64) N)))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) N)
✓	accuracy	100.0%	(*.f64 N (+.f64 #s(literal 1 binary64) N))
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
✓	accuracy	100.0%	(*.f64 N N)
✓	accuracy	99.5%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
✓	accuracy	100.0%	(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Results

48.0ms

256×

valid

Compiler

Compiled 52 to 11 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-atan2: 9.0ms (43.5% of total)

ival-mult: 5.0ms (24.2% of total)

compiled-spec: 3.0ms (14.5% of total)

ival-add: 2.0ms (9.7% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

8 → 84

Calls

Call 1

Inputs
#<alt (atan2 1 1)>
#<alt (atan2 1 (* N N))>
#<alt (* N N)>
#<alt (atan2 1 (* N (+ 1 N)))>
#<alt (* N (+ 1 N))>
#<alt (+ 1 N)>
#<alt (+ (* N N) (+ 1 N))>
#<alt (atan2 1 (+ (* N N) (+ 1 N)))>

Outputs
#<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 (* N (+ 1 N)))>
#<alt (atan2 1 (* N (+ 1 N)))>
#<alt (atan2 1 (* N (+ 1 N)))>
#<alt (atan2 1 (* N (+ 1 N)))>
#<alt (atan2 1 (* N (+ 1 N)))>
#<alt (atan2 1 (* N (+ 1 N)))>
#<alt (atan2 1 (* N (+ 1 N)))>
#<alt (atan2 1 (* N (+ 1 N)))>
#<alt (atan2 1 (* N (- 1 (* -1 N))))>
#<alt (atan2 1 (* N (- 1 (* -1 N))))>
#<alt (atan2 1 (* N (- 1 (* -1 N))))>
#<alt (atan2 1 (* N (- 1 (* -1 N))))>
#<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 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 (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)))>

Calls

21 calls:

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

rewrite20.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

58×	`fma-define`
50×	`fma-lowering-fma.f32`
50×	`fma-lowering-fma.f64`
34×	`+-lowering-+.f64`
34×	`+-lowering-+.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	25	34
2	41	34
3	67	34
4	100	34
5	120	34
6	129	34
0	129	34

Stop Event

1×	iter limit
1×	saturated

Counts

8 → 48

Calls

Call 1

Inputs
(atan2 1 1)
(atan2 1 (* N N))
(* N N)
(atan2 1 (* N (+ 1 N)))
(* N (+ 1 N))
(+ 1 N)
(+ (* N N) (+ 1 N))
(atan2 1 (+ (* N N) (+ 1 N)))

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

simplify146.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1694×	`-lowering-.f32`
1694×	`-lowering-.f64`
1526×	`fmsub-define`
1338×	`fmm-def`
1218×	`fnmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	432
1	76	345
2	165	345
3	570	345
4	3685	345
0	8517	345

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(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 (* N (+ 1 N)))
(atan2 1 (* N (+ 1 N)))
(atan2 1 (* N (+ 1 N)))
(atan2 1 (* N (+ 1 N)))
(atan2 1 (* N (+ 1 N)))
(atan2 1 (* N (+ 1 N)))
(atan2 1 (* N (+ 1 N)))
(atan2 1 (* N (+ 1 N)))
(atan2 1 (* N (- 1 (* -1 N))))
(atan2 1 (* N (- 1 (* -1 N))))
(atan2 1 (* N (- 1 (* -1 N))))
(atan2 1 (* N (- 1 (* -1 N))))
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)))
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 (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)))

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

eval17.0ms (0.4%)

Compiler: Compiled 1091 to 121 computations (88.9% saved)

prune29.0ms (0.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	0	0	0
Picked	2	2	4
Done	0	1	1
Total	148	7	155

Accuracy

99.6%

Counts

155 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 N N N))
▶	87.9%	(atan2.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N)))
▶	97.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) N))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
✓	97.3%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
✓	94.9%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
▶	7.8%	(atan2.f64 #s(literal 1 binary64) N)

Compiler

Compiled 51 to 34 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (fma.f64 N N N))
✓	cost-diff	6272	(fma.f64 N N N)
✓	cost-diff	0	(log.f64 N)
✓	cost-diff	0	(exp.f64 #s(literal 2 binary64))
✓	cost-diff	0	(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N)))
✓	cost-diff	0	(*.f64 N N)
✓	cost-diff	0	(+.f64 (*.f64 N N) N)
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) N))
✓	cost-diff	0	(atan2.f64 #s(literal 1 binary64) N)

Rules

22×	`-lowering-.f32`
22×	`-lowering-.f64`
18×	`fma-define`
14×	`fma-lowering-fma.f32`
14×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	50
1	18	50
2	20	50
3	26	50
4	30	50
5	40	50
6	42	50
0	42	50

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize91.0ms (2.1%)

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 N N N)
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (fma.f64 N N N))
✓	accuracy	100.0%	(log.f64 N)
✓	accuracy	100.0%	(exp.f64 #s(literal 2 binary64))
✓	accuracy	99.5%	(atan2.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N)))
✓	accuracy	91.9%	(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N))
✓	accuracy	100.0%	(*.f64 N N)
✓	accuracy	99.9%	(+.f64 (*.f64 N N) N)
✓	accuracy	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) N))
✓	accuracy	100.0%	(atan2.f64 #s(literal 1 binary64) N)

Results

71.0ms

256×

valid

Compiler

Compiled 55 to 14 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-atan2: 8.0ms (24.2% of total)

ival-log: 7.0ms (21.1% of total)

ival-pow: 5.0ms (15.1% of total)

ival-mult: 4.0ms (12.1% of total)

compiled-spec: 4.0ms (12.1% of total)

ival-add: 3.0ms (9.1% of total)

ival-exp: 3.0ms (9.1% of total)

const: 1.0ms (3% of total)

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

series80.0ms (1.8%)

Counts

10 → 108

Calls

Call 1

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

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

Calls

27 calls:

Time	Variable		Point	Expression
52.0ms	N	@	0	(pow (exp 2) (log N))
19.0ms	N	@	-inf	(pow (exp 2) (log N))
6.0ms	N	@	inf	(pow (exp 2) (log N))
0.0ms	N	@	inf	(atan2 1 (pow (exp 2) (log N)))
0.0ms	N	@	-inf	(atan2 1 (+ (* N N) N))

rewrite18.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

28×	`fma-define`
26×	`-lowering-.f32`
26×	`-lowering-.f64`
18×	`fma-lowering-fma.f32`
18×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	24	35
2	31	35
3	40	35
4	53	35
5	68	35
6	84	35
7	93	35
0	93	35

Stop Event

1×	iter limit
1×	saturated

Counts

10 → 42

Calls

Call 1

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

Outputs
(atan2.f64 #s(literal 1 binary64) N)
(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
(+.f64 N (*.f64 N N))
(+.f64 (*.f64 N N) 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)
(.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))
(*.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) N) N)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 N)))
(pow.f64 N #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N))
(.f64 #s(literal 1 binary64) (.f64 N N))
(*.f64 N N)
(.f64 (.f64 N N) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 N)))
(pow.f64 N #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N))
(.f64 #s(literal 1 binary64) (.f64 N N))
(*.f64 N N)
(.f64 (.f64 N N) #s(literal 1 binary64))
(exp.f64 #s(literal 2 binary64))
(log.f64 N)
(+.f64 (log.f64 N) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (log.f64 N))
(+.f64 N (*.f64 N N))
(+.f64 (*.f64 N N) 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)
(.f64 #s(literal 1 binary64) (.f64 N (+.f64 #s(literal 1 binary64) N)))
(*.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) N) N)
(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))

simplify187.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

2134×	`fnmadd-define`
1254×	`+-lowering-+.f64`
1254×	`+-lowering-+.f32`
1082×	`fmsub-define`
1076×	`fnmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	488
1	68	418
2	135	418
3	347	418
4	1251	382
5	4121	382
0	8345	382

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

eval16.0ms (0.4%)

Compiler: Compiled 955 to 59 computations (93.8% saved)

prune8.0ms (0.2%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	0	0
Picked	0	4	4
Done	0	3	3
Total	150	7	157

Accuracy

99.6%

Counts

157 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.3%	(atan2.f64 #s(literal 1 binary64) (fma.f64 N N N))
✓	87.9%	(atan2.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N)))
✓	97.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) N))
✓	99.6%	(atan2.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 N (+.f64 N #s(literal 1 binary64)))))
✓	97.3%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
✓	94.9%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
✓	7.8%	(atan2.f64 #s(literal 1 binary64) N)

Compiler

Compiled 114 to 61 computations (46.5% saved)

regimes7.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	N
3.0ms	(-.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)

regimes8.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	N
2.0ms	(-.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 (0.1%)

Counts

5 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) N)
(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 (*.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
97.3%	1	`N`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 1

Calls

Call 1

Inputs
(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(atan2.f64 #s(literal 1 binary64) N)
(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
94.9%	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) N)

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
7.8%	1	`N`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (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
6.2%	1	`N`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify10.0ms (0.2%)

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	15	35
1	21	35

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.0s (23.3%)

Rules

1896×	`sum5-define`
1840×	`fnmadd-define`
1836×	`fma-lowering-fma.f32`
1836×	`fma-lowering-fma.f64`
1790×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	285
1	69	201
2	148	201
3	548	201
4	3615	201
0	8278	201
0	28	432
1	76	345
2	165	345
3	570	345
4	3685	345
0	8517	345
0	6	24
1	16	19
2	32	19
3	55	19
4	81	19
5	106	19
6	122	19
7	130	19
0	130	19
0	6	16
1	15	16
2	27	16
3	54	16
4	91	16
5	171	16
6	288	16
7	477	16
8	2204	16
9	3650	16
10	6570	16
0	8423	16

Stop Event

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

Compiler

Compiled 135 to 74 computations (45.2% saved)

preprocess44.0ms (1%)

Compiler: Compiled 110 to 52 computations (52.7% saved)

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

analyze3.0ms (0.1%)

sample1.8s (41%)

preprocess40.0ms (0.9%)

explain177.0ms (4.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify14.0ms (0.3%)

localize67.0ms (1.5%)

series1.0ms (0%)

rewrite179.0ms (4.1%)

simplify34.0ms (0.8%)

eval39.0ms (0.9%)

prune32.0ms (0.7%)

simplify8.0ms (0.2%)

localize38.0ms (0.9%)

series2.0ms (0%)

rewrite20.0ms (0.5%)

simplify120.0ms (2.8%)

eval10.0ms (0.2%)

prune6.0ms (0.1%)

simplify10.0ms (0.2%)

localize64.0ms (1.5%)

series2.0ms (0%)

rewrite20.0ms (0.5%)

simplify146.0ms (3.3%)

eval17.0ms (0.4%)

prune29.0ms (0.7%)

simplify7.0ms (0.2%)

localize91.0ms (2.1%)

series80.0ms (1.8%)

rewrite18.0ms (0.4%)

simplify187.0ms (4.3%)

eval16.0ms (0.4%)

prune8.0ms (0.2%)

regimes7.0ms (0.2%)

regimes8.0ms (0.2%)

regimes3.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify10.0ms (0.2%)

soundness1.0s (23.3%)

preprocess44.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18