Metrics for 2atan (example 3.5)

analyze4.0ms (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: 2.0ms

ival->: 1.0ms (44% of total)

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)

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

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

sample2.1s (49.2%)

Results

1.6s	7330×	1	valid
165.0ms	651×	2	valid
26.0ms	275×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-atan: 602.0ms (45.9% of total)

backward-pass: 171.0ms (13% of total)

...c/correct-round.rkt:119:19: 164.0ms (12.5% of total)

ival-add: 119.0ms (9.1% of total)

ival-sub: 104.0ms (7.9% of total)

ival->: 73.0ms (5.6% of total)

ival-and: 34.0ms (2.6% of total)

ival-<: 29.0ms (2.2% of total)

const: 15.0ms (1.1% of total)

Bogosity

preprocess37.0ms (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)))

explain138.0ms (3.3%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
255	-	-	`(-.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

95.0ms	454×	1	valid
11.0ms	40×	2	valid
2.0ms	18×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-atan: 23.0ms (46.7% of total)

backward-pass: 13.0ms (26.4% of total)

ival-add: 7.0ms (14.2% of total)

ival-sub: 6.0ms (12.2% of total)

const: 1.0ms (2% 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
▶	8.9%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify13.0ms (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)

localize63.0ms (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	8.9%	(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))

Results

47.0ms	227×	1	valid
5.0ms	20×	2	valid
1.0ms	9×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-atan: 11.0ms (46.2% of total)

backward-pass: 6.0ms (25.2% of total)

ival-add: 4.0ms (16.8% of total)

ival-sub: 3.0ms (12.6% of total)

const: 1.0ms (4.2% 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)

rewrite156.0ms (3.7%)

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)))

simplify36.0ms (0.9%)

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)

eval35.0ms (0.8%)

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

prune33.0ms (0.8%)

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)

simplify6.0ms (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)

localize30.0ms (0.7%)

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

20.0ms

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 (41.4% of total)

ival-atan2: 2.0ms (27.6% of total)

ival-mult: 2.0ms (27.6% 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	(+ 1 (* N (+ N 1)))
0.0ms	N	@	-inf	(* N (+ N 1))

rewrite17.0ms (0.4%)

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))

simplify136.0ms (3.2%)

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)

eval8.0ms (0.2%)

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

prune13.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Accuracy

99.6%

Counts

88 → 4

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)))))
▶	96.4%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
▶	92.8%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
▶	6.5%	(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Compiler

Compiled 28 to 18 computations (35.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	17	27
2	21	27
3	32	27
4	34	27
0	34	27

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)

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)

localize44.0ms (1%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	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	99.7%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
✓	accuracy	100.0%	(atan2.f64 #s(literal 1 binary64) #s(literal 1 binary64))

Results

32.0ms

256×

valid

Compiler

Compiled 33 to 9 computations (72.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-atan2: 5.0ms (46.1% of total)

ival-mult: 4.0ms (36.9% of total)

ival-add: 1.0ms (9.2% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

6 → 60

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)>

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)))>

Calls

15 calls:

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

rewrite14.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	19	22
2	26	22
3	45	22
4	65	22
5	80	22
6	88	22
0	88	22

Stop Event

1×	iter limit
1×	saturated

Counts

6 → 26

Calls

Call 1

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

simplify119.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1534×	`-lowering-.f32`
1534×	`-lowering-.f64`
1530×	`fnmsub-define`
1468×	`fmsub-define`
1292×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	262
1	47	215
2	71	215
3	235	215
4	1748	215
5	4688	215
0	8149	215

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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)))

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)

eval8.0ms (0.2%)

Compiler: Compiled 544 to 60 computations (89% saved)

prune8.0ms (0.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	85	5	90

Accuracy

99.6%

Counts

90 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.4%	(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)))))
✓	96.4%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
✓	92.8%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
▶	8.0%	(atan2.f64 #s(literal 1 binary64) N)

Compiler

Compiled 36 to 23 computations (36.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 N N)
✓	cost-diff	(+.f64 (*.f64 N N) N)
✓	cost-diff	(atan2.f64 #s(literal 1 binary64) (+.f64 (*.f64 N N) N))
✓	cost-diff	(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	6	19
1	13	19
2	15	19
3	21	19
4	25	19
5	35	19
6	37	19
0	37	19

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

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

localize39.0ms (0.9%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	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

27.0ms

256×

valid

Compiler

Compiled 24 to 7 computations (70.8% saved)

Precisions

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

ival-atan2: 4.0ms (51.9% of total)

ival-mult: 2.0ms (25.9% of total)

ival-add: 1.0ms (13% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

4 → 48

Calls

Call 1

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

Calls

12 calls:

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

rewrite14.0ms (0.3%)

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: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	15	15
2	20	15
3	30	15
4	45	15
5	63	15
6	82	15
7	91	15
0	91	15

Stop Event

1×	iter limit
1×	saturated

Counts

4 → 19

Calls

Call 1

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

simplify108.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1550×	`fnmadd-define`
1396×	`-lowering-.f32`
1396×	`-lowering-.f64`
1274×	`div-sub`
960×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	208
1	41	173
2	71	173
3	217	173
4	1101	173
5	3251	173
6	6717	173
0	8142	173

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

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)

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)

eval6.0ms (0.1%)

Compiler: Compiled 425 to 47 computations (88.9% saved)

prune19.0ms (0.4%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	65	7	72

Accuracy

99.7%

Counts

72 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	89.3%	(atan2.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N)) N))
	96.4%	(atan2.f64 #s(literal 1 binary64) (+.f64 (pow.f64 N #s(literal 2 binary64)) N))
✓	96.4%	(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)))))
✓	96.4%	(atan2.f64 #s(literal 1 binary64) (*.f64 N (+.f64 #s(literal 1 binary64) N)))
✓	92.8%	(atan2.f64 #s(literal 1 binary64) (*.f64 N N))
✓	8.0%	(atan2.f64 #s(literal 1 binary64) N)

Compiler

Compiled 112 to 64 computations (42.9% saved)

regimes18.0ms (0.4%)

Counts

9 → 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)))))
(-.f64 (atan.f64 (+.f64 N #s(literal 1 binary64))) (atan.f64 N))
(atan2.f64 #s(literal 1 binary64) (+.f64 (pow.f64 N #s(literal 2 binary64)) N))
(atan2.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 N)) N))

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

Calls

2 calls:

15.0ms	N
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)

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
96.4%	1	`N`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0.1%)

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
92.8%	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
8.0%	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
6.5%	1	`N`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (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	13	27
1	19	27

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness943.0ms (22.4%)

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	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
0	17	262
1	47	215
2	71	215
3	235	215
4	1748	215
5	4688	215
0	8149	215

Stop Event

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

Compiler

Compiled 108 to 61 computations (43.5% saved)

preprocess46.0ms (1.1%)

Compiler: Compiled 94 to 48 computations (48.9% 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

analyze4.0ms (0.1%)

sample2.1s (49.2%)

preprocess37.0ms (0.9%)

explain138.0ms (3.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.3%)

localize63.0ms (1.5%)

series1.0ms (0%)

rewrite156.0ms (3.7%)

simplify36.0ms (0.9%)

eval35.0ms (0.8%)

prune33.0ms (0.8%)

simplify6.0ms (0.2%)

localize30.0ms (0.7%)

series2.0ms (0%)

rewrite17.0ms (0.4%)

simplify136.0ms (3.2%)

eval8.0ms (0.2%)

prune13.0ms (0.3%)

simplify5.0ms (0.1%)

localize44.0ms (1%)

series1.0ms (0%)

rewrite14.0ms (0.3%)

simplify119.0ms (2.8%)

eval8.0ms (0.2%)

prune8.0ms (0.2%)

simplify5.0ms (0.1%)

localize39.0ms (0.9%)

series1.0ms (0%)

rewrite14.0ms (0.3%)

simplify108.0ms (2.6%)

eval6.0ms (0.1%)

prune19.0ms (0.4%)

regimes18.0ms (0.4%)

regimes3.0ms (0.1%)

regimes2.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify7.0ms (0.2%)

soundness943.0ms (22.4%)

preprocess46.0ms (1.1%)

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