Metrics for Maksimov and Kolovsky, Equation (32)

analyze1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
100%	99.8%	0%	0.2%	0%	0%	0%	1

Compiler

Compiled 31 to 23 computations (25.8% saved)

sample2.1s (14.4%)

Memory

57.0MiB live, 2 263.2MiB allocated

Samples

1.4s	7 866×	0	valid
121.0ms	390×	1	valid

Precisions

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

ival-sub: 341.0ms (29.2% of total)

ival-div: 201.0ms (17.2% of total)

ival-mult: 170.0ms (14.5% of total)

ival-pow2: 126.0ms (10.8% of total)

ival-cos: 81.0ms (6.9% of total)

ival-neg: 64.0ms (5.5% of total)

ival-exp: 55.0ms (4.7% of total)

ival-fabs: 52.0ms (4.4% of total)

ival-add: 48.0ms (4.1% of total)

adjust: 17.0ms (1.5% of total)

ival-true: 6.0ms (0.5% of total)

exact: 5.0ms (0.4% of total)

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

Bogosity

preprocess346.0ms (2.4%)

Memory

-24.3MiB live, 549.4MiB allocated

Algorithm

1×	egg-herbie

Rules

7 472×	`lower-fma.f64`
7 472×	`lower-fma.f32`
3 222×	`lower-*.f32`
3 218×	`lower-*.f64`
2 026×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	209	597
1	575	589
2	1511	565
3	5225	565
0	21	29
0	36	29
1	67	29
2	134	28
3	376	28
4	1307	28
5	4682	28
0	8522	27

Stop Event

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

Calls

Call 1

Inputs

(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs

(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

(*.f64 (cos.f64 (fma.f64 K (*.f64 (+.f64 m n) #s(literal -1/2 binary64)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l))))

Symmetry

(sort m n)

explain453.0ms (3.1%)

Memory

32.3MiB live, 856.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
175	40	(5.136781697644427e-233 1.867108585763016e-159 1.0575587121075125e-150 -7611.643785463953 -9.09584853580877e+188)	-	`(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))`
0	0	-	-	`(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))`
0	0	-	-	`K`
0	0	-	-	`(/.f64 (+.f64 m n) #s(literal 2 binary64))`
0	0	-	-	`(-.f64 l (fabs.f64 (-.f64 m n)))`
0	0	-	-	`(neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))`
0	0	-	-	`(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))`
0	0	-	-	`(+.f64 m n)`
0	0	-	-	`(fabs.f64 (-.f64 m n))`
0	0	-	-	`m`
0	0	-	-	`(*.f64 K (+.f64 m n))`
0	0	-	-	`n`
0	0	-	-	`(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))`
0	0	-	-	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`
0	0	-	-	`(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)`
0	0	-	-	`(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))`
0	0	-	-	`(-.f64 m n)`
0	0	-	-	`(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`l`
0	0	-	-	`M`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`cos.f64`	`(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))`	sensitivity	168	0
`cos.f64`	`(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))`	oflow-rescue	47	0
↳	`(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))`	overflow	47
↳	`(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)`	overflow	47
↳	`(*.f64 K (+.f64 m n))`	overflow	47

Confusion

	Predicted +	Predicted -
+	62	0
-	153	41

Precision

0.28837209302325584

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	62	0	0
-	153	0	41

Precision?

0.28837209302325584

Recall?

1.0

Freqs

test

number	freq
0	41
1	215

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

178.0ms	424×	1	valid
13.0ms	88×	0	valid

Compiler

Compiled 368 to 88 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 146.0ms

ival-sub: 48.0ms (32.9% of total)

adjust: 29.0ms (19.9% of total)

ival-cos: 19.0ms (13% of total)

ival-div: 12.0ms (8.2% of total)

ival-mult: 11.0ms (7.5% of total)

ival-pow2: 9.0ms (6.2% of total)

ival-add: 5.0ms (3.4% of total)

ival-exp: 4.0ms (2.7% of total)

ival-neg: 4.0ms (2.7% of total)

ival-fabs: 4.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 5 to 5 computations (0% saved)

prune1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.1%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Status

Accuracy

Program

▶

76.1%

(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 34 to 21 computations (38.2% saved)

simplify524.0ms (3.6%)

Memory

-259.0MiB live, 455.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	256	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	cost-diff	384	(/.f64 (+.f64 m n) #s(literal 2 binary64))
✓	cost-diff	384	(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
✓	cost-diff	5696	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))

Rules

7 472×	`lower-fma.f64`
7 472×	`lower-fma.f32`
3 222×	`lower-*.f32`
3 218×	`lower-*.f64`
2 026×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	148
0	36	148
1	67	148
2	134	145
3	376	145
4	1307	145
5	4682	145
0	8522	143

Stop Event

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

Calls

Call 1

Inputs
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
(*.f64 K (+.f64 m n))
K
(+.f64 m n)
m
n
#s(literal 2 binary64)
M
(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
(/.f64 (+.f64 m n) #s(literal 2 binary64))
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)

Outputs
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) #s(literal -1/2 binary64)) M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l))))
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
(cos.f64 (fma.f64 K (*.f64 (+.f64 m n) #s(literal -1/2 binary64)) M))
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
(fma.f64 K (*.f64 (+.f64 m n) #s(literal 1/2 binary64)) (neg.f64 M))
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
(.f64 K (.f64 (+.f64 m n) #s(literal 1/2 binary64)))
(*.f64 K (+.f64 m n))
K
(+.f64 m n)
m
n
#s(literal 2 binary64)
M
(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l)))
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l))
(neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))
(*.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M))
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(*.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M))
(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
(fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))
(/.f64 (+.f64 m n) #s(literal 2 binary64))
(*.f64 (+.f64 m n) #s(literal 1/2 binary64))
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)

localize116.0ms (0.8%)

Memory

9.7MiB live, 199.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	accuracy	100.0%	(*.f64 K (+.f64 m n))
✓	accuracy	100.0%	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
✓	accuracy	37.6%	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))

Samples

78.0ms	212×	1	valid
8.0ms	44×	0	valid

Compiler

Compiled 150 to 23 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-sub: 15.0ms (24.6% of total)

ival-cos: 12.0ms (19.7% of total)

adjust: 9.0ms (14.8% of total)

ival-div: 6.0ms (9.8% of total)

ival-mult: 6.0ms (9.8% of total)

ival-pow2: 5.0ms (8.2% of total)

ival-add: 3.0ms (4.9% of total)

ival-exp: 2.0ms (3.3% of total)

ival-neg: 2.0ms (3.3% of total)

ival-fabs: 2.0ms (3.3% of total)

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

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

exact: 0.0ms (0% of total)

series24.0ms (0.2%)

Memory

10.3MiB live, 46.5MiB allocated

Counts

6 → 228

Calls

Call 1

Inputs
#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) (patch (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 m n) #s(literal 2 binary64)) (patch (/.f64 (+.f64 m n) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))) (patch (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))) #<representation binary64>) () ())
#s(alt (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (patch (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) #<representation binary64>) () ())
#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())

Outputs
#s(alt (pow (- (* 1/2 n) M) 2) (taylor 0 m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* m (- (* 1/2 n) M)) (pow (- (* 1/2 n) M) 2)) (taylor 0 m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2)) (taylor 0 m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2)) (taylor 0 m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow m 2)) (taylor inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m))) (taylor inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m))) (taylor inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m))) (taylor inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow m 2)) (taylor -inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m))) (taylor -inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m)))) (taylor -inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m)))) (taylor -inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (- (* 1/2 m) M) 2) (taylor 0 n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* n (- (* 1/2 m) M)) (pow (- (* 1/2 m) M) 2)) (taylor 0 n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* K (+ m n)) (taylor inf K) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K (+ m n)) (taylor inf K) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K (+ m n)) (taylor inf K) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K (+ m n)) (taylor -inf K) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K (+ m n)) (taylor -inf K) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K (+ m n)) (taylor -inf K) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K (+ m n)) (taylor -inf K) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K n) (taylor 0 m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (+ (* K m) (* K n)) (taylor 0 m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (+ (* K m) (* K n)) (taylor 0 m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (+ (* K m) (* K n)) (taylor 0 m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K m) (taylor inf m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* m (+ K (/ (* K n) m))) (taylor inf m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* m (+ K (/ (* K n) m))) (taylor inf m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* m (+ K (/ (* K n) m))) (taylor inf m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K m) (taylor -inf m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* m (+ (* -1 K) (* -1 (/ (* K n) m))))) (taylor -inf m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* m (+ (* -1 K) (* -1 (/ (* K n) m))))) (taylor -inf m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* m (+ (* -1 K) (* -1 (/ (* K n) m))))) (taylor -inf m) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K m) (taylor 0 n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (+ (* K m) (* K n)) (taylor 0 n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (+ (* K m) (* K n)) (taylor 0 n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (+ (* K m) (* K n)) (taylor 0 n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K n) (taylor inf n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* n (+ K (/ (* K m) n))) (taylor inf n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* n (+ K (/ (* K m) n))) (taylor inf n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* n (+ K (/ (* K m) n))) (taylor inf n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* K n) (taylor -inf n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (+ (* -1 K) (* -1 (/ (* K m) n))))) (taylor -inf n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (+ (* -1 K) (* -1 (/ (* K m) n))))) (taylor -inf n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (+ (* -1 K) (* -1 (/ (* K m) n))))) (taylor -inf n) (#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())) ())

Calls

57 calls:

Time	Variable		Point	Expression
4.0ms	m	@	0	(cos (- (/ (* K (+ m n)) 2) M))
1.0ms	m	@	-inf	(/ (+ m n) 2)
1.0ms	K	@	0	(cos (- (/ (* K (+ m n)) 2) M))
1.0ms	K	@	0	(/ (* K (+ m n)) 2)
1.0ms	M	@	-inf	(pow (- (/ (+ m n) 2) M) 2)

simplify349.0ms (2.4%)

Memory

-4.0MiB live, 623.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10 032×	`lower-fma.f64`
10 032×	`lower-fma.f32`
7 192×	`lower-*.f64`
7 192×	`lower-*.f32`
4 352×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	388	3016
1	1162	2963
2	3519	2940
0	8866	2818

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(pow (- (* 1/2 n) M) 2)
(+ (* m (- (* 1/2 n) M)) (pow (- (* 1/2 n) M) 2))
(+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))
(+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))
(* 1/4 (pow m 2))
(* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))
(* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))
(* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))
(* 1/4 (pow m 2))
(* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))
(* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))
(* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))
(pow (- (* 1/2 m) M) 2)
(+ (* n (- (* 1/2 m) M)) (pow (- (* 1/2 m) M) 2))
(+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))
(+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))
(* 1/4 (pow n 2))
(* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))
(* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))
(* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))
(* 1/4 (pow n 2))
(* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))
(* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))
(* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))
(* 1/4 (pow (+ m n) 2))
(+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2)))
(+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))
(+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))
(pow M 2)
(* (pow M 2) (+ 1 (* -1 (/ (+ m n) M))))
(* (pow M 2) (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
(* (pow M 2) (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
(pow M 2)
(* (pow M 2) (+ 1 (* -1 (/ (+ m n) M))))
(* (pow M 2) (+ 1 (* -1 (/ (+ m (+ n (* -1/4 (/ (pow (+ m n) 2) M)))) M))))
(* (pow M 2) (+ 1 (* -1 (/ (+ m (+ n (* -1/4 (/ (pow (+ m n) 2) M)))) M))))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K (+ m n)))
(* 1/2 (* K n))
(+ (* 1/2 (* K m)) (* 1/2 (* K n)))
(+ (* 1/2 (* K m)) (* 1/2 (* K n)))
(+ (* 1/2 (* K m)) (* 1/2 (* K n)))
(* 1/2 (* K m))
(* m (+ (* 1/2 K) (* 1/2 (/ (* K n) m))))
(* m (+ (* 1/2 K) (* 1/2 (/ (* K n) m))))
(* m (+ (* 1/2 K) (* 1/2 (/ (* K n) m))))
(* 1/2 (* K m))
(* -1 (* m (+ (* -1/2 K) (* -1/2 (/ (* K n) m)))))
(* -1 (* m (+ (* -1/2 K) (* -1/2 (/ (* K n) m)))))
(* -1 (* m (+ (* -1/2 K) (* -1/2 (/ (* K n) m)))))
(* 1/2 (* K m))
(+ (* 1/2 (* K m)) (* 1/2 (* K n)))
(+ (* 1/2 (* K m)) (* 1/2 (* K n)))
(+ (* 1/2 (* K m)) (* 1/2 (* K n)))
(* 1/2 (* K n))
(* n (+ (* 1/2 K) (* 1/2 (/ (* K m) n))))
(* n (+ (* 1/2 K) (* 1/2 (/ (* K m) n))))
(* n (+ (* 1/2 K) (* 1/2 (/ (* K m) n))))
(* 1/2 (* K n))
(* -1 (* n (+ (* -1/2 K) (* -1/2 (/ (* K m) n)))))
(* -1 (* n (+ (* -1/2 K) (* -1/2 (/ (* K m) n)))))
(* -1 (* n (+ (* -1/2 K) (* -1/2 (/ (* K m) n)))))
(* 1/2 n)
(+ (* 1/2 m) (* 1/2 n))
(+ (* 1/2 m) (* 1/2 n))
(+ (* 1/2 m) (* 1/2 n))
(* 1/2 m)
(* m (+ 1/2 (* 1/2 (/ n m))))
(* m (+ 1/2 (* 1/2 (/ n m))))
(* m (+ 1/2 (* 1/2 (/ n m))))
(* 1/2 m)
(* -1 (* m (- (* -1/2 (/ n m)) 1/2)))
(* -1 (* m (- (* -1/2 (/ n m)) 1/2)))
(* -1 (* m (- (* -1/2 (/ n m)) 1/2)))
(* 1/2 m)
(+ (* 1/2 m) (* 1/2 n))
(+ (* 1/2 m) (* 1/2 n))
(+ (* 1/2 m) (* 1/2 n))
(* 1/2 n)
(* n (+ 1/2 (* 1/2 (/ m n))))
(* n (+ 1/2 (* 1/2 (/ m n))))
(* n (+ 1/2 (* 1/2 (/ m n))))
(* 1/2 n)
(* -1 (* n (- (* -1/2 (/ m n)) 1/2)))
(* -1 (* n (- (* -1/2 (/ m n)) 1/2)))
(* -1 (* n (- (* -1/2 (/ m n)) 1/2)))
(- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))
(- (+ (fabs (- m n)) (* m (- M (* 1/2 n)))) (+ l (pow (- (* 1/2 n) M) 2)))
(- (+ (fabs (- m n)) (* m (- (+ M (* -1/4 m)) (* 1/2 n)))) (+ l (pow (- (* 1/2 n) M) 2)))
(- (+ (fabs (- m n)) (* m (- (+ M (* -1/4 m)) (* 1/2 n)))) (+ l (pow (- (* 1/2 n) M) 2)))
(* -1/4 (pow m 2))
(* (pow m 2) (- (/ M m) (+ 1/4 (* 1/2 (/ n m)))))
(* (pow m 2) (- (+ (/ M m) (/ (fabs (- m n)) (pow m 2))) (+ 1/4 (+ (* 1/2 (/ n m)) (+ (/ l (pow m 2)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))))))
(* (pow m 2) (- (+ (/ M m) (/ (fabs (- m n)) (pow m 2))) (+ 1/4 (+ (* 1/2 (/ n m)) (+ (/ l (pow m 2)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))))))
(* -1/4 (pow m 2))
(* (pow m 2) (- (* -1 (/ (- (* 1/2 n) M) m)) 1/4))
(* (pow m 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 n) M) 2))) m)) (* -1 (- (* 1/2 n) M))) m)) 1/4))
(* (pow m 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 n) M) 2))) m)) (* -1 (- (* 1/2 n) M))) m)) 1/4))
(- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))
(- (+ (fabs (- m n)) (* n (- M (* 1/2 m)))) (+ l (pow (- (* 1/2 m) M) 2)))
(- (+ (fabs (- m n)) (* n (- (+ M (* -1/4 n)) (* 1/2 m)))) (+ l (pow (- (* 1/2 m) M) 2)))
(- (+ (fabs (- m n)) (* n (- (+ M (* -1/4 n)) (* 1/2 m)))) (+ l (pow (- (* 1/2 m) M) 2)))
(* -1/4 (pow n 2))
(* (pow n 2) (- (/ M n) (+ 1/4 (* 1/2 (/ m n)))))
(* (pow n 2) (- (+ (/ M n) (/ (fabs (- m n)) (pow n 2))) (+ 1/4 (+ (* 1/2 (/ m n)) (+ (/ l (pow n 2)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))))))
(* (pow n 2) (- (+ (/ M n) (/ (fabs (- m n)) (pow n 2))) (+ 1/4 (+ (* 1/2 (/ m n)) (+ (/ l (pow n 2)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))))))
(* -1/4 (pow n 2))
(* (pow n 2) (- (* -1 (/ (- (* 1/2 m) M) n)) 1/4))
(* (pow n 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 m) M) 2))) n)) (* -1 (- (* 1/2 m) M))) n)) 1/4))
(* (pow n 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 m) M) 2))) n)) (* -1 (- (* 1/2 m) M))) n)) 1/4))
(- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))
(- (+ (fabs (- m n)) (* M (+ m n))) (+ l (* 1/4 (pow (+ m n) 2))))
(- (+ (fabs (- m n)) (* M (- (* -1 M) (* -1 (+ m n))))) (+ l (* 1/4 (pow (+ m n) 2))))
(- (+ (fabs (- m n)) (* M (- (* -1 M) (* -1 (+ m n))))) (+ l (* 1/4 (pow (+ m n) 2))))
(* -1 (pow M 2))
(* (pow M 2) (- (+ (/ m M) (/ n M)) 1))
(* (pow M 2) (- (/ (fabs (- m n)) (pow M 2)) (+ 1 (+ (* -1 (/ (+ m n) M)) (+ (* 1/4 (/ (pow (+ m n) 2) (pow M 2))) (/ l (pow M 2)))))))
(* (pow M 2) (- (/ (fabs (- m n)) (pow M 2)) (+ 1 (+ (* -1 (/ (+ m n) M)) (+ (* 1/4 (/ (pow (+ m n) 2) (pow M 2))) (/ l (pow M 2)))))))
(* -1 (pow M 2))
(* (pow M 2) (- (+ (/ m M) (/ n M)) 1))
(* (pow M 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))) M)) (+ m n)) M)) 1))
(* (pow M 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))) M)) (+ m n)) M)) 1))
(- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))
(- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2))
(- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2))
(- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2))
(* -1 l)
(* l (- (/ (fabs (- m n)) l) (+ 1 (/ (pow (- (* 1/2 (+ m n)) M) 2) l))))
(* l (- (/ (fabs (- m n)) l) (+ 1 (/ (pow (- (* 1/2 (+ m n)) M) 2) l))))
(* l (- (/ (fabs (- m n)) l) (+ 1 (/ (pow (- (* 1/2 (+ m n)) M) 2) l))))
(* -1 l)
(* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)) l)))))
(* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)) l)))))
(* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)) l)))))
(cos (neg M))
(+ (cos (neg M)) (* -1/2 (* K (* (sin (neg M)) (+ m n)))))
(+ (cos (neg M)) (* K (- (* -1/8 (* K (* (cos (neg M)) (pow (+ m n) 2)))) (* 1/2 (* (sin (neg M)) (+ m n))))))
(+ (cos (neg M)) (* K (- (* K (+ (* -1/8 (* (cos (neg M)) (pow (+ m n) 2))) (* 1/48 (* K (* (sin (neg M)) (pow (+ m n) 3)))))) (* 1/2 (* (sin (neg M)) (+ m n))))))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K n)) M))
(+ (cos (- (* 1/2 (* K n)) M)) (* -1/2 (* K (* m (sin (- (* 1/2 (* K n)) M))))))
(+ (cos (- (* 1/2 (* K n)) M)) (* m (- (* -1/8 (* (pow K 2) (* m (cos (- (* 1/2 (* K n)) M))))) (* 1/2 (* K (sin (- (* 1/2 (* K n)) M)))))))
(+ (cos (- (* 1/2 (* K n)) M)) (* m (- (* m (+ (* -1/8 (* (pow K 2) (cos (- (* 1/2 (* K n)) M)))) (* 1/48 (* (pow K 3) (* m (sin (- (* 1/2 (* K n)) M))))))) (* 1/2 (* K (sin (- (* 1/2 (* K n)) M)))))))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (- n (* -1 m)))) M))
(cos (- (* 1/2 (* K (- n (* -1 m)))) M))
(cos (- (* 1/2 (* K (- n (* -1 m)))) M))
(cos (- (* 1/2 (* K (- n (* -1 m)))) M))
(cos (- (* 1/2 (* K m)) M))
(+ (cos (- (* 1/2 (* K m)) M)) (* -1/2 (* K (* n (sin (- (* 1/2 (* K m)) M))))))
(+ (cos (- (* 1/2 (* K m)) M)) (* n (- (* -1/8 (* (pow K 2) (* n (cos (- (* 1/2 (* K m)) M))))) (* 1/2 (* K (sin (- (* 1/2 (* K m)) M)))))))
(+ (cos (- (* 1/2 (* K m)) M)) (* n (- (* n (+ (* -1/8 (* (pow K 2) (cos (- (* 1/2 (* K m)) M)))) (* 1/48 (* (pow K 3) (* n (sin (- (* 1/2 (* K m)) M))))))) (* 1/2 (* K (sin (- (* 1/2 (* K m)) M)))))))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (- m (* -1 n)))) M))
(cos (- (* 1/2 (* K (- m (* -1 n)))) M))
(cos (- (* 1/2 (* K (- m (* -1 n)))) M))
(cos (- (* 1/2 (* K (- m (* -1 n)))) M))
(cos (* 1/2 (* K (+ m n))))
(+ (cos (* 1/2 (* K (+ m n)))) (* M (sin (* 1/2 (* K (+ m n))))))
(+ (cos (* 1/2 (* K (+ m n)))) (* M (- (* -1/2 (* M (cos (* 1/2 (* K (+ m n)))))) (* -1 (sin (* 1/2 (* K (+ m n))))))))
(+ (cos (* 1/2 (* K (+ m n)))) (* M (- (* M (+ (* -1/2 (cos (* 1/2 (* K (+ m n))))) (* -1/6 (* M (sin (* 1/2 (* K (+ m n)))))))) (* -1 (sin (* 1/2 (* K (+ m n))))))))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))
(cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))
(cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))
(cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K (+ m n))
(* K n)
(+ (* K m) (* K n))
(+ (* K m) (* K n))
(+ (* K m) (* K n))
(* K m)
(* m (+ K (/ (* K n) m)))
(* m (+ K (/ (* K n) m)))
(* m (+ K (/ (* K n) m)))
(* K m)
(* -1 (* m (+ (* -1 K) (* -1 (/ (* K n) m)))))
(* -1 (* m (+ (* -1 K) (* -1 (/ (* K n) m)))))
(* -1 (* m (+ (* -1 K) (* -1 (/ (* K n) m)))))
(* K m)
(+ (* K m) (* K n))
(+ (* K m) (* K n))
(+ (* K m) (* K n))
(* K n)
(* n (+ K (/ (* K m) n)))
(* n (+ K (/ (* K m) n)))
(* n (+ K (/ (* K m) n)))
(* K n)
(* -1 (* n (+ (* -1 K) (* -1 (/ (* K m) n)))))
(* -1 (* n (+ (* -1 K) (* -1 (/ (* K m) n)))))
(* -1 (* n (+ (* -1 K) (* -1 (/ (* K m) n)))))

Outputs
(pow (- (* 1/2 n) M) 2)
(*.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M))
(+ (* m (- (* 1/2 n) M)) (pow (- (* 1/2 n) M) 2))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (-.f64 m (fma.f64 n #s(literal -1/2 binary64) M)))
(+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))
(fma.f64 m (-.f64 (fma.f64 m #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) n)) M) (.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M)))
(+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))
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(*.f64 (+.f64 n m) K)
(* K (+ m n))
(*.f64 (+.f64 n m) K)
(* K (+ m n))
(*.f64 (+.f64 n m) K)
(* K n)
(*.f64 n K)
(+ (* K m) (* K n))
(*.f64 (+.f64 n m) K)
(+ (* K m) (* K n))
(*.f64 (+.f64 n m) K)
(+ (* K m) (* K n))
(*.f64 (+.f64 n m) K)
(* K m)
(*.f64 m K)
(* m (+ K (/ (* K n) m)))
(*.f64 m (fma.f64 n (/.f64 K m) K))
(* m (+ K (/ (* K n) m)))
(*.f64 m (fma.f64 n (/.f64 K m) K))
(* m (+ K (/ (* K n) m)))
(*.f64 m (fma.f64 n (/.f64 K m) K))
(* K m)
(*.f64 m K)
(* -1 (* m (+ (* -1 K) (* -1 (/ (* K n) m)))))
(*.f64 m (fma.f64 n (/.f64 K m) K))
(* -1 (* m (+ (* -1 K) (* -1 (/ (* K n) m)))))
(*.f64 m (fma.f64 n (/.f64 K m) K))
(* -1 (* m (+ (* -1 K) (* -1 (/ (* K n) m)))))
(*.f64 m (fma.f64 n (/.f64 K m) K))
(* K m)
(*.f64 m K)
(+ (* K m) (* K n))
(*.f64 (+.f64 n m) K)
(+ (* K m) (* K n))
(*.f64 (+.f64 n m) K)
(+ (* K m) (* K n))
(*.f64 (+.f64 n m) K)
(* K n)
(*.f64 n K)
(* n (+ K (/ (* K m) n)))
(*.f64 n (fma.f64 m (/.f64 K n) K))
(* n (+ K (/ (* K m) n)))
(*.f64 n (fma.f64 m (/.f64 K n) K))
(* n (+ K (/ (* K m) n)))
(*.f64 n (fma.f64 m (/.f64 K n) K))
(* K n)
(*.f64 n K)
(* -1 (* n (+ (* -1 K) (* -1 (/ (* K m) n)))))
(*.f64 n (fma.f64 m (/.f64 K n) K))
(* -1 (* n (+ (* -1 K) (* -1 (/ (* K m) n)))))
(*.f64 n (fma.f64 m (/.f64 K n) K))
(* -1 (* n (+ (* -1 K) (* -1 (/ (* K m) n)))))
(*.f64 n (fma.f64 m (/.f64 K n) K))

rewrite350.0ms (2.4%)

Memory

1.8MiB live, 566.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 100×	`lower-fma.f64`
5 100×	`lower-fma.f32`
4 482×	`lower-/.f32`
4 478×	`lower-/.f64`
4 324×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	53
0	32	53
1	152	53
2	1217	53
0	8384	53

Stop Event

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

Counts

6 → 319

Calls

Call 1

Inputs
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
(/.f64 (+.f64 m n) #s(literal 2 binary64))
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
(*.f64 K (+.f64 m n))

Outputs
(+.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (+.f64 m n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (neg.f64 M)))
(+.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (*.f64 (neg.f64 M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))) #s(literal 1 binary64)))
(exp.f64 (+.f64 (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))))
(fma.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (neg.f64 M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))))
(fma.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (neg.f64 M)))
(/.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))) (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)) (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (*.f64 M M)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (*.f64 M M))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))) (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (*.f64 M M)))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (*.f64 M M))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M)))) (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))
(/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M)))) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))
(/.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (*.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))))
(/.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (*.f64 M M)))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (*.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))))
(/.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (*.f64 M M))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))))) (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))))) (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))))) (neg.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (.f64 M M))))) (neg.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))))
(/.f64 (neg.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (*.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (*.f64 M M))))) (neg.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (*.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (neg.f64 (*.f64 M M))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))) (neg.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (+.f64 m n) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (neg.f64 M)) #s(literal 3 binary64))) (fma.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (+.f64 m n) #s(literal 1/2 binary64))) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (+.f64 m n) #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (neg.f64 M)) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (neg.f64 M))) (.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (+.f64 m n) #s(literal 1/2 binary64))) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (neg.f64 M))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (-.f64 (.f64 (.f64 (neg.f64 M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (.f64 (neg.f64 M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))) (.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (.f64 (neg.f64 M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))))))
(pow.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))))
(*.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))
(.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))) #s(literal 2 binary64)))
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(-.f64 (/.f64 (.f64 (.f64 m K) (.f64 m K)) (-.f64 (.f64 m K) (.f64 n K))) (/.f64 (.f64 (.f64 n K) (.f64 n K)) (-.f64 (.f64 m K) (.f64 n K))))
(fma.f64 m K (*.f64 n K))
(fma.f64 n K (*.f64 m K))
(fma.f64 K m (*.f64 n K))
(fma.f64 K n (*.f64 m K))
(/.f64 K (/.f64 #s(literal 1 binary64) (+.f64 m n)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 m K) (.f64 m K) (-.f64 (.f64 (.f64 n K) (.f64 n K)) (.f64 (.f64 m K) (.f64 n K)))) (fma.f64 (.f64 m (.f64 m m)) (.f64 K (.f64 K K)) (.f64 (.f64 n (.f64 n n)) (.f64 K (*.f64 K K))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 m K) (.f64 n K)) (-.f64 (.f64 (.f64 m K) (.f64 m K)) (.f64 (.f64 n K) (.f64 n K)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 m m (.f64 n (-.f64 n m))) (.f64 K (fma.f64 m (.f64 m m) (.f64 n (*.f64 n n))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 m n) (.f64 K (.f64 (+.f64 m n) (-.f64 m n)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 m m (.f64 n (-.f64 n m))) (.f64 (fma.f64 m (.f64 m m) (.f64 n (*.f64 n n))) K)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 m n) (.f64 (.f64 (+.f64 m n) (-.f64 m n)) K)))
(/.f64 (fma.f64 (.f64 m (.f64 m m)) (.f64 K (.f64 K K)) (.f64 (.f64 n (.f64 n n)) (.f64 K (.f64 K K)))) (fma.f64 (.f64 m K) (.f64 m K) (-.f64 (.f64 (.f64 n K) (.f64 n K)) (.f64 (.f64 m K) (*.f64 n K)))))
(/.f64 (-.f64 (.f64 (.f64 m K) (.f64 m K)) (.f64 (.f64 n K) (.f64 n K))) (-.f64 (.f64 m K) (.f64 n K)))
(/.f64 (.f64 K (fma.f64 m (.f64 m m) (.f64 n (.f64 n n)))) (fma.f64 m m (*.f64 n (-.f64 n m))))
(/.f64 (.f64 K (.f64 (+.f64 m n) (-.f64 m n))) (-.f64 m n))
(/.f64 (.f64 (fma.f64 m (.f64 m m) (.f64 n (.f64 n n))) K) (fma.f64 m m (*.f64 n (-.f64 n m))))
(/.f64 (.f64 (.f64 (+.f64 m n) (-.f64 m n)) K) (-.f64 m n))
(/.f64 (neg.f64 (fma.f64 (.f64 m (.f64 m m)) (.f64 K (.f64 K K)) (.f64 (.f64 n (.f64 n n)) (.f64 K (.f64 K K))))) (neg.f64 (fma.f64 (.f64 m K) (.f64 m K) (-.f64 (.f64 (.f64 n K) (.f64 n K)) (.f64 (.f64 m K) (*.f64 n K))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 m K) (.f64 m K)) (.f64 (.f64 n K) (.f64 n K)))) (neg.f64 (-.f64 (.f64 m K) (.f64 n K))))
(/.f64 (neg.f64 (.f64 K (fma.f64 m (.f64 m m) (.f64 n (.f64 n n))))) (neg.f64 (fma.f64 m m (*.f64 n (-.f64 n m)))))
(/.f64 (neg.f64 (.f64 K (.f64 (+.f64 m n) (-.f64 m n)))) (neg.f64 (-.f64 m n)))
(/.f64 (neg.f64 (.f64 (fma.f64 m (.f64 m m) (.f64 n (.f64 n n))) K)) (neg.f64 (fma.f64 m m (*.f64 n (-.f64 n m)))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 m n) (-.f64 m n)) K)) (neg.f64 (-.f64 m n)))
(/.f64 (fma.f64 (.f64 n (.f64 n n)) (.f64 K (.f64 K K)) (.f64 (.f64 m (.f64 m m)) (.f64 K (.f64 K K)))) (fma.f64 (.f64 n K) (.f64 n K) (-.f64 (.f64 (.f64 m K) (.f64 m K)) (.f64 (.f64 n K) (*.f64 m K)))))
(*.f64 (+.f64 m n) K)
(*.f64 K (+.f64 m n))
(.f64 (fma.f64 (.f64 m (.f64 m m)) (.f64 K (.f64 K K)) (.f64 (.f64 n (.f64 n n)) (.f64 K (.f64 K K)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 m K) (.f64 m K) (-.f64 (.f64 (.f64 n K) (.f64 n K)) (.f64 (.f64 m K) (.f64 n K))))))
(.f64 (-.f64 (.f64 (.f64 m K) (.f64 m K)) (.f64 (.f64 n K) (.f64 n K))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 m K) (*.f64 n K))))
(.f64 (.f64 K (fma.f64 m (.f64 m m) (.f64 n (.f64 n n)))) (/.f64 #s(literal 1 binary64) (fma.f64 m m (.f64 n (-.f64 n m)))))
(.f64 (.f64 K (*.f64 (+.f64 m n) (-.f64 m n))) (/.f64 #s(literal 1 binary64) (-.f64 m n)))
(.f64 (.f64 (fma.f64 m (.f64 m m) (.f64 n (.f64 n n))) K) (/.f64 #s(literal 1 binary64) (fma.f64 m m (.f64 n (-.f64 n m)))))
(.f64 (.f64 (*.f64 (+.f64 m n) (-.f64 m n)) K) (/.f64 #s(literal 1 binary64) (-.f64 m n)))
(.f64 (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (.f64 (+.f64 m n) (-.f64 m n))) (.f64 (+.f64 m n) K))
(.f64 (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (.f64 (fma.f64 m m (.f64 n (+.f64 m n))) (-.f64 m n))) (/.f64 K (/.f64 #s(literal 1 binary64) (fma.f64 m m (*.f64 n (+.f64 m n))))))
(.f64 (/.f64 K (.f64 (fma.f64 m m (.f64 n (+.f64 m n))) (-.f64 m n))) (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (/.f64 #s(literal 1 binary64) (fma.f64 m m (*.f64 n (+.f64 m n))))))
(.f64 (/.f64 K (.f64 (+.f64 m n) (-.f64 m n))) (/.f64 (*.f64 (+.f64 m n) (-.f64 m n)) (/.f64 #s(literal 1 binary64) (+.f64 m n))))
(.f64 (/.f64 K (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (fma.f64 m (.f64 m m) (.f64 n (.f64 n n))))) (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (fma.f64 m m (*.f64 n (-.f64 n m)))))
(.f64 (/.f64 K (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (*.f64 (+.f64 m n) (-.f64 m n)))) (+.f64 m n))
(.f64 (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (fma.f64 m (.f64 m m) (.f64 n (.f64 n n))))) (/.f64 K (fma.f64 m m (*.f64 n (-.f64 n m)))))
(.f64 (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (/.f64 (.f64 (+.f64 m n) (-.f64 m n)) (.f64 (+.f64 m n) (-.f64 m n)))) (/.f64 K (-.f64 m n)))

eval113.0ms (0.8%)

Memory: 23.9MiB live, 137.6MiB allocated
Compiler: Compiled 32 016 to 2 350 computations (92.7% saved)

prune157.0ms (1.1%)

Memory

-30.7MiB live, 177.6MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	531	16	547
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	532	16	548

Accuracy

97.2%

Counts

548 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	76.1%	(.f64 (cos.f64 (-.f64 (/.f64 (fma.f64 n K (.f64 m K)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	59.4%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (fma.f64 (.f64 (+.f64 n m) (+.f64 n m)) (/.f64 #s(literal 1/4 binary64) (*.f64 M M)) (/.f64 (+.f64 n m) (neg.f64 M))) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	72.7%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	37.2%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
	39.8%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 n (.f64 n #s(literal -1/4 binary64))))))
	75.3%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 m (.f64 m (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (fma.f64 n #s(literal -1/2 binary64) M) (/.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M) l)) m)) m)))))))
	41.3%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
▶	31.6%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	76.7%	(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	48.0%	(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 m n) (-.f64 m n)))) (/.f64 #s(literal 1 binary64) (-.f64 m n))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	36.6%	(.f64 (cos.f64 (-.f64 (exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 m n) K))) #s(literal -1 binary64))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	83.4%	(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	82.4%	(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 m K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	77.0%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 (.f64 m (.f64 K #s(literal -1/2 binary64))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 n K)) M)) (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 n K)) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	84.7%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	96.2%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 1 124 to 698 computations (37.9% saved)

simplify221.0ms (1.5%)

Memory

14.5MiB live, 366.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	cost-diff	256	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	cost-diff	384	(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
✓	cost-diff	5696	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	cost-diff	256	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	cost-diff	384	(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
✓	cost-diff	5696	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
✓	cost-diff	128	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	cost-diff	192	(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
✓	cost-diff	384	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
✓	cost-diff	1024	(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
✓	cost-diff	0	(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	cost-diff	128	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	cost-diff	384	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
✓	cost-diff	0	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	cost-diff	256	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	cost-diff	384	(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
✓	cost-diff	5696	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))

Rules

6 342×	`lower-fma.f32`
6 336×	`lower-fma.f64`
3 332×	`lower-*.f32`
3 308×	`lower-*.f64`
1 560×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	968
0	117	968
1	204	968
2	432	953
3	1177	923
4	3357	915
5	7925	915
0	8162	891

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
(cos.f64 M)
M
(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
(/.f64 (+.f64 m n) #s(literal 2 binary64))
(+.f64 m n)
m
n
#s(literal 2 binary64)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
(*.f64 K (+.f64 m n))
K
(+.f64 m n)
m
n
#s(literal 2 binary64)
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
(*.f64 K (+.f64 m n))
K
(+.f64 m n)
m
n
#s(literal 2 binary64)
M
(exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
(neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))))
#s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))
(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
(/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M))
(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)
#s(literal -1/4 binary64)
(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
(*.f64 (+.f64 n m) (+.f64 n m))
(+.f64 n m)
(neg.f64 M)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(cos.f64 (-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M))
(-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)
#s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K)))
(.f64 #s(literal 1/2 binary64) (.f64 n K))
#s(literal 1/2 binary64)
(*.f64 n K)
n
K
M
(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
(/.f64 (+.f64 m n) #s(literal 2 binary64))
(+.f64 m n)
m
#s(literal 2 binary64)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)))
(fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))
K
(.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M)))
(+.f64 n m)
n
m
(*.f64 #s(literal 1/2 binary64) (sin.f64 M))
#s(literal 1/2 binary64)
(sin.f64 M)
M
(cos.f64 M)
(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
(/.f64 (+.f64 m n) #s(literal 2 binary64))
(+.f64 m n)
#s(literal 2 binary64)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)

Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
(cos.f64 M)
M
(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l)))
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l))
(neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))
(neg.f64 (*.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M)))
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(*.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M))
(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
(neg.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M))
(/.f64 (+.f64 m n) #s(literal 2 binary64))
(+.f64 m n)
m
n
#s(literal 2 binary64)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) #s(literal -1/2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
(cos.f64 (fma.f64 K (*.f64 (+.f64 m n) #s(literal -1/2 binary64)) M))
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
(neg.f64 (fma.f64 K (*.f64 (+.f64 m n) #s(literal -1/2 binary64)) M))
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
(*.f64 K (+.f64 m n))
K
(+.f64 m n)
m
n
#s(literal 2 binary64)
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (fma.f64 K (.f64 (+.f64 m n) #s(literal -1/2 binary64)) M)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M))))))
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
(cos.f64 (fma.f64 K (*.f64 (+.f64 m n) #s(literal -1/2 binary64)) M))
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
(neg.f64 (fma.f64 K (*.f64 (+.f64 m n) #s(literal -1/2 binary64)) M))
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
(*.f64 K (+.f64 m n))
K
(+.f64 m n)
m
n
#s(literal 2 binary64)
M
(exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M)))))
(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
(-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M))))
(neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))))
(neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M))))
#s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))
#s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M)))
(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
(*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M))
(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
(fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M)
(/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M))
(/.f64 (*.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64))) M)
(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
(*.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal -1/4 binary64) M) #s(literal 1 binary64)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)
(fma.f64 (+.f64 m n) (/.f64 (*.f64 #s(literal -1/4 binary64) (+.f64 m n)) M) m)
#s(literal -1/4 binary64)
(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
(/.f64 (*.f64 (+.f64 m n) (+.f64 m n)) M)
(*.f64 (+.f64 n m) (+.f64 n m))
(*.f64 (+.f64 m n) (+.f64 m n))
(+.f64 n m)
(+.f64 m n)
(neg.f64 M)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l))) (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)))
(cos.f64 (-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M))
(cos.f64 (-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M))
(-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)
(-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)
#s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K)))
#s(approx (/ (* K (+ m n)) 2) (.f64 n (.f64 K #s(literal 1/2 binary64))))
(.f64 #s(literal 1/2 binary64) (.f64 n K))
(.f64 n (.f64 K #s(literal 1/2 binary64)))
#s(literal 1/2 binary64)
(*.f64 n K)
(*.f64 K n)
n
K
M
(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l)))
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l))
(neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))
(neg.f64 (*.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M)))
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(*.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M))
(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
(neg.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M))
(/.f64 (+.f64 m n) #s(literal 2 binary64))
(+.f64 m n)
m
#s(literal 2 binary64)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l))) #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 m n) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 m n) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)))
(fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))
(fma.f64 K (.f64 (+.f64 m n) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))
K
(.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M)))
(.f64 (+.f64 m n) (.f64 #s(literal 1/2 binary64) (sin.f64 M)))
(+.f64 n m)
(+.f64 m n)
n
m
(*.f64 #s(literal 1/2 binary64) (sin.f64 M))
#s(literal 1/2 binary64)
(sin.f64 M)
M
(cos.f64 M)
(exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l)))
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) l))
(neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))
(neg.f64 (*.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M)))
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(*.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M))
(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
(neg.f64 (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) M))
(/.f64 (+.f64 m n) #s(literal 2 binary64))
(+.f64 m n)
#s(literal 2 binary64)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)

localize394.0ms (2.7%)

Memory

26.9MiB live, 620.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
✓	accuracy	99.8%	(fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))
✓	accuracy	99.8%	(.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M)))
✓	accuracy	36.6%	#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)))
✓	accuracy	100.0%	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 n K))
✓	accuracy	51.9%	#s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K)))
✓	accuracy	37.6%	(cos.f64 (-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M))
✓	accuracy	94.1%	(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
✓	accuracy	90.7%	(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
✓	accuracy	88.7%	(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
✓	accuracy	37.6%	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	accuracy	100.0%	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
✓	accuracy	100.0%	(*.f64 K (+.f64 m n))
✓	accuracy	37.6%	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	accuracy	19.9%	#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
✓	accuracy	100.0%	(cos.f64 M)
✓	accuracy	100.0%	(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	accuracy	100.0%	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
✓	accuracy	40.2%	#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))

Samples

230.0ms	212×	1	valid
17.0ms	44×	0	valid

Compiler

Compiled 798 to 45 computations (94.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

ival-mult: 31.0ms (23.8% of total)

ival-cos: 26.0ms (20% of total)

adjust: 17.0ms (13.1% of total)

ival-add: 13.0ms (10% of total)

ival-div: 11.0ms (8.4% of total)

ival-sub: 10.0ms (7.7% of total)

ival-sin: 8.0ms (6.1% of total)

ival-pow2: 5.0ms (3.8% of total)

ival-neg: 4.0ms (3.1% of total)

ival-fabs: 4.0ms (3.1% of total)

ival-exp: 2.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series109.0ms (0.7%)

Memory

10.1MiB live, 238.9MiB allocated

Counts

24 → 1 020

Calls

Call 1

Inputs
#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) (patch (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #<representation binary64>) () ())
#s(alt (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))) (patch (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (patch (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M) (patch (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M) #<representation binary64>) () ())
#s(alt (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (patch (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (patch (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) (patch (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())
#s(alt (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (patch (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (patch (.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (patch (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #<representation binary64>) () ())
#s(alt #s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M)) (patch #s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M)) #<representation binary64>) () ())
#s(alt (cos.f64 M) (patch (cos.f64 M) #<representation binary64>) () ())
#s(alt #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)) (patch #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)) #<representation binary64>) () ())
#s(alt (.f64 K (+.f64 m n)) (patch (.f64 K (+.f64 m n)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (patch (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) #<representation binary64>) () ())
#s(alt (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)) (patch (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)) #<representation binary64>) () ())
#s(alt (cos.f64 (-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (patch (cos.f64 (-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) #<representation binary64>) () ())
#s(alt #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) (patch #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (.f64 n K)) (patch (.f64 #s(literal 1/2 binary64) (.f64 n K)) #<representation binary64>) () ())
#s(alt #s(approx (cos (- (/ (* K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) (patch #s(approx (cos (- (/ (* K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (patch (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) #<representation binary64>) () ())
#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())

Outputs
#s(alt (pow (- (* 1/2 n) M) 2) (taylor 0 m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* m (- (* 1/2 n) M)) (pow (- (* 1/2 n) M) 2)) (taylor 0 m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2)) (taylor 0 m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2)) (taylor 0 m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow m 2)) (taylor inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m))) (taylor inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m))) (taylor inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m))) (taylor inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow m 2)) (taylor -inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m))) (taylor -inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m)))) (taylor -inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m)))) (taylor -inf m) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (- (* 1/2 m) M) 2) (taylor 0 n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* n (- (* 1/2 m) M)) (pow (- (* 1/2 m) M) 2)) (taylor 0 n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2)) (taylor 0 n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2)) (taylor 0 n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow n 2)) (taylor inf n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n))) (taylor inf n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n))) (taylor inf n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n))) (taylor inf n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow n 2)) (taylor -inf n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n))) (taylor -inf n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n)))) (taylor -inf n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n)))) (taylor -inf n) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (pow (+ m n) 2)) (taylor 0 M) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2))) (taylor 0 M) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) (taylor 0 M) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) (taylor 0 M) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow M 2) (taylor inf M) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow M 2) (+ 1 (* -1 (/ (+ m n) M)))) (taylor inf M) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow M 2) (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2)))))) (taylor inf M) (#s(alt (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) (patch (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (cos M) (taylor 0 K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor 0 K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor 0 K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor 0 K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* K (* (sin M) (+ m n)))) (taylor inf K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* K (+ (* 1/2 (* (sin M) (+ m n))) (/ (cos M) K))) (taylor inf K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* K (+ (* 1/2 (* (sin M) (+ m n))) (/ (cos M) K))) (taylor inf K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* K (+ (* 1/2 (* (sin M) (+ m n))) (/ (cos M) K))) (taylor inf K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* K (* (sin M) (+ m n)))) (taylor -inf K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* K (+ (* -1 (/ (cos M) K)) (* -1/2 (* (sin M) (+ m n)))))) (taylor -inf K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* K (+ (* -1 (/ (cos M) K)) (* -1/2 (* (sin M) (+ m n)))))) (taylor -inf K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* K (+ (* -1 (/ (cos M) K)) (* -1/2 (* (sin M) (+ m n)))))) (taylor -inf K) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* m (sin M))))) (taylor 0 n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M)))))) (taylor 0 n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M)))))) (taylor 0 n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M)))))) (taylor 0 n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* K (* n (sin M)))) (taylor inf n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* n (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* m (sin M))) n)) (/ (cos M) n)))) (taylor inf n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* n (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* m (sin M))) n)) (/ (cos M) n)))) (taylor inf n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* n (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* m (sin M))) n)) (/ (cos M) n)))) (taylor inf n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* K (* n (sin M)))) (taylor -inf n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* m (sin M))))) n)) (* -1/2 (* K (sin M)))))) (taylor -inf n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* m (sin M))))) n)) (* -1/2 (* K (sin M)))))) (taylor -inf n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* n (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* m (sin M))))) n)) (* -1/2 (* K (sin M)))))) (taylor -inf n) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* n (sin M))))) (taylor 0 m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M)))))) (taylor 0 m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M)))))) (taylor 0 m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M)))))) (taylor 0 m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* K (* m (sin M)))) (taylor inf m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* m (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* n (sin M))) m)) (/ (cos M) m)))) (taylor inf m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* m (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* n (sin M))) m)) (/ (cos M) m)))) (taylor inf m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* m (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* n (sin M))) m)) (/ (cos M) m)))) (taylor inf m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (* K (* m (sin M)))) (taylor -inf m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* m (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* n (sin M))))) m)) (* -1/2 (* K (sin M)))))) (taylor -inf m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* m (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* n (sin M))))) m)) (* -1/2 (* K (sin M)))))) (taylor -inf m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* m (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* n (sin M))))) m)) (* -1/2 (* K (sin M)))))) (taylor -inf m) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (* K (* M (+ m n))))) (taylor 0 M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* M (+ (* -1/2 M) (* 1/2 (* K (+ m n)))))) (taylor 0 M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* M (+ (* 1/2 (* K (+ m n))) (* M (- (* -1/12 (* K (* M (+ m n)))) 1/2))))) (taylor 0 M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor inf M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor inf M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor inf M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor inf M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor -inf M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor -inf M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor -inf M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())
#s(alt (+ (cos M) (* 1/2 (* K (* (sin M) (+ m n))))) (taylor -inf M) (#s(alt (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) (patch (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)) #<representation binary64>) () ())) ())

Calls

255 calls:

Time	Variable		Point	Expression
12.0ms	n	@	-inf	(* 1/2 (* n K))
3.0ms	n	@	0	(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
3.0ms	m	@	inf	(+ (* M (/ (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (neg M))) M)
3.0ms	m	@	-inf	(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
2.0ms	M	@	0	(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

simplify528.0ms (3.6%)

Memory

-11.8MiB live, 683.5MiB allocated

Algorithm

1×	egg-herbie

Rules

8 956×	`lower-fma.f64`
8 956×	`lower-fma.f32`
6 738×	`lower-+.f64`
6 738×	`lower-+.f32`
6 016×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1036	25459
1	3361	24621
0	8060	23823

Stop Event

1×	iter limit
1×	node limit

Counts

1 020 → 1 018

Calls

Call 1

Inputs
(pow (- (* 1/2 n) M) 2)
(+ (* m (- (* 1/2 n) M)) (pow (- (* 1/2 n) M) 2))
(+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))
(+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))
(* 1/4 (pow m 2))
(* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))
(* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))
(* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))
(* 1/4 (pow m 2))
(* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))
(* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))
(* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))
(pow (- (* 1/2 m) M) 2)
(+ (* n (- (* 1/2 m) M)) (pow (- (* 1/2 m) M) 2))
(+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))
(+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))
(* 1/4 (pow n 2))
(* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))
(* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))
(* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))
(* 1/4 (pow n 2))
(* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))
(* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))
(* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))
(* 1/4 (pow (+ m n) 2))
(+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2)))
(+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))
(+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))
(pow M 2)
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(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K n)) M))
(+ (cos (- (* 1/2 (* K n)) M)) (* -1/2 (* K (* m (sin (- (* 1/2 (* K n)) M))))))
(+ (cos (- (* 1/2 (* K n)) M)) (* m (- (* -1/8 (* (pow K 2) (* m (cos (- (* 1/2 (* K n)) M))))) (* 1/2 (* K (sin (- (* 1/2 (* K n)) M)))))))
(+ (cos (- (* 1/2 (* K n)) M)) (* m (- (* m (+ (* -1/8 (* (pow K 2) (cos (- (* 1/2 (* K n)) M)))) (* 1/48 (* (pow K 3) (* m (sin (- (* 1/2 (* K n)) M))))))) (* 1/2 (* K (sin (- (* 1/2 (* K n)) M)))))))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (- n (* -1 m)))) M))
(cos (- (* 1/2 (* K (- n (* -1 m)))) M))
(cos (- (* 1/2 (* K (- n (* -1 m)))) M))
(cos (- (* 1/2 (* K (- n (* -1 m)))) M))
(cos (- (* 1/2 (* K m)) M))
(+ (cos (- (* 1/2 (* K m)) M)) (* -1/2 (* K (* n (sin (- (* 1/2 (* K m)) M))))))
(+ (cos (- (* 1/2 (* K m)) M)) (* n (- (* -1/8 (* (pow K 2) (* n (cos (- (* 1/2 (* K m)) M))))) (* 1/2 (* K (sin (- (* 1/2 (* K m)) M)))))))
(+ (cos (- (* 1/2 (* K m)) M)) (* n (- (* n (+ (* -1/8 (* (pow K 2) (cos (- (* 1/2 (* K m)) M)))) (* 1/48 (* (pow K 3) (* n (sin (- (* 1/2 (* K m)) M))))))) (* 1/2 (* K (sin (- (* 1/2 (* K m)) M)))))))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (- m (* -1 n)))) M))
(cos (- (* 1/2 (* K (- m (* -1 n)))) M))
(cos (- (* 1/2 (* K (- m (* -1 n)))) M))
(cos (- (* 1/2 (* K (- m (* -1 n)))) M))
(cos (* 1/2 (* K (+ m n))))
(+ (cos (* 1/2 (* K (+ m n)))) (* M (sin (* 1/2 (* K (+ m n))))))
(+ (cos (* 1/2 (* K (+ m n)))) (* M (- (* -1/2 (* M (cos (* 1/2 (* K (+ m n)))))) (* -1 (sin (* 1/2 (* K (+ m n))))))))
(+ (cos (* 1/2 (* K (+ m n)))) (* M (- (* M (+ (* -1/2 (cos (* 1/2 (* K (+ m n))))) (* -1/6 (* M (sin (* 1/2 (* K (+ m n)))))))) (* -1 (sin (* 1/2 (* K (+ m n))))))))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (- (* 1/2 (* K (+ m n))) M))
(cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))
(cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))
(cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))
(cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))
(* 1/2 (* m (sin M)))
(+ (* 1/2 (* m (sin M))) (* 1/2 (* n (sin M))))
(+ (* 1/2 (* m (sin M))) (* 1/2 (* n (sin M))))
(+ (* 1/2 (* m (sin M))) (* 1/2 (* n (sin M))))
(* 1/2 (* n (sin M)))
(* n (+ (* 1/2 (sin M)) (* 1/2 (/ (* m (sin M)) n))))
(* n (+ (* 1/2 (sin M)) (* 1/2 (/ (* m (sin M)) n))))
(* n (+ (* 1/2 (sin M)) (* 1/2 (/ (* m (sin M)) n))))
(* 1/2 (* n (sin M)))
(* -1 (* n (+ (* -1/2 (sin M)) (* -1/2 (/ (* m (sin M)) n)))))
(* -1 (* n (+ (* -1/2 (sin M)) (* -1/2 (/ (* m (sin M)) n)))))
(* -1 (* n (+ (* -1/2 (sin M)) (* -1/2 (/ (* m (sin M)) n)))))
(* 1/2 (* n (sin M)))
(+ (* 1/2 (* m (sin M))) (* 1/2 (* n (sin M))))
(+ (* 1/2 (* m (sin M))) (* 1/2 (* n (sin M))))
(+ (* 1/2 (* m (sin M))) (* 1/2 (* n (sin M))))
(* 1/2 (* m (sin M)))
(* m (+ (* 1/2 (sin M)) (* 1/2 (/ (* n (sin M)) m))))
(* m (+ (* 1/2 (sin M)) (* 1/2 (/ (* n (sin M)) m))))
(* m (+ (* 1/2 (sin M)) (* 1/2 (/ (* n (sin M)) m))))
(* 1/2 (* m (sin M)))
(* -1 (* m (+ (* -1/2 (sin M)) (* -1/2 (/ (* n (sin M)) m)))))
(* -1 (* m (+ (* -1/2 (sin M)) (* -1/2 (/ (* n (sin M)) m)))))
(* -1 (* m (+ (* -1/2 (sin M)) (* -1/2 (/ (* n (sin M)) m)))))
(* 1/2 (* M (+ m n)))
(* M (+ (* -1/12 (* (pow M 2) (+ m n))) (* 1/2 (+ m n))))
(* M (+ (* 1/2 (+ m n)) (* (pow M 2) (+ (* -1/12 (+ m n)) (* 1/240 (* (pow M 2) (+ m n)))))))
(* M (+ (* 1/2 (+ m n)) (* (pow M 2) (+ (* -1/12 (+ m n)) (* (pow M 2) (+ (* -1/10080 (* (pow M 2) (+ m n))) (* 1/240 (+ m n))))))))
(* 1/2 (* (sin M) (+ m n)))
(* 1/2 (* (sin M) (+ m n)))
(* 1/2 (* (sin M) (+ m n)))
(* 1/2 (* (sin M) (+ m n)))
(* 1/2 (* (sin M) (+ m n)))
(* 1/2 (* (sin M) (+ m n)))
(* 1/2 (* (sin M) (+ m n)))
(* 1/2 (* (sin M) (+ m n)))
(cos M)
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(* 1/2 (* K (* (sin M) (+ m n))))
(* K (+ (* 1/2 (* (sin M) (+ m n))) (/ (cos M) K)))
(* K (+ (* 1/2 (* (sin M) (+ m n))) (/ (cos M) K)))
(* K (+ (* 1/2 (* (sin M) (+ m n))) (/ (cos M) K)))
(* 1/2 (* K (* (sin M) (+ m n))))
(* -1 (* K (+ (* -1 (/ (cos M) K)) (* -1/2 (* (sin M) (+ m n))))))
(* -1 (* K (+ (* -1 (/ (cos M) K)) (* -1/2 (* (sin M) (+ m n))))))
(* -1 (* K (+ (* -1 (/ (cos M) K)) (* -1/2 (* (sin M) (+ m n))))))
(+ (cos M) (* 1/2 (* K (* m (sin M)))))
(+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M))))))
(+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M))))))
(+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M))))))
(* 1/2 (* K (* n (sin M))))
(* n (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* m (sin M))) n)) (/ (cos M) n))))
(* n (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* m (sin M))) n)) (/ (cos M) n))))
(* n (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* m (sin M))) n)) (/ (cos M) n))))
(* 1/2 (* K (* n (sin M))))
(* -1 (* n (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* m (sin M))))) n)) (* -1/2 (* K (sin M))))))
(* -1 (* n (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* m (sin M))))) n)) (* -1/2 (* K (sin M))))))
(* -1 (* n (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* m (sin M))))) n)) (* -1/2 (* K (sin M))))))
(+ (cos M) (* 1/2 (* K (* n (sin M)))))
(+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M))))))
(+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M))))))
(+ (cos M) (+ (* 1/2 (* K (* m (sin M)))) (* 1/2 (* K (* n (sin M))))))
(* 1/2 (* K (* m (sin M))))
(* m (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* n (sin M))) m)) (/ (cos M) m))))
(* m (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* n (sin M))) m)) (/ (cos M) m))))
(* m (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* n (sin M))) m)) (/ (cos M) m))))
(* 1/2 (* K (* m (sin M))))
(* -1 (* m (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* n (sin M))))) m)) (* -1/2 (* K (sin M))))))
(* -1 (* m (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* n (sin M))))) m)) (* -1/2 (* K (sin M))))))
(* -1 (* m (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* n (sin M))))) m)) (* -1/2 (* K (sin M))))))
1
(+ 1 (* 1/2 (* K (* M (+ m n)))))
(+ 1 (* M (+ (* -1/2 M) (* 1/2 (* K (+ m n))))))
(+ 1 (* M (+ (* 1/2 (* K (+ m n))) (* M (- (* -1/12 (* K (* M (+ m n)))) 1/2)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))

Outputs
(pow (- (* 1/2 n) M) 2)
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (-.f64 (*.f64 #s(literal 1/2 binary64) n) M))
(+ (* m (- (* 1/2 n) M)) (pow (- (* 1/2 n) M) 2))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) n) M) m))
(+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (.f64 m (-.f64 (fma.f64 m #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) n)) M)))
(+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))
(fma.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (.f64 m (-.f64 (fma.f64 m #s(literal 1/4 binary64) (.f64 #s(literal 1/2 binary64) n)) M)))
(* 1/4 (pow m 2))
(.f64 #s(literal 1/4 binary64) (.f64 m m))
(* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))
(.f64 (.f64 m m) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) n) M) m)))
(* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))
(.f64 (.f64 m m) (-.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 n m) #s(literal 1/4 binary64)) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (-.f64 (.f64 #s(literal 1/2 binary64) n) M)) (.f64 m m))) (/.f64 M m)))
(* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))
(.f64 (.f64 m m) (-.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 n m) #s(literal 1/4 binary64)) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (-.f64 (.f64 #s(literal 1/2 binary64) n) M)) (.f64 m m))) (/.f64 M m)))
(* 1/4 (pow m 2))
(.f64 #s(literal 1/4 binary64) (.f64 m m))
(* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))
(.f64 (.f64 m m) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) n) M) m)))
(* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))
(.f64 (.f64 m m) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M)) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (-.f64 (.f64 #s(literal 1/2 binary64) n) M)) m)) m)))
(* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))
(.f64 (.f64 m m) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M)) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (-.f64 (.f64 #s(literal 1/2 binary64) n) M)) m)) m)))
(pow (- (* 1/2 m) M) 2)
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) (-.f64 (*.f64 #s(literal 1/2 binary64) m) M))
(+ (* n (- (* 1/2 m) M)) (pow (- (* 1/2 m) M) 2))
(.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) (+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) m) M) n))
(+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))
(fma.f64 n (-.f64 (fma.f64 #s(literal 1/2 binary64) m (.f64 n #s(literal 1/4 binary64))) M) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) (-.f64 (.f64 #s(literal 1/2 binary64) m) M)))
(+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))
(fma.f64 n (-.f64 (fma.f64 #s(literal 1/2 binary64) m (.f64 n #s(literal 1/4 binary64))) M) (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) (-.f64 (.f64 #s(literal 1/2 binary64) m) M)))
(* 1/4 (pow n 2))
(.f64 #s(literal 1/4 binary64) (.f64 n n))
(* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))
(.f64 (.f64 n n) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) m) M) n)))
(* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))
(.f64 (.f64 n n) (-.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 m n) #s(literal 1/4 binary64)) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) (-.f64 (.f64 #s(literal 1/2 binary64) m) M)) (.f64 n n))) (/.f64 M n)))
(* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))
(.f64 (.f64 n n) (-.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 m n) #s(literal 1/4 binary64)) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) (-.f64 (.f64 #s(literal 1/2 binary64) m) M)) (.f64 n n))) (/.f64 M n)))
(* 1/4 (pow n 2))
(.f64 #s(literal 1/4 binary64) (.f64 n n))
(* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))
(.f64 (.f64 n n) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) m) M) n)))
(* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))
(.f64 (.f64 n n) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M)) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) (-.f64 (.f64 #s(literal 1/2 binary64) m) M)) n)) n)))
(* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))
(.f64 (.f64 n n) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M)) (/.f64 (.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) (-.f64 (.f64 #s(literal 1/2 binary64) m) M)) n)) n)))
(* 1/4 (pow (+ m n) 2))
(.f64 #s(literal 1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m)))
(+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2)))
(fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m)) (.f64 M (-.f64 (neg.f64 m) n)))
(+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))
(fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m)) (.f64 M (-.f64 M (+.f64 n m))))
(+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))
(fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m)) (.f64 M (-.f64 M (+.f64 n m))))
(pow M 2)
(*.f64 M M)
(* (pow M 2) (+ 1 (* -1 (/ (+ m n) M))))
(.f64 (.f64 M M) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 n m) M)))
(* (pow M 2) (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
(.f64 (.f64 M M) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) (.f64 M M)) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 n m) M))))
(* (pow M 2) (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
(.f64 (.f64 M M) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) (.f64 M M)) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 n m) M))))
(pow M 2)
(*.f64 M M)
(* (pow M 2) (+ 1 (* -1 (/ (+ m n) M))))
(.f64 (.f64 M M) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 n m) M)))
(* (pow M 2) (+ 1 (* -1 (/ (+ m (+ n (* -1/4 (/ (pow (+ m n) 2) M)))) M))))
(.f64 (.f64 M M) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M)))
(* (pow M 2) (+ 1 (* -1 (/ (+ m (+ n (* -1/4 (/ (pow (+ m n) 2) M)))) M))))
(.f64 (.f64 M M) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M)))
(- (* 1/2 n) M)
(-.f64 (*.f64 #s(literal 1/2 binary64) n) M)
(- (+ (* 1/2 m) (* 1/2 n)) M)
(fma.f64 #s(literal 1/2 binary64) (+.f64 n m) (neg.f64 M))
(- (+ (* 1/2 m) (* 1/2 n)) M)
(fma.f64 #s(literal 1/2 binary64) (+.f64 n m) (neg.f64 M))
(- (+ (* 1/2 m) (* 1/2 n)) M)
(fma.f64 #s(literal 1/2 binary64) (+.f64 n m) (neg.f64 M))
(* 1/2 m)
(*.f64 #s(literal 1/2 binary64) m)
(* m (- (+ 1/2 (* 1/2 (/ n m))) (/ M m)))
(.f64 m (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) m)))
(* m (- (+ 1/2 (* 1/2 (/ n m))) (/ M m)))
(.f64 m (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) m)))
(* m (- (+ 1/2 (* 1/2 (/ n m))) (/ M m)))
(.f64 m (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) m)))
(* 1/2 m)
(*.f64 #s(literal 1/2 binary64) m)
(* -1 (* m (- (* -1 (/ (- (* 1/2 n) M) m)) 1/2)))
(neg.f64 (.f64 m (+.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (neg.f64 m)) #s(literal -1/2 binary64))))
(* -1 (* m (- (* -1 (/ (- (* 1/2 n) M) m)) 1/2)))
(neg.f64 (.f64 m (+.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (neg.f64 m)) #s(literal -1/2 binary64))))
(* -1 (* m (- (* -1 (/ (- (* 1/2 n) M) m)) 1/2)))
(neg.f64 (.f64 m (+.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) n) M) (neg.f64 m)) #s(literal -1/2 binary64))))
(- (* 1/2 m) M)
(-.f64 (*.f64 #s(literal 1/2 binary64) m) M)
(- (+ (* 1/2 m) (* 1/2 n)) M)
(fma.f64 #s(literal 1/2 binary64) (+.f64 n m) (neg.f64 M))
(- (+ (* 1/2 m) (* 1/2 n)) M)
(fma.f64 #s(literal 1/2 binary64) (+.f64 n m) (neg.f64 M))
(- (+ (* 1/2 m) (* 1/2 n)) M)
(fma.f64 #s(literal 1/2 binary64) (+.f64 n m) (neg.f64 M))
(* 1/2 n)
(*.f64 #s(literal 1/2 binary64) n)
(* n (- (+ 1/2 (* 1/2 (/ m n))) (/ M n)))
(.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) n)))
(* n (- (+ 1/2 (* 1/2 (/ m n))) (/ M n)))
(.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) n)))
(* n (- (+ 1/2 (* 1/2 (/ m n))) (/ M n)))
(.f64 n (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) n)))
(* 1/2 n)
(*.f64 #s(literal 1/2 binary64) n)
(* -1 (* n (- (* -1 (/ (- (* 1/2 m) M) n)) 1/2)))
(.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) n)) #s(literal -1/2 binary64)) (neg.f64 n))
(* -1 (* n (- (* -1 (/ (- (* 1/2 m) M) n)) 1/2)))
(.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) n)) #s(literal -1/2 binary64)) (neg.f64 n))
(* -1 (* n (- (* -1 (/ (- (* 1/2 m) M) n)) 1/2)))
(.f64 (+.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) m) M) n)) #s(literal -1/2 binary64)) (neg.f64 n))
(* 1/2 (+ m n))
(*.f64 #s(literal 1/2 binary64) (+.f64 n m))
(+ (* -1 M) (* 1/2 (+ m n)))
(fma.f64 #s(literal 1/2 binary64) (+.f64 n m) (neg.f64 M))
(+ (* -1 M) (* 1/2 (+ m n)))
(fma.f64 #s(literal 1/2 binary64) (+.f64 n m) (neg.f64 M))
(+ (* -1 M) (* 1/2 (+ m n)))
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(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (neg.f64 M))
(* 1/2 (* K m))
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(* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))
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(* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))
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(* 1/2 (* K m))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(.f64 (.f64 #s(literal 1/2 binary64) K) (*.f64 m (sin.f64 M)))
(* m (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* n (sin M))) m)) (/ (cos M) m))))
(.f64 m (fma.f64 #s(literal 1/2 binary64) (fma.f64 K (sin.f64 M) (/.f64 (.f64 K (*.f64 n (sin.f64 M))) m)) (/.f64 (cos.f64 M) m)))
(* m (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* n (sin M))) m)) (/ (cos M) m))))
(.f64 m (fma.f64 #s(literal 1/2 binary64) (fma.f64 K (sin.f64 M) (/.f64 (.f64 K (*.f64 n (sin.f64 M))) m)) (/.f64 (cos.f64 M) m)))
(* m (+ (* 1/2 (* K (sin M))) (+ (* 1/2 (/ (* K (* n (sin M))) m)) (/ (cos M) m))))
(.f64 m (fma.f64 #s(literal 1/2 binary64) (fma.f64 K (sin.f64 M) (/.f64 (.f64 K (*.f64 n (sin.f64 M))) m)) (/.f64 (cos.f64 M) m)))
(* 1/2 (* K (* m (sin M))))
(.f64 (.f64 #s(literal 1/2 binary64) K) (*.f64 m (sin.f64 M)))
(* -1 (* m (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* n (sin M))))) m)) (* -1/2 (* K (sin M))))))
(neg.f64 (.f64 m (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) K) (sin.f64 M)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 K (*.f64 n (sin.f64 M))) (cos.f64 M)) m))))
(* -1 (* m (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* n (sin M))))) m)) (* -1/2 (* K (sin M))))))
(neg.f64 (.f64 m (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) K) (sin.f64 M)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 K (*.f64 n (sin.f64 M))) (cos.f64 M)) m))))
(* -1 (* m (+ (* -1 (/ (+ (cos M) (* 1/2 (* K (* n (sin M))))) m)) (* -1/2 (* K (sin M))))))
(neg.f64 (.f64 m (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) K) (sin.f64 M)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 K (*.f64 n (sin.f64 M))) (cos.f64 M)) m))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* K (* M (+ m n)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 M (+.f64 n m)) K) #s(literal 1 binary64))
(+ 1 (* M (+ (* -1/2 M) (* 1/2 (* K (+ m n))))))
(fma.f64 M (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 n m) K) (.f64 M #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* M (+ (* 1/2 (* K (+ m n))) (* M (- (* -1/12 (* K (* M (+ m n)))) 1/2)))))
(fma.f64 M (fma.f64 M (fma.f64 (.f64 #s(literal -1/12 binary64) K) (.f64 M (+.f64 n m)) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (+.f64 n m) K))) #s(literal 1 binary64))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 n m) (sin.f64 M))) (cos.f64 M))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 n m) (sin.f64 M))) (cos.f64 M))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 n m) (sin.f64 M))) (cos.f64 M))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 n m) (sin.f64 M))) (cos.f64 M))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 n m) (sin.f64 M))) (cos.f64 M))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 n m) (sin.f64 M))) (cos.f64 M))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 n m) (sin.f64 M))) (cos.f64 M))
(+ (cos M) (* 1/2 (* K (* (sin M) (+ m n)))))
(fma.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 n m) (sin.f64 M))) (cos.f64 M))

rewrite373.0ms (2.5%)

Memory

16.7MiB live, 601.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 006×	`lower-*.f32`
5 984×	`lower-*.f64`
3 980×	`lower-fma.f32`
3 974×	`lower-fma.f64`
3 458×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	382
0	107	374
1	356	374
2	2711	374
0	8811	374

Stop Event

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

Counts

24 → 659

Calls

Call 1

Inputs
(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
(-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M)
(-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
(cos.f64 M)
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(*.f64 K (+.f64 m n))
(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
(cos.f64 (-.f64 #s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M))
#s(approx (/ (* K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K)))
(.f64 #s(literal 1/2 binary64) (.f64 n K))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M)))
(.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M)))
(fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))

Outputs
(+.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (+.f64 m n) #s(literal 1/2 binary64))) (*.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (neg.f64 M)))
(+.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (*.f64 (neg.f64 M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))) #s(literal 1 binary64)))
(exp.f64 (+.f64 (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))))
(fma.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (neg.f64 M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))))
(fma.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (neg.f64 M)))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))) (.f64 (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64))) (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M))) (.f64 (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M)) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M)) (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M))) (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))
(/.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))) (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (*.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64))))
(/.f64 (.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (*.f64 (neg.f64 M) M))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (*.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (*.f64 (neg.f64 M) M)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))
(pow.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) #s(literal 2 binary64))
(pow.f64 (*.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))))
(*.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M)))
(.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64)))) #s(literal 2 binary64)))
(.f64 (.f64 (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M)) (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)) #s(literal 2 binary64)))
(+.f64 (*.f64 (+.f64 m n) #s(literal 1/2 binary64)) (neg.f64 M))
(+.f64 (neg.f64 M) (*.f64 (+.f64 m n) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))))
(-.f64 (*.f64 (+.f64 m n) #s(literal 1/2 binary64)) M)
(-.f64 (/.f64 (.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64)) (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64)))) (/.f64 (.f64 M (.f64 M M)) (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (*.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)) (/.f64 (*.f64 M M) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))
(-.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) #s(literal 0 binary64)) M)
(fma.f64 M #s(literal -1 binary64) (*.f64 (+.f64 m n) #s(literal 1/2 binary64)))
(fma.f64 (+.f64 m n) #s(literal 1/2 binary64) (neg.f64 M))
(fma.f64 #s(literal 1/2 binary64) (+.f64 m n) (neg.f64 M))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 m n)) #s(literal -1 binary64)) (neg.f64 M))
(fma.f64 (neg.f64 (+.f64 m n)) #s(literal -1/2 binary64) (neg.f64 M))
(fma.f64 #s(literal 1 binary64) (*.f64 (+.f64 m n) #s(literal 1/2 binary64)) (neg.f64 M))
(fma.f64 #s(literal -1 binary64) M (*.f64 (+.f64 m n) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fma.f64 m (.f64 m m) (.f64 n (.f64 n n)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 n (-.f64 n m) (.f64 m m))) (neg.f64 M))
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fma.f64 m (.f64 m m) (.f64 n (.f64 n n)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 m (-.f64 m n) (.f64 n n))) (neg.f64 M))
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 m n) (-.f64 m n))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 m n)) (neg.f64 M))
(fma.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 m n) (-.f64 n m))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 n m)) (neg.f64 M))
(/.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))) (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (-.f64 (.f64 M M) (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (neg.f64 M)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64))) (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M))))
(/.f64 (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M)) (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))
(/.f64 (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M)) (-.f64 (*.f64 (+.f64 m n) #s(literal 1/2 binary64)) (neg.f64 M)))
(/.f64 (neg.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M))))) (neg.f64 (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M))) (neg.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M)))
(/.f64 (exp.f64 (log.f64 (fma.f64 (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n))) #s(literal 1/8 binary64) (neg.f64 (.f64 M (.f64 M M)))))) (exp.f64 (log.f64 (fma.f64 M (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64))))))
(/.f64 (exp.f64 (log.f64 (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/4 binary64) (.f64 (neg.f64 M) M)))) (exp.f64 (log.f64 (fma.f64 (+.f64 m n) #s(literal 1/2 binary64) M))))
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(pow.f64 (/.f64 (-.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (.f64 (sin.f64 M) K)) (cos.f64 M)) (-.f64 (pow.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (.f64 (sin.f64 M) K)) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 M M)))))) #s(literal -1 binary64))
(.f64 (fma.f64 (pow.f64 (.f64 (.f64 K (+.f64 m n)) (sin.f64 M)) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (cos.f64 M) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 M) (-.f64 (cos.f64 M) (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (.f64 (sin.f64 M) K))) (pow.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (*.f64 (sin.f64 M) K)) #s(literal 2 binary64)))))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (.f64 (sin.f64 M) K)) #s(literal 2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 M M))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (.f64 (sin.f64 M) K)) (cos.f64 M))))

eval633.0ms (4.3%)

Memory: 16.4MiB live, 626.9MiB allocated
Compiler: Compiled 128 528 to 6 795 computations (94.7% saved)

prune454.0ms (3.1%)

Memory

-12.2MiB live, 738.6MiB allocated

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	2 565	16	2 581
Fresh	11	0	11
Picked	5	0	5
Done	0	0	0
Total	2 581	16	2 597

Accuracy

97.2%

Counts

2 597 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	9.5%	(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	21.1%	(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M M)) (/.f64 #s(literal 2 binary64) (+.f64 m n)) (.f64 (+.f64 #s(literal 0 binary64) M) K)) (.f64 (+.f64 #s(literal 0 binary64) M) (/.f64 #s(literal 2 binary64) (+.f64 m n))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	31.6%	(.f64 (cos.f64 (-.f64 (/.f64 (fma.f64 n K (.f64 m K)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
▶	32.2%	(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	13.8%	(.f64 (cos.f64 (-.f64 (exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))) #s(literal -1 binary64))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	28.2%	(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 n (.f64 #s(literal 1/2 binary64) (fma.f64 K (/.f64 m n) K)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	44.0%	(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
	33.2%	(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
▶	31.9%	(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	32.5%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 m K) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 n K) (neg.f64 M)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 n K) (neg.f64 M))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
▶	92.3%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	54.5%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 n n) #s(literal -1/4 binary64)))))
	50.8%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
	49.2%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
▶	38.4%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	65.2%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (+ (* K (* (+ n m) (* 1/2 (sin M)))) (cos M)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 M (+.f64 n m)) K) #s(literal 1 binary64)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Compiler

Compiled 808 to 498 computations (38.4% saved)

simplify219.0ms (1.5%)

Memory

2.2MiB live, 475.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	320	(*.f64 #s(literal 0 binary64) M)
✓	cost-diff	320	(.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))
✓	cost-diff	384	(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))
✓	cost-diff	448	(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64)))
✓	cost-diff	0	(-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)
✓	cost-diff	0	(cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M))
✓	cost-diff	0	(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	cost-diff	384	(/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n)))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (.f64 m K))
✓	cost-diff	0	#s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))
✓	cost-diff	0	(cos.f64 #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K))))
✓	cost-diff	0	(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	cost-diff	0	(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
✓	cost-diff	0	(cos.f64 M)
✓	cost-diff	0	#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
✓	cost-diff	0	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	cost-diff	128	(/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M))
✓	cost-diff	128	(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	cost-diff	192	(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
✓	cost-diff	1024	(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)

Rules

5 994×	`lower-fma.f32`
5 986×	`lower-fma.f64`
3 354×	`lower-*.f32`
3 326×	`lower-*.f64`
1 854×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	973
0	119	899
1	234	891
2	523	876
3	1580	846
4	5048	832
0	8123	815

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
(cos.f64 M)
M
(exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
(neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))))
#s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))
(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
(/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M))
(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
n
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)
#s(literal -1/4 binary64)
(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
(*.f64 (+.f64 n m) (+.f64 n m))
(+.f64 n m)
m
(neg.f64 M)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
(cos.f64 M)
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K))))
#s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))
(.f64 #s(literal 1/2 binary64) (.f64 m K))
#s(literal 1/2 binary64)
(*.f64 m K)
m
K
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M))
(-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)
(/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n)))
K
(/.f64 #s(literal 2 binary64) (+.f64 m n))
#s(literal 2 binary64)
(+.f64 m n)
m
n
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M)))
#s(literal 0 binary64)
(.f64 M (.f64 M M))
M
(*.f64 M M)
(/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))
#s(literal 2 binary64)
(*.f64 K (+.f64 m n))
K
(+.f64 m n)
m
n
(.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))
(+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M)))
(fma.f64 M M (*.f64 #s(literal 0 binary64) M))
(*.f64 #s(literal 0 binary64) M)
#s(literal 1 binary64)
(.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n))))
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l

Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M))) l))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
(cos.f64 M)
M
(exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (+.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M))) l)))
(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M))) l))
(neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))))
(neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M))))
#s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))
#s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M)))
(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
(*.f64 M (fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M))
(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
(fma.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64)) M)
(/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M))
(/.f64 (*.f64 (+.f64 m n) (fma.f64 (+.f64 m n) (/.f64 #s(literal 1/4 binary64) M) #s(literal -1 binary64))) M)
(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
(*.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n))
n
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)
(fma.f64 (/.f64 (+.f64 m n) M) (*.f64 #s(literal -1/4 binary64) (+.f64 m n)) m)
#s(literal -1/4 binary64)
(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
(/.f64 (*.f64 (+.f64 m n) (+.f64 m n)) M)
(*.f64 (+.f64 n m) (+.f64 n m))
(*.f64 (+.f64 m n) (+.f64 m n))
(+.f64 n m)
(+.f64 m n)
m
(neg.f64 M)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
(cos.f64 M)
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 K m)))))
(cos.f64 #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K))))
(cos.f64 #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 K m))))
#s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))
#s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 K m)))
(.f64 #s(literal 1/2 binary64) (.f64 m K))
(.f64 #s(literal 1/2 binary64) (.f64 K m))
#s(literal 1/2 binary64)
(*.f64 m K)
(*.f64 K m)
m
K
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) (cos.f64 (fma.f64 K (/.f64 (+.f64 m n) #s(literal 2 binary64)) (neg.f64 M))))
(cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M))
(cos.f64 (fma.f64 K (/.f64 (+.f64 m n) #s(literal 2 binary64)) (neg.f64 M)))
(-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)
(fma.f64 K (/.f64 (+.f64 m n) #s(literal 2 binary64)) (neg.f64 M))
(/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n)))
(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
K
(/.f64 #s(literal 2 binary64) (+.f64 m n))
#s(literal 2 binary64)
(+.f64 m n)
m
n
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) (cos.f64 (/.f64 (.f64 (.f64 K (+.f64 m n)) (.f64 M (fma.f64 M (.f64 #s(literal -2 binary64) (/.f64 M (.f64 K (+.f64 m n)))) M))) (.f64 #s(literal 2 binary64) (.f64 M M)))))
(cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))))))
(cos.f64 (/.f64 (.f64 (.f64 K (+.f64 m n)) (.f64 M (fma.f64 M (.f64 #s(literal -2 binary64) (/.f64 M (.f64 K (+.f64 m n)))) M))) (.f64 #s(literal 2 binary64) (*.f64 M M))))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))
(/.f64 (.f64 (.f64 K (+.f64 m n)) (.f64 M (fma.f64 M (.f64 #s(literal -2 binary64) (/.f64 M (.f64 K (+.f64 m n)))) M))) (.f64 #s(literal 2 binary64) (*.f64 M M)))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64)))
(.f64 M (fma.f64 M (.f64 #s(literal -2 binary64) (/.f64 M (*.f64 K (+.f64 m n)))) M))
(-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M)))
(.f64 M (.f64 M (neg.f64 M)))
#s(literal 0 binary64)
(.f64 M (.f64 M M))
M
(*.f64 M M)
(/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))
#s(literal 2 binary64)
(*.f64 K (+.f64 m n))
K
(+.f64 m n)
m
n
(.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))
(*.f64 M M)
(+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M)))
(*.f64 M M)
(fma.f64 M M (*.f64 #s(literal 0 binary64) M))
(*.f64 M M)
(*.f64 #s(literal 0 binary64) M)
#s(literal 0 binary64)
#s(literal 1 binary64)
(.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n))))
(.f64 #s(literal 2 binary64) (.f64 M (/.f64 M (*.f64 K (+.f64 m n)))))
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l

localize386.0ms (2.6%)

Memory

-10.3MiB live, 589.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	79.5%	(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64)))
✓	accuracy	43.3%	(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))
✓	accuracy	37.6%	(cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))))))
✓	accuracy	19.9%	#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) (+.f64 m n))
✓	accuracy	99.6%	(/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n)))
✓	accuracy	37.6%	(cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M))
✓	accuracy	19.9%	#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
✓	accuracy	100.0%	(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
✓	accuracy	37.6%	(cos.f64 #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K))))
✓	accuracy	34.3%	#s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))
✓	accuracy	19.9%	#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
✓	accuracy	100.0%	(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
✓	accuracy	100.0%	(cos.f64 M)
✓	accuracy	40.2%	#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
✓	accuracy	19.9%	#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
✓	accuracy	94.1%	(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
✓	accuracy	90.7%	(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
✓	accuracy	88.7%	(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
✓	accuracy	40.2%	#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))

Samples

198.0ms	212×	1	valid
17.0ms	44×	0	valid

Compiler

Compiled 816 to 61 computations (92.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 163.0ms

ival-mult: 37.0ms (22.7% of total)

ival-cos: 31.0ms (19% of total)

adjust: 25.0ms (15.3% of total)

ival-div: 23.0ms (14.1% of total)

ival-add: 19.0ms (11.6% of total)

ival-sub: 14.0ms (8.6% of total)

ival-pow2: 6.0ms (3.7% of total)

ival-neg: 4.0ms (2.4% of total)

ival-exp: 2.0ms (1.2% of total)

ival-fabs: 2.0ms (1.2% of total)

exact: 1.0ms (0.6% of total)

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

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

series114.0ms (0.8%)

Memory

-0.8MiB live, 200.6MiB allocated

Counts

25 → 1 008

Calls

Call 1

Inputs
#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())
#s(alt (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (patch (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) #<representation binary64>) () ())
#s(alt (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))) (patch (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) (patch (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (patch (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) #<representation binary64>) () ())
#s(alt #s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M)) (patch #s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M)) #<representation binary64>) () ())
#s(alt (cos.f64 M) (patch (cos.f64 M) #<representation binary64>) () ())
#s(alt (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) (patch (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (patch (.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) #<representation binary64>) () ())
#s(alt (cos.f64 #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (patch (cos.f64 #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) #<representation binary64>) () ())
#s(alt #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K))) (patch #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (.f64 m K)) (patch (.f64 #s(literal 1/2 binary64) (.f64 m K)) #<representation binary64>) () ())
#s(alt (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) (patch (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (patch (.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) #<representation binary64>) () ())
#s(alt (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (patch (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M) (patch (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (patch (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))))) (patch (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))))) #<representation binary64>) () ())
#s(alt (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64)) (patch (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 0 binary64) M) (patch (.f64 #s(literal 0 binary64) M) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (patch (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) #<representation binary64>) () ())
#s(alt (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)) (patch (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)) #<representation binary64>) () ())
#s(alt #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)) (patch #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 2 binary64) (+.f64 m n)) (patch (/.f64 #s(literal 2 binary64) (+.f64 m n)) #<representation binary64>) () ())
#s(alt (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/4 (/ (pow (+ m n) 2) M)) (taylor 0 M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2))) M) (taylor 0 M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M) (taylor 0 M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M) (taylor 0 M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt M (taylor inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* M (+ 1 (* -1 (/ (+ m n) M)))) (taylor inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2)))))) (taylor inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2)))))) (taylor inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt M (taylor -inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* -1 (* M (- (+ (/ m M) (/ n M)) 1))) (taylor -inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1))) (taylor -inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1))) (taylor -inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) (taylor 0 n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (+ (* -1 (* n (+ 1 (* -1/2 (/ m M))))) (* -1 (+ m (* -1/4 (/ (pow m 2) M)))))) (taylor 0 n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M)))))) (taylor 0 n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M)))))) (taylor 0 n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow n 2) M)) (taylor inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (* 1/4 (/ 1 M)))) (taylor inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2)))))) (taylor inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2)))))) (taylor inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow n 2) M)) (taylor -inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (- (+ (* 1/2 (/ m (* M n))) (* 1/4 (/ 1 M))) (/ 1 n))) (taylor -inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ m M)) 1)) (* -1 (/ (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) n))) n)) (* 1/4 (/ 1 M)))) (taylor -inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ m M)) 1)) (* -1 (/ (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) n))) n)) (* 1/4 (/ 1 M)))) (taylor -inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M))))) (taylor 0 m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (+ (* -1 (* m (+ 1 (* -1/2 (/ n M))))) (* -1 (+ n (* -1/4 (/ (pow n 2) M)))))) (taylor 0 m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (+ (* -1 (+ n (* -1/4 (/ (pow n 2) M)))) (* m (+ (* -1 (+ 1 (* -1/2 (/ n M)))) (* 1/4 (/ m M)))))) (taylor 0 m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (+ (* -1 (+ n (* -1/4 (/ (pow n 2) M)))) (* m (+ (* -1 (+ 1 (* -1/2 (/ n M)))) (* 1/4 (/ m M)))))) (taylor 0 m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow m 2) M)) (taylor inf m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (* 1/4 (/ 1 M)))) (taylor inf m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (+ (* -1 (/ (+ n (* -1/4 (/ (pow n 2) M))) (pow m 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow m 2)))))) (taylor inf m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (+ (* -1 (/ (+ n (* -1/4 (/ (pow n 2) M))) (pow m 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow m 2)))))) (taylor inf m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow m 2) M)) (taylor -inf m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (- (+ (* 1/2 (/ n (* M m))) (* 1/4 (/ 1 M))) (/ 1 m))) (taylor -inf m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow m 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ n M)) 1)) (* -1 (/ (+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M))))) m))) m)) (* 1/4 (/ 1 M)))) (taylor -inf m) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
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Calls

252 calls:

Time	Variable		Point	Expression
12.0ms	m	@	0	(cos (/ (+ (* (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))))
4.0ms	m	@	0	(* 1/2 (* m K))
2.0ms	n	@	-inf	(/ 2 (+ m n))
2.0ms	n	@	0	(cos (/ (+ (* (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))))
2.0ms	m	@	inf	(/ (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (neg M))

simplify736.0ms (5%)

Memory

23.1MiB live, 565.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6 750×	`lower-fma.f64`
6 750×	`lower-fma.f32`
6 432×	`lower-*.f64`
6 432×	`lower-*.f32`
4 448×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1581	26444
1	5247	25218
0	8342	24337

Stop Event

1×	iter limit
1×	node limit

Counts

1 008 → 1 006

Calls

Call 1

Inputs
(* 1/4 (/ (pow (+ m n) 2) M))
(/ (+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2))) M)
(/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M)
(/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M)
M
(* M (+ 1 (* -1 (/ (+ m n) M))))
(* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
(* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
M
(* -1 (* M (- (+ (/ m M) (/ n M)) 1)))
(* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1)))
(* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1)))
(+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M)))))
(+ M (+ (* -1 (* n (+ 1 (* -1/2 (/ m M))))) (* -1 (+ m (* -1/4 (/ (pow m 2) M))))))
(+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M))))))
(+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M))))))
(* 1/4 (/ (pow n 2) M))
(* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (* 1/4 (/ 1 M))))
(* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2))))))
(* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2))))))
(* 1/4 (/ (pow n 2) M))
(* (pow n 2) (- (+ (* 1/2 (/ m (* M n))) (* 1/4 (/ 1 M))) (/ 1 n)))
(* (pow n 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ m M)) 1)) (* -1 (/ (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) n))) n)) (* 1/4 (/ 1 M))))
(* (pow n 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ m M)) 1)) (* -1 (/ (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) n))) n)) (* 1/4 (/ 1 M))))
(+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M)))))
(+ M (+ (* -1 (* m (+ 1 (* -1/2 (/ n M))))) (* -1 (+ n (* -1/4 (/ (pow n 2) M))))))
(+ M (+ (* -1 (+ n (* -1/4 (/ (pow n 2) M)))) (* m (+ (* -1 (+ 1 (* -1/2 (/ n M)))) (* 1/4 (/ m M))))))
(+ M (+ (* -1 (+ n (* -1/4 (/ (pow n 2) M)))) (* m (+ (* -1 (+ 1 (* -1/2 (/ n M)))) (* 1/4 (/ m M))))))
(* 1/4 (/ (pow m 2) M))
(* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (* 1/4 (/ 1 M))))
(* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (+ (* -1 (/ (+ n (* -1/4 (/ (pow n 2) M))) (pow m 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow m 2))))))
(* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (+ (* -1 (/ (+ n (* -1/4 (/ (pow n 2) M))) (pow m 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow m 2))))))
(* 1/4 (/ (pow m 2) M))
(* (pow m 2) (- (+ (* 1/2 (/ n (* M m))) (* 1/4 (/ 1 M))) (/ 1 m)))
(* (pow m 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ n M)) 1)) (* -1 (/ (+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M))))) m))) m)) (* 1/4 (/ 1 M))))
(* (pow m 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ n M)) 1)) (* -1 (/ (+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M))))) m))) m)) (* 1/4 (/ 1 M))))
(+ m (* -1/4 (/ (pow m 2) M)))
(+ m (+ (* -1/4 (/ (pow m 2) M)) (* n (+ 1 (* -1/2 (/ m M))))))
(+ m (+ (* -1/4 (/ (pow m 2) M)) (* n (+ 1 (+ (* -1/2 (/ m M)) (* -1/4 (/ n M)))))))
(+ m (+ (* -1/4 (/ (pow m 2) M)) (* n (+ 1 (+ (* -1/2 (/ m M)) (* -1/4 (/ n M)))))))
(* -1/4 (/ (pow n 2) M))
(* (pow n 2) (- (+ (* -1/2 (/ m (* M n))) (/ 1 n)) (* 1/4 (/ 1 M))))
(* (pow n 2) (- (+ (* -1/2 (/ m (* M n))) (+ (* -1/4 (/ (pow m 2) (* M (pow n 2)))) (+ (/ 1 n) (/ m (pow n 2))))) (* 1/4 (/ 1 M))))
(* (pow n 2) (- (+ (* -1/2 (/ m (* M n))) (+ (* -1/4 (/ (pow m 2) (* M (pow n 2)))) (+ (/ 1 n) (/ m (pow n 2))))) (* 1/4 (/ 1 M))))
(* -1/4 (/ (pow n 2) M))
(* (pow n 2) (- (* -1 (/ (- (* 1/2 (/ m M)) 1) n)) (* 1/4 (/ 1 M))))
(* (pow n 2) (- (* -1 (/ (- (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) n)) (* 1/2 (/ m M))) 1) n)) (* 1/4 (/ 1 M))))
(* (pow n 2) (- (* -1 (/ (- (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) n)) (* 1/2 (/ m M))) 1) n)) (* 1/4 (/ 1 M))))
(+ n (* -1/4 (/ (pow n 2) M)))
(+ n (+ (* -1/4 (/ (pow n 2) M)) (* m (+ 1 (* -1/2 (/ n M))))))
(+ n (+ (* -1/4 (/ (pow n 2) M)) (* m (+ 1 (+ (* -1/2 (/ n M)) (* -1/4 (/ m M)))))))
(+ n (+ (* -1/4 (/ (pow n 2) M)) (* m (+ 1 (+ (* -1/2 (/ n M)) (* -1/4 (/ m M)))))))
(* -1/4 (/ (pow m 2) M))
(* (pow m 2) (- (+ (* -1/2 (/ n (* M m))) (/ 1 m)) (* 1/4 (/ 1 M))))
(* (pow m 2) (- (+ (* -1/2 (/ n (* M m))) (+ (* -1/4 (/ (pow n 2) (* M (pow m 2)))) (+ (/ 1 m) (/ n (pow m 2))))) (* 1/4 (/ 1 M))))
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(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* -1 M))
(+ (cos (* -1 M)) (* -1/2 (* K (* (sin (* -1 M)) (+ m n)))))
(+ (cos (* -1 M)) (* K (- (* -1/8 (* K (* (cos (* -1 M)) (pow (+ m n) 2)))) (* 1/2 (* (sin (* -1 M)) (+ m n))))))
(+ (cos (* -1 M)) (* K (- (* K (+ (* -1/8 (* (cos (* -1 M)) (pow (+ m n) 2))) (* 1/48 (* K (* (sin (* -1 M)) (pow (+ m n) 3)))))) (* 1/2 (* (sin (* -1 M)) (+ m n))))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2))))
(+ (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* -1/2 (/ (* K (* m (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2)))))) (pow M 2))))
(+ (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* m (- (* m (- (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) 2))) (pow M 4))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow n 2)))) (* 2 (/ (pow M 3) (* K (pow n 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))))) (pow M 2))))))
(+ (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* m (- (* m (- (+ (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) 2))) (pow M 4))) (* m (- (* -1/4 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) (+ (* -2 (/ (pow M 3) (* K (pow n 2)))) (* 2 (/ (pow M 3) (* K (pow n 2)))))))) (pow M 4))) (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -1/48 (/ (* (pow K 3) (pow (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) 3)) (pow M 6))) (* 1/2 (/ (* K (+ (* -2 (/ (pow M 3) (* K (pow n 3)))) (* 2 (/ (pow M 3) (* K (pow n 3)))))) (pow M 2)))))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow n 2)))) (* 2 (/ (pow M 3) (* K (pow n 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))))) (pow M 2))))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2))))
(+ (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* -1/2 (/ (* K (* n (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2)))))) (pow M 2))))
(+ (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* n (- (* n (- (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) 2))) (pow M 4))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow m 2)))) (* 2 (/ (pow M 3) (* K (pow m 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))))) (pow M 2))))))
(+ (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* n (- (* n (- (+ (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) 2))) (pow M 4))) (* n (- (* -1/4 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) (+ (* -2 (/ (pow M 3) (* K (pow m 2)))) (* 2 (/ (pow M 3) (* K (pow m 2)))))))) (pow M 4))) (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -1/48 (/ (* (pow K 3) (pow (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) 3)) (pow M 6))) (* 1/2 (/ (* K (+ (* -2 (/ (pow M 3) (* K (pow m 3)))) (* 2 (/ (pow M 3) (* K (pow m 3)))))) (pow M 2)))))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow m 2)))) (* 2 (/ (pow M 3) (* K (pow m 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))))) (pow M 2))))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))

Outputs
(* 1/4 (/ (pow (+ m n) 2) M))
(.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (+.f64 m n) (+.f64 m n)) M))
(/ (+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2))) M)
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n))) (*.f64 (+.f64 m n) M)) M)
(/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M)
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (-.f64 M (+.f64 m n)))) M)
(/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M)
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (-.f64 M (+.f64 m n)))) M)
M
(* M (+ 1 (* -1 (/ (+ m n) M))))
(*.f64 M (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 m n) M)))
(* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
(+.f64 M (.f64 M (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n))) (.f64 M M)) (/.f64 (+.f64 m n) M))))
(* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
(+.f64 M (.f64 M (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n))) (.f64 M M)) (/.f64 (+.f64 m n) M))))
M
(* -1 (* M (- (+ (/ m M) (/ n M)) 1)))
(*.f64 (+.f64 (/.f64 m M) (+.f64 (/.f64 n M) #s(literal -1 binary64))) (neg.f64 M))
(* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1)))
(.f64 (+.f64 (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (+.f64 m n) (+.f64 m n)) M)) (+.f64 m n)) (neg.f64 M)) #s(literal -1 binary64)) (neg.f64 M))
(* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1)))
(.f64 (+.f64 (/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (*.f64 (+.f64 m n) (+.f64 m n)) M)) (+.f64 m n)) (neg.f64 M)) #s(literal -1 binary64)) (neg.f64 M))
(+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M)))))
(-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m))
(+ M (+ (* -1 (* n (+ 1 (* -1/2 (/ m M))))) (* -1 (+ m (* -1/4 (/ (pow m 2) M))))))
(-.f64 (-.f64 M (.f64 n (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 m m) M) m))
(+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M))))))
(+.f64 M (-.f64 (.f64 n (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) n) M) (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)))
(+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M))))))
(+.f64 M (-.f64 (.f64 n (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) n) M) (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)))
(* 1/4 (/ (pow n 2) M))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 n n)) M)
(* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (* 1/4 (/ 1 M))))
(.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)) n)))
(* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2))))))
(.f64 (.f64 n n) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 M (.f64 n n))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 m m) M) m) (*.f64 n n))) (/.f64 (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)) n)))
(* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2))))))
(.f64 (.f64 n n) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 M (.f64 n n))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 m m) M) m) (*.f64 n n))) (/.f64 (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)) n)))
(* 1/4 (/ (pow n 2) M))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 n n)) M)
(* (pow n 2) (- (+ (* 1/2 (/ m (* M n))) (* 1/4 (/ 1 M))) (/ 1 n)))
(.f64 (.f64 n n) (+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 m (*.f64 n M)) (/.f64 #s(literal 1/4 binary64) M)) (/.f64 #s(literal -1 binary64) n)))
(* (pow n 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ m M)) 1)) (* -1 (/ (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) n))) n)) (* 1/4 (/ 1 M))))
(.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (neg.f64 (fma.f64 (/.f64 m M) #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)) n)) n)))
(* (pow n 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ m M)) 1)) (* -1 (/ (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) n))) n)) (* 1/4 (/ 1 M))))
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(+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M)))))
(-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 n n) M) n))
(+ M (+ (* -1 (* m (+ 1 (* -1/2 (/ n M))))) (* -1 (+ n (* -1/4 (/ (pow n 2) M))))))
(+.f64 M (neg.f64 (fma.f64 m (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 n n) M) n))))
(+ M (+ (* -1 (+ n (* -1/4 (/ (pow n 2) M)))) (* m (+ (* -1 (+ 1 (* -1/2 (/ n M)))) (* 1/4 (/ m M))))))
(+.f64 M (fma.f64 m (-.f64 (.f64 #s(literal 1/4 binary64) (/.f64 m M)) (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 n n) M) n))))
(+ M (+ (* -1 (+ n (* -1/4 (/ (pow n 2) M)))) (* m (+ (* -1 (+ 1 (* -1/2 (/ n M)))) (* 1/4 (/ m M))))))
(+.f64 M (fma.f64 m (-.f64 (.f64 #s(literal 1/4 binary64) (/.f64 m M)) (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 n n) M) n))))
(* 1/4 (/ (pow m 2) M))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 m m)) M)
(* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (* 1/4 (/ 1 M))))
(.f64 (.f64 m m) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64)) m)))
(* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (+ (* -1 (/ (+ n (* -1/4 (/ (pow n 2) M))) (pow m 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow m 2))))))
(.f64 (.f64 m m) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 M (.f64 m m))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 n n) M) n) (*.f64 m m))) (/.f64 (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64)) m)))
(* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (+ (* -1 (/ (+ n (* -1/4 (/ (pow n 2) M))) (pow m 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow m 2))))))
(.f64 (.f64 m m) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 M (.f64 m m))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 n n) M) n) (*.f64 m m))) (/.f64 (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64)) m)))
(* 1/4 (/ (pow m 2) M))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 m m)) M)
(* (pow m 2) (- (+ (* 1/2 (/ n (* M m))) (* 1/4 (/ 1 M))) (/ 1 m)))
(.f64 (.f64 m m) (+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 n (*.f64 m M)) (/.f64 #s(literal 1/4 binary64) M)) (/.f64 #s(literal -1 binary64) m)))
(* (pow m 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ n M)) 1)) (* -1 (/ (+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M))))) m))) m)) (* 1/4 (/ 1 M))))
(.f64 (.f64 m m) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (neg.f64 (fma.f64 (/.f64 n M) #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 n n) M) n)) m)) m)))
(* (pow m 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ n M)) 1)) (* -1 (/ (+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M))))) m))) m)) (* 1/4 (/ 1 M))))
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(+ m (* -1/4 (/ (pow m 2) M)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)
(+ m (+ (* -1/4 (/ (pow m 2) M)) (* n (+ 1 (* -1/2 (/ m M))))))
(fma.f64 n (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m))
(+ m (+ (* -1/4 (/ (pow m 2) M)) (* n (+ 1 (+ (* -1/2 (/ m M)) (* -1/4 (/ n M)))))))
(+.f64 m (fma.f64 n (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 n M) #s(literal -1/4 binary64) (.f64 (/.f64 m M) #s(literal -1/2 binary64)))) (/.f64 (.f64 #s(literal -1/4 binary64) (*.f64 m m)) M)))
(+ m (+ (* -1/4 (/ (pow m 2) M)) (* n (+ 1 (+ (* -1/2 (/ m M)) (* -1/4 (/ n M)))))))
(+.f64 m (fma.f64 n (+.f64 #s(literal 1 binary64) (fma.f64 (/.f64 n M) #s(literal -1/4 binary64) (.f64 (/.f64 m M) #s(literal -1/2 binary64)))) (/.f64 (.f64 #s(literal -1/4 binary64) (*.f64 m m)) M)))
(* -1/4 (/ (pow n 2) M))
(/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)
(* (pow n 2) (- (+ (* -1/2 (/ m (* M n))) (/ 1 n)) (* 1/4 (/ 1 M))))
(.f64 (.f64 n n) (+.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 m (*.f64 n M)) (/.f64 #s(literal 1 binary64) n)) (/.f64 #s(literal -1/4 binary64) M)))
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(* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 m n) K) (neg.f64 M)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow M 2)))
(fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow M 2) (- (* 1/24 (pow M 2)) 1/2)))
(fma.f64 (.f64 M M) (fma.f64 (.f64 M M) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow M 2) (- (* (pow M 2) (+ 1/24 (* -1/720 (pow M 2)))) 1/2)))
(fma.f64 (.f64 M M) (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos M)
(cos.f64 M)
(cos M)
(cos.f64 M)
(cos M)
(cos.f64 M)
(cos M)
(cos.f64 M)
(cos M)
(cos.f64 M)
(cos M)
(cos.f64 M)
(cos M)
(cos.f64 M)
(cos M)
(cos.f64 M)
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l)))
(+ (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (* m (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- M (* 1/2 n)))))
(fma.f64 m (.f64 (+.f64 M (.f64 n #s(literal -1/2 binary64))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l))))
(+ (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (* m (+ (* m (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- (* 1/2 (pow (- M (* 1/2 n)) 2)) 1/4))) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- M (* 1/2 n))))))
(fma.f64 m (fma.f64 m (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l))) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 M (.f64 n #s(literal -1/2 binary64))) (+.f64 M (.f64 n #s(literal -1/2 binary64)))) #s(literal -1/4 binary64))) (.f64 (+.f64 M (.f64 n #s(literal -1/2 binary64))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l))))
(+ (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (* m (+ (* m (+ (* m (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (+ (* -1/4 (- M (* 1/2 n))) (* 1/6 (pow (- M (* 1/2 n)) 3))))) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- (* 1/2 (pow (- M (* 1/2 n)) 2)) 1/4)))) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- M (* 1/2 n))))))
(fma.f64 m (fma.f64 m (fma.f64 (.f64 m (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l)))) (fma.f64 #s(literal -1/4 binary64) (+.f64 M (.f64 n #s(literal -1/2 binary64))) (.f64 #s(literal 1/6 binary64) (.f64 (+.f64 M (.f64 n #s(literal -1/2 binary64))) (.f64 (+.f64 M (.f64 n #s(literal -1/2 binary64))) (+.f64 M (.f64 n #s(literal -1/2 binary64))))))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l))) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 M (.f64 n #s(literal -1/2 binary64))) (+.f64 M (.f64 n #s(literal -1/2 binary64)))) #s(literal -1/4 binary64)))) (.f64 (+.f64 M (.f64 n #s(literal -1/2 binary64))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) (fma.f64 n #s(literal 1/2 binary64) (neg.f64 M)) l))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l)))
(+ (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (* n (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- M (* 1/2 m)))))
(fma.f64 n (.f64 (+.f64 M (.f64 m #s(literal -1/2 binary64))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l))))
(+ (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (* n (+ (* n (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- (* 1/2 (pow (- M (* 1/2 m)) 2)) 1/4))) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- M (* 1/2 m))))))
(fma.f64 n (fma.f64 n (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l))) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 M (.f64 m #s(literal -1/2 binary64))) (+.f64 M (.f64 m #s(literal -1/2 binary64)))) #s(literal -1/4 binary64))) (.f64 (+.f64 M (.f64 m #s(literal -1/2 binary64))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l))))
(+ (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (* n (+ (* n (+ (* n (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (+ (* -1/4 (- M (* 1/2 m))) (* 1/6 (pow (- M (* 1/2 m)) 3))))) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- (* 1/2 (pow (- M (* 1/2 m)) 2)) 1/4)))) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- M (* 1/2 m))))))
(fma.f64 n (fma.f64 n (fma.f64 n (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l))) (fma.f64 #s(literal 1/6 binary64) (.f64 (+.f64 M (.f64 m #s(literal -1/2 binary64))) (.f64 (+.f64 M (.f64 m #s(literal -1/2 binary64))) (+.f64 M (.f64 m #s(literal -1/2 binary64))))) (.f64 #s(literal -1/4 binary64) (+.f64 M (.f64 m #s(literal -1/2 binary64)))))) (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l))) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 M (.f64 m #s(literal -1/2 binary64))) (+.f64 M (.f64 m #s(literal -1/2 binary64)))) #s(literal -1/4 binary64)))) (.f64 (+.f64 M (.f64 m #s(literal -1/2 binary64))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 m #s(literal 1/2 binary64)) M) (-.f64 (.f64 m #s(literal 1/2 binary64)) M) l))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 m n) (+.f64 m n)) l)))
(+ (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (* M (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (+ m n))))
(fma.f64 M (.f64 (+.f64 m n) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) l)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 m n) (+.f64 m n)) l))))
(+ (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (* M (+ (* M (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (- (* 1/2 (pow (+ m n) 2)) 1))) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (+ m n)))))
(fma.f64 M (fma.f64 M (.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) l))) (fma.f64 (.f64 (+.f64 m n) (+.f64 m n)) #s(literal 1/2 binary64) #s(literal -1 binary64))) (.f64 (+.f64 m n) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) l))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) l))))
(+ (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (* M (+ (* M (+ (* M (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (+ (* -1 (+ m n)) (* 1/6 (pow (+ m n) 3))))) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (- (* 1/2 (pow (+ m n) 2)) 1)))) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (+ m n)))))
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(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
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(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (*.f64 (+.f64 m n) #s(literal 1/2 binary64)) M))))
(+ (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))) (* -1 (* l (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))))))
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(+ (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))) (* l (+ (* -1 (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)))) (* 1/2 (* l (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))))))))
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(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
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(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
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(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
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(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
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(exp (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2)))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(exp (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2)))
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(exp (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2)))
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(exp (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2)))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l)))
(* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))) (* (sin (neg M)) (+ m n))))) (* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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(* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))))
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(+ (* n (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (sin (- (* 1/2 (* K m)) M))))) (* (cos (- (* 1/2 (* K m)) M)) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- M (* 1/2 m)))))) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2))))))
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(+ (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* m (- (* m (- (+ (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) 2))) (pow M 4))) (* m (- (* -1/4 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) (+ (* -2 (/ (pow M 3) (* K (pow n 2)))) (* 2 (/ (pow M 3) (* K (pow n 2)))))))) (pow M 4))) (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -1/48 (/ (* (pow K 3) (pow (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) 3)) (pow M 6))) (* 1/2 (/ (* K (+ (* -2 (/ (pow M 3) (* K (pow n 3)))) (* 2 (/ (pow M 3) (* K (pow n 3)))))) (pow M 2)))))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow n 2)))) (* 2 (/ (pow M 3) (* K (pow n 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))))) (pow M 2))))))
(fma.f64 m (fma.f64 m (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 K K) (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 n K))))) (.f64 M M))) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M))))) (pow.f64 M #s(literal 4 binary64))) (fma.f64 m (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 (.f64 K K) (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 n K))))) (.f64 M M)))) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) #s(literal 0 binary64))) (pow.f64 M #s(literal 4 binary64))) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 K (/.f64 #s(literal 0 binary64) (.f64 M M))) (/.f64 (.f64 #s(literal -1/48 binary64) (.f64 (.f64 K (.f64 K K)) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)))))) (pow.f64 M #s(literal 6 binary64)))) (neg.f64 (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 n K))))) (.f64 M M)))))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 K (.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 n K))))) (.f64 M M))))) (.f64 M M))))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 K (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 n K))))) (.f64 M M))))) (.f64 M M)))) (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 n K))))) (*.f64 M M))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M)))
(+ (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* -1/2 (/ (* K (* n (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2)))))) (pow M 2))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (.f64 n K) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M)) (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))))) (.f64 M M)) (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))))
(+ (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* n (- (* n (- (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) 2))) (pow M 4))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow m 2)))) (* 2 (/ (pow M 3) (* K (pow m 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))))) (pow M 2))))))
(fma.f64 n (fma.f64 n (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 K K) (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M)) (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M))))) (pow.f64 M #s(literal 4 binary64))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 K (.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))))) (.f64 M M)))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 K (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M)) (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))))) (.f64 M M)))) (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))))
(+ (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* n (- (* n (- (+ (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) 2))) (pow M 4))) (* n (- (* -1/4 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) (+ (* -2 (/ (pow M 3) (* K (pow m 2)))) (* 2 (/ (pow M 3) (* K (pow m 2)))))))) (pow M 4))) (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -1/48 (/ (* (pow K 3) (pow (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) 3)) (pow M 6))) (* 1/2 (/ (* K (+ (* -2 (/ (pow M 3) (* K (pow m 3)))) (* 2 (/ (pow M 3) (* K (pow m 3)))))) (pow M 2)))))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow m 2)))) (* 2 (/ (pow M 3) (* K (pow m 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))))) (pow M 2))))))
(fma.f64 n (fma.f64 n (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 K K) (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M)) (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M))))) (pow.f64 M #s(literal 4 binary64))) (fma.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 K K) (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M)) #s(literal 0 binary64)))) (pow.f64 M #s(literal 4 binary64))) (.f64 (fma.f64 #s(literal -1/48 binary64) (/.f64 (.f64 (.f64 K (.f64 K K)) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M)) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M)) (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M))))) (pow.f64 M #s(literal 6 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K #s(literal 0 binary64))) (.f64 M M))) (neg.f64 (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M)))))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 K (.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))))) (.f64 M M))))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 K (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) #s(literal 0 binary64) (.f64 M M)) (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (.f64 M M))))) (.f64 M M)))) (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 m K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 m K)) (.f64 M M)))) (*.f64 M M))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K (.f64 (+.f64 m n) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K)))))) (.f64 M M)))

rewrite449.0ms (3.1%)

Memory

-7.8MiB live, 368.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 024×	`lower-*.f32`
4 000×	`lower-*.f64`
3 562×	`lower-fma.f32`
3 554×	`lower-fma.f64`
2 838×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	473
0	113	418
1	471	412
2	4152	412
0	8214	412

Stop Event

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

Counts

25 → 481

Calls

Call 1

Inputs
(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
(/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M))
(cos.f64 M)
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 #s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K))))
#s(approx (- (/ (* K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))
(.f64 #s(literal 1/2 binary64) (.f64 m K))
(/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n)))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M))
(-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64)))
(/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))
(.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))
(*.f64 #s(literal 0 binary64) M)
(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(/.f64 #s(literal 2 binary64) (+.f64 m n))
(cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))))))

Outputs
(+.f64 M (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)))
(+.f64 (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)) M)
(-.f64 (/.f64 (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M)) (-.f64 (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)) M)) (/.f64 (.f64 M M) (-.f64 (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)) M)))
(fma.f64 M (/.f64 (+.f64 m (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)) (neg.f64 M)) M)
(fma.f64 (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)) (.f64 (/.f64 #s(literal -1 binary64) M) M) M)
(fma.f64 (/.f64 (+.f64 m (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)) (neg.f64 M)) M M)
(fma.f64 #s(literal 1 binary64) M (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)))
(fma.f64 #s(literal -1 binary64) (neg.f64 M) (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)))
(fma.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 M) #s(literal 1 binary64)) (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)))
(fma.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (/.f64 #s(literal -1 binary64) M) M)
(fma.f64 (/.f64 M #s(literal -1 binary64)) (/.f64 (+.f64 m (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)) M) M)
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 M (-.f64 M (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M))) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M))) (fma.f64 M (.f64 M M) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))))) (.f64 (*.f64 (neg.f64 M) M) M)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)) M) (-.f64 (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M)) (*.f64 M M))))
(/.f64 (fma.f64 M (.f64 M M) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))))) (.f64 (.f64 (neg.f64 M) M) M))) (fma.f64 M (-.f64 M (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M))) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (*.f64 M M))))
(/.f64 (fma.f64 M (.f64 M M) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))))) (.f64 (.f64 (neg.f64 M) M) M))) (fma.f64 M M (/.f64 (-.f64 (.f64 (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))))) (neg.f64 M))))
(/.f64 (-.f64 (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M)) (.f64 M M)) (-.f64 (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)) M))
(/.f64 (neg.f64 (fma.f64 M (.f64 M M) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))))) (.f64 (.f64 (neg.f64 M) M) M)))) (neg.f64 (fma.f64 M (-.f64 M (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M))) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (*.f64 M M)))))
(/.f64 (neg.f64 (-.f64 (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M)) (.f64 M M))) (neg.f64 (-.f64 (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)) M)))
(/.f64 (-.f64 (.f64 M M) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M))) (-.f64 M (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M))))
(pow.f64 (/.f64 (fma.f64 M (-.f64 M (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M))) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M))) (fma.f64 M (.f64 M M) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))))) (.f64 (*.f64 (neg.f64 M) M) M)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)) M) (-.f64 (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M)) (*.f64 M M))) #s(literal -1 binary64))
(.f64 (fma.f64 M (.f64 M M) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))))) (.f64 (.f64 (neg.f64 M) M) M))) (/.f64 #s(literal 1 binary64) (fma.f64 M (-.f64 M (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M))) (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M)))))
(.f64 (-.f64 (/.f64 (.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)))) (.f64 M M)) (.f64 M M)) (/.f64 #s(literal 1 binary64) (-.f64 (neg.f64 (/.f64 (.f64 M (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))) M)) M)))
(.f64 (+.f64 (/.f64 (+.f64 m (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n)) (neg.f64 M)) #s(literal 1 binary64)) M)
(+.f64 n (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) m))
(+.f64 m (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n))
(+.f64 (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) m) n)
(+.f64 (+.f64 n m) (.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64))))
(+.f64 (.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64))) (+.f64 n m))
(+.f64 (fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) n) m)
(-.f64 (/.f64 (.f64 n n) (-.f64 n (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) m))) (/.f64 (.f64 (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) m) (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) m)) (-.f64 n (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) m))))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m))
(fma.f64 (.f64 (+.f64 n m) (+.f64 n m)) (.f64 (/.f64 #s(literal 1 binary64) M) #s(literal -1/4 binary64)) (+.f64 n m))
(fma.f64 (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) #s(literal -1/4 binary64) (+.f64 n m))
(fma.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) (+.f64 n m))
(fma.f64 (fma.f64 m (.f64 m m) (/.f64 (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m))) (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m))) (.f64 #s(literal -1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m))))) (.f64 M (.f64 M M)))) (/.f64 #s(literal 1 binary64) (fma.f64 m (-.f64 m (.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)))) (/.f64 (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m))) (.f64 #s(literal -1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m)))) (*.f64 M M)))) n)
(fma.f64 (fma.f64 n (.f64 n n) (.f64 m (.f64 m m))) (/.f64 #s(literal 1 binary64) (fma.f64 m (-.f64 m n) (.f64 n n))) (.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64))))
(fma.f64 (fma.f64 n (.f64 n n) (.f64 m (.f64 m m))) (/.f64 #s(literal 1 binary64) (fma.f64 n (-.f64 n m) (.f64 m m))) (.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64))))
(fma.f64 (-.f64 (/.f64 (.f64 (.f64 #s(literal -1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m))) (.f64 #s(literal -1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m)))) (.f64 M M)) (.f64 m m)) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64)) (neg.f64 m))) n)
(fma.f64 (.f64 (+.f64 n m) (-.f64 n m)) (/.f64 #s(literal 1 binary64) (-.f64 n m)) (.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64))))
(fma.f64 (.f64 (+.f64 n m) (-.f64 m n)) (/.f64 #s(literal 1 binary64) (-.f64 m n)) (.f64 (+.f64 n m) (*.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64))))
(fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m))) (/.f64 #s(literal 1 binary64) M) (+.f64 n m))
(fma.f64 (*.f64 #s(literal -1/4 binary64) (+.f64 n m)) (/.f64 (+.f64 n m) M) (+.f64 n m))
(fma.f64 (/.f64 (.f64 (+.f64 n m) (-.f64 m n)) (.f64 (fma.f64 n (+.f64 n m) (.f64 m m)) (-.f64 m n))) (fma.f64 n (+.f64 n m) (.f64 m m)) (.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64))))
(fma.f64 (/.f64 (.f64 (+.f64 n m) (-.f64 m n)) (.f64 (+.f64 n m) (-.f64 m n))) (+.f64 n m) (.f64 (+.f64 n m) (.f64 (/.f64 (+.f64 n m) M) #s(literal -1/4 binary64))))
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#s(literal 0 binary64)
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#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m))) #s(literal -1 binary64)))
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(.f64 (/.f64 #s(literal 2 binary64) (fma.f64 n (.f64 n n) (.f64 m (.f64 m m)))) (fma.f64 m (-.f64 m n) (*.f64 n n)))
(.f64 (/.f64 #s(literal 2 binary64) (fma.f64 n (.f64 n n) (.f64 m (.f64 m m)))) (fma.f64 n (-.f64 n m) (*.f64 m m)))
(.f64 (/.f64 #s(literal 2 binary64) (.f64 (+.f64 n m) (-.f64 n m))) (-.f64 n m))
(.f64 (/.f64 #s(literal 2 binary64) (.f64 (+.f64 n m) (-.f64 m n))) (-.f64 m n))
(cos.f64 (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K) (/.f64 (fma.f64 (.f64 (.f64 (neg.f64 M) M) M) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 n m))) (.f64 M M)) (.f64 M M))))
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(cos.f64 (/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (neg.f64 M) M) M) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 n m))) (.f64 M M))) (.f64 (.f64 (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 n m))) M) M)))

eval493.0ms (3.4%)

Memory: 27.3MiB live, 435.3MiB allocated
Compiler: Compiled 77 828 to 4 834 computations (93.8% saved)

prune264.0ms (1.8%)

Memory

-35.0MiB live, 581.3MiB allocated

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	1 848	16	1 864
Fresh	8	3	11
Picked	4	1	5
Done	0	0	0
Total	1 860	20	1 880

Accuracy

97.3%

Counts

1 880 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.4%	(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (exp.f64 (.f64 #s(literal 2 binary64) (log.f64 M)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
▶	8.4%	(.f64 (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	5.3%	(.f64 (cos.f64 (/.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (.f64 K (+.f64 n m)) (.f64 (.f64 M M) (.f64 #s(literal 2 binary64) (.f64 (.f64 (neg.f64 M) M) M)))) (.f64 (.f64 M M) (.f64 K (+.f64 n m)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	5.7%	(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (-.f64 (.f64 M M) (/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 m (.f64 M (.f64 M M))) (.f64 n K)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 M (.f64 M M))) K)) n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	9.7%	(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (.f64 (.f64 M (.f64 M M)) (+.f64 (/.f64 #s(literal 1 binary64) M) (/.f64 #s(literal -2 binary64) (.f64 (+.f64 m n) K))))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	13.2%	(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (.f64 M M)) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
▶	31.6%	(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	36.2%	(.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
▶	35.8%	(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	35.2%	(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	33.9%	(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	13.8%	(.f64 (cos.f64 (-.f64 (exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 n m)))) #s(literal -1 binary64))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	28.2%	(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 n (.f64 #s(literal 1/2 binary64) (fma.f64 K (/.f64 m n) K)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	33.2%	(.f64 (cos.f64 #s(approx (/ (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	31.9%	(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	32.5%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 m K) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 n K) (neg.f64 M)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 n K) (neg.f64 M))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	49.2%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
	31.5%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
▶	90.3%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	36.5%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Compiler

Compiled 1 211 to 732 computations (39.6% saved)

simplify293.0ms (2%)

Memory

37.1MiB live, 431.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	192	(+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M)))
✓	cost-diff	320	(*.f64 #s(literal 0 binary64) M)
✓	cost-diff	1536	(/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))
✓	cost-diff	2304	(fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K)))
✓	cost-diff	0	(/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n)))
✓	cost-diff	0	(-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)
✓	cost-diff	0	(cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M))
✓	cost-diff	0	(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	cost-diff	0	(-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M)
✓	cost-diff	0	(cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M))
✓	cost-diff	0	(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	cost-diff	512	(fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64))))
✓	cost-diff	0	(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
✓	cost-diff	0	#s(approx (cos M) #s(literal 1 binary64))
✓	cost-diff	0	#s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64)))
✓	cost-diff	0	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	cost-diff	0	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	cost-diff	128	(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	cost-diff	192	(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
✓	cost-diff	896	(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)

Rules

7 236×	`lower-fma.f32`
7 224×	`lower-fma.f64`
3 090×	`lower-*.f32`
3 052×	`lower-*.f64`
2 848×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	1097
0	142	1062
1	282	1017
2	655	981
3	1989	939
4	7120	927
0	8162	917

Stop Event

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

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64)))
#s(approx (cos M) #s(literal 1 binary64))
#s(literal 1 binary64)
(exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
(neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))))
#s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))
(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
M
(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
(/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M))
(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
n
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)
#s(literal -1/4 binary64)
(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
(*.f64 (+.f64 n m) (+.f64 n m))
(+.f64 n m)
m
(neg.f64 M)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64)))
#s(approx (cos M) #s(literal 1 binary64))
#s(literal 1 binary64)
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M))
(-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M)
(fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64))))
(*.f64 m K)
m
K
#s(literal 1/2 binary64)
(.f64 n (.f64 K #s(literal 1/2 binary64)))
n
(*.f64 K #s(literal 1/2 binary64))
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M))
(-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)
(/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n)))
K
#s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))
(/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n)
(fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64))
(/.f64 m n)
m
n
#s(literal -2 binary64)
#s(literal 2 binary64)
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n))))))
(/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))
(fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K)))
(.f64 M (.f64 M (*.f64 M M)))
M
(.f64 M (.f64 M M))
(*.f64 M M)
(/.f64 #s(literal 1 binary64) (*.f64 M M))
#s(literal 1 binary64)
(/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))
(.f64 (.f64 (neg.f64 M) M) M)
(*.f64 (neg.f64 M) M)
(neg.f64 M)
(.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K)
(*.f64 #s(literal 1/2 binary64) (+.f64 n m))
#s(literal 1/2 binary64)
(+.f64 n m)
n
m
K
(.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n))))
(+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M)))
#s(literal 0 binary64)
(fma.f64 M M (*.f64 #s(literal 0 binary64) M))
(*.f64 #s(literal 0 binary64) M)
(/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))
#s(literal 2 binary64)
(*.f64 K (+.f64 m n))
(+.f64 m n)
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l

Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (+.f64 M (neg.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n)))))))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64)))
#s(approx (cos M) #s(literal 1 binary64))
#s(literal 1 binary64)
(exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))
(exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (+.f64 M (neg.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n))))))))
(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
(-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (+.f64 M (neg.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n)))))))
(neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))))
(neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (+.f64 M (neg.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n)))))))
#s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))
#s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (+.f64 M (neg.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n))))))
(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
(.f64 M (+.f64 M (neg.f64 (.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n)))))
M
(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
(+.f64 M (neg.f64 (*.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n))))
(/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M))
(/.f64 (*.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n)) (neg.f64 M))
(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
(*.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 m n) M) #s(literal 1 binary64)) (+.f64 m n))
n
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)
(fma.f64 (+.f64 m n) (/.f64 (*.f64 #s(literal -1/4 binary64) (+.f64 m n)) M) m)
#s(literal -1/4 binary64)
(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
(*.f64 (+.f64 m n) (/.f64 (+.f64 m n) M))
(*.f64 (+.f64 n m) (+.f64 n m))
(*.f64 (+.f64 m n) (+.f64 m n))
(+.f64 n m)
(+.f64 m n)
m
(neg.f64 M)
(-.f64 l (fabs.f64 (-.f64 m n)))
l
(fabs.f64 (-.f64 m n))
(-.f64 m n)
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64)))
#s(approx (cos M) #s(literal 1 binary64))
#s(literal 1 binary64)
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) (cos.f64 (fma.f64 K (.f64 (+.f64 m n) #s(literal 1/2 binary64)) (neg.f64 M))))
(cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M))
(cos.f64 (fma.f64 K (*.f64 (+.f64 m n) #s(literal 1/2 binary64)) (neg.f64 M)))
(-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M)
(fma.f64 K (*.f64 (+.f64 m n) #s(literal 1/2 binary64)) (neg.f64 M))
(fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64))))
(.f64 K (.f64 (+.f64 m n) #s(literal 1/2 binary64)))
(*.f64 m K)
(*.f64 K m)
m
K
#s(literal 1/2 binary64)
(.f64 n (.f64 K #s(literal 1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 K n))
n
(*.f64 K #s(literal 1/2 binary64))
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 m (/.f64 #s(literal -2 binary64) n) #s(literal 2 binary64)) n))) M)))
(cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M))
(cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 m (/.f64 #s(literal -2 binary64) n) #s(literal 2 binary64)) n))) M))
(-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)
(-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 m (/.f64 #s(literal -2 binary64) n) #s(literal 2 binary64)) n))) M)
(/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n)))
(/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 m (/.f64 #s(literal -2 binary64) n) #s(literal 2 binary64)) n)))
K
#s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))
#s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 m (/.f64 #s(literal -2 binary64) n) #s(literal 2 binary64)) n))
(/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n)
(/.f64 (fma.f64 m (/.f64 #s(literal -2 binary64) n) #s(literal 2 binary64)) n)
(fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64))
(fma.f64 m (/.f64 #s(literal -2 binary64) n) #s(literal 2 binary64))
(/.f64 m n)
m
n
#s(literal -2 binary64)
#s(literal 2 binary64)
M
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l
(.f64 (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) (cos.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 M (.f64 K (+.f64 m n))))) (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)))))
(cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n))))))
(cos.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 M (.f64 K (+.f64 m n))))) (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64))))
(/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) (/.f64 M (.f64 K (+.f64 m n))))) (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)))
(fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K)))
(.f64 M (fma.f64 #s(literal -2 binary64) (.f64 M (/.f64 M (*.f64 K (+.f64 m n)))) M))
(.f64 M (.f64 M (*.f64 M M)))
M
(.f64 M (.f64 M M))
(*.f64 M M)
(/.f64 #s(literal 1 binary64) (*.f64 M M))
#s(literal 1 binary64)
(/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))
(/.f64 (.f64 M (.f64 M (.f64 M #s(literal -2 binary64)))) (.f64 K (+.f64 m n)))
(.f64 (.f64 (neg.f64 M) M) M)
(neg.f64 (.f64 M (.f64 M M)))
(*.f64 (neg.f64 M) M)
(neg.f64 (*.f64 M M))
(neg.f64 M)
(.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K)
(.f64 K (.f64 (+.f64 m n) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (+.f64 n m))
(*.f64 (+.f64 m n) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(+.f64 n m)
(+.f64 m n)
n
m
K
(.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n))))
(/.f64 (.f64 M M) (.f64 K (*.f64 (+.f64 m n) #s(literal 1/2 binary64))))
(+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M)))
(*.f64 M M)
#s(literal 0 binary64)
(fma.f64 M M (*.f64 #s(literal 0 binary64) M))
(*.f64 M M)
(*.f64 #s(literal 0 binary64) M)
#s(literal 0 binary64)
(/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))
#s(literal 2 binary64)
(*.f64 K (+.f64 m n))
(+.f64 m n)
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
(neg.f64 l)
l

localize476.0ms (3.2%)

Memory

11.7MiB live, 708.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	43.3%	(/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))
✓	accuracy	37.6%	(cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n))))))
✓	accuracy	33.9%	(fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K)))
✓	accuracy	19.9%	#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
✓	accuracy	99.6%	(/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n)))
✓	accuracy	48.6%	#s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))
✓	accuracy	37.6%	(cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M))
✓	accuracy	19.9%	#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
✓	accuracy	100.0%	(-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M)
✓	accuracy	97.1%	(fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64))))
✓	accuracy	37.6%	(cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M))
✓	accuracy	19.9%	#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
✓	accuracy	100.0%	(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
✓	accuracy	58.4%	#s(approx (cos M) #s(literal 1 binary64))
✓	accuracy	40.2%	#s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64)))
✓	accuracy	19.9%	#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
✓	accuracy	90.7%	(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
✓	accuracy	88.7%	(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
✓	accuracy	58.4%	#s(approx (cos M) #s(literal 1 binary64))
✓	accuracy	40.2%	#s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64)))

Samples

272.0ms	212×	1	valid
28.0ms	44×	0	valid

Compiler

Compiled 902 to 77 computations (91.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 224.0ms

ival-mult: 61.0ms (27.3% of total)

ival-div: 47.0ms (21% of total)

ival-cos: 39.0ms (17.4% of total)

adjust: 29.0ms (13% of total)

ival-add: 19.0ms (8.5% of total)

ival-sub: 15.0ms (6.7% of total)

ival-pow2: 5.0ms (2.2% of total)

ival-neg: 4.0ms (1.8% of total)

ival-exp: 2.0ms (0.9% of total)

ival-fabs: 2.0ms (0.9% of total)

exact: 1.0ms (0.4% of total)

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

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

series126.0ms (0.9%)

Memory

-57.7MiB live, 137.8MiB allocated

Counts

25 → 1 044

Calls

Call 1

Inputs
#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())
#s(alt (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (patch (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) #<representation binary64>) () ())
#s(alt (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))) (patch (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (patch (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (patch (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) #<representation binary64>) () ())
#s(alt #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (patch #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (cos M) #s(literal 1 binary64)) (patch #s(approx (cos M) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) (patch (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) (patch (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (patch (.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) #<representation binary64>) () ())
#s(alt (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (patch (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M) (patch (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M) #<representation binary64>) () ())
#s(alt (.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (patch (.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) #<representation binary64>) () ())
#s(alt (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (patch (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M) (patch (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M) #<representation binary64>) () ())
#s(alt (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) (patch (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (patch (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))))) (patch (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 0 binary64) M) (patch (.f64 #s(literal 0 binary64) M) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (patch (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (patch (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) #<representation binary64>) () ())
#s(alt (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)) (patch (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)) #<representation binary64>) () ())
#s(alt #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)) (patch #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)) #<representation binary64>) () ())
#s(alt #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n)) (patch #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n)) #<representation binary64>) () ())
#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())

Outputs
#s(alt (* 1/4 (/ (pow (+ m n) 2) M)) (taylor 0 M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2))) M) (taylor 0 M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M) (taylor 0 M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M) (taylor 0 M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt M (taylor inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* M (+ 1 (* -1 (/ (+ m n) M)))) (taylor inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2)))))) (taylor inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2)))))) (taylor inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt M (taylor -inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* -1 (* M (- (+ (/ m M) (/ n M)) 1))) (taylor -inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1))) (taylor -inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1))) (taylor -inf M) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) (taylor 0 n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (+ (* -1 (* n (+ 1 (* -1/2 (/ m M))))) (* -1 (+ m (* -1/4 (/ (pow m 2) M)))))) (taylor 0 n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M)))))) (taylor 0 n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M)))))) (taylor 0 n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow n 2) M)) (taylor inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (* 1/4 (/ 1 M)))) (taylor inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2)))))) (taylor inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2)))))) (taylor inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* 1/4 (/ (pow n 2) M)) (taylor -inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (- (+ (* 1/2 (/ m (* M n))) (* 1/4 (/ 1 M))) (/ 1 n))) (taylor -inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
#s(alt (* (pow n 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ m M)) 1)) (* -1 (/ (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) n))) n)) (* 1/4 (/ 1 M)))) (taylor -inf n) (#s(alt (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) (patch (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M) #<representation binary64>) () ())) ())
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#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor inf m) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor inf m) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2)))) (taylor -inf m) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2)))) (taylor -inf m) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2)))) (taylor -inf m) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2)))) (taylor -inf m) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* -1 M)) (taylor 0 K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 M)) (* -1/2 (* K (* (sin (* -1 M)) (+ m n))))) (taylor 0 K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 M)) (* K (- (* -1/8 (* K (* (cos (* -1 M)) (pow (+ m n) 2)))) (* 1/2 (* (sin (* -1 M)) (+ m n)))))) (taylor 0 K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (+ (cos (* -1 M)) (* K (- (* K (+ (* -1/8 (* (cos (* -1 M)) (pow (+ m n) 2))) (* 1/48 (* K (* (sin (* -1 M)) (pow (+ m n) 3)))))) (* 1/2 (* (sin (* -1 M)) (+ m n)))))) (taylor 0 K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor inf K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor inf K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor inf K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor inf K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor -inf K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor -inf K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor -inf K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())
#s(alt (cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2)))) (taylor -inf K) (#s(alt (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (patch (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) #<representation binary64>) () ())) ())

Calls

261 calls:

Time	Variable		Point	Expression
24.0ms	M	@	0	(* (cos (- (/ K (/ 2 (+ m n))) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
1.0ms	M	@	0	(* (cos (- (+ (* (* m K) 1/2) (* n (* K 1/2))) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
1.0ms	l	@	inf	(* (cos (- (+ (* (* m K) 1/2) (* n (* K 1/2))) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
1.0ms	K	@	0	(* (cos (- (+ (* (* m K) 1/2) (* n (* K 1/2))) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
1.0ms	l	@	0	(* (cos (- (+ (* (* m K) 1/2) (* n (* K 1/2))) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

simplify496.0ms (3.4%)

Memory

24.1MiB live, 772.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6 746×	`lower-fma.f64`
6 746×	`lower-fma.f32`
6 388×	`lower-*.f64`
6 388×	`lower-*.f32`
4 368×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1632	29337
1	5507	27968
0	8545	27030

Stop Event

1×	iter limit
1×	node limit

Counts

1 044 → 1 042

Calls

Call 1

Inputs
(* 1/4 (/ (pow (+ m n) 2) M))
(/ (+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2))) M)
(/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M)
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(cos (* 1/2 (* K (+ m n))))
(+ (cos (* 1/2 (* K (+ m n)))) (* M (sin (* 1/2 (* K (+ m n))))))
(+ (cos (* 1/2 (* K (+ m n)))) (* M (- (* -1/2 (* M (cos (* 1/2 (* K (+ m n)))))) (* -1 (sin (* 1/2 (* K (+ m n))))))))
(+ (cos (* 1/2 (* K (+ m n)))) (* M (- (* M (+ (* -1/2 (cos (* 1/2 (* K (+ m n))))) (* -1/6 (* M (sin (* 1/2 (* K (+ m n)))))))) (* -1 (sin (* 1/2 (* K (+ m n))))))))
(cos (* 1/2 (/ (* K (* (+ m n) (- (pow M 2) (* 2 (/ (pow M 3) (* K (+ m n))))))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (- (pow M 2) (* 2 (/ (pow M 3) (* K (+ m n))))))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (- (pow M 2) (* 2 (/ (pow M 3) (* K (+ m n))))))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (- (pow M 2) (* 2 (/ (pow M 3) (* K (+ m n))))))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2))))
(+ (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* -1/2 (/ (* K (* n (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2)))))) (pow M 2))))
(+ (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* n (- (* n (- (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) 2))) (pow M 4))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow m 2)))) (* 2 (/ (pow M 3) (* K (pow m 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))))) (pow M 2))))))
(+ (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* n (- (* n (- (+ (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) 2))) (pow M 4))) (* n (- (* -1/4 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (* (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) (+ (* -2 (/ (pow M 3) (* K (pow m 2)))) (* 2 (/ (pow M 3) (* K (pow m 2)))))))) (pow M 4))) (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -1/48 (/ (* (pow K 3) (pow (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))) 3)) (pow M 6))) (* 1/2 (/ (* K (+ (* -2 (/ (pow M 3) (* K (pow m 3)))) (* 2 (/ (pow M 3) (* K (pow m 3)))))) (pow M 2)))))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow m 2)))) (* 2 (/ (pow M 3) (* K (pow m 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* m (+ (* -2 (/ (pow M 3) (* K m))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K m))) (+ (* 2 (/ (pow M 3) (* K m))) (pow M 2))))) (pow M 2))))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- m (* -1 n))))) (pow M 2)) (- m (* -1 n)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2))))
(+ (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* -1/2 (/ (* K (* m (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2)))))) (pow M 2))))
(+ (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* m (- (* m (- (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) 2))) (pow M 4))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow n 2)))) (* 2 (/ (pow M 3) (* K (pow n 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))))) (pow M 2))))))
(+ (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* m (- (* m (- (+ (* -1/8 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (pow (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) 2))) (pow M 4))) (* m (- (* -1/4 (/ (* (pow K 2) (* (cos (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (* (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) (+ (* -2 (/ (pow M 3) (* K (pow n 2)))) (* 2 (/ (pow M 3) (* K (pow n 2)))))))) (pow M 4))) (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -1/48 (/ (* (pow K 3) (pow (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))) 3)) (pow M 6))) (* 1/2 (/ (* K (+ (* -2 (/ (pow M 3) (* K (pow n 3)))) (* 2 (/ (pow M 3) (* K (pow n 3)))))) (pow M 2)))))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K (pow n 2)))) (* 2 (/ (pow M 3) (* K (pow n 2))))))) (pow M 2))))) (* 1/2 (/ (* K (* (sin (* 1/2 (/ (* K (* n (+ (* -2 (/ (pow M 3) (* K n))) (pow M 2)))) (pow M 2)))) (+ (* -2 (/ (pow M 3) (* K n))) (+ (* 2 (/ (pow M 3) (* K n))) (pow M 2))))) (pow M 2))))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos (* -1 M))
(+ (cos (* -1 M)) (* -1/2 (* K (* (sin (* -1 M)) (+ m n)))))
(+ (cos (* -1 M)) (* K (- (* -1/8 (* K (* (cos (* -1 M)) (pow (+ m n) 2)))) (* 1/2 (* (sin (* -1 M)) (+ m n))))))
(+ (cos (* -1 M)) (* K (- (* K (+ (* -1/8 (* (cos (* -1 M)) (pow (+ m n) 2))) (* 1/48 (* K (* (sin (* -1 M)) (pow (+ m n) 3)))))) (* 1/2 (* (sin (* -1 M)) (+ m n))))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))

Outputs
(* 1/4 (/ (pow (+ m n) 2) M))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n))) M)
(/ (+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2))) M)
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (-.f64 (neg.f64 m) n))) M)
(/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M)
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (-.f64 M (+.f64 m n)))) M)
(/ (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n))))) M)
(/.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) (.f64 M (-.f64 M (+.f64 m n)))) M)
M
(* M (+ 1 (* -1 (/ (+ m n) M))))
(*.f64 M (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 m n) M)))
(* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
(.f64 M (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (+.f64 m n) (+.f64 m n)) (*.f64 M M)) (neg.f64 (/.f64 (+.f64 m n) M)))))
(* M (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))
(.f64 M (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (+.f64 m n) (+.f64 m n)) (*.f64 M M)) (neg.f64 (/.f64 (+.f64 m n) M)))))
M
(* -1 (* M (- (+ (/ m M) (/ n M)) 1)))
(*.f64 (+.f64 (/.f64 m M) (+.f64 (/.f64 n M) #s(literal -1 binary64))) (neg.f64 M))
(* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1)))
(.f64 (+.f64 (/.f64 (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 m n) (+.f64 m n))) M) (+.f64 m n)) (neg.f64 M)) #s(literal -1 binary64)) (neg.f64 M))
(* -1 (* M (- (* -1 (/ (+ (* -1 (+ m n)) (* 1/4 (/ (pow (+ m n) 2) M))) M)) 1)))
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(+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M)))))
(-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m))
(+ M (+ (* -1 (* n (+ 1 (* -1/2 (/ m M))))) (* -1 (+ m (* -1/4 (/ (pow m 2) M))))))
(+.f64 M (neg.f64 (fma.f64 n (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m))))
(+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M))))))
(+.f64 M (fma.f64 n (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) n) M) (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 m m) M) m))))
(+ M (+ (* -1 (+ m (* -1/4 (/ (pow m 2) M)))) (* n (+ (* -1 (+ 1 (* -1/2 (/ m M)))) (* 1/4 (/ n M))))))
(+.f64 M (fma.f64 n (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) n) M) (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 m m) M) m))))
(* 1/4 (/ (pow n 2) M))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 n n)) M)
(* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (* 1/4 (/ 1 M))))
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(* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2))))))
(.f64 (.f64 n n) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 M (.f64 n n))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 m m) M) m) (*.f64 n n))) (/.f64 (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)) n)))
(* (pow n 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ m M))) n)) (+ (* -1 (/ (+ m (* -1/4 (/ (pow m 2) M))) (pow n 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow n 2))))))
(.f64 (.f64 n n) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 M (.f64 n n))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 m m) M) m) (*.f64 n n))) (/.f64 (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)) n)))
(* 1/4 (/ (pow n 2) M))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 n n)) M)
(* (pow n 2) (- (+ (* 1/2 (/ m (* M n))) (* 1/4 (/ 1 M))) (/ 1 n)))
(.f64 (.f64 n n) (fma.f64 #s(literal 1/2 binary64) (/.f64 m (*.f64 n M)) (+.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 #s(literal -1 binary64) n))))
(* (pow n 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ m M)) 1)) (* -1 (/ (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) n))) n)) (* 1/4 (/ 1 M))))
(.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)) (neg.f64 n)) (fma.f64 (/.f64 m M) #s(literal 1/2 binary64) #s(literal -1 binary64))) n)))
(* (pow n 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ m M)) 1)) (* -1 (/ (+ M (* -1 (+ m (* -1/4 (/ (pow m 2) M))))) n))) n)) (* 1/4 (/ 1 M))))
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(+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M)))))
(-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 n n) M) n))
(+ M (+ (* -1 (* m (+ 1 (* -1/2 (/ n M))))) (* -1 (+ n (* -1/4 (/ (pow n 2) M))))))
(+.f64 M (neg.f64 (fma.f64 m (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 n n) M) n))))
(+ M (+ (* -1 (+ n (* -1/4 (/ (pow n 2) M)))) (* m (+ (* -1 (+ 1 (* -1/2 (/ n M)))) (* 1/4 (/ m M))))))
(+.f64 M (fma.f64 m (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) m) M) (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 n n) M) n))))
(+ M (+ (* -1 (+ n (* -1/4 (/ (pow n 2) M)))) (* m (+ (* -1 (+ 1 (* -1/2 (/ n M)))) (* 1/4 (/ m M))))))
(+.f64 M (fma.f64 m (-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) m) M) (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 n n) M) n))))
(* 1/4 (/ (pow m 2) M))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 m m)) M)
(* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (* 1/4 (/ 1 M))))
(.f64 (.f64 m m) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64)) m)))
(* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (+ (* -1 (/ (+ n (* -1/4 (/ (pow n 2) M))) (pow m 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow m 2))))))
(.f64 (.f64 m m) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 M (.f64 m m))) (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 n n) M) n) (*.f64 m m))) (/.f64 (fma.f64 (/.f64 n M) #s(literal -1/2 binary64) #s(literal 1 binary64)) m)))
(* (pow m 2) (+ (* -1 (/ (+ 1 (* -1/2 (/ n M))) m)) (+ (* -1 (/ (+ n (* -1/4 (/ (pow n 2) M))) (pow m 2))) (+ (* 1/4 (/ 1 M)) (/ M (pow m 2))))))
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(* 1/4 (/ (pow m 2) M))
(/.f64 (.f64 #s(literal 1/4 binary64) (.f64 m m)) M)
(* (pow m 2) (- (+ (* 1/2 (/ n (* M m))) (* 1/4 (/ 1 M))) (/ 1 m)))
(.f64 (.f64 m m) (+.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 n (*.f64 m M)) (/.f64 #s(literal 1/4 binary64) M)) (/.f64 #s(literal -1 binary64) m)))
(* (pow m 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ n M)) 1)) (* -1 (/ (+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M))))) m))) m)) (* 1/4 (/ 1 M))))
(.f64 (.f64 m m) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (neg.f64 (fma.f64 (/.f64 n M) #s(literal 1/2 binary64) #s(literal -1 binary64))) (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 n n) M) n)) m)) m)))
(* (pow m 2) (+ (* -1 (/ (+ (* -1 (- (* 1/2 (/ n M)) 1)) (* -1 (/ (+ M (* -1 (+ n (* -1/4 (/ (pow n 2) M))))) m))) m)) (* 1/4 (/ 1 M))))
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(+ m (* -1/4 (/ (pow m 2) M)))
(fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)
(+ m (+ (* -1/4 (/ (pow m 2) M)) (* n (+ 1 (* -1/2 (/ m M))))))
(fma.f64 n (fma.f64 (/.f64 m M) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l))) (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 m n) K)) M)))
(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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(* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))))
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(+ (* n (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (sin (- (* 1/2 (* K m)) M))))) (* (cos (- (* 1/2 (* K m)) M)) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- M (* 1/2 m)))))) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2))))))
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(+ (* n (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (sin (- (* 1/2 (* K m)) M))))) (+ (* n (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (* (sin (- (* 1/2 (* K m)) M)) (- M (* 1/2 m)))))) (+ (* -1/8 (* (pow K 2) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2))))))) (* (cos (- (* 1/2 (* K m)) M)) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- (* 1/2 (pow (- M (* 1/2 m)) 2)) 1/4)))))) (* (cos (- (* 1/2 (* K m)) M)) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- M (* 1/2 m))))))) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2))))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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1
#s(literal 1 binary64)
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(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
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(* (cos (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2)))))
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(* (cos (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))))
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(+ (* m (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (sin (- (* 1/2 (* K n)) M))))) (* (cos (- (* 1/2 (* K n)) M)) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- M (* 1/2 n)))))) (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2))))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l))) (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 m n) K)) M)))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
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(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l))) (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 m n) K)) M)))
(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
(.f64 (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) (-.f64 (.f64 (+.f64 m n) #s(literal 1/2 binary64)) M) l))) (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 m n) K)) M)))
(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
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(fma.f64 m (fma.f64 m (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 K K) (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) (.f64 M M)))) (.f64 M M))) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M))))) (pow.f64 M #s(literal 4 binary64))) (fma.f64 m (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 K K) (.f64 (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) (.f64 M M)))) (.f64 M M))) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) #s(literal 0 binary64)))) (pow.f64 M #s(literal 4 binary64))) (.f64 (fma.f64 #s(literal -1/48 binary64) (/.f64 (.f64 (.f64 K (.f64 K K)) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M))))) (pow.f64 M #s(literal 6 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 K #s(literal 0 binary64))) (.f64 M M))) (neg.f64 (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) (.f64 M M)))) (.f64 M M)))))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 K (.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) (.f64 M M)))) (.f64 M M))))) (.f64 M M))))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 K (.f64 (fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) #s(literal 0 binary64) (.f64 M M)) (sin.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) (.f64 M M)))) (.f64 M M))))) (.f64 M M)))) (cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 n K) (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 M (.f64 M M)) (.f64 n K)) (.f64 M M)))) (*.f64 M M))))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ (* -2 (/ (pow M 3) (* K (- n (* -1 m))))) (pow M 2)) (- n (* -1 m)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* -1 M))
(cos.f64 M)
(+ (cos (* -1 M)) (* -1/2 (* K (* (sin (* -1 M)) (+ m n)))))
(fma.f64 #s(literal -1/2 binary64) (.f64 (neg.f64 (.f64 K (sin.f64 M))) (+.f64 m n)) (cos.f64 M))
(+ (cos (* -1 M)) (* K (- (* -1/8 (* K (* (cos (* -1 M)) (pow (+ m n) 2)))) (* 1/2 (* (sin (* -1 M)) (+ m n))))))
(fma.f64 K (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 K (cos.f64 M)) (.f64 (+.f64 m n) (+.f64 m n))) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 m n) (sin.f64 (neg.f64 M))))) (cos.f64 M))
(+ (cos (* -1 M)) (* K (- (* K (+ (* -1/8 (* (cos (* -1 M)) (pow (+ m n) 2))) (* 1/48 (* K (* (sin (* -1 M)) (pow (+ m n) 3)))))) (* 1/2 (* (sin (* -1 M)) (+ m n))))))
(fma.f64 K (fma.f64 K (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 (+.f64 m n) (+.f64 m n)) (cos.f64 M)) (.f64 #s(literal 1/48 binary64) (.f64 (neg.f64 (.f64 K (sin.f64 M))) (.f64 (+.f64 m n) (.f64 (+.f64 m n) (+.f64 m n)))))) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 m n) (sin.f64 (neg.f64 M))))) (cos.f64 M))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))
(cos (* 1/2 (/ (* K (* (+ m n) (+ (* -2 (/ (pow M 3) (* K (+ m n)))) (pow M 2)))) (pow M 2))))
(cos.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (+.f64 m n) K) (fma.f64 M M (/.f64 (.f64 #s(literal -2 binary64) (.f64 M (.f64 M M))) (.f64 (+.f64 m n) K))))) (.f64 M M)))

rewrite376.0ms (2.6%)

Memory

9.2MiB live, 553.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 034×	`lower-fma.f32`
6 022×	`lower-fma.f64`
5 006×	`lower-*.f32`
4 970×	`lower-*.f64`
2 442×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	564
0	140	526
1	581	487
2	5198	487
0	8220	484

Stop Event

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

Counts

25 → 583

Calls

Call 1

Inputs
(fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)
(+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m))
(-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
#s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64)))
#s(approx (cos M) #s(literal 1 binary64))
(exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))
(fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64))))
(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M))
(-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (*.f64 K #s(literal 1/2 binary64)))) M)
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M))
(-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)
(/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n)))
(fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K)))
(/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))
(*.f64 #s(literal 0 binary64) M)
(+.f64 #s(literal 0 binary64) (fma.f64 M M (*.f64 #s(literal 0 binary64) M)))
(/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M)
(.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M))
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
#s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))
(cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n))))))

Outputs
(+.f64 M (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)))
(+.f64 (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)) M)
(-.f64 (/.f64 (/.f64 (.f64 (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m))) (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (.f64 (neg.f64 M) (neg.f64 M))) (-.f64 (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)) M)) (/.f64 (.f64 M M) (-.f64 (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)) M)))
(fma.f64 M (neg.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M)) M)
(fma.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) (.f64 (/.f64 #s(literal -1 binary64) M) M) M)
(fma.f64 (neg.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M)) M M)
(fma.f64 #s(literal 1 binary64) M (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)))
(fma.f64 #s(literal -1 binary64) (neg.f64 M) (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)))
(fma.f64 (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m))) (/.f64 #s(literal -1 binary64) M) M)
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(fma.f64 #s(literal 1 binary64) (.f64 M M) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 M) #s(literal 2 binary64)) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (.f64 M M) (neg.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M)) (*.f64 M M))
(fma.f64 (.f64 M M) #s(literal 1 binary64) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (.f64 M M) (.f64 (.f64 M M) (/.f64 #s(literal 1 binary64) (.f64 M M))) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (.f64 M M) (/.f64 (.f64 M M) (.f64 M M)) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (.f64 M (.f64 M M)) (.f64 M (/.f64 #s(literal 1 binary64) (.f64 M M))) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (.f64 M (.f64 M M)) (/.f64 M (.f64 M M)) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 M M)) (.f64 M (.f64 M (.f64 M M))) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)) M (*.f64 M M))
(fma.f64 (.f64 (.f64 M M) (.f64 M (.f64 M (.f64 M M)))) (/.f64 #s(literal 1 binary64) (.f64 M (.f64 M (.f64 M M)))) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (neg.f64 (.f64 M (.f64 M (.f64 M M)))) (/.f64 #s(literal 1 binary64) (.f64 M (neg.f64 M))) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (/.f64 (.f64 M (.f64 M M)) (.f64 M M)) M (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (/.f64 M M) (/.f64 (.f64 M (.f64 M M)) M) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (/.f64 (.f64 M (.f64 M M)) M) (/.f64 M M) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (/.f64 (.f64 M M) M) (/.f64 (.f64 M M) M) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (/.f64 (.f64 M (.f64 M (.f64 M M))) M) (/.f64 #s(literal 1 binary64) M) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (pow.f64 M #s(literal 1 binary64)) (pow.f64 M #s(literal 1 binary64)) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 M M)) M) (.f64 M (.f64 M M)) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 M M)) (.f64 M M)) (.f64 M M) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)) #s(literal 3 binary64)) (.f64 (.f64 M M) (.f64 M (.f64 M (.f64 M M))))) (fma.f64 (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)) (-.f64 (.f64 M (.f64 M (.f64 M M))) (.f64 (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)) (.f64 M M)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)) (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M))) (.f64 M (.f64 M (.f64 M M)))) (-.f64 (/.f64 (.f64 M (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (neg.f64 M)) (.f64 M M)))
(/.f64 (.f64 M (fma.f64 M (.f64 M M) (pow.f64 (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)) #s(literal 3 binary64)))) (fma.f64 M (-.f64 M (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M))) (/.f64 (.f64 (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m))) (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (.f64 (neg.f64 M) (neg.f64 M)))))
(/.f64 (.f64 M (-.f64 (/.f64 (.f64 (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m))) (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (.f64 (neg.f64 M) (neg.f64 M))) (.f64 M M))) (-.f64 (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)) M))
(/.f64 (.f64 (fma.f64 M (.f64 M M) (pow.f64 (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)) #s(literal 3 binary64))) M) (fma.f64 M (-.f64 M (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M))) (/.f64 (.f64 (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m))) (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (.f64 (neg.f64 M) (neg.f64 M)))))
(/.f64 (.f64 (-.f64 (/.f64 (.f64 (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m))) (.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)))) (.f64 (neg.f64 M) (neg.f64 M))) (.f64 M M)) M) (-.f64 (neg.f64 (.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M) M)) M))
(.f64 M (fma.f64 M (neg.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M)) M))
(.f64 (fma.f64 M (neg.f64 (/.f64 (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) (+.f64 n m)) M)) M) M)
#s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))
#s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 m (/.f64 #s(literal -2 binary64) n) #s(literal 2 binary64)) n))
(cos.f64 (.f64 (fma.f64 M M (/.f64 (.f64 M (.f64 M M)) (.f64 (.f64 (+.f64 n m) K) #s(literal -1/2 binary64)))) (/.f64 (.f64 (+.f64 n m) (.f64 K #s(literal 1/2 binary64))) (.f64 M M))))
(cos.f64 (/.f64 (fma.f64 M M (/.f64 (.f64 M (.f64 M M)) (.f64 (.f64 (+.f64 n m) K) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 M M) (.f64 (+.f64 n m) (*.f64 K #s(literal 1/2 binary64)))))))
(cos.f64 (/.f64 (neg.f64 (fma.f64 M M (/.f64 (.f64 M (.f64 M M)) (.f64 (.f64 (+.f64 n m) K) #s(literal -1/2 binary64))))) (/.f64 (.f64 M M) (.f64 (+.f64 n m) (*.f64 K #s(literal 1/2 binary64))))))

eval313.0ms (2.1%)

Memory: 41.8MiB live, 547.0MiB allocated
Compiler: Compiled 86 171 to 5 064 computations (94.1% saved)

prune363.0ms (2.5%)

Memory

-46.9MiB live, 613.2MiB allocated

Pruning

23 alts after pruning (19 fresh and 4 done)

	Pruned	Kept	Total
New	1 973	8	1 981
Fresh	3	11	14
Picked	2	3	5
Done	0	1	1
Total	1 978	23	2 001

Accuracy

97.3%

Counts

2 001 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	9.3%	(.f64 (cos.f64 (/.f64 (fma.f64 (/.f64 (.f64 M (.f64 M (.f64 M M))) M) (/.f64 #s(literal 1 binary64) M) (/.f64 (.f64 M (.f64 M M)) (.f64 (.f64 (+.f64 n m) K) #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	5.4%	(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (exp.f64 (.f64 #s(literal 2 binary64) (log.f64 M)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	8.4%	(.f64 (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (.f64 M M) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	5.7%	(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (-.f64 (.f64 M M) (/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 m (.f64 M (.f64 M M))) (.f64 n K)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 M (.f64 M M))) K)) n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	9.7%	(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (.f64 (.f64 M (.f64 M M)) (+.f64 (/.f64 #s(literal 1 binary64) M) (/.f64 #s(literal -2 binary64) (.f64 (+.f64 m n) K))))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	13.2%	(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (.f64 M M)) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	31.6%	(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	36.2%	(.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	35.8%	(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	35.2%	(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	33.9%	(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	13.8%	(.f64 (cos.f64 (-.f64 (exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 n m) K))) #s(literal -1 binary64))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	28.2%	(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 n (.f64 #s(literal 1/2 binary64) (fma.f64 K (/.f64 m n) K)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	33.2%	(.f64 (cos.f64 #s(approx (/ (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
✓	31.9%	(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	32.5%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 m K) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 n K) (neg.f64 M)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 n K) (neg.f64 M))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	31.5%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
	83.8%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ ( -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	67.1%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M #s(approx (+ ( M (/ (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (neg M))) M) (.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)) (neg.f64 n)) (fma.f64 (/.f64 m M) #s(literal 1/2 binary64) #s(literal -1 binary64))) n))))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	54.5%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
	50.7%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
	49.2%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
✓	36.5%	(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Compiler

Compiled 2 185 to 743 computations (66% saved)

regimes102.0ms (0.7%)

Memory

5.8MiB live, 201.6MiB allocated

Counts

57 → 1

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ ( -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 n n) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M #s(approx (+ ( M (/ (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (neg M))) M) (.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)) (neg.f64 n)) (fma.f64 (/.f64 m M) #s(literal 1/2 binary64) #s(literal -1 binary64))) n))))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (/ (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (fma.f64 n K (.f64 m K)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 n (.f64 #s(literal 1/2 binary64) (fma.f64 K (/.f64 m n) K)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 n (.f64 n #s(literal -1/4 binary64))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (+ (* K (* (+ n m) (* 1/2 (sin M)))) (cos M)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 M (+.f64 n m)) K) #s(literal 1 binary64)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (.f64 M M)) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M M)) (/.f64 #s(literal 2 binary64) (+.f64 m n)) (.f64 (+.f64 #s(literal 0 binary64) M) K)) (.f64 (+.f64 #s(literal 0 binary64) M) (/.f64 #s(literal 2 binary64) (+.f64 m n))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 m (.f64 m (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (fma.f64 n #s(literal -1/2 binary64) M) (/.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M) l)) m)) m)))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (fma.f64 (.f64 (+.f64 n m) (+.f64 n m)) (/.f64 #s(literal 1/4 binary64) (*.f64 M M)) (/.f64 (+.f64 n m) (neg.f64 M))) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (.f64 (.f64 M (.f64 M M)) (+.f64 (/.f64 #s(literal 1 binary64) M) (/.f64 #s(literal -2 binary64) (.f64 (+.f64 m n) K))))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (.f64 M M) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (/.f64 (fma.f64 (/.f64 (.f64 M (.f64 M (.f64 M M))) M) (/.f64 #s(literal 1 binary64) M) (/.f64 (.f64 M (.f64 M M)) (.f64 (.f64 (+.f64 n m) K) #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (-.f64 (.f64 M M) (/.f64 (fma.f64 #s(literal -2 binary64) (/.f64 (.f64 m (.f64 M (.f64 M M))) (.f64 n K)) (/.f64 (.f64 #s(literal 2 binary64) (.f64 M (.f64 M M))) K)) n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (/.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (.f64 K (+.f64 n m)) (.f64 (.f64 M M) (.f64 #s(literal 2 binary64) (.f64 (.f64 (neg.f64 M) M) M)))) (.f64 (.f64 M M) (.f64 K (+.f64 n m)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 m K) (sin.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 n K) (neg.f64 M)))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 n K) (neg.f64 M))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 m K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (fma.f64 n K (.f64 m K)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 m n) (-.f64 m n)))) (/.f64 #s(literal 1 binary64) (-.f64 m n))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))) #s(literal -1 binary64))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 n m)))) #s(literal -1 binary64))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 n m) K))) #s(literal -1 binary64))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 K (.f64 (+.f64 n m) (.f64 #s(literal 1/2 binary64) (sin.f64 M))) (cos.f64 M))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (fma.f64 (.f64 m (.f64 K #s(literal -1/2 binary64))) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 n K)) M)) (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 n K)) M)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (exp.f64 (.f64 #s(literal 2 binary64) (log.f64 M)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (*.f64 (+.f64 m n) K))) #s(literal -1 binary64))) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Calls

6 calls:

18.0ms	m
17.0ms	M
17.0ms	l
17.0ms	K
16.0ms	n

Results

Accuracy	Segments	Branch
96.2%	1	`K`
96.2%	1	`m`
96.2%	1	`n`
96.2%	1	`M`
96.2%	1	`l`
96.2%	1	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes72.0ms (0.5%)

Memory

13.3MiB live, 133.0MiB allocated

Counts

40 → 3

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ ( -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 n n) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M #s(approx (+ ( M (/ (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (neg M))) M) (.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)) (neg.f64 n)) (fma.f64 (/.f64 m M) #s(literal 1/2 binary64) #s(literal -1 binary64))) n))))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (/ (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (fma.f64 n K (.f64 m K)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 n (.f64 #s(literal 1/2 binary64) (fma.f64 K (/.f64 m n) K)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 n (.f64 n #s(literal -1/4 binary64))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (+ (* K (* (+ n m) (* 1/2 (sin M)))) (cos M)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 M (+.f64 n m)) K) #s(literal 1 binary64)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (.f64 M M)) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M M)) (/.f64 #s(literal 2 binary64) (+.f64 m n)) (.f64 (+.f64 #s(literal 0 binary64) M) K)) (.f64 (+.f64 #s(literal 0 binary64) M) (/.f64 #s(literal 2 binary64) (+.f64 m n))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 m (.f64 m (+.f64 #s(literal -1/4 binary64) (/.f64 (+.f64 (fma.f64 n #s(literal -1/2 binary64) M) (/.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M) l)) m)) m)))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (fma.f64 (.f64 (+.f64 n m) (+.f64 n m)) (/.f64 #s(literal 1/4 binary64) (*.f64 M M)) (/.f64 (+.f64 n m) (neg.f64 M))) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (.f64 (.f64 M (.f64 M M)) (+.f64 (/.f64 #s(literal 1 binary64) M) (/.f64 #s(literal -2 binary64) (.f64 (+.f64 m n) K))))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (/.f64 (fma.f64 (-.f64 #s(literal 0 binary64) (.f64 M (.f64 M M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (.f64 M M) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (/.f64 (fma.f64 (.f64 M (.f64 M (.f64 M M))) (/.f64 #s(literal 1 binary64) (.f64 M M)) (/.f64 (.f64 (.f64 (neg.f64 M) M) M) (.f64 (.f64 #s(literal 1/2 binary64) (+.f64 n m)) K))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (/.f64 (fma.f64 (/.f64 (.f64 M (.f64 M (.f64 M M))) M) (/.f64 #s(literal 1 binary64) M) (/.f64 (.f64 M (.f64 M M)) (.f64 (.f64 (+.f64 n m) K) #s(literal -1/2 binary64)))) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (*.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Outputs

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (+ (* K (* (+ n m) (* 1/2 (sin M)))) (cos M)) (fma.f64 #s(literal 1/2 binary64) (*.f64 (*.f64 M (+.f64 n m)) K) #s(literal 1 binary64)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Calls

6 calls:

13.0ms	K
12.0ms	M
12.0ms	m
12.0ms	l
11.0ms	n

Results

Accuracy	Segments	Branch
92.3%	1	`K`
92.3%	1	`n`
95.8%	3	`M`
92.3%	1	`l`
92.3%	1	`m`
96.1%	3	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes82.0ms (0.6%)

Memory

-3.3MiB live, 74.2MiB allocated

Counts

30 → 4

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ ( -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 n n) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M #s(approx (+ ( M (/ (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (neg M))) M) (.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)) (neg.f64 n)) (fma.f64 (/.f64 m M) #s(literal 1/2 binary64) #s(literal -1 binary64))) n))))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (/ (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (fma.f64 n K (.f64 m K)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 n (.f64 #s(literal 1/2 binary64) (fma.f64 K (/.f64 m n) K)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 n (.f64 n #s(literal -1/4 binary64))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (+ (* K (* (+ n m) (* 1/2 (sin M)))) (cos M)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 M (+.f64 n m)) K) #s(literal 1 binary64)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 (/.f64 #s(approx (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (.f64 M M)) (.f64 (+.f64 #s(literal 0 binary64) (fma.f64 M M (.f64 #s(literal 0 binary64) M))) (/.f64 #s(literal 2 binary64) (.f64 K (+.f64 m n)))))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Outputs
(.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (+ (* K (* (+ n m) (* 1/2 (sin M)))) (cos M)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 M (+.f64 n m)) K) #s(literal 1 binary64)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Calls

6 calls:

36.0ms	M
10.0ms	m
9.0ms	K
9.0ms	n
9.0ms	l

Results

Accuracy	Segments	Branch
90.3%	1	`m`
90.3%	1	`K`
90.3%	1	`n`
90.3%	1	`l`
93.8%	3	`M`
96.6%	4	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes9.0ms (0.1%)

Memory

17.2MiB live, 17.2MiB allocated

Counts

28 → 4

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ ( -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 n n) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M #s(approx (+ ( M (/ (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (neg M))) M) (.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)) (neg.f64 n)) (fma.f64 (/.f64 m M) #s(literal 1/2 binary64) #s(literal -1 binary64))) n))))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (/ (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (fma.f64 n K (.f64 m K)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 n (.f64 #s(literal 1/2 binary64) (fma.f64 K (/.f64 m n) K)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 n (.f64 n #s(literal -1/4 binary64))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Outputs
(.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Calls

1 calls:

7.0ms

(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Results

Accuracy	Segments	Branch
96.2%	4	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`

Compiler

Compiled 34 to 21 computations (38.2% saved)

regimes10.0ms (0.1%)

Memory

-21.2MiB live, 16.6MiB allocated

Counts

27 → 4

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ ( -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 n n) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M #s(approx (+ ( M (/ (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (neg M))) M) (.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)) (neg.f64 n)) (fma.f64 (/.f64 m M) #s(literal 1/2 binary64) #s(literal -1 binary64))) n))))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (/ (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (fma.f64 n K (.f64 m K)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (+.f64 m n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 n (.f64 #s(literal 1/2 binary64) (fma.f64 K (/.f64 m n) K)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 n (.f64 n #s(literal -1/4 binary64))))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 (fma.f64 (/.f64 m n) #s(literal -2 binary64) #s(literal 2 binary64)) n))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Calls

1 calls:

8.0ms

(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Results

Accuracy	Segments	Branch
96.2%	4	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`

Compiler

Compiled 34 to 21 computations (38.2% saved)

regimes6.0ms (0%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

18 → 4

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ ( -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 m m) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 (.f64 n n) #s(literal -1/4 binary64)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M #s(approx (+ ( M (/ (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (neg M))) M) (.f64 (.f64 n n) (-.f64 (/.f64 #s(literal 1/4 binary64) M) (/.f64 (-.f64 (/.f64 (-.f64 M (fma.f64 #s(literal -1/4 binary64) (/.f64 (*.f64 m m) M) m)) (neg.f64 n)) (fma.f64 (/.f64 m M) #s(literal 1/2 binary64) #s(literal -1 binary64))) n))))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 m K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (- (/ ( K (+ m n)) 2) M) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 #s(approx (/ (+ ( (- 0 (* M (* M M))) (/ 2 (* K (+ m n)))) (* (+ 0 (+ (* M M) (* 0 M))) 1)) (* (+ 0 (+ (* M M) (* 0 M))) (/ 2 (* K (+ m n))))) (.f64 #s(literal 1/2 binary64) (.f64 n K)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 #s(approx (/ ( K (+ m n)) 2) (.f64 #s(literal 1/2 binary64) (.f64 n K))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 (cos.f64 (-.f64 (fma.f64 (.f64 m K) #s(literal 1/2 binary64) (.f64 n (.f64 K #s(literal 1/2 binary64)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Calls

1 calls:

5.0ms

(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Results

Accuracy	Segments	Branch
96.2%	4	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`

Compiler

Compiled 34 to 21 computations (38.2% saved)

regimes3.0ms (0%)

Memory

10.6MiB live, 10.6MiB allocated

Counts

7 → 4

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ ( -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Calls

1 calls:

2.0ms

(*.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Results

Accuracy	Segments	Branch
96.2%	4	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`

Compiler

Compiled 34 to 21 computations (38.2% saved)

regimes20.0ms (0.1%)

Memory

-1.9MiB live, 36.9MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ ( -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 #s(literal -1/4 binary64) (*.f64 m m)))))

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (*.f64 M (fma.f64 M (/.f64 #s(approx (+ n (+ (* -1/4 (/ (* (+ n m) (+ n m)) M)) m)) (/.f64 (*.f64 #s(literal -1/4 binary64) (*.f64 n n)) M)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Calls

6 calls:

6.0ms	M
3.0ms	n
3.0ms	l
3.0ms	K
3.0ms	m

Results

Accuracy	Segments	Branch
83.8%	1	`K`
91.1%	2	`m`
83.8%	1	`n`
83.8%	1	`l`
83.8%	1	`M`
85.4%	2	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes19.0ms (0.1%)

Memory

2.1MiB live, 38.8MiB allocated

Counts

5 → 4

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) (fma.f64 (*.f64 M M) #s(literal -1/2 binary64) #s(literal 1 binary64)))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n)))))

Calls

6 calls:

5.0ms	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
3.0ms	l
2.0ms	K
2.0ms	m
2.0ms	n

Results

Accuracy	Segments	Branch
60.2%	4	`K`
76.1%	3	`M`
77.6%	3	`n`
70.4%	5	`l`
66.3%	4	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`
79.5%	4	`m`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes9.0ms (0.1%)

Memory

-21.8MiB live, 17.1MiB allocated

Counts

3 → 4

Calls

Call 1

Inputs

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 #s(literal -1/4 binary64) (*.f64 m m)))))

Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m)))))

Calls

3 calls:

4.0ms	M
2.0ms	m
2.0ms	n

Results

Accuracy	Segments	Branch
72.3%	3	`M`
56.8%	3	`n`
74.2%	4	`m`

Compiler

Compiled 18 to 15 computations (16.7% saved)

regimes4.0ms (0%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

2 → 3

Calls

Call 1

Inputs

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))

Outputs

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

(*.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))

Calls

2 calls:

2.0ms	m
2.0ms	M

Results

Accuracy	Segments	Branch
67.3%	3	`M`
49.2%	1	`m`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes11.0ms (0.1%)

Memory

-14.1MiB live, 24.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

Calls

6 calls:

4.0ms	m
1.0ms	K
1.0ms	M
1.0ms	l
1.0ms	n

Results

Accuracy	Segments	Branch
36.5%	1	`m`
36.5%	1	`n`
36.5%	1	`K`
36.5%	1	`(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))`
36.5%	1	`l`
36.5%	1	`M`

Compiler

Compiled 64 to 46 computations (28.1% saved)

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	0.9705712466018273	1.0

Compiler

Compiled 37 to 29 computations (21.6% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	0.9705712466018273	1.0
0.0ms	-0.24754836297261354	-0.0

Compiler

Compiled 37 to 29 computations (21.6% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	-0.0	0.7559817380965503
0.0ms	-0.24754836297261354	-0.0

Compiler

Compiled 37 to 29 computations (21.6% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	-0.0	0.7559817380965503
0.0ms	-0.24754836297261354	-0.0

Compiler

Compiled 37 to 29 computations (21.6% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	-0.0	0.7559817380965503
0.0ms	-0.24754836297261354	-0.0

Compiler

Compiled 37 to 29 computations (21.6% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN
0.0ms	0.7559817380965503	0.802548141155688
0.0ms	-0.9556933618412676	-0.24754836297261354

Compiler

Compiled 37 to 29 computations (21.6% saved)

bsearch24.0ms (0.2%)

Memory

-18.1MiB live, 33.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
13.0ms	-4.924088840362706e+20	-6893915113138.98

Samples

9.0ms	76×	0	valid
1.0ms	4×	1	valid

Compiler

Compiled 302 to 199 computations (34.1% saved)

Precisions

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

ival-sub: 2.0ms (27.7% of total)

ival-div: 1.0ms (13.8% of total)

ival-mult: 1.0ms (13.8% of total)

ival-pow2: 1.0ms (13.8% of total)

ival-cos: 1.0ms (13.8% of total)

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

adjust: 0.0ms (0% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

bsearch223.0ms (1.5%)

Memory

10.6MiB live, 124.2MiB allocated

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
160.0ms	-1.6645376367098033e-295	-1.9898566026127867e-298
18.0ms	-4.747491351399878e-37	-8.284568164035093e-39
34.0ms	-274386289841.6482	-0.3445555006060969

Samples

188.0ms	369×	0	valid
9.0ms	31×	1	valid

Compiler

Compiled 821 to 580 computations (29.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 184.0ms

ival-sub: 147.0ms (80% of total)

ival-div: 12.0ms (6.5% of total)

ival-mult: 5.0ms (2.7% of total)

ival-pow2: 4.0ms (2.2% of total)

ival-cos: 4.0ms (2.2% of total)

ival-exp: 3.0ms (1.6% of total)

ival-add: 2.0ms (1.1% of total)

ival-neg: 2.0ms (1.1% of total)

ival-fabs: 2.0ms (1.1% of total)

adjust: 1.0ms (0.5% of total)

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

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

exact: 0.0ms (0% of total)

bsearch32.0ms (0.2%)

Memory

2.0MiB live, 47.3MiB allocated

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
26.0ms	61632.85968299131	29512594404.06904
1.0ms	-4.747491351399878e-37	-8.284568164035093e-39
1.0ms	-274386289841.6482	-0.3445555006060969

Samples

15.0ms	130×	0	valid
6.0ms	14×	1	valid

Compiler

Compiled 854 to 603 computations (29.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-div: 4.0ms (24.9% of total)

ival-sub: 3.0ms (18.7% of total)

ival-mult: 2.0ms (12.5% of total)

ival-pow2: 2.0ms (12.5% of total)

ival-add: 1.0ms (6.2% of total)

adjust: 1.0ms (6.2% of total)

ival-exp: 1.0ms (6.2% of total)

ival-cos: 1.0ms (6.2% of total)

ival-neg: 1.0ms (6.2% of total)

ival-fabs: 1.0ms (6.2% of total)

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

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

exact: 0.0ms (0% of total)

bsearch57.0ms (0.4%)

Memory

24.6MiB live, 63.2MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	1.181638286420504e-17	2.004433550817977e-16
33.0ms	-7611.643785463953	-7.194524909231858e-7

Samples

37.0ms	259×	0	valid
4.0ms	13×	1	valid

Compiler

Compiled 547 to 386 computations (29.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-div: 9.0ms (27.9% of total)

ival-sub: 6.0ms (18.6% of total)

ival-cos: 4.0ms (12.4% of total)

ival-mult: 3.0ms (9.3% of total)

ival-pow2: 3.0ms (9.3% of total)

ival-add: 2.0ms (6.2% of total)

ival-exp: 2.0ms (6.2% of total)

adjust: 1.0ms (3.1% of total)

ival-neg: 1.0ms (3.1% of total)

ival-fabs: 1.0ms (3.1% of total)

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

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

exact: 0.0ms (0% of total)

simplify110.0ms (0.7%)

Memory

-0.9MiB live, 75.0MiB allocated

Algorithm

1×	egg-herbie

Rules

446×	`distribute-lft-neg-in_binary64`
388×	`neg-mul-1_binary64`
306×	`unsub-neg_binary64`
266×	`cancel-sign-sub_binary64`
248×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	2333
1	233	2333
2	278	2333
3	326	2300
4	364	2300
5	387	2300
6	469	2300
7	687	2300
8	931	2300
9	971	2300
10	1093	2300
11	1250	2300
12	1434	2300
13	1568	2300
14	1634	2300
15	1700	2300
16	1749	2300
17	1799	2300
18	1835	2300
19	1847	2300

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(if (<=.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #s(literal 4371064304532507/4503599627370496 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (if (<=.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #s(literal +inf.0 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (+ (* K (* (+ n m) (* 1/2 (sin M)))) (cos M)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 M (+.f64 n m)) K) #s(literal 1 binary64)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n))))))))
(if (<=.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #s(literal -3602879701896397/18014398509481984 binary64)) (.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (if (<=.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #s(literal 4371064304532507/4503599627370496 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (if (<=.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #s(literal +inf.0 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (+ (* K (* (+ n m) (* 1/2 (sin M)))) (cos M)) (fma.f64 #s(literal 1/2 binary64) (.f64 (.f64 M (+.f64 n m)) K) #s(literal 1 binary64)))) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))))))
(if (<=.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #s(literal -3602879701896397/18014398509481984 binary64)) (.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (fma.f64 (/.f64 m (.f64 n n)) #s(literal -2 binary64) (/.f64 #s(literal 2 binary64) n)))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (if (<=.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #s(literal 0 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (if (<=.f64 (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n)))))) #s(literal +inf.0 binary64)) (.f64 (cos.f64 (-.f64 (/.f64 K #s(approx (/ 2 (+ m n)) (/.f64 #s(literal 2 binary64) m))) M)) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 (-.f64 (neg.f64 #s(approx (pow (- (/ (+ m n) 2) M) 2) (.f64 M (fma.f64 M (/.f64 (+.f64 n (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 n m) (+.f64 n m)) M) m)) (neg.f64 M)) M)))) (-.f64 l (fabs.f64 (-.f64 m n)))))))))
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Outputs
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (neg.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) (cos.f64 M)) (exp.f64 (-.f64 (-.f64 (fabs.f64 (-.f64 m n)) l) (pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64)))))
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(if (<=.f64 m #s(literal -54 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m))))) (if (<=.f64 m #s(literal -7901930132589739/47890485652059026823698344598447161988085597568237568 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (if (<=.f64 m #s(literal -1122911039760397/92041888504950574475740425768398066361240421321846096523996201552759130012416493123946740389072658442813498306494153399121300361632981310716337884487410751681417161433531128461466736435838000189159978471467522953645133149359340995314643512596903545427635461470508184698852989920501614748075702440767602758254592 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (.f64 M M))))) (.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n))))))))
(if (<=.f64 m #s(literal -54 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 m m))))) (if (<=.f64 m #s(literal -7901930132589739/47890485652059026823698344598447161988085597568237568 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (if (<=.f64 m #s(literal -1122911039760397/92041888504950574475740425768398066361240421321846096523996201552759130012416493123946740389072658442813498306494153399121300361632981310716337884487410751681417161433531128461466736435838000189159978471467522953645133149359340995314643512596903545427635461470508184698852989920501614748075702440767602758254592 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 M (neg.f64 M))))) (.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 #s(literal -1/4 binary64) (.f64 n n))))))))
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(if (<=.f64 M #s(literal -51 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (.f64 M M))))) (if (<=.f64 M #s(literal 2028240960365167/10141204801825835211973625643008 binary64)) (.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 (*.f64 M M)))))))
(if (<=.f64 M #s(literal -51 binary64)) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (.f64 M (neg.f64 M))))) (if (<=.f64 M #s(literal 2028240960365167/10141204801825835211973625643008 binary64)) (.f64 #s(approx (cos (- (/ (* K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l)))) (.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (*.f64 M (neg.f64 M)))))))
(.f64 #s(approx (cos (- (/ ( K (+ m n)) 2) M)) #s(approx (cos M) #s(literal 1 binary64))) (exp.f64 #s(approx (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) (neg.f64 l))))

soundness1.2s (8%)

Memory

-3.4MiB live, 1 250.1MiB allocated

Rules

10 032×	`lower-fma.f64`
10 032×	`lower-fma.f32`
8 956×	`lower-fma.f64`
8 956×	`lower-fma.f32`
7 192×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1632	29337
1	5507	27968
0	8545	27030
0	1581	26444
1	5247	25218
0	8342	24337
0	1036	25459
1	3361	24621
0	8060	23823
0	388	3016
1	1162	2963
2	3519	2940
0	8866	2818
0	63	382
0	107	374
1	356	374
2	2711	374
0	8811	374

Stop Event

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

Compiler

Compiled 3 472 to 1 470 computations (57.7% saved)

preprocess369.0ms (2.5%)

Memory: -71.1MiB live, 284.4MiB allocated
Compiler: Compiled 3 654 to 530 computations (85.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

sample2.1s (14.4%)

preprocess346.0ms (2.4%)

explain453.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify524.0ms (3.6%)

localize116.0ms (0.8%)

series24.0ms (0.2%)

simplify349.0ms (2.4%)

rewrite350.0ms (2.4%)

eval113.0ms (0.8%)

prune157.0ms (1.1%)

simplify221.0ms (1.5%)

localize394.0ms (2.7%)

series109.0ms (0.7%)

simplify528.0ms (3.6%)

rewrite373.0ms (2.5%)

eval633.0ms (4.3%)

prune454.0ms (3.1%)

simplify219.0ms (1.5%)

localize386.0ms (2.6%)

series114.0ms (0.8%)

simplify736.0ms (5%)

rewrite449.0ms (3.1%)

eval493.0ms (3.4%)

prune264.0ms (1.8%)

simplify293.0ms (2%)

localize476.0ms (3.2%)

series126.0ms (0.9%)

simplify496.0ms (3.4%)

rewrite376.0ms (2.6%)

eval313.0ms (2.1%)

prune363.0ms (2.5%)

regimes102.0ms (0.7%)

regimes72.0ms (0.5%)

regimes82.0ms (0.6%)

regimes9.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes3.0ms (0%)

regimes20.0ms (0.1%)

regimes19.0ms (0.1%)

regimes9.0ms (0.1%)

regimes4.0ms (0%)

regimes11.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch24.0ms (0.2%)

bsearch223.0ms (1.5%)

bsearch32.0ms (0.2%)

bsearch57.0ms (0.4%)

simplify110.0ms (0.7%)

soundness1.2s (8%)

preprocess369.0ms (2.5%)

end0.0ms (0%)

Profiling