Metrics for Maksimov and Kolovsky, Equation (32)

analyze4.0ms (0%)

Memory

-37.6MiB live, 0.9MiB 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)

sample1.6s (13.2%)

Memory

32.6MiB live, 2 444.8MiB allocated

Samples

1.1s	7 839×	0	valid
155.0ms	417×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 910.0ms

ival-div: 205.0ms (22.5% of total)

ival-sub: 195.0ms (21.4% of total)

ival-mult: 112.0ms (12.3% of total)

ival-pow2: 93.0ms (10.2% of total)

ival-cos: 69.0ms (7.6% of total)

ival-exp: 60.0ms (6.6% of total)

ival-add: 55.0ms (6% of total)

ival-fabs: 48.0ms (5.3% of total)

ival-neg: 38.0ms (4.2% of total)

adjust: 17.0ms (1.9% of total)

exact: 8.0ms (0.9% of total)

ival-true: 6.0ms (0.7% of total)

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

Bogosity

preprocess409.0ms (3.3%)

Memory

14.7MiB live, 534.6MiB allocated

Algorithm

2×	egg-herbie

Rules

7 472×	`accelerator-lowering-fma.f32`
7 472×	`accelerator-lowering-fma.f64`
3 222×	`-lowering-.f32`
3 222×	`-lowering-.f64`
2 026×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	210	626
1	575	618
2	1513	593
3	5215	593
0	21	29
1	52	29
2	119	28
3	364	28
4	1293	28
5	4695	28
0	8537	27

Stop Event

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

Calls

Call 1

Inputs
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

Outputs

(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

(*.f64 (cos.f64 (fma.f64 K (fma.f64 (+.f64 m n) #s(literal -1/2 binary64) #s(literal 0 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))))

Call 2

Inputs
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
(* (cos (- (/ (* (neg K) (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
(* (cos (- (/ (* K (+ (neg m) n)) 2) M)) (exp (- (neg (pow (- (/ (+ (neg m) n) 2) M) 2)) (- l (fabs (- (neg m) n))))))
(* (cos (- (/ (* K (+ m (neg n))) 2) M)) (exp (- (neg (pow (- (/ (+ m (neg n)) 2) M) 2)) (- l (fabs (- m (neg n)))))))
(* (cos (- (/ (* K (+ m n)) 2) (neg M))) (exp (- (neg (pow (- (/ (+ m n) 2) (neg M)) 2)) (- l (fabs (- m n))))))
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- (neg l) (fabs (- m n))))))
(neg (* (cos (- (/ (* (neg K) (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))
(neg (* (cos (- (/ (* K (+ (neg m) n)) 2) M)) (exp (- (neg (pow (- (/ (+ (neg m) n) 2) M) 2)) (- l (fabs (- (neg m) n)))))))
(neg (* (cos (- (/ (* K (+ m (neg n))) 2) M)) (exp (- (neg (pow (- (/ (+ m (neg n)) 2) M) 2)) (- l (fabs (- m (neg n))))))))
(neg (* (cos (- (/ (* K (+ m n)) 2) (neg M))) (exp (- (neg (pow (- (/ (+ m n) 2) (neg M)) 2)) (- l (fabs (- m n)))))))
(neg (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- (neg l) (fabs (- m n)))))))
(* (cos (- (/ (* m (+ K n)) 2) M)) (exp (- (neg (pow (- (/ (+ K n) 2) M) 2)) (- l (fabs (- K n))))))
(* (cos (- (/ (* n (+ m K)) 2) M)) (exp (- (neg (pow (- (/ (+ m K) 2) M) 2)) (- l (fabs (- m K))))))
(* (cos (- (/ (* M (+ m n)) 2) K)) (exp (- (neg (pow (- (/ (+ m n) 2) K) 2)) (- l (fabs (- m n))))))
(* (cos (- (/ (* l (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- K (fabs (- m n))))))
(* (cos (- (/ (* K (+ n m)) 2) M)) (exp (- (neg (pow (- (/ (+ n m) 2) M) 2)) (- l (fabs (- n m))))))
(* (cos (- (/ (* K (+ M n)) 2) m)) (exp (- (neg (pow (- (/ (+ M n) 2) m) 2)) (- l (fabs (- M n))))))
(* (cos (- (/ (* K (+ l n)) 2) M)) (exp (- (neg (pow (- (/ (+ l n) 2) M) 2)) (- m (fabs (- l n))))))
(* (cos (- (/ (* K (+ m M)) 2) n)) (exp (- (neg (pow (- (/ (+ m M) 2) n) 2)) (- l (fabs (- m M))))))
(* (cos (- (/ (* K (+ m l)) 2) M)) (exp (- (neg (pow (- (/ (+ m l) 2) M) 2)) (- n (fabs (- m l))))))
(* (cos (- (/ (* K (+ m n)) 2) l)) (exp (- (neg (pow (- (/ (+ m n) 2) l) 2)) (- M (fabs (- m n))))))

Outputs
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
(* (cos (- (* (+ m n) (/ K 2)) M)) (exp (- (- (fabs (- n m)) l) (pow (- (/ (+ m n) 2) M) 2))))
(* (cos (- (/ (* (neg K) (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
(* (exp (- (- (fabs (- n m)) l) (pow (- (/ (+ m n) 2) M) 2))) (cos (- (* (+ m n) (* K -1/2)) M)))
(* (cos (- (/ (* K (+ (neg m) n)) 2) M)) (exp (- (neg (pow (- (/ (+ (neg m) n) 2) M) 2)) (- l (fabs (- (neg m) n))))))
(* (cos (- (* (- n m) (/ K 2)) M)) (exp (- (- (fabs (+ m n)) l) (pow (- (/ (- n m) 2) M) 2))))
(* (cos (- (/ (* K (+ m (neg n))) 2) M)) (exp (- (neg (pow (- (/ (+ m (neg n)) 2) M) 2)) (- l (fabs (- m (neg n)))))))
(* (cos (- (* (- m n) (/ K 2)) M)) (exp (- (- (fabs (+ m n)) l) (pow (- (/ (- m n) 2) M) 2))))
(* (cos (- (/ (* K (+ m n)) 2) (neg M))) (exp (- (neg (pow (- (/ (+ m n) 2) (neg M)) 2)) (- l (fabs (- m n))))))
(* (cos (- (* (+ m n) (* K -1/2)) M)) (exp (- (- (fabs (- n m)) l) (pow (+ M (/ (+ m n) 2)) 2))))
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- (neg l) (fabs (- m n))))))
(* (cos (- (* (+ m n) (/ K 2)) M)) (exp (+ l (- (fabs (- n m)) (pow (- (/ (+ m n) 2) M) 2)))))
(neg (* (cos (- (/ (* (neg K) (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))
(* (exp (- (- (fabs (- n m)) l) (pow (- (/ (+ m n) 2) M) 2))) (neg (cos (- (* (+ m n) (* K -1/2)) M))))
(neg (* (cos (- (/ (* K (+ (neg m) n)) 2) M)) (exp (- (neg (pow (- (/ (+ (neg m) n) 2) M) 2)) (- l (fabs (- (neg m) n)))))))
(* (exp (- (- (fabs (+ m n)) l) (pow (- (/ (- n m) 2) M) 2))) (neg (cos (- (* (- n m) (/ K 2)) M))))
(neg (* (cos (- (/ (* K (+ m (neg n))) 2) M)) (exp (- (neg (pow (- (/ (+ m (neg n)) 2) M) 2)) (- l (fabs (- m (neg n))))))))
(* (exp (- (- (fabs (+ m n)) l) (pow (- (/ (- m n) 2) M) 2))) (neg (cos (- (* (- m n) (/ K 2)) M))))
(neg (* (cos (- (/ (* K (+ m n)) 2) (neg M))) (exp (- (neg (pow (- (/ (+ m n) 2) (neg M)) 2)) (- l (fabs (- m n)))))))
(* (exp (- (- (fabs (- n m)) l) (pow (+ M (/ (+ m n) 2)) 2))) (neg (cos (- (* (+ m n) (* K -1/2)) M))))
(neg (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- (neg l) (fabs (- m n)))))))
(* (exp (+ l (- (fabs (- n m)) (pow (- (/ (+ m n) 2) M) 2)))) (neg (cos (- (* (+ m n) (/ K 2)) M))))
(* (cos (- (/ (* m (+ K n)) 2) M)) (exp (- (neg (pow (- (/ (+ K n) 2) M) 2)) (- l (fabs (- K n))))))
(* (cos (- (* (+ K n) (/ m 2)) M)) (exp (- (- (fabs (- K n)) l) (pow (- (/ (+ K n) 2) M) 2))))
(* (cos (- (/ (* n (+ m K)) 2) M)) (exp (- (neg (pow (- (/ (+ m K) 2) M) 2)) (- l (fabs (- m K))))))
(* (cos (- (* (+ K m) (/ n 2)) M)) (exp (- (- (fabs (- m K)) l) (pow (- (/ (+ K m) 2) M) 2))))
(* (cos (- (/ (* M (+ m n)) 2) K)) (exp (- (neg (pow (- (/ (+ m n) 2) K) 2)) (- l (fabs (- m n))))))
(* (cos (- (* (+ m n) (/ M 2)) K)) (exp (- (- (fabs (- n m)) l) (pow (- (/ (+ m n) 2) K) 2))))
(* (cos (- (/ (* l (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- K (fabs (- m n))))))
(* (cos (- (* (+ m n) (/ l 2)) M)) (exp (- (- (fabs (- n m)) K) (pow (- (/ (+ m n) 2) M) 2))))
(* (cos (- (/ (* K (+ n m)) 2) M)) (exp (- (neg (pow (- (/ (+ n m) 2) M) 2)) (- l (fabs (- n m))))))
(* (cos (- (* (+ m n) (/ K 2)) M)) (exp (- (- (fabs (- n m)) l) (pow (- (/ (+ m n) 2) M) 2))))
(* (cos (- (/ (* K (+ M n)) 2) m)) (exp (- (neg (pow (- (/ (+ M n) 2) m) 2)) (- l (fabs (- M n))))))
(* (cos (- (* (+ n M) (/ K 2)) m)) (exp (- (- (fabs (- M n)) l) (pow (- (/ (+ n M) 2) m) 2))))
(* (cos (- (/ (* K (+ l n)) 2) M)) (exp (- (neg (pow (- (/ (+ l n) 2) M) 2)) (- m (fabs (- l n))))))
(* (cos (- (* (+ n l) (/ K 2)) M)) (exp (- (- (fabs (- l n)) m) (pow (- (/ (+ n l) 2) M) 2))))
(* (cos (- (/ (* K (+ m M)) 2) n)) (exp (- (neg (pow (- (/ (+ m M) 2) n) 2)) (- l (fabs (- m M))))))
(* (cos (- (* K (/ (+ m M) 2)) n)) (exp (- (- (fabs (- m M)) l) (pow (- (/ (+ m M) 2) n) 2))))
(* (cos (- (/ (* K (+ m l)) 2) M)) (exp (- (neg (pow (- (/ (+ m l) 2) M) 2)) (- n (fabs (- m l))))))
(* (cos (- (* K (/ (+ m l) 2)) M)) (exp (- (fabs (- m l)) (+ n (pow (- (/ (+ m l) 2) M) 2)))))
(* (cos (- (/ (* K (+ m n)) 2) l)) (exp (- (neg (pow (- (/ (+ m n) 2) l) 2)) (- M (fabs (- m n))))))
(* (cos (- (* (+ m n) (/ K 2)) l)) (exp (- (- (fabs (- n m)) M) (pow (- (/ (+ m n) 2) l) 2))))

Symmetry

(sort m n)

explain530.0ms (4.3%)

Memory

16.1MiB live, 768.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
164	39	(1.478410095232548e-291 -3.5143974520616126e-37 -5.767059969841576e-254 -7.576674980028176e+76 -1.50106544442423e-85)	-	`(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	145	0
`cos.f64`	`(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))`	oflow-rescue	58	0
↳	`(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))`	overflow	58
↳	`(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)`	overflow	58
↳	`(*.f64 K (+.f64 m n))`	overflow	58

Confusion

	Predicted +	Predicted -
+	62	0
-	141	53

Precision

0.3054187192118227

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	62	0	0
-	141	0	53

Precision?

0.3054187192118227

Recall?

1.0

Freqs

test

number	freq
0	53
1	203

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

187.0ms	396×	1	valid
90.0ms	108×	0	valid
3.0ms	8×	2	valid

Compiler

Compiled 368 to 88 computations (76.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 166.0ms

adjust: 39.0ms (23.5% of total)

ival-neg: 39.0ms (23.5% of total)

ival-sub: 22.0ms (13.2% of total)

ival-cos: 18.0ms (10.8% of total)

ival-div: 12.0ms (7.2% of total)

ival-mult: 10.0ms (6% of total)

ival-pow2: 9.0ms (5.4% of total)

ival-exp: 6.0ms (3.6% of total)

ival-fabs: 6.0ms (3.6% of total)

ival-add: 5.0ms (3% of total)

exact: 1.0ms (0.6% of total)

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

ival-true: 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

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.9%	(.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

▶

75.9%

(*.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)

simplify633.0ms (5.2%)

Memory

9.5MiB live, 489.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	256	(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
✓	cost-diff	320	(/.f64 (+.f64 m n) #s(literal 2 binary64))
✓	cost-diff	384	(-.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	5696	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))

Rules

7 472×	`accelerator-lowering-fma.f32`
7 472×	`accelerator-lowering-fma.f64`
3 222×	`-lowering-.f32`
3 222×	`-lowering-.f64`
2 026×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	148
1	52	148
2	119	145
3	364	145
4	1293	145
5	4695	145
0	8537	143

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
(cos (- (/ (* K (+ m n)) 2) M))
(- (/ (* K (+ m n)) 2) M)
(/ (* K (+ m n)) 2)
(* K (+ m n))
K
(+ m n)
m
n
2
M
(exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
(- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
(neg (pow (- (/ (+ m n) 2) M) 2))
(pow (- (/ (+ m n) 2) M) 2)
(- (/ (+ m n) 2) M)
(/ (+ m n) 2)
(- l (fabs (- m n)))
l
(fabs (- m n))
(- m n)

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

localize164.0ms (1.3%)

Memory

-24.4MiB live, 131.6MiB allocated

Localize:

Found 4 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	100.0%	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) 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	41.2%	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))

Samples

73.0ms	198×	1	valid
33.0ms	54×	0	valid
2.0ms	4×	2	valid

Compiler

Compiled 150 to 23 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-div: 32.0ms (36.5% of total)

adjust: 19.0ms (21.7% of total)

ival-sub: 9.0ms (10.3% of total)

ival-cos: 9.0ms (10.3% of total)

ival-mult: 5.0ms (5.7% of total)

ival-pow2: 4.0ms (4.6% of total)

ival-exp: 3.0ms (3.4% of total)

ival-add: 3.0ms (3.4% of total)

ival-neg: 2.0ms (2.3% of total)

ival-fabs: 2.0ms (2.3% of total)

exact: 0.0ms (0% of total)

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

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

series18.0ms (0.1%)

Memory

30.5MiB live, 30.5MiB allocated

Counts

6 → 240

Calls

Call 1

Inputs
#<alt (pow (- (/ (+ m n) 2) M) 2)>
#<alt (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))>
#<alt (/ (+ m n) 2)>
#<alt (/ (* K (+ m n)) 2)>
#<alt (cos (- (/ (* K (+ m n)) 2) M))>
#<alt (- (/ (* K (+ m n)) 2) M)>

Outputs
#<alt (pow (- (* 1/2 n) M) 2)>
#<alt (+ (* m (- (* 1/2 n) M)) (pow (- (* 1/2 n) M) 2))>
#<alt (+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))>
#<alt (+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))>
#<alt (* 1/4 (pow m 2))>
#<alt (* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))>
#<alt (* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))>
#<alt (* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))>
#<alt (* 1/4 (pow m 2))>
#<alt (* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))>
#<alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))>
#<alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))>
#<alt (pow (- (* 1/2 m) M) 2)>
#<alt (+ (* n (- (* 1/2 m) M)) (pow (- (* 1/2 m) M) 2))>
#<alt (+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))>
#<alt (+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))>
#<alt (* 1/4 (pow n 2))>
#<alt (* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))>
#<alt (* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))>
#<alt (* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))>
#<alt (* 1/4 (pow n 2))>
#<alt (* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))>
#<alt (* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))>
#<alt (* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))>
#<alt (* 1/4 (pow (+ m n) 2))>
#<alt (+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2)))>
#<alt (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))>
#<alt (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))>
#<alt (pow M 2)>
#<alt (* (pow M 2) (+ 1 (* -1 (/ (+ m n) M))))>
#<alt (* (pow M 2) (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))>
#<alt (* (pow M 2) (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))>
#<alt (pow M 2)>
#<alt (* (pow M 2) (+ 1 (* -1 (/ (+ m n) M))))>
#<alt (* (pow M 2) (+ 1 (* -1 (/ (+ m (+ n (* -1/4 (/ (pow (+ m n) 2) M)))) M))))>
#<alt (* (pow M 2) (+ 1 (* -1 (/ (+ m (+ n (* -1/4 (/ (pow (+ m n) 2) M)))) M))))>
#<alt (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* m (- M (* 1/2 n)))) (+ l (pow (- (* 1/2 n) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* m (- (+ M (* -1/4 m)) (* 1/2 n)))) (+ l (pow (- (* 1/2 n) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* m (- (+ M (* -1/4 m)) (* 1/2 n)))) (+ l (pow (- (* 1/2 n) M) 2)))>
#<alt (* -1/4 (pow m 2))>
#<alt (* (pow m 2) (- (/ M m) (+ 1/4 (* 1/2 (/ n m)))))>
#<alt (* (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)))))))>
#<alt (* (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)))))))>
#<alt (* -1/4 (pow m 2))>
#<alt (* (pow m 2) (- (* -1 (/ (- (* 1/2 n) M) m)) 1/4))>
#<alt (* (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))>
#<alt (* (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))>
#<alt (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* n (- M (* 1/2 m)))) (+ l (pow (- (* 1/2 m) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* n (- (+ M (* -1/4 n)) (* 1/2 m)))) (+ l (pow (- (* 1/2 m) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* n (- (+ M (* -1/4 n)) (* 1/2 m)))) (+ l (pow (- (* 1/2 m) M) 2)))>
#<alt (* -1/4 (pow n 2))>
#<alt (* (pow n 2) (- (/ M n) (+ 1/4 (* 1/2 (/ m n)))))>
#<alt (* (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)))))))>
#<alt (* (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)))))))>
#<alt (* -1/4 (pow n 2))>
#<alt (* (pow n 2) (- (* -1 (/ (- (* 1/2 m) M) n)) 1/4))>
#<alt (* (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))>
#<alt (* (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))>
#<alt (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))>
#<alt (- (+ (fabs (- m n)) (* M (+ m n))) (+ l (* 1/4 (pow (+ m n) 2))))>
#<alt (- (+ (fabs (- m n)) (* M (- (* -1 M) (* -1 (+ m n))))) (+ l (* 1/4 (pow (+ m n) 2))))>
#<alt (- (+ (fabs (- m n)) (* M (- (* -1 M) (* -1 (+ m n))))) (+ l (* 1/4 (pow (+ m n) 2))))>
#<alt (* -1 (pow M 2))>
#<alt (* (pow M 2) (- (+ (/ m M) (/ n M)) 1))>
#<alt (* (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)))))))>
#<alt (* (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)))))))>
#<alt (* -1 (pow M 2))>
#<alt (* (pow M 2) (- (+ (/ m M) (/ n M)) 1))>
#<alt (* (pow M 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))) M)) (+ m n)) M)) 1))>
#<alt (* (pow M 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))) M)) (+ m n)) M)) 1))>
#<alt (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))>
#<alt (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2))>
#<alt (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2))>
#<alt (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2))>
#<alt (* -1 l)>
#<alt (* l (- (/ (fabs (- m n)) l) (+ 1 (/ (pow (- (* 1/2 (+ m n)) M) 2) l))))>
#<alt (* l (- (/ (fabs (- m n)) l) (+ 1 (/ (pow (- (* 1/2 (+ m n)) M) 2) l))))>
#<alt (* l (- (/ (fabs (- m n)) l) (+ 1 (/ (pow (- (* 1/2 (+ m n)) M) 2) l))))>
#<alt (* -1 l)>
#<alt (* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)) l)))))>
#<alt (* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)) l)))))>
#<alt (* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)) l)))))>
#<alt (* 1/2 n)>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (* 1/2 m)>
#<alt (* m (+ 1/2 (* 1/2 (/ n m))))>
#<alt (* m (+ 1/2 (* 1/2 (/ n m))))>
#<alt (* m (+ 1/2 (* 1/2 (/ n m))))>
#<alt (* 1/2 m)>
#<alt (* -1 (* m (- (* -1/2 (/ n m)) 1/2)))>
#<alt (* -1 (* m (- (* -1/2 (/ n m)) 1/2)))>
#<alt (* -1 (* m (- (* -1/2 (/ n m)) 1/2)))>
#<alt (* 1/2 m)>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (* 1/2 n)>
#<alt (* n (+ 1/2 (* 1/2 (/ m n))))>
#<alt (* n (+ 1/2 (* 1/2 (/ m n))))>
#<alt (* n (+ 1/2 (* 1/2 (/ m n))))>
#<alt (* 1/2 n)>
#<alt (* -1 (* n (- (* -1/2 (/ m n)) 1/2)))>
#<alt (* -1 (* n (- (* -1/2 (/ m n)) 1/2)))>
#<alt (* -1 (* n (- (* -1/2 (/ m n)) 1/2)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K n))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (* 1/2 (* K m))>
#<alt (* m (+ (* 1/2 K) (* 1/2 (/ (* K n) m))))>
#<alt (* m (+ (* 1/2 K) (* 1/2 (/ (* K n) m))))>
#<alt (* m (+ (* 1/2 K) (* 1/2 (/ (* K n) m))))>
#<alt (* 1/2 (* K m))>
#<alt (* -1 (* m (+ (* -1/2 K) (* -1/2 (/ (* K n) m)))))>
#<alt (* -1 (* m (+ (* -1/2 K) (* -1/2 (/ (* K n) m)))))>
#<alt (* -1 (* m (+ (* -1/2 K) (* -1/2 (/ (* K n) m)))))>
#<alt (* 1/2 (* K m))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (* 1/2 (* K n))>
#<alt (* n (+ (* 1/2 K) (* 1/2 (/ (* K m) n))))>
#<alt (* n (+ (* 1/2 K) (* 1/2 (/ (* K m) n))))>
#<alt (* n (+ (* 1/2 K) (* 1/2 (/ (* K m) n))))>
#<alt (* 1/2 (* K n))>
#<alt (* -1 (* n (+ (* -1/2 K) (* -1/2 (/ (* K m) n)))))>
#<alt (* -1 (* n (+ (* -1/2 K) (* -1/2 (/ (* K m) n)))))>
#<alt (* -1 (* n (+ (* -1/2 K) (* -1/2 (/ (* K m) n)))))>
#<alt (cos (neg M))>
#<alt (+ (cos (neg M)) (* -1/2 (* K (* (sin (neg M)) (+ m n)))))>
#<alt (+ (cos (neg M)) (* K (- (* -1/8 (* K (* (cos (neg M)) (pow (+ m n) 2)))) (* 1/2 (* (sin (neg M)) (+ m n))))))>
#<alt (+ (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))))))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K n)) M))>
#<alt (+ (cos (- (* 1/2 (* K n)) M)) (* -1/2 (* K (* m (sin (- (* 1/2 (* K n)) M))))))>
#<alt (+ (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)))))))>
#<alt (+ (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)))))))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (- n (* -1 m)))) M))>
#<alt (cos (- (* 1/2 (* K (- n (* -1 m)))) M))>
#<alt (cos (- (* 1/2 (* K (- n (* -1 m)))) M))>
#<alt (cos (- (* 1/2 (* K (- n (* -1 m)))) M))>
#<alt (cos (- (* 1/2 (* K m)) M))>
#<alt (+ (cos (- (* 1/2 (* K m)) M)) (* -1/2 (* K (* n (sin (- (* 1/2 (* K m)) M))))))>
#<alt (+ (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)))))))>
#<alt (+ (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)))))))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (- m (* -1 n)))) M))>
#<alt (cos (- (* 1/2 (* K (- m (* -1 n)))) M))>
#<alt (cos (- (* 1/2 (* K (- m (* -1 n)))) M))>
#<alt (cos (- (* 1/2 (* K (- m (* -1 n)))) M))>
#<alt (cos (* 1/2 (* K (+ m n))))>
#<alt (+ (cos (* 1/2 (* K (+ m n)))) (* M (sin (* 1/2 (* K (+ m n))))))>
#<alt (+ (cos (* 1/2 (* K (+ m n)))) (* M (- (* -1/2 (* M (cos (* 1/2 (* K (+ m n)))))) (* -1 (sin (* 1/2 (* K (+ m n))))))))>
#<alt (+ (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))))))))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))>
#<alt (cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))>
#<alt (cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))>
#<alt (cos (+ (* -1 M) (* 1/2 (* K (+ m n)))))>
#<alt (* -1 M)>
#<alt (- (* 1/2 (* K (+ m n))) M)>
#<alt (- (* 1/2 (* K (+ m n))) M)>
#<alt (- (* 1/2 (* K (+ m n))) M)>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* K (+ (* -1 (/ M K)) (* 1/2 (+ m n))))>
#<alt (* K (+ (* -1 (/ M K)) (* 1/2 (+ m n))))>
#<alt (* K (+ (* -1 (/ M K)) (* 1/2 (+ m n))))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* -1 (* K (+ (* -1/2 (+ m n)) (/ M K))))>
#<alt (* -1 (* K (+ (* -1/2 (+ m n)) (/ M K))))>
#<alt (* -1 (* K (+ (* -1/2 (+ m n)) (/ M K))))>
#<alt (- (* 1/2 (* K n)) M)>
#<alt (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)>
#<alt (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)>
#<alt (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)>
#<alt (* 1/2 (* K m))>
#<alt (* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))>
#<alt (* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))>
#<alt (* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))>
#<alt (* 1/2 (* K m))>
#<alt (* -1 (* m (+ (* -1 (/ (- (* 1/2 (* K n)) M) m)) (* -1/2 K))))>
#<alt (* -1 (* m (+ (* -1 (/ (- (* 1/2 (* K n)) M) m)) (* -1/2 K))))>
#<alt (* -1 (* m (+ (* -1 (/ (- (* 1/2 (* K n)) M) m)) (* -1/2 K))))>
#<alt (- (* 1/2 (* K m)) M)>
#<alt (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)>
#<alt (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)>
#<alt (- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)>
#<alt (* 1/2 (* K n))>
#<alt (* n (- (+ (* 1/2 K) (* 1/2 (/ (* K m) n))) (/ M n)))>
#<alt (* n (- (+ (* 1/2 K) (* 1/2 (/ (* K m) n))) (/ M n)))>
#<alt (* n (- (+ (* 1/2 K) (* 1/2 (/ (* K m) n))) (/ M n)))>
#<alt (* 1/2 (* K n))>
#<alt (* -1 (* n (+ (* -1 (/ (- (* 1/2 (* K m)) M) n)) (* -1/2 K))))>
#<alt (* -1 (* n (+ (* -1 (/ (- (* 1/2 (* K m)) M) n)) (* -1/2 K))))>
#<alt (* -1 (* n (+ (* -1 (/ (- (* 1/2 (* K m)) M) n)) (* -1/2 K))))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (+ (* -1 M) (* 1/2 (* K (+ m n))))>
#<alt (+ (* -1 M) (* 1/2 (* K (+ m n))))>
#<alt (+ (* -1 M) (* 1/2 (* K (+ m n))))>
#<alt (* -1 M)>
#<alt (* M (- (* 1/2 (/ (* K (+ m n)) M)) 1))>
#<alt (* M (- (* 1/2 (/ (* K (+ m n)) M)) 1))>
#<alt (* M (- (* 1/2 (/ (* K (+ m n)) M)) 1))>
#<alt (* -1 M)>
#<alt (* -1 (* M (+ 1 (* -1/2 (/ (* K (+ m n)) M)))))>
#<alt (* -1 (* M (+ 1 (* -1/2 (/ (* K (+ m n)) M)))))>
#<alt (* -1 (* M (+ 1 (* -1/2 (/ (* K (+ m n)) M)))))>

Calls

60 calls:

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

rewrite648.0ms (5.3%)

Memory

-45.4MiB live, 691.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 100×	`accelerator-lowering-fma.f32`
5 100×	`accelerator-lowering-fma.f64`
4 482×	`/-lowering-/.f32`
4 482×	`/-lowering-/.f64`
4 324×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	57
1	139	57
2	1204	57
0	8367	57

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 329

Calls

Call 1

Inputs
(pow (- (/ (+ m n) 2) M) 2)
(- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
(/ (+ m n) 2)
(/ (* K (+ m n)) 2)
(cos (- (/ (* K (+ m n)) 2) M))
(- (/ (* K (+ m n)) 2) M)

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

simplify449.0ms (3.7%)

Memory

8.9MiB live, 796.1MiB allocated

Algorithm

1×	egg-herbie

Rules

9 836×	`accelerator-lowering-fma.f32`
9 836×	`accelerator-lowering-fma.f64`
6 674×	`-lowering-.f32`
6 674×	`-lowering-.f64`
3 438×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	405	3302
1	1220	3243
2	3733	3220
0	8309	3092

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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))))
(- (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)))))
(* 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)))
(* 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)))))
(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)))))
(* -1 M)
(- (* 1/2 (* K (+ m n))) M)
(- (* 1/2 (* K (+ m n))) M)
(- (* 1/2 (* K (+ m n))) M)
(* 1/2 (* K (+ m n)))
(* K (+ (* -1 (/ M K)) (* 1/2 (+ m n))))
(* K (+ (* -1 (/ M K)) (* 1/2 (+ m n))))
(* K (+ (* -1 (/ M K)) (* 1/2 (+ m n))))
(* 1/2 (* K (+ m n)))
(* -1 (* K (+ (* -1/2 (+ m n)) (/ M K))))
(* -1 (* K (+ (* -1/2 (+ m n)) (/ M K))))
(* -1 (* K (+ (* -1/2 (+ m n)) (/ M K))))
(- (* 1/2 (* K n)) M)
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(* 1/2 (* K m))
(* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))
(* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))
(* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))
(* 1/2 (* K m))
(* -1 (* m (+ (* -1 (/ (- (* 1/2 (* K n)) M) m)) (* -1/2 K))))
(* -1 (* m (+ (* -1 (/ (- (* 1/2 (* K n)) M) m)) (* -1/2 K))))
(* -1 (* m (+ (* -1 (/ (- (* 1/2 (* K n)) M) m)) (* -1/2 K))))
(- (* 1/2 (* K m)) M)
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(* 1/2 (* K n))
(* n (- (+ (* 1/2 K) (* 1/2 (/ (* K m) n))) (/ M n)))
(* n (- (+ (* 1/2 K) (* 1/2 (/ (* K m) n))) (/ M n)))
(* n (- (+ (* 1/2 K) (* 1/2 (/ (* K m) n))) (/ M n)))
(* 1/2 (* K n))
(* -1 (* n (+ (* -1 (/ (- (* 1/2 (* K m)) M) n)) (* -1/2 K))))
(* -1 (* n (+ (* -1 (/ (- (* 1/2 (* K m)) M) n)) (* -1/2 K))))
(* -1 (* n (+ (* -1 (/ (- (* 1/2 (* K m)) M) n)) (* -1/2 K))))
(* 1/2 (* K (+ m n)))
(+ (* -1 M) (* 1/2 (* K (+ m n))))
(+ (* -1 M) (* 1/2 (* K (+ m n))))
(+ (* -1 M) (* 1/2 (* K (+ m n))))
(* -1 M)
(* M (- (* 1/2 (/ (* K (+ m n)) M)) 1))
(* M (- (* 1/2 (/ (* K (+ m n)) M)) 1))
(* M (- (* 1/2 (/ (* K (+ m n)) M)) 1))
(* -1 M)
(* -1 (* M (+ 1 (* -1/2 (/ (* K (+ m n)) M)))))
(* -1 (* M (+ 1 (* -1/2 (/ (* K (+ m n)) M)))))
(* -1 (* M (+ 1 (* -1/2 (/ (* K (+ m n)) M)))))

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 (fma.f64 #s(literal 1/2 binary64) n #s(literal 0 binary64)) 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 (fma.f64 m #s(literal 1/4 binary64) (-.f64 (fma.f64 #s(literal 1/2 binary64) n #s(literal 0 binary64)) 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))
(fma.f64 m (fma.f64 m #s(literal 1/4 binary64) (-.f64 (fma.f64 #s(literal 1/2 binary64) n #s(literal 0 binary64)) M)) (*.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M)))
(* 1/4 (pow m 2))
(.f64 m (.f64 m #s(literal 1/4 binary64)))
(* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))
(.f64 m (.f64 m (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) n #s(literal 0 binary64)) 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 #s(literal 1/4 binary64) (+.f64 (/.f64 (.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M)) (.f64 m m)) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) n #s(literal 0 binary64)) 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 #s(literal 1/4 binary64) (+.f64 (/.f64 (.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M)) (.f64 m m)) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) n #s(literal 0 binary64)) M) m))))
(* 1/4 (pow m 2))
(.f64 m (.f64 m #s(literal 1/4 binary64)))
(* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))
(.f64 m (.f64 m (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) n #s(literal 0 binary64)) 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 (/.f64 (*.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M)) m) (fma.f64 n #s(literal -1/2 binary64) 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 (/.f64 (*.f64 (fma.f64 n #s(literal -1/2 binary64) M) (fma.f64 n #s(literal -1/2 binary64) M)) m) (fma.f64 n #s(literal -1/2 binary64) M)) m)))
(pow (- (* 1/2 m) M) 2)
(*.f64 (fma.f64 m #s(literal -1/2 binary64) M) (fma.f64 m #s(literal -1/2 binary64) M))
(+ (* n (- (* 1/2 m) M)) (pow (- (* 1/2 m) M) 2))
(*.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) (-.f64 n (fma.f64 m #s(literal -1/2 binary64) M)))
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(-.f64 #s(literal 0 binary64) M)
(- (* 1/2 (* K (+ m n))) M)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(- (* 1/2 (* K (+ m n))) M)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(- (* 1/2 (* K (+ m n))) M)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(* 1/2 (* K (+ m n)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) #s(literal 0 binary64))
(* K (+ (* -1 (/ M K)) (* 1/2 (+ m n))))
(-.f64 #s(literal 0 binary64) (*.f64 K (fma.f64 (+.f64 n m) #s(literal -1/2 binary64) (/.f64 M K))))
(* K (+ (* -1 (/ M K)) (* 1/2 (+ m n))))
(-.f64 #s(literal 0 binary64) (*.f64 K (fma.f64 (+.f64 n m) #s(literal -1/2 binary64) (/.f64 M K))))
(* K (+ (* -1 (/ M K)) (* 1/2 (+ m n))))
(-.f64 #s(literal 0 binary64) (*.f64 K (fma.f64 (+.f64 n m) #s(literal -1/2 binary64) (/.f64 M K))))
(* 1/2 (* K (+ m n)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) #s(literal 0 binary64))
(* -1 (* K (+ (* -1/2 (+ m n)) (/ M K))))
(-.f64 #s(literal 0 binary64) (*.f64 K (fma.f64 (+.f64 n m) #s(literal -1/2 binary64) (/.f64 M K))))
(* -1 (* K (+ (* -1/2 (+ m n)) (/ M K))))
(-.f64 #s(literal 0 binary64) (*.f64 K (fma.f64 (+.f64 n m) #s(literal -1/2 binary64) (/.f64 M K))))
(* -1 (* K (+ (* -1/2 (+ m n)) (/ M K))))
(-.f64 #s(literal 0 binary64) (*.f64 K (fma.f64 (+.f64 n m) #s(literal -1/2 binary64) (/.f64 M K))))
(- (* 1/2 (* K n)) M)
(-.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 n K) #s(literal 0 binary64)) M)
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(* 1/2 (* K m))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) K #s(literal 0 binary64))
(* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))
(-.f64 #s(literal 0 binary64) (.f64 m (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 n (.f64 #s(literal -1/2 binary64) K) M) m))))
(* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))
(-.f64 #s(literal 0 binary64) (.f64 m (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 n (.f64 #s(literal -1/2 binary64) K) M) m))))
(* m (- (+ (* 1/2 K) (* 1/2 (/ (* K n) m))) (/ M m)))
(-.f64 #s(literal 0 binary64) (.f64 m (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 n (.f64 #s(literal -1/2 binary64) K) M) m))))
(* 1/2 (* K m))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) K #s(literal 0 binary64))
(* -1 (* m (+ (* -1 (/ (- (* 1/2 (* K n)) M) m)) (* -1/2 K))))
(-.f64 #s(literal 0 binary64) (.f64 m (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 n (.f64 #s(literal -1/2 binary64) K) M) m))))
(* -1 (* m (+ (* -1 (/ (- (* 1/2 (* K n)) M) m)) (* -1/2 K))))
(-.f64 #s(literal 0 binary64) (.f64 m (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 n (.f64 #s(literal -1/2 binary64) K) M) m))))
(* -1 (* m (+ (* -1 (/ (- (* 1/2 (* K n)) M) m)) (* -1/2 K))))
(-.f64 #s(literal 0 binary64) (.f64 m (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 n (.f64 #s(literal -1/2 binary64) K) M) m))))
(- (* 1/2 (* K m)) M)
(-.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) K #s(literal 0 binary64)) M)
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(- (+ (* 1/2 (* K m)) (* 1/2 (* K n))) M)
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(* 1/2 (* K n))
(fma.f64 #s(literal 1/2 binary64) (*.f64 n K) #s(literal 0 binary64))
(* n (- (+ (* 1/2 K) (* 1/2 (/ (* K m) n))) (/ M n)))
(-.f64 #s(literal 0 binary64) (.f64 n (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 m (.f64 #s(literal -1/2 binary64) K) M) n))))
(* n (- (+ (* 1/2 K) (* 1/2 (/ (* K m) n))) (/ M n)))
(-.f64 #s(literal 0 binary64) (.f64 n (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 m (.f64 #s(literal -1/2 binary64) K) M) n))))
(* n (- (+ (* 1/2 K) (* 1/2 (/ (* K m) n))) (/ M n)))
(-.f64 #s(literal 0 binary64) (.f64 n (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 m (.f64 #s(literal -1/2 binary64) K) M) n))))
(* 1/2 (* K n))
(fma.f64 #s(literal 1/2 binary64) (*.f64 n K) #s(literal 0 binary64))
(* -1 (* n (+ (* -1 (/ (- (* 1/2 (* K m)) M) n)) (* -1/2 K))))
(-.f64 #s(literal 0 binary64) (.f64 n (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 m (.f64 #s(literal -1/2 binary64) K) M) n))))
(* -1 (* n (+ (* -1 (/ (- (* 1/2 (* K m)) M) n)) (* -1/2 K))))
(-.f64 #s(literal 0 binary64) (.f64 n (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 m (.f64 #s(literal -1/2 binary64) K) M) n))))
(* -1 (* n (+ (* -1 (/ (- (* 1/2 (* K m)) M) n)) (* -1/2 K))))
(-.f64 #s(literal 0 binary64) (.f64 n (fma.f64 #s(literal -1/2 binary64) K (/.f64 (fma.f64 m (.f64 #s(literal -1/2 binary64) K) M) n))))
(* 1/2 (* K (+ m n)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) #s(literal 0 binary64))
(+ (* -1 M) (* 1/2 (* K (+ m n))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(+ (* -1 M) (* 1/2 (* K (+ m n))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(+ (* -1 M) (* 1/2 (* K (+ m n))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (+.f64 n m) K) (-.f64 #s(literal 0 binary64) M))
(* -1 M)
(-.f64 #s(literal 0 binary64) M)
(* M (- (* 1/2 (/ (* K (+ m n)) M)) 1))
(.f64 M (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (+.f64 n m) K) M) #s(literal -1 binary64)))
(* M (- (* 1/2 (/ (* K (+ m n)) M)) 1))
(.f64 M (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (+.f64 n m) K) M) #s(literal -1 binary64)))
(* M (- (* 1/2 (/ (* K (+ m n)) M)) 1))
(.f64 M (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (+.f64 n m) K) M) #s(literal -1 binary64)))
(* -1 M)
(-.f64 #s(literal 0 binary64) M)
(* -1 (* M (+ 1 (* -1/2 (/ (* K (+ m n)) M)))))
(.f64 (-.f64 #s(literal 0 binary64) M) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 n m) K) M) #s(literal 1 binary64)))
(* -1 (* M (+ 1 (* -1/2 (/ (* K (+ m n)) M)))))
(.f64 (-.f64 #s(literal 0 binary64) M) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 n m) K) M) #s(literal 1 binary64)))
(* -1 (* M (+ 1 (* -1/2 (/ (* K (+ m n)) M)))))
(.f64 (-.f64 #s(literal 0 binary64) M) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (+.f64 n m) K) M) #s(literal 1 binary64)))

eval82.0ms (0.7%)

Memory: 26.6MiB live, 213.2MiB allocated
Compiler: Compiled 34 830 to 2 321 computations (93.3% saved)

prune92.0ms (0.8%)

Memory

29.4MiB live, 258.3MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	556	13	569
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	557	13	570

Accuracy

99.4%

Counts

570 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.8%	(*.f64 (cos.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) K #s(literal 0 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))))))
	72.8%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) (/.f64 (fma.f64 m #s(literal -1/2 binary64) M) n) (fma.f64 m #s(literal -1/2 binary64) M)) n))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	56.5%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (.f64 (fma.f64 m #s(literal -1/2 binary64) M) (fma.f64 m #s(literal -1/2 binary64) M)) (.f64 n n)) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) n)))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
▶	48.8%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n #s(literal 1/4 binary64)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	48.6%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (.f64 m (.f64 m #s(literal 1/4 binary64)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
	48.6%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (*.f64 M M)) (-.f64 l (fabs.f64 (-.f64 m n))))))
	38.9%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M))))
▶	29.4%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
▶	38.9%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 (.f64 n n) #s(literal -1/4 binary64))))
	37.8%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 m (.f64 m #s(literal -1/4 binary64)))))
	31.0%	(.f64 (cos.f64 (-.f64 (.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (fma.f64 m (.f64 m m) (.f64 n (.f64 n n))))) (/.f64 #s(literal 1 binary64) (fma.f64 n (-.f64 n m) (.f64 m 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))))))
	46.6%	(.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))))))
▶	98.1%	(*.f64 (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 862 to 566 computations (34.3% saved)

simplify284.0ms (2.3%)

Memory

-56.0MiB live, 694.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	64	(fma.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) K #s(literal 0 binary64))
✓	cost-diff	320	(/.f64 (+.f64 m n) #s(literal 2 binary64))
✓	cost-diff	384	(-.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	5696	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
✓	cost-diff	128	(neg.f64 (.f64 n (.f64 n #s(literal 1/4 binary64))))
✓	cost-diff	192	(-.f64 (neg.f64 (.f64 n (.f64 n #s(literal 1/4 binary64)))) (-.f64 l (fabs.f64 (-.f64 m n))))
✓	cost-diff	192	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	cost-diff	256	(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
✓	cost-diff	0	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
✓	cost-diff	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 (.f64 n n) #s(literal -1/4 binary64))))
✓	cost-diff	192	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	cost-diff	256	(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
✓	cost-diff	0	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
✓	cost-diff	0	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
✓	cost-diff	192	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	cost-diff	256	(/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 (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	320	(/.f64 (+.f64 m n) #s(literal 2 binary64))
✓	cost-diff	384	(-.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	5696	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))

Rules

6 366×	`accelerator-lowering-fma.f32`
6 366×	`accelerator-lowering-fma.f64`
3 112×	`-lowering-.f32`
3 112×	`-lowering-.f64`
1 672×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	489
1	109	486
2	248	479
3	635	479
4	1858	479
5	5438	479
0	8312	470

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (cos M) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
(cos M)
M
(exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
(- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
(neg (pow (- (/ (+ m n) 2) M) 2))
(pow (- (/ (+ m n) 2) M) 2)
(- (/ (+ m n) 2) M)
(/ (+ m n) 2)
(+ m n)
m
n
2
(- l (fabs (- m n)))
l
(fabs (- m n))
(- m n)
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- 0 l)))
(cos (- (/ (* K (+ m n)) 2) M))
(- (/ (* K (+ m n)) 2) M)
(/ (* K (+ m n)) 2)
(* K (+ m n))
K
(+ m n)
m
n
2
M
(exp (- 0 l))
(- 0 l)
0
l
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (* (* n n) -1/4)))
(cos (- (/ (* K (+ m n)) 2) M))
(- (/ (* K (+ m n)) 2) M)
(/ (* K (+ m n)) 2)
(* K (+ m n))
K
(+ m n)
m
n
2
M
(exp (* (* n n) -1/4))
(* (* n n) -1/4)
(* n n)
-1/4
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (* n (* n 1/4))) (- l (fabs (- m n))))))
(cos (- (/ (* K (+ m n)) 2) M))
(- (/ (* K (+ m n)) 2) M)
(/ (* K (+ m n)) 2)
(* K (+ m n))
K
(+ m n)
m
n
2
M
(exp (- (neg (* n (* n 1/4))) (- l (fabs (- m n)))))
(- (neg (* n (* n 1/4))) (- l (fabs (- m n))))
(neg (* n (* n 1/4)))
(* n (* n 1/4))
(* n 1/4)
1/4
(- l (fabs (- m n)))
l
(fabs (- m n))
(- m n)
(* (cos (+ (* (+ (* 1/2 m) 0) K) 0)) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
(cos (+ (* (+ (* 1/2 m) 0) K) 0))
(+ (* (+ (* 1/2 m) 0) K) 0)
(+ (* 1/2 m) 0)
1/2
m
0
K
(exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
(- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
(neg (pow (- (/ (+ m n) 2) M) 2))
(pow (- (/ (+ m n) 2) M) 2)
(- (/ (+ m n) 2) M)
(/ (+ m n) 2)
(+ m n)
n
2
M
(- l (fabs (- m n)))
l
(fabs (- m n))
(- m n)

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

localize362.0ms (3%)

Memory

8.7MiB live, 644.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(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)))))
✓	accuracy	100.0%	(pow.f64 (-.f64 (/.f64 (+.f64 m n) #s(literal 2 binary64)) M) #s(literal 2 binary64))
✓	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	58.0%	(cos.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) K #s(literal 0 binary64)))
✓	accuracy	100.0%	(*.f64 K (+.f64 m n))
✓	accuracy	100.0%	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
✓	accuracy	100.0%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n #s(literal 1/4 binary64)))) (-.f64 l (fabs.f64 (-.f64 m n))))))
✓	accuracy	41.2%	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	accuracy	100.0%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 (.f64 n n) #s(literal -1/4 binary64))))
✓	accuracy	100.0%	(*.f64 K (+.f64 m n))
✓	accuracy	100.0%	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
✓	accuracy	41.2%	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	accuracy	100.0%	(*.f64 K (+.f64 m n))
✓	accuracy	100.0%	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)
✓	accuracy	100.0%	(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
✓	accuracy	41.2%	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))
✓	accuracy	100.0%	(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)))))
✓	accuracy	100.0%	(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 (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))))

Samples

199.0ms	198×	1	valid
17.0ms	54×	0	valid
3.0ms	4×	2	valid

Compiler

Compiled 502 to 47 computations (90.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 165.0ms

ival-sub: 65.0ms (39.3% of total)

ival-mult: 24.0ms (14.5% of total)

ival-cos: 20.0ms (12.1% of total)

ival-exp: 17.0ms (10.3% of total)

adjust: 13.0ms (7.9% of total)

ival-add: 8.0ms (4.8% of total)

ival-div: 6.0ms (3.6% of total)

ival-pow2: 4.0ms (2.4% of total)

ival-neg: 3.0ms (1.8% 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)

series63.0ms (0.5%)

Memory

15.6MiB live, 132.7MiB allocated

Counts

17 → 648

Calls

Call 1

Inputs
#<alt (pow (- (/ (+ m n) 2) M) 2)>
#<alt (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))>
#<alt (/ (+ m n) 2)>
#<alt (* (cos M) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))>
#<alt (/ (* K (+ m n)) 2)>
#<alt (cos (- (/ (* K (+ m n)) 2) M))>
#<alt (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- 0 l)))>
#<alt (- (/ (* K (+ m n)) 2) M)>
#<alt (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (* (* n n) -1/4)))>
#<alt (- (neg (* n (* n 1/4))) (- l (fabs (- m n))))>
#<alt (neg (* n (* n 1/4)))>
#<alt (+ (* (+ (* 1/2 m) 0) K) 0)>
#<alt (cos M)>
#<alt (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))>
#<alt (* K (+ m n))>
#<alt (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (* n (* n 1/4))) (- l (fabs (- m n))))))>
#<alt (cos (+ (* (+ (* 1/2 m) 0) K) 0))>

Outputs
#<alt (pow (- (* 1/2 n) M) 2)>
#<alt (+ (* m (- (* 1/2 n) M)) (pow (- (* 1/2 n) M) 2))>
#<alt (+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))>
#<alt (+ (* m (- (+ (* 1/4 m) (* 1/2 n)) M)) (pow (- (* 1/2 n) M) 2))>
#<alt (* 1/4 (pow m 2))>
#<alt (* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))>
#<alt (* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))>
#<alt (* (pow m 2) (- (+ 1/4 (+ (* 1/2 (/ n m)) (/ (pow (- (* 1/2 n) M) 2) (pow m 2)))) (/ M m)))>
#<alt (* 1/4 (pow m 2))>
#<alt (* (pow m 2) (- (+ 1/4 (* 1/2 (/ n m))) (/ M m)))>
#<alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))>
#<alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 n) M)) (* -1 (/ (pow (- (* 1/2 n) M) 2) m))) m))))>
#<alt (pow (- (* 1/2 m) M) 2)>
#<alt (+ (* n (- (* 1/2 m) M)) (pow (- (* 1/2 m) M) 2))>
#<alt (+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))>
#<alt (+ (* n (- (+ (* 1/4 n) (* 1/2 m)) M)) (pow (- (* 1/2 m) M) 2))>
#<alt (* 1/4 (pow n 2))>
#<alt (* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))>
#<alt (* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))>
#<alt (* (pow n 2) (- (+ 1/4 (+ (* 1/2 (/ m n)) (/ (pow (- (* 1/2 m) M) 2) (pow n 2)))) (/ M n)))>
#<alt (* 1/4 (pow n 2))>
#<alt (* (pow n 2) (- (+ 1/4 (* 1/2 (/ m n))) (/ M n)))>
#<alt (* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))>
#<alt (* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (- (* 1/2 m) M)) (* -1 (/ (pow (- (* 1/2 m) M) 2) n))) n))))>
#<alt (* 1/4 (pow (+ m n) 2))>
#<alt (+ (* -1 (* M (+ m n))) (* 1/4 (pow (+ m n) 2)))>
#<alt (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))>
#<alt (+ (* 1/4 (pow (+ m n) 2)) (* M (+ M (* -1 (+ m n)))))>
#<alt (pow M 2)>
#<alt (* (pow M 2) (+ 1 (* -1 (/ (+ m n) M))))>
#<alt (* (pow M 2) (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))>
#<alt (* (pow M 2) (+ 1 (+ (* -1 (/ (+ m n) M)) (* 1/4 (/ (pow (+ m n) 2) (pow M 2))))))>
#<alt (pow M 2)>
#<alt (* (pow M 2) (+ 1 (* -1 (/ (+ m n) M))))>
#<alt (* (pow M 2) (+ 1 (* -1 (/ (+ m (+ n (* -1/4 (/ (pow (+ m n) 2) M)))) M))))>
#<alt (* (pow M 2) (+ 1 (* -1 (/ (+ m (+ n (* -1/4 (/ (pow (+ m n) 2) M)))) M))))>
#<alt (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* m (- M (* 1/2 n)))) (+ l (pow (- (* 1/2 n) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* m (- (+ M (* -1/4 m)) (* 1/2 n)))) (+ l (pow (- (* 1/2 n) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* m (- (+ M (* -1/4 m)) (* 1/2 n)))) (+ l (pow (- (* 1/2 n) M) 2)))>
#<alt (* -1/4 (pow m 2))>
#<alt (* (pow m 2) (- (/ M m) (+ 1/4 (* 1/2 (/ n m)))))>
#<alt (* (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)))))))>
#<alt (* (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)))))))>
#<alt (* -1/4 (pow m 2))>
#<alt (* (pow m 2) (- (* -1 (/ (- (* 1/2 n) M) m)) 1/4))>
#<alt (* (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))>
#<alt (* (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))>
#<alt (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* n (- M (* 1/2 m)))) (+ l (pow (- (* 1/2 m) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* n (- (+ M (* -1/4 n)) (* 1/2 m)))) (+ l (pow (- (* 1/2 m) M) 2)))>
#<alt (- (+ (fabs (- m n)) (* n (- (+ M (* -1/4 n)) (* 1/2 m)))) (+ l (pow (- (* 1/2 m) M) 2)))>
#<alt (* -1/4 (pow n 2))>
#<alt (* (pow n 2) (- (/ M n) (+ 1/4 (* 1/2 (/ m n)))))>
#<alt (* (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)))))))>
#<alt (* (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)))))))>
#<alt (* -1/4 (pow n 2))>
#<alt (* (pow n 2) (- (* -1 (/ (- (* 1/2 m) M) n)) 1/4))>
#<alt (* (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))>
#<alt (* (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))>
#<alt (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))>
#<alt (- (+ (fabs (- m n)) (* M (+ m n))) (+ l (* 1/4 (pow (+ m n) 2))))>
#<alt (- (+ (fabs (- m n)) (* M (- (* -1 M) (* -1 (+ m n))))) (+ l (* 1/4 (pow (+ m n) 2))))>
#<alt (- (+ (fabs (- m n)) (* M (- (* -1 M) (* -1 (+ m n))))) (+ l (* 1/4 (pow (+ m n) 2))))>
#<alt (* -1 (pow M 2))>
#<alt (* (pow M 2) (- (+ (/ m M) (/ n M)) 1))>
#<alt (* (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)))))))>
#<alt (* (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)))))))>
#<alt (* -1 (pow M 2))>
#<alt (* (pow M 2) (- (+ (/ m M) (/ n M)) 1))>
#<alt (* (pow M 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))) M)) (+ m n)) M)) 1))>
#<alt (* (pow M 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))) M)) (+ m n)) M)) 1))>
#<alt (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))>
#<alt (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2))>
#<alt (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2))>
#<alt (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2))>
#<alt (* -1 l)>
#<alt (* l (- (/ (fabs (- m n)) l) (+ 1 (/ (pow (- (* 1/2 (+ m n)) M) 2) l))))>
#<alt (* l (- (/ (fabs (- m n)) l) (+ 1 (/ (pow (- (* 1/2 (+ m n)) M) 2) l))))>
#<alt (* l (- (/ (fabs (- m n)) l) (+ 1 (/ (pow (- (* 1/2 (+ m n)) M) 2) l))))>
#<alt (* -1 l)>
#<alt (* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)) l)))))>
#<alt (* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)) l)))))>
#<alt (* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)) l)))))>
#<alt (* 1/2 n)>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (* 1/2 m)>
#<alt (* m (+ 1/2 (* 1/2 (/ n m))))>
#<alt (* m (+ 1/2 (* 1/2 (/ n m))))>
#<alt (* m (+ 1/2 (* 1/2 (/ n m))))>
#<alt (* 1/2 m)>
#<alt (* -1 (* m (- (* -1/2 (/ n m)) 1/2)))>
#<alt (* -1 (* m (- (* -1/2 (/ n m)) 1/2)))>
#<alt (* -1 (* m (- (* -1/2 (/ n m)) 1/2)))>
#<alt (* 1/2 m)>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (+ (* 1/2 m) (* 1/2 n))>
#<alt (* 1/2 n)>
#<alt (* n (+ 1/2 (* 1/2 (/ m n))))>
#<alt (* n (+ 1/2 (* 1/2 (/ m n))))>
#<alt (* n (+ 1/2 (* 1/2 (/ m n))))>
#<alt (* 1/2 n)>
#<alt (* -1 (* n (- (* -1/2 (/ m n)) 1/2)))>
#<alt (* -1 (* n (- (* -1/2 (/ m n)) 1/2)))>
#<alt (* -1 (* n (- (* -1/2 (/ m n)) 1/2)))>
#<alt (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (+ (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))))>
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#<alt (* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (* (sin (neg M)) (+ m n))))) (* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))>
#<alt (+ (* K (+ (* -1/2 (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (* (sin (neg M)) (+ m n)))) (* -1/8 (* K (* (cos (neg M)) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (pow (+ m n) 2))))))) (* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))>
#<alt (+ (* K (+ (* -1/2 (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (* (sin (neg M)) (+ m n)))) (* K (+ (* -1/8 (* (cos (neg M)) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (pow (+ m n) 2)))) (* 1/48 (* K (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (* (sin (neg M)) (pow (+ m n) 3))))))))) (* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (+ (* -1/2 (* K (* m (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (- (* 1/2 (* K n)) M)))))) (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))>
#<alt (+ (* m (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (- (* 1/2 (* K n)) M))))) (* -1/8 (* (pow K 2) (* m (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))))))) (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))>
#<alt (+ (* m (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (- (* 1/2 (* K n)) M))))) (* m (+ (* -1/8 (* (pow K 2) (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))) (* 1/48 (* (pow K 3) (* m (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (- (* 1/2 (* K n)) M)))))))))) (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l)))>
#<alt (+ (* -1/2 (* K (* n (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M)))))) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))>
#<alt (+ (* n (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M))))) (* n (+ (* -1/4 (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l)))) (* -1/8 (* (pow K 2) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))))))) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))>
#<alt (+ (* n (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M))))) (* n (+ (* -1/4 (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l)))) (+ (* -1/8 (* (pow K 2) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))) (* n (+ (* 1/48 (* (pow K 3) (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M))))) (* 1/8 (* K (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M)))))))))))) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (+ (* M (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (* 1/2 (* K (+ m n)))))) (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))>
#<alt (+ (* M (+ (* -1/2 (* M (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (* 1/2 (* K (+ m n))))))) (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))>
#<alt (+ (* M (+ (* M (+ (* -1/2 (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))) (* -1/6 (* M (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (* 1/2 (* K (+ m n))))))))) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (* 1/2 (* K (+ m n))))))) (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2)))))>
#<alt (+ (* -1 (* l (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))) (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))>
#<alt (+ (* l (+ (* -1 (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2)))))) (* 1/2 (* l (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))))) (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))>
#<alt (+ (* l (+ (* -1 (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2)))))) (* l (+ (* -1/6 (* l (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))) (* 1/2 (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2)))))))))) (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/8 (* (pow K 2) (pow m 2))))>
#<alt (+ 1 (* (pow m 2) (+ (* -1/8 (pow K 2)) (* 1/384 (* (pow K 4) (pow m 2))))))>
#<alt (+ 1 (* (pow m 2) (+ (* -1/8 (pow K 2)) (* (pow m 2) (+ (* -1/46080 (* (pow K 6) (pow m 2))) (* 1/384 (pow K 4)))))))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt 1>
#<alt (+ 1 (* -1/8 (* (pow K 2) (pow m 2))))>
#<alt (+ 1 (* (pow K 2) (+ (* -1/8 (pow m 2)) (* 1/384 (* (pow K 2) (pow m 4))))))>
#<alt (+ 1 (* (pow K 2) (+ (* -1/8 (pow m 2)) (* (pow K 2) (+ (* -1/46080 (* (pow K 2) (pow m 6))) (* 1/384 (pow m 4)))))))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>

Calls

162 calls:

Time	Variable		Point	Expression
6.0ms	l	@	inf	(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- 0 l)))
5.0ms	K	@	-inf	(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (* n (* n 1/4))) (- l (fabs (- m n))))))
3.0ms	m	@	inf	(* (cos M) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
1.0ms	m	@	inf	(* K (+ m n))
1.0ms	K	@	0	(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- 0 l)))

rewrite383.0ms (3.1%)

Memory

-6.9MiB live, 699.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 484×	`-lowering-.f32`
4 484×	`-lowering-.f64`
4 012×	`/-lowering-/.f32`
4 012×	`/-lowering-/.f64`
2 932×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	189
1	244	186
2	2114	186
0	8527	186

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 512

Calls

Call 1

Inputs
(pow (- (/ (+ m n) 2) M) 2)
(- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
(/ (+ m n) 2)
(* (cos M) (exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
(/ (* K (+ m n)) 2)
(cos (- (/ (* K (+ m n)) 2) M))
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- 0 l)))
(- (/ (* K (+ m n)) 2) M)
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (* (* n n) -1/4)))
(- (neg (* n (* n 1/4))) (- l (fabs (- m n))))
(neg (* n (* n 1/4)))
(+ (* (+ (* 1/2 m) 0) K) 0)
(cos M)
(exp (- (neg (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
(* K (+ m n))
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (neg (* n (* n 1/4))) (- l (fabs (- m n))))))
(cos (+ (* (+ (* 1/2 m) 0) K) 0))

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

simplify629.0ms (5.1%)

Memory

-1.1MiB live, 1 041.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 890×	`accelerator-lowering-fma.f32`
10 890×	`accelerator-lowering-fma.f64`
7 460×	`-lowering-.f32`
7 460×	`-lowering-.f64`
5 428×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	978	12249
1	3100	11805
2	7237	11805
0	8664	11362

Stop Event

1×	iter limit
1×	node limit

Counts

648 → 648

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))))
(- (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)))))
(* 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)))
(exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))))
(+ (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))))
(+ (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (* M (+ (* M (+ (* -1/2 (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))))) (* (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)))))
(+ (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (* M (+ (* M (+ (* -1/2 (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))))) (+ (* M (+ (* -1/2 (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2))))) (+ m n))) (* (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)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))))
(+ (* m (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- M (* 1/2 n))))) (* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2))))))
(+ (* m (+ (* m (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- (* 1/2 (pow (- M (* 1/2 n)) 2)) 1/4)))) (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- M (* 1/2 n)))))) (* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2))))))
(+ (* m (+ (* m (+ (* m (* (cos 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)))))) (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- (* 1/2 (pow (- M (* 1/2 n)) 2)) 1/4))))) (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2)))) (- M (* 1/2 n)))))) (* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2))))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
(* (cos M) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
(* (cos M) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
(* (cos M) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))))
(+ (* n (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- M (* 1/2 m))))) (* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2))))))
(+ (* n (+ (* n (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- (* 1/2 (pow (- M (* 1/2 m)) 2)) 1/4)))) (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- M (* 1/2 m)))))) (* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2))))))
(+ (* n (+ (* n (+ (* n (* (cos M) (* (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)))))) (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- (* 1/2 (pow (- M (* 1/2 m)) 2)) 1/4))))) (* (cos M) (* (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2)))) (- M (* 1/2 m)))))) (* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2))))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2)))))
(* (cos M) (exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2)))))
(* (cos M) (exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2)))))
(* (cos M) (exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2)))))
(* (cos M) (exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2)))))
(* (cos M) (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))))
(+ (* -1 (* l (* (cos M) (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)))))) (* (cos M) (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)))))
(+ (* l (+ (* -1 (* (cos M) (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))))) (* 1/2 (* l (* (cos M) (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)))))))) (* (cos M) (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)))))
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(- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))
(- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))
(* -1 l)
(* l (- (/ (fabs (- m n)) l) (+ 1 (* 1/4 (/ (pow n 2) l)))))
(* l (- (/ (fabs (- m n)) l) (+ 1 (* 1/4 (/ (pow n 2) l)))))
(* l (- (/ (fabs (- m n)) l) (+ 1 (* 1/4 (/ (pow n 2) l)))))
(* -1 l)
(* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (* 1/4 (pow n 2))) l)))))
(* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (* 1/4 (pow n 2))) l)))))
(* -1 (* l (+ 1 (* -1 (/ (- (fabs (- m n)) (* 1/4 (pow n 2))) l)))))
(- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))
(- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))
(- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))
(- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))
(- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))
(- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))
(- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))
(- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))
(- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))
(- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))
(- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))
(- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
1
(+ 1 (* -1/2 (pow M 2)))
(+ 1 (* (pow M 2) (- (* 1/24 (pow M 2)) 1/2)))
(+ 1 (* (pow M 2) (- (* (pow M 2) (+ 1/24 (* -1/720 (pow M 2)))) 1/2)))
(cos M)
(cos M)
(cos M)
(cos M)
(cos M)
(cos M)
(cos M)
(cos M)
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 n) M) 2))))
(+ (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)))))
(+ (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))))))
(+ (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))))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2))))
(exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2))))
(exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2))))
(exp (- (fabs (neg (+ n (* -1 m)))) (+ l (pow (- (* 1/2 (- n (* -1 m))) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 m) M) 2))))
(+ (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)))))
(+ (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))))))
(+ (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))))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2))))
(exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2))))
(exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2))))
(exp (- (fabs (+ m (* -1 n))) (+ l (pow (- (* 1/2 (- m (* -1 n))) M) 2))))
(exp (- (fabs (- m n)) (+ l (* 1/4 (pow (+ m n) 2)))))
(+ (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))))
(+ (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)))))
(+ (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)))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2))))
(exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2))))
(exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2))))
(exp (- (fabs (- m n)) (+ l (pow (+ (* -1 M) (* 1/2 (+ m n))) 2))))
(exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)))
(+ (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))) (* -1 (* l (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))))))
(+ (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))))))))
(+ (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))) (* l (+ (* -1 (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)))) (* l (+ (* -1/6 (* l (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2))))) (* 1/2 (exp (- (fabs (- m n)) (pow (- (* 1/2 (+ m n)) M) 2)))))))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (fabs (- m n)) (+ l (pow (- (* 1/2 (+ m n)) M) 2))))
(exp (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2)))
(exp (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2)))
(exp (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 2)))
(exp (- (+ (fabs (- m n)) (* -1 l)) (pow (- (* 1/2 (+ m n)) M) 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 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)))))
(* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (* (sin (neg M)) (+ m n))))) (* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))
(+ (* K (+ (* -1/2 (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (* (sin (neg M)) (+ m n)))) (* -1/8 (* K (* (cos (neg M)) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (pow (+ m n) 2))))))) (* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))
(+ (* K (+ (* -1/2 (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (* (sin (neg M)) (+ m n)))) (* K (+ (* -1/8 (* (cos (neg M)) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (pow (+ m n) 2)))) (* 1/48 (* K (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (* (sin (neg M)) (pow (+ m n) 3))))))))) (* (cos (neg M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(+ (* -1/2 (* K (* m (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (- (* 1/2 (* K n)) M)))))) (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))
(+ (* m (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (- (* 1/2 (* K n)) M))))) (* -1/8 (* (pow K 2) (* m (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))))))) (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))
(+ (* m (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (- (* 1/2 (* K n)) M))))) (* m (+ (* -1/8 (* (pow K 2) (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))) (* 1/48 (* (pow K 3) (* m (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (- (* 1/2 (* K n)) M)))))))))) (* (cos (- (* 1/2 (* K n)) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (exp (- (fabs (neg (+ n (* -1 m)))) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l)))
(+ (* -1/2 (* K (* n (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M)))))) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))
(+ (* n (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M))))) (* n (+ (* -1/4 (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l)))) (* -1/8 (* (pow K 2) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))))))) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))
(+ (* n (+ (* -1/2 (* K (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M))))) (* n (+ (* -1/4 (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l)))) (+ (* -1/8 (* (pow K 2) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))) (* n (+ (* 1/48 (* (pow K 3) (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M))))) (* 1/8 (* K (* (exp (- (fabs (- m n)) l)) (sin (- (* 1/2 (* K m)) M)))))))))))) (* (cos (- (* 1/2 (* K m)) M)) (exp (- (fabs (- m n)) l))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (exp (- (fabs (+ m (* -1 n))) (+ l (* 1/4 (pow n 2))))))
(* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(+ (* M (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (* 1/2 (* K (+ m n)))))) (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))
(+ (* M (+ (* -1/2 (* M (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (* 1/2 (* K (+ m n))))))) (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))
(+ (* M (+ (* M (+ (* -1/2 (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))) (* -1/6 (* M (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (* 1/2 (* K (+ m n))))))))) (* (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))) (sin (* 1/2 (* K (+ m n))))))) (* (cos (* 1/2 (* K (+ m n)))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2)))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2)))))
(+ (* -1 (* l (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))) (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))
(+ (* l (+ (* -1 (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2)))))) (* 1/2 (* l (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))))) (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))
(+ (* l (+ (* -1 (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2)))))) (* l (+ (* -1/6 (* l (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))) (* 1/2 (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2)))))))))) (* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (fabs (- m n)) (+ l (* 1/4 (pow n 2))))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))))
(* (cos (- (* 1/2 (* K (+ m n))) M)) (exp (- (+ (fabs (- m n)) (* -1 l)) (* 1/4 (pow n 2)))))
1
(+ 1 (* -1/8 (* (pow K 2) (pow m 2))))
(+ 1 (* (pow m 2) (+ (* -1/8 (pow K 2)) (* 1/384 (* (pow K 4) (pow m 2))))))
(+ 1 (* (pow m 2) (+ (* -1/8 (pow K 2)) (* (pow m 2) (+ (* -1/46080 (* (pow K 6) (pow m 2))) (* 1/384 (pow K 4)))))))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
1
(+ 1 (* -1/8 (* (pow K 2) (pow m 2))))
(+ 1 (* (pow K 2) (+ (* -1/8 (pow m 2)) (* 1/384 (* (pow K 2) (pow m 4))))))
(+ 1 (* (pow K 2) (+ (* -1/8 (pow m 2)) (* (pow K 2) (+ (* -1/46080 (* (pow K 2) (pow m 6))) (* 1/384 (pow m 4)))))))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))

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))
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(cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)))
(cos (* 1/2 (* K m)))
(cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)))
(cos (* 1/2 (* K m)))
(cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)))
(cos (* 1/2 (* K m)))
(cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)))
(cos (* 1/2 (* K m)))
(cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)))
(cos (* 1/2 (* K m)))
(cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)))
(cos (* 1/2 (* K m)))
(cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)))

eval326.0ms (2.7%)

Memory: 46.5MiB live, 563.1MiB allocated
Compiler: Compiled 82 171 to 3 894 computations (95.3% saved)

prune230.0ms (1.9%)

Memory

18.9MiB live, 545.4MiB allocated

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	2 016	11	2 027
Fresh	8	0	8
Picked	5	0	5
Done	0	0	0
Total	2 029	11	2 040

Accuracy

99.4%

Counts

2 040 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.4%	(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M)))
	79.8%	(*.f64 (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 K (fma.f64 m #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 0 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))))))
	26.7%	(.f64 (cos.f64 (.f64 M (fma.f64 (*.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
	31.7%	(.f64 (cos.f64 (.f64 M (fma.f64 (.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (.f64 (*.f64 n n) #s(literal -1/4 binary64))))
▶	32.3%	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
	29.8%	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 m K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
▶	50.9%	(.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
	36.7%	(*.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
▶	87.8%	(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l)))
	8.3%	(cos.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M))
▶	8.4%	(cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M))

Compiler

Compiled 428 to 316 computations (26.2% saved)

simplify274.0ms (2.2%)

Memory

-12.3MiB live, 462.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(exp.f64 (-.f64 #s(literal 0 binary64) l))
✓	cost-diff	0	(*.f64 n K)
✓	cost-diff	0	(cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 n K)))
✓	cost-diff	0	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) (*.f64 M M))
✓	cost-diff	0	(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M)))
✓	cost-diff	0	(cos.f64 M)
✓	cost-diff	0	(.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
✓	cost-diff	0	(-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M)
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) l)
✓	cost-diff	192	(cos.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M))
✓	cost-diff	192	(+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64))
✓	cost-diff	-64	(.f64 #s(literal 1/2 binary64) (.f64 m K))
✓	cost-diff	0	(*.f64 m K)
✓	cost-diff	0	(-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M)
✓	cost-diff	192	(cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M))
✓	cost-diff	0	(-.f64 n m)
✓	cost-diff	0	(fabs.f64 (-.f64 n m))
✓	cost-diff	0	(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l))
✓	cost-diff	0	(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l)))

Rules

8 058×	`accelerator-lowering-fma.f32`
8 058×	`accelerator-lowering-fma.f64`
3 092×	`-lowering-.f32`
3 092×	`-lowering-.f64`
2 634×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	211
1	107	209
2	267	207
3	679	207
4	2091	207
5	5721	207
0	8069	201

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(exp (- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l)))
(- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l))
(fabs (- n m))
(- n m)
n
m
(+ (* 1/4 (* (+ n m) (+ n m))) l)
1/4
(* (+ n m) (+ n m))
(+ n m)
l
(cos (- (* 1/2 (* m K)) M))
(- (* 1/2 (* m K)) M)
(* 1/2 (* m K))
1/2
(* m K)
m
K
M
(* (+ (- 0 l) 1) (cos (- (+ (* (* 1/2 K) (+ n m)) 0) M)))
(+ (- 0 l) 1)
(- 0 l)
0
l
1
(cos (- (+ (* (* 1/2 K) (+ n m)) 0) M))
(- (+ (* (* 1/2 K) (+ n m)) 0) M)
(+ (* (* 1/2 K) (+ n m)) 0)
(* 1/2 K)
1/2
K
(+ n m)
n
m
M
(* (cos M) (exp (- 0 (* M M))))
(cos M)
M
(exp (- 0 (* M M)))
(- 0 (* M M))
0
(* M M)
(* (cos (* 1/2 (* n K))) (exp (- 0 l)))
(cos (* 1/2 (* n K)))
(* 1/2 (* n K))
1/2
(* n K)
n
K
(exp (- 0 l))
(- 0 l)
0
l

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

localize237.0ms (1.9%)

Memory

30.4MiB live, 337.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 (-.f64 #s(literal 0 binary64) l))
✓	accuracy	100.0%	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 n K))
✓	accuracy	58.5%	(cos.f64 (.f64 #s(literal 1/2 binary64) (.f64 n K)))
✓	accuracy	100.0%	(*.f64 M M)
✓	accuracy	100.0%	(cos.f64 M)
✓	accuracy	100.0%	(.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
✓	accuracy	100.0%	(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M)))
✓	accuracy	100.0%	(fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64))
✓	accuracy	100.0%	(-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M)
✓	accuracy	99.8%	(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M)))
✓	accuracy	41.2%	(cos.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M))
✓	accuracy	100.0%	(*.f64 m K)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (.f64 m K))
✓	accuracy	100.0%	(-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M)
✓	accuracy	56.4%	(cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M))
✓	accuracy	100.0%	(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l)))
✓	accuracy	100.0%	(*.f64 (+.f64 n m) (+.f64 n m))
✓	accuracy	100.0%	(-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l))
✓	accuracy	99.7%	(fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l)

Samples

171.0ms	201×	1	valid
14.0ms	55×	0	valid

Compiler

Compiled 223 to 41 computations (81.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-cos: 50.0ms (35.4% of total)

ival-add: 29.0ms (20.5% of total)

ival-mult: 28.0ms (19.8% of total)

adjust: 14.0ms (9.9% of total)

ival-sub: 10.0ms (7.1% of total)

ival-exp: 8.0ms (5.7% of total)

exact: 1.0ms (0.7% of total)

ival-fabs: 1.0ms (0.7% of total)

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

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

series72.0ms (0.6%)

Memory

-33.5MiB live, 56.5MiB allocated

Counts

26 → 696

Calls

Call 1

Inputs
#<alt (exp (- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l)))>
#<alt (- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l))>
#<alt (fabs (- n m))>
#<alt (- n m)>
#<alt (cos (- (* 1/2 (* m K)) M))>
#<alt (- (* 1/2 (* m K)) M)>
#<alt (* m K)>
#<alt (* 1/2 (* m K))>
#<alt (+ (- 0 l) 1)>
#<alt (cos (- (+ (* (* 1/2 K) (+ n m)) 0) M))>
#<alt (- 0 l)>
#<alt (- (+ (* (* 1/2 K) (+ n m)) 0) M)>
#<alt (* (cos M) (exp (- 0 (* M M))))>
#<alt (cos M)>
#<alt (exp (- 0 (* M M)))>
#<alt (- 0 (* M M))>
#<alt (* (cos (* 1/2 (* n K))) (exp (- 0 l)))>
#<alt (cos (* 1/2 (* n K)))>
#<alt (* n K)>
#<alt (exp (- 0 l))>
#<alt (+ (* 1/4 (* (+ n m) (+ n m))) l)>
#<alt (* (+ n m) (+ n m))>
#<alt (* (+ (- 0 l) 1) (cos (- (+ (* (* 1/2 K) (+ n m)) 0) M)))>
#<alt (+ (* (* 1/2 K) (+ n m)) 0)>
#<alt (* M M)>
#<alt (* 1/2 (* n K))>

Outputs
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2)))))>
#<alt (+ (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2))))) (* -1/2 (* m (* n (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2)))))))))>
#<alt (+ (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2))))) (* n (+ (* -1/2 (* m (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2))))))) (* n (* (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2))))) (- (* 1/8 (pow m 2)) 1/4))))))>
#<alt (+ (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2))))) (* n (+ (* -1/2 (* m (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2))))))) (* n (+ (* n (* (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2))))) (+ (* -1/48 (pow m 3)) (* 1/8 m)))) (* (exp (- (fabs (- n m)) (+ l (* 1/4 (pow m 2))))) (- (* 1/8 (pow m 2)) 1/4)))))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (neg (+ m (* -1 n)))) (+ l (* 1/4 (pow (- m (* -1 n)) 2)))))>
#<alt (exp (- (fabs (neg (+ m (* -1 n)))) (+ l (* 1/4 (pow (- m (* -1 n)) 2)))))>
#<alt (exp (- (fabs (neg (+ m (* -1 n)))) (+ l (* 1/4 (pow (- m (* -1 n)) 2)))))>
#<alt (exp (- (fabs (neg (+ m (* -1 n)))) (+ l (* 1/4 (pow (- m (* -1 n)) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2)))))>
#<alt (+ (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2))))) (* -1/2 (* m (* n (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2)))))))))>
#<alt (+ (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2))))) (* m (+ (* -1/2 (* n (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2))))))) (* m (* (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2))))) (- (* 1/8 (pow n 2)) 1/4))))))>
#<alt (+ (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2))))) (* m (+ (* -1/2 (* n (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2))))))) (* m (+ (* m (* (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2))))) (+ (* -1/48 (pow n 3)) (* 1/8 n)))) (* (exp (- (fabs (- n m)) (+ l (* 1/4 (pow n 2))))) (- (* 1/8 (pow n 2)) 1/4)))))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (+ n (* -1 m))) (+ l (* 1/4 (pow (- n (* -1 m)) 2)))))>
#<alt (exp (- (fabs (+ n (* -1 m))) (+ l (* 1/4 (pow (- n (* -1 m)) 2)))))>
#<alt (exp (- (fabs (+ n (* -1 m))) (+ l (* 1/4 (pow (- n (* -1 m)) 2)))))>
#<alt (exp (- (fabs (+ n (* -1 m))) (+ l (* 1/4 (pow (- n (* -1 m)) 2)))))>
#<alt (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2))))>
#<alt (+ (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2)))) (* -1 (* l (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2)))))))>
#<alt (+ (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2)))) (* l (+ (* -1 (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2))))) (* 1/2 (* l (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2)))))))))>
#<alt (+ (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2)))) (* l (+ (* -1 (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2))))) (* l (+ (* -1/6 (* l (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2)))))) (* 1/2 (exp (- (fabs (- n m)) (* 1/4 (pow (+ m n) 2))))))))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (fabs (- n m)) (+ l (* 1/4 (pow (+ m n) 2)))))>
#<alt (exp (- (+ (fabs (- n m)) (* -1 l)) (* 1/4 (pow (+ m n) 2))))>
#<alt (exp (- (+ (fabs (- n m)) (* -1 l)) (* 1/4 (pow (+ m n) 2))))>
#<alt (exp (- (+ (fabs (- n m)) (* -1 l)) (* 1/4 (pow (+ m n) 2))))>
#<alt (exp (- (+ (fabs (- n m)) (* -1 l)) (* 1/4 (pow (+ m n) 2))))>
#<alt (- (fabs (- n m)) (+ l (* 1/4 (pow m 2))))>
#<alt (- (+ (fabs (- n m)) (* -1/2 (* m n))) (+ l (* 1/4 (pow m 2))))>
#<alt (- (+ (fabs (- n m)) (* n (- (* -1/4 n) (* 1/2 m)))) (+ l (* 1/4 (pow m 2))))>
#<alt (- (+ (fabs (- n m)) (* n (- (* -1/4 n) (* 1/2 m)))) (+ l (* 1/4 (pow m 2))))>
#<alt (* -1/4 (pow n 2))>
#<alt (* (pow n 2) (- (* -1/2 (/ m n)) 1/4))>
#<alt (* (pow n 2) (- (/ (fabs (- n m)) (pow n 2)) (+ 1/4 (+ (* 1/4 (/ (pow m 2) (pow n 2))) (+ (* 1/2 (/ m n)) (/ l (pow n 2)))))))>
#<alt (* (pow n 2) (- (/ (fabs (- n m)) (pow n 2)) (+ 1/4 (+ (* 1/4 (/ (pow m 2) (pow n 2))) (+ (* 1/2 (/ m n)) (/ l (pow n 2)))))))>
#<alt (* -1/4 (pow n 2))>
#<alt (* (pow n 2) (- (* -1/2 (/ m n)) 1/4))>
#<alt (* (pow n 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (neg (+ m (* -1 n)))) (+ l (* 1/4 (pow m 2)))) n)) (* -1/2 m)) n)) 1/4))>
#<alt (* (pow n 2) (- (* -1 (/ (- (* -1 (/ (- (fabs (neg (+ m (* -1 n)))) (+ l (* 1/4 (pow m 2)))) n)) (* -1/2 m)) n)) 1/4))>
#<alt (- (fabs (- n m)) (+ l (* 1/4 (pow n 2))))>
#<alt (- (+ (fabs (- n m)) (* -1/2 (* m n))) (+ l (* 1/4 (pow n 2))))>
#<alt (- (+ (fabs (- n m)) (* m (- (* -1/4 m) (* 1/2 n)))) (+ l (* 1/4 (pow n 2))))>
#<alt (- (+ (fabs (- n m)) (* m (- (* -1/4 m) (* 1/2 n)))) (+ l (* 1/4 (pow n 2))))>
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#<alt (+ (cos (* 1/2 (* K n))) (* -1 (* l (cos (* 1/2 (* K n))))))>
#<alt (+ (cos (* 1/2 (* K n))) (* l (+ (* -1 (cos (* 1/2 (* K n)))) (* 1/2 (* l (cos (* 1/2 (* K n))))))))>
#<alt (+ (cos (* 1/2 (* K n))) (* l (+ (* -1 (cos (* 1/2 (* K n)))) (* l (+ (* -1/6 (* l (cos (* 1/2 (* K n))))) (* 1/2 (cos (* 1/2 (* K n)))))))))>
#<alt (* (cos (* 1/2 (* K n))) (exp (neg l)))>
#<alt (* (cos (* 1/2 (* K n))) (exp (neg l)))>
#<alt (* (cos (* 1/2 (* K n))) (exp (neg l)))>
#<alt (* (cos (* 1/2 (* K n))) (exp (neg l)))>
#<alt (* (cos (* 1/2 (* K n))) (exp (* -1 l)))>
#<alt (* (cos (* 1/2 (* K n))) (exp (* -1 l)))>
#<alt (* (cos (* 1/2 (* K n))) (exp (* -1 l)))>
#<alt (* (cos (* 1/2 (* K n))) (exp (* -1 l)))>
#<alt 1>
#<alt (+ 1 (* -1/8 (* (pow K 2) (pow n 2))))>
#<alt (+ 1 (* (pow n 2) (+ (* -1/8 (pow K 2)) (* 1/384 (* (pow K 4) (pow n 2))))))>
#<alt (+ 1 (* (pow n 2) (+ (* -1/8 (pow K 2)) (* (pow n 2) (+ (* -1/46080 (* (pow K 6) (pow n 2))) (* 1/384 (pow K 4)))))))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt 1>
#<alt (+ 1 (* -1/8 (* (pow K 2) (pow n 2))))>
#<alt (+ 1 (* (pow K 2) (+ (* -1/8 (pow n 2)) (* 1/384 (* (pow K 2) (pow n 4))))))>
#<alt (+ 1 (* (pow K 2) (+ (* -1/8 (pow n 2)) (* (pow K 2) (+ (* -1/46080 (* (pow K 2) (pow n 6))) (* 1/384 (pow n 4)))))))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (cos (* 1/2 (* K n)))>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt (* K n)>
#<alt 1>
#<alt (+ 1 (* -1 l))>
#<alt (+ 1 (* l (- (* 1/2 l) 1)))>
#<alt (+ 1 (* l (- (* l (+ 1/2 (* -1/6 l))) 1)))>
#<alt (exp (neg l))>
#<alt (exp (neg l))>
#<alt (exp (neg l))>
#<alt (exp (neg l))>
#<alt (exp (* -1 l))>
#<alt (exp (* -1 l))>
#<alt (exp (* -1 l))>
#<alt (exp (* -1 l))>
#<alt (+ l (* 1/4 (pow m 2)))>
#<alt (+ l (+ (* 1/4 (pow m 2)) (* 1/2 (* m n))))>
#<alt (+ l (+ (* 1/4 (pow m 2)) (* n (+ (* 1/4 n) (* 1/2 m)))))>
#<alt (+ l (+ (* 1/4 (pow m 2)) (* n (+ (* 1/4 n) (* 1/2 m)))))>
#<alt (* 1/4 (pow n 2))>
#<alt (* (pow n 2) (+ 1/4 (* 1/2 (/ m n))))>
#<alt (* (pow n 2) (+ 1/4 (+ (* 1/4 (/ (pow m 2) (pow n 2))) (+ (* 1/2 (/ m n)) (/ l (pow n 2))))))>
#<alt (* (pow n 2) (+ 1/4 (+ (* 1/4 (/ (pow m 2) (pow n 2))) (+ (* 1/2 (/ m n)) (/ l (pow n 2))))))>
#<alt (* 1/4 (pow n 2))>
#<alt (* (pow n 2) (+ 1/4 (* 1/2 (/ m n))))>
#<alt (* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ l (* 1/4 (pow m 2))) n)) (* -1/2 m)) n))))>
#<alt (* (pow n 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ l (* 1/4 (pow m 2))) n)) (* -1/2 m)) n))))>
#<alt (+ l (* 1/4 (pow n 2)))>
#<alt (+ l (+ (* 1/4 (pow n 2)) (* 1/2 (* m n))))>
#<alt (+ l (+ (* 1/4 (pow n 2)) (* m (+ (* 1/4 m) (* 1/2 n)))))>
#<alt (+ l (+ (* 1/4 (pow n 2)) (* m (+ (* 1/4 m) (* 1/2 n)))))>
#<alt (* 1/4 (pow m 2))>
#<alt (* (pow m 2) (+ 1/4 (* 1/2 (/ n m))))>
#<alt (* (pow m 2) (+ 1/4 (+ (* 1/4 (/ (pow n 2) (pow m 2))) (+ (* 1/2 (/ n m)) (/ l (pow m 2))))))>
#<alt (* (pow m 2) (+ 1/4 (+ (* 1/4 (/ (pow n 2) (pow m 2))) (+ (* 1/2 (/ n m)) (/ l (pow m 2))))))>
#<alt (* 1/4 (pow m 2))>
#<alt (* (pow m 2) (+ 1/4 (* 1/2 (/ n m))))>
#<alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ l (* 1/4 (pow n 2))) m)) (* -1/2 n)) m))))>
#<alt (* (pow m 2) (+ 1/4 (* -1 (/ (+ (* -1 (/ (+ l (* 1/4 (pow n 2))) m)) (* -1/2 n)) m))))>
#<alt (* 1/4 (pow (+ m n) 2))>
#<alt (+ l (* 1/4 (pow (+ m n) 2)))>
#<alt (+ l (* 1/4 (pow (+ m n) 2)))>
#<alt (+ l (* 1/4 (pow (+ m n) 2)))>
#<alt l>
#<alt (* l (+ 1 (* 1/4 (/ (pow (+ m n) 2) l))))>
#<alt (* l (+ 1 (* 1/4 (/ (pow (+ m n) 2) l))))>
#<alt (* l (+ 1 (* 1/4 (/ (pow (+ m n) 2) l))))>
#<alt l>
#<alt (* -1 (* l (- (* -1/4 (/ (pow (+ m n) 2) l)) 1)))>
#<alt (* -1 (* l (- (* -1/4 (/ (pow (+ m n) 2) l)) 1)))>
#<alt (* -1 (* l (- (* -1/4 (/ (pow (+ m n) 2) l)) 1)))>
#<alt (pow m 2)>
#<alt (+ (* 2 (* m n)) (pow m 2))>
#<alt (+ (* n (+ n (* 2 m))) (pow m 2))>
#<alt (+ (* n (+ n (* 2 m))) (pow m 2))>
#<alt (pow n 2)>
#<alt (* (pow n 2) (+ 1 (* 2 (/ m n))))>
#<alt (* (pow n 2) (+ 1 (+ (* 2 (/ m n)) (/ (pow m 2) (pow n 2)))))>
#<alt (* (pow n 2) (+ 1 (+ (* 2 (/ m n)) (/ (pow m 2) (pow n 2)))))>
#<alt (pow n 2)>
#<alt (* (pow n 2) (+ 1 (* 2 (/ m n))))>
#<alt (* (pow n 2) (+ 1 (* -1 (/ (+ (* -2 m) (* -1 (/ (pow m 2) n))) n))))>
#<alt (* (pow n 2) (+ 1 (* -1 (/ (+ (* -2 m) (* -1 (/ (pow m 2) n))) n))))>
#<alt (pow n 2)>
#<alt (+ (* 2 (* m n)) (pow n 2))>
#<alt (+ (* m (+ m (* 2 n))) (pow n 2))>
#<alt (+ (* m (+ m (* 2 n))) (pow n 2))>
#<alt (pow m 2)>
#<alt (* (pow m 2) (+ 1 (* 2 (/ n m))))>
#<alt (* (pow m 2) (+ 1 (+ (* 2 (/ n m)) (/ (pow n 2) (pow m 2)))))>
#<alt (* (pow m 2) (+ 1 (+ (* 2 (/ n m)) (/ (pow n 2) (pow m 2)))))>
#<alt (pow m 2)>
#<alt (* (pow m 2) (+ 1 (* 2 (/ n m))))>
#<alt (* (pow m 2) (+ 1 (* -1 (/ (+ (* -2 n) (* -1 (/ (pow n 2) m))) m))))>
#<alt (* (pow m 2) (+ 1 (* -1 (/ (+ (* -2 n) (* -1 (/ (pow n 2) m))) m))))>
#<alt (cos (- (* 1/2 (* K (+ m n))) M))>
#<alt (+ (cos (- (* 1/2 (* K (+ m n))) M)) (* -1 (* l (cos (- (* 1/2 (* K (+ m n))) M)))))>
#<alt (+ (cos (- (* 1/2 (* K (+ m n))) M)) (* -1 (* l (cos (- (* 1/2 (* K (+ m n))) M)))))>
#<alt (+ (cos (- (* 1/2 (* K (+ m n))) M)) (* -1 (* l (cos (- (* 1/2 (* K (+ m n))) M)))))>
#<alt (* -1 (* l (cos (- (* 1/2 (* K (+ m n))) M))))>
#<alt (* l (+ (* -1 (cos (- (* 1/2 (* K (+ m n))) M))) (/ (cos (- (* 1/2 (* K (+ m n))) M)) l)))>
#<alt (* l (+ (* -1 (cos (- (* 1/2 (* K (+ m n))) M))) (/ (cos (- (* 1/2 (* K (+ m n))) M)) l)))>
#<alt (* l (+ (* -1 (cos (- (* 1/2 (* K (+ m n))) M))) (/ (cos (- (* 1/2 (* K (+ m n))) M)) l)))>
#<alt (* -1 (* l (cos (- (* 1/2 (* K (+ m n))) M))))>
#<alt (* -1 (* l (+ (cos (- (* 1/2 (* K (+ m n))) M)) (* -1 (/ (cos (- (* 1/2 (* K (+ m n))) M)) l)))))>
#<alt (* -1 (* l (+ (cos (- (* 1/2 (* K (+ m n))) M)) (* -1 (/ (cos (- (* 1/2 (* K (+ m n))) M)) l)))))>
#<alt (* -1 (* l (+ (cos (- (* 1/2 (* K (+ m n))) M)) (* -1 (/ (cos (- (* 1/2 (* K (+ m n))) M)) l)))))>
#<alt (* (cos (neg M)) (- 1 l))>
#<alt (+ (* -1/2 (* K (* (sin (neg M)) (* (+ m n) (- 1 l))))) (* (cos (neg M)) (- 1 l)))>
#<alt (+ (* K (+ (* -1/2 (* (sin (neg M)) (* (+ m n) (- 1 l)))) (* -1/8 (* K (* (cos (neg M)) (* (pow (+ m n) 2) (- 1 l))))))) (* (cos (neg M)) (- 1 l)))>
#<alt (+ (* K (+ (* -1/2 (* (sin (neg M)) (* (+ m n) (- 1 l)))) (* K (+ (* -1/8 (* (cos (neg M)) (* (pow (+ m n) 2) (- 1 l)))) (* 1/48 (* K (* (sin (neg M)) (* (pow (+ m n) 3) (- 1 l))))))))) (* (cos (neg M)) (- 1 l)))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K m)) M)) (- 1 l))>
#<alt (+ (* -1/2 (* K (* n (* (sin (- (* 1/2 (* K m)) M)) (- 1 l))))) (* (cos (- (* 1/2 (* K m)) M)) (- 1 l)))>
#<alt (+ (* n (+ (* -1/2 (* K (* (sin (- (* 1/2 (* K m)) M)) (- 1 l)))) (* -1/8 (* (pow K 2) (* n (* (cos (- (* 1/2 (* K m)) M)) (- 1 l))))))) (* (cos (- (* 1/2 (* K m)) M)) (- 1 l)))>
#<alt (+ (* n (+ (* -1/2 (* K (* (sin (- (* 1/2 (* K m)) M)) (- 1 l)))) (* n (+ (* -1/8 (* (pow K 2) (* (cos (- (* 1/2 (* K m)) M)) (- 1 l)))) (* 1/48 (* (pow K 3) (* n (* (sin (- (* 1/2 (* K m)) M)) (- 1 l))))))))) (* (cos (- (* 1/2 (* K m)) M)) (- 1 l)))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (- m (* -1 n)))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K n)) M)) (- 1 l))>
#<alt (+ (* -1/2 (* K (* m (* (sin (- (* 1/2 (* K n)) M)) (- 1 l))))) (* (cos (- (* 1/2 (* K n)) M)) (- 1 l)))>
#<alt (+ (* m (+ (* -1/2 (* K (* (sin (- (* 1/2 (* K n)) M)) (- 1 l)))) (* -1/8 (* (pow K 2) (* m (* (cos (- (* 1/2 (* K n)) M)) (- 1 l))))))) (* (cos (- (* 1/2 (* K n)) M)) (- 1 l)))>
#<alt (+ (* m (+ (* -1/2 (* K (* (sin (- (* 1/2 (* K n)) M)) (- 1 l)))) (* m (+ (* -1/8 (* (pow K 2) (* (cos (- (* 1/2 (* K n)) M)) (- 1 l)))) (* 1/48 (* (pow K 3) (* m (* (sin (- (* 1/2 (* K n)) M)) (- 1 l))))))))) (* (cos (- (* 1/2 (* K n)) M)) (- 1 l)))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (- n (* -1 m)))) M)) (- 1 l))>
#<alt (* (cos (* 1/2 (* K (+ m n)))) (- 1 l))>
#<alt (+ (* M (* (sin (* 1/2 (* K (+ m n)))) (- 1 l))) (* (cos (* 1/2 (* K (+ m n)))) (- 1 l)))>
#<alt (+ (* M (+ (* -1/2 (* M (* (cos (* 1/2 (* K (+ m n)))) (- 1 l)))) (* (sin (* 1/2 (* K (+ m n)))) (- 1 l)))) (* (cos (* 1/2 (* K (+ m n)))) (- 1 l)))>
#<alt (+ (* M (+ (* M (+ (* -1/2 (* (cos (* 1/2 (* K (+ m n)))) (- 1 l))) (* -1/6 (* M (* (sin (* 1/2 (* K (+ m n)))) (- 1 l)))))) (* (sin (* 1/2 (* K (+ m n)))) (- 1 l)))) (* (cos (* 1/2 (* K (+ m n)))) (- 1 l)))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (- (* 1/2 (* K (+ m n))) M)) (- 1 l))>
#<alt (* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (- 1 l))>
#<alt (* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (- 1 l))>
#<alt (* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (- 1 l))>
#<alt (* (cos (+ (* -1 M) (* 1/2 (* K (+ m n))))) (- 1 l))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K (+ m n)))>
#<alt (* 1/2 (* K m))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (* 1/2 (* K n))>
#<alt (* n (+ (* 1/2 K) (* 1/2 (/ (* K m) n))))>
#<alt (* n (+ (* 1/2 K) (* 1/2 (/ (* K m) n))))>
#<alt (* n (+ (* 1/2 K) (* 1/2 (/ (* K m) n))))>
#<alt (* 1/2 (* K n))>
#<alt (* -1 (* n (+ (* -1/2 K) (* -1/2 (/ (* K m) n)))))>
#<alt (* -1 (* n (+ (* -1/2 K) (* -1/2 (/ (* K m) n)))))>
#<alt (* -1 (* n (+ (* -1/2 K) (* -1/2 (/ (* K m) n)))))>
#<alt (* 1/2 (* K n))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (+ (* 1/2 (* K m)) (* 1/2 (* K n)))>
#<alt (* 1/2 (* K m))>
#<alt (* m (+ (* 1/2 K) (* 1/2 (/ (* K n) m))))>
#<alt (* m (+ (* 1/2 K) (* 1/2 (/ (* K n) m))))>
#<alt (* m (+ (* 1/2 K) (* 1/2 (/ (* K n) m))))>
#<alt (* 1/2 (* K m))>
#<alt (* -1 (* m (+ (* -1/2 K) (* -1/2 (/ (* K n) m)))))>
#<alt (* -1 (* m (+ (* -1/2 K) (* -1/2 (/ (* K n) m)))))>
#<alt (* -1 (* m (+ (* -1/2 K) (* -1/2 (/ (* K n) m)))))>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (pow M 2)>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>
#<alt (* 1/2 (* K n))>

Calls

174 calls:

Time	Variable		Point	Expression
24.0ms	m	@	-inf	(- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l))
2.0ms	n	@	inf	(- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l))
1.0ms	l	@	inf	(* (cos (* 1/2 (* n K))) (exp (- 0 l)))
1.0ms	n	@	0	(exp (- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l)))
1.0ms	m	@	0	(exp (- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l)))

rewrite524.0ms (4.3%)

Memory

40.5MiB live, 579.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 696×	`-lowering-.f32`
4 696×	`-lowering-.f64`
3 652×	`/-lowering-/.f32`
3 652×	`/-lowering-/.f64`
3 308×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	169
1	230	165
2	2038	165
0	8323	162

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 766

Calls

Call 1

Inputs
(exp (- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l)))
(- (fabs (- n m)) (+ (* 1/4 (* (+ n m) (+ n m))) l))
(fabs (- n m))
(- n m)
(cos (- (* 1/2 (* m K)) M))
(- (* 1/2 (* m K)) M)
(* m K)
(* 1/2 (* m K))
(+ (- 0 l) 1)
(cos (- (+ (* (* 1/2 K) (+ n m)) 0) M))
(- 0 l)
(- (+ (* (* 1/2 K) (+ n m)) 0) M)
(* (cos M) (exp (- 0 (* M M))))
(cos M)
(exp (- 0 (* M M)))
(- 0 (* M M))
(* (cos (* 1/2 (* n K))) (exp (- 0 l)))
(cos (* 1/2 (* n K)))
(* n K)
(exp (- 0 l))
(+ (* 1/4 (* (+ n m) (+ n m))) l)
(* (+ n m) (+ n m))
(* (+ (- 0 l) 1) (cos (- (+ (* (* 1/2 K) (+ n m)) 0) M)))
(+ (* (* 1/2 K) (+ n m)) 0)
(* M M)
(* 1/2 (* n K))

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

simplify617.0ms (5%)

Memory

-69.9MiB live, 1 063.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 686×	`accelerator-lowering-fma.f32`
13 686×	`accelerator-lowering-fma.f64`
9 614×	`-lowering-.f32`
9 614×	`-lowering-.f64`
3 286×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	791	8019
1	2389	7510
2	7522	7510
0	8859	7162

Stop Event

1×	iter limit
1×	node limit

Counts

696 → 696

Calls

Call 1

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

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

eval218.0ms (1.8%)

Memory: 14.6MiB live, 477.4MiB allocated
Compiler: Compiled 43 433 to 3 928 computations (91% saved)

prune249.0ms (2%)

Memory

35.5MiB live, 308.2MiB allocated

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	1 491	21	1 512
Fresh	5	1	6
Picked	5	0	5
Done	0	0	0
Total	1 501	22	1 523

Accuracy

99.4%

Counts

1 523 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	8.6%	(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
	9.0%	(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
	8.4%	(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
	23.5%	(.f64 (fma.f64 n (.f64 n (.f64 #s(literal -1/8 binary64) (.f64 K K))) #s(literal 1 binary64)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
	8.6%	(.f64 (-.f64 #s(literal 1 binary64) l) (cos.f64 (.f64 n (*.f64 #s(literal 1/2 binary64) K))))
	7.6%	(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (+.f64 n m) (-.f64 n m)) (.f64 #s(literal 1/2 binary64) K)) (-.f64 n m)) M)))
▶	8.3%	(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
	31.7%	(.f64 (cos.f64 (.f64 M (fma.f64 (.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (.f64 (*.f64 n n) #s(literal -1/4 binary64))))
	11.4%	(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
	8.8%	(*.f64 (cos.f64 M) (-.f64 #s(literal 1 binary64) l))
	50.9%	(.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
	46.9%	(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 n n))))
	51.2%	(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 m m))))
	27.1%	(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
▶	36.0%	(exp.f64 (-.f64 #s(literal 0 binary64) l))
▶	55.8%	(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
▶	51.3%	(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
	8.6%	(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))
	8.3%	(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
	8.3%	(cos.f64 (.f64 M (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 m K) M) #s(literal -1 binary64))))
	8.9%	(cos.f64 M)
▶	8.9%	#s(literal 1 binary64)

Compiler

Compiled 646 to 496 computations (23.2% saved)

simplify18.0ms (0.2%)

Memory

-12.2MiB live, 26.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 m (.f64 #s(literal 1/2 binary64) K))
✓	cost-diff	0	(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) l)
✓	cost-diff	192	(+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 n #s(literal -1/4 binary64))
✓	cost-diff	0	(.f64 n (.f64 n #s(literal -1/4 binary64)))
✓	cost-diff	0	(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) l)
✓	cost-diff	0	(exp.f64 (-.f64 #s(literal 0 binary64) l))
✓	cost-diff	0	(*.f64 m m)
✓	cost-diff	0	(.f64 (.f64 m m) #s(literal -1/4 binary64))
✓	cost-diff	0	(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))

Rules

176×	`accelerator-lowering-fma.f32`
176×	`accelerator-lowering-fma.f64`
172×	`-lowering-.f32`
172×	`-lowering-.f64`
64×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	77
1	47	75
2	87	75
3	133	75
4	218	75
5	262	75
6	317	75
7	367	75
8	406	75
9	410	75
0	410	75

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(exp (* (* m m) -1/4))
(* (* m m) -1/4)
(* m m)
m
-1/4
1
(exp (- 0 l))
(- 0 l)
0
l
(exp (* n (* n -1/4)))
(* n (* n -1/4))
n
(* n -1/4)
-1/4
(* (+ (- 0 l) 1) (cos (* m (* 1/2 K))))
(+ (- 0 l) 1)
(- 0 l)
0
l
1
(cos (* m (* 1/2 K)))
(* m (* 1/2 K))
m
(* 1/2 K)
1/2
K

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

localize84.0ms (0.7%)

Memory

-0.7MiB live, 177.6MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 m (.f64 #s(literal 1/2 binary64) K))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) K)
✓	accuracy	99.9%	(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
✓	accuracy	58.0%	(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
✓	accuracy	100.0%	(.f64 n (.f64 n #s(literal -1/4 binary64)))
✓	accuracy	100.0%	(*.f64 n #s(literal -1/4 binary64))
✓	accuracy	100.0%	(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) l)
✓	accuracy	100.0%	(exp.f64 (-.f64 #s(literal 0 binary64) l))
✓	accuracy	100.0%	(*.f64 m m)
✓	accuracy	100.0%	(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 m m) #s(literal -1/4 binary64))

Samples

35.0ms	114×	1	valid
25.0ms	142×	0	valid

Compiler

Compiled 84 to 24 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-mult: 18.0ms (44.7% of total)

ival-exp: 9.0ms (22.3% of total)

ival-cos: 6.0ms (14.9% of total)

adjust: 3.0ms (7.4% of total)

ival-sub: 1.0ms (2.5% of total)

ival-add: 1.0ms (2.5% of total)

exact: 1.0ms (2.5% of total)

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

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

series11.0ms (0.1%)

Memory

-15.4MiB live, 21.1MiB allocated

Counts

13 → 204

Calls

Call 1

Inputs
#<alt (exp (* (* m m) -1/4))>
#<alt (* (* m m) -1/4)>
#<alt (* m m)>
#<alt (exp (- 0 l))>
#<alt (- 0 l)>
#<alt (exp (* n (* n -1/4)))>
#<alt (* n (* n -1/4))>
#<alt (* n -1/4)>
#<alt (+ (- 0 l) 1)>
#<alt (cos (* m (* 1/2 K)))>
#<alt (* m (* 1/2 K))>
#<alt (* (+ (- 0 l) 1) (cos (* m (* 1/2 K))))>
#<alt (* 1/2 K)>

Outputs
#<alt 1>
#<alt (+ 1 (* -1/4 (pow m 2)))>
#<alt (+ 1 (* (pow m 2) (- (* 1/32 (pow m 2)) 1/4)))>
#<alt (+ 1 (* (pow m 2) (- (* (pow m 2) (+ 1/32 (* -1/384 (pow m 2)))) 1/4)))>
#<alt (exp (* -1/4 (pow m 2)))>
#<alt (exp (* -1/4 (pow m 2)))>
#<alt (exp (* -1/4 (pow m 2)))>
#<alt (exp (* -1/4 (pow m 2)))>
#<alt (exp (* -1/4 (pow m 2)))>
#<alt (exp (* -1/4 (pow m 2)))>
#<alt (exp (* -1/4 (pow m 2)))>
#<alt (exp (* -1/4 (pow m 2)))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (* -1/4 (pow m 2))>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt (pow m 2)>
#<alt 1>
#<alt (+ 1 (* -1 l))>
#<alt (+ 1 (* l (- (* 1/2 l) 1)))>
#<alt (+ 1 (* l (- (* l (+ 1/2 (* -1/6 l))) 1)))>
#<alt (exp (neg l))>
#<alt (exp (neg l))>
#<alt (exp (neg l))>
#<alt (exp (neg l))>
#<alt (exp (* -1 l))>
#<alt (exp (* -1 l))>
#<alt (exp (* -1 l))>
#<alt (exp (* -1 l))>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt (* -1 l)>
#<alt 1>
#<alt (+ 1 (* -1/4 (pow n 2)))>
#<alt (+ 1 (* (pow n 2) (- (* 1/32 (pow n 2)) 1/4)))>
#<alt (+ 1 (* (pow n 2) (- (* (pow n 2) (+ 1/32 (* -1/384 (pow n 2)))) 1/4)))>
#<alt (exp (* -1/4 (pow n 2)))>
#<alt (exp (* -1/4 (pow n 2)))>
#<alt (exp (* -1/4 (pow n 2)))>
#<alt (exp (* -1/4 (pow n 2)))>
#<alt (exp (* -1/4 (pow n 2)))>
#<alt (exp (* -1/4 (pow n 2)))>
#<alt (exp (* -1/4 (pow n 2)))>
#<alt (exp (* -1/4 (pow n 2)))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 (pow n 2))>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt (* -1/4 n)>
#<alt 1>
#<alt (+ 1 (* -1 l))>
#<alt (+ 1 (* -1 l))>
#<alt (+ 1 (* -1 l))>
#<alt (* -1 l)>
#<alt (* l (- (/ 1 l) 1))>
#<alt (* l (- (/ 1 l) 1))>
#<alt (* l (- (/ 1 l) 1))>
#<alt (* -1 l)>
#<alt (* -1 (* l (- 1 (/ 1 l))))>
#<alt (* -1 (* l (- 1 (/ 1 l))))>
#<alt (* -1 (* l (- 1 (/ 1 l))))>
#<alt 1>
#<alt (+ 1 (* -1/8 (* (pow K 2) (pow m 2))))>
#<alt (+ 1 (* (pow m 2) (+ (* -1/8 (pow K 2)) (* 1/384 (* (pow K 4) (pow m 2))))))>
#<alt (+ 1 (* (pow m 2) (+ (* -1/8 (pow K 2)) (* (pow m 2) (+ (* -1/46080 (* (pow K 6) (pow m 2))) (* 1/384 (pow K 4)))))))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt 1>
#<alt (+ 1 (* -1/8 (* (pow K 2) (pow m 2))))>
#<alt (+ 1 (* (pow K 2) (+ (* -1/8 (pow m 2)) (* 1/384 (* (pow K 2) (pow m 4))))))>
#<alt (+ 1 (* (pow K 2) (+ (* -1/8 (pow m 2)) (* (pow K 2) (+ (* -1/46080 (* (pow K 2) (pow m 6))) (* 1/384 (pow m 4)))))))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (* 1/2 (* K m))>
#<alt (cos (* 1/2 (* K m)))>
#<alt (+ (cos (* 1/2 (* K m))) (* -1 (* l (cos (* 1/2 (* K m))))))>
#<alt (+ (cos (* 1/2 (* K m))) (* -1 (* l (cos (* 1/2 (* K m))))))>
#<alt (+ (cos (* 1/2 (* K m))) (* -1 (* l (cos (* 1/2 (* K m))))))>
#<alt (* -1 (* l (cos (* 1/2 (* K m)))))>
#<alt (* l (+ (* -1 (cos (* 1/2 (* K m)))) (/ (cos (* 1/2 (* K m))) l)))>
#<alt (* l (+ (* -1 (cos (* 1/2 (* K m)))) (/ (cos (* 1/2 (* K m))) l)))>
#<alt (* l (+ (* -1 (cos (* 1/2 (* K m)))) (/ (cos (* 1/2 (* K m))) l)))>
#<alt (* -1 (* l (cos (* 1/2 (* K m)))))>
#<alt (* -1 (* l (+ (cos (* 1/2 (* K m))) (* -1 (/ (cos (* 1/2 (* K m))) l)))))>
#<alt (* -1 (* l (+ (cos (* 1/2 (* K m))) (* -1 (/ (cos (* 1/2 (* K m))) l)))))>
#<alt (* -1 (* l (+ (cos (* 1/2 (* K m))) (* -1 (/ (cos (* 1/2 (* K m))) l)))))>
#<alt (- 1 l)>
#<alt (- (+ 1 (* -1/8 (* (pow K 2) (* (pow m 2) (- 1 l))))) l)>
#<alt (- (+ 1 (* (pow m 2) (+ (* -1/8 (* (pow K 2) (- 1 l))) (* 1/384 (* (pow K 4) (* (pow m 2) (- 1 l))))))) l)>
#<alt (- (+ 1 (* (pow m 2) (+ (* -1/8 (* (pow K 2) (- 1 l))) (* (pow m 2) (+ (* -1/46080 (* (pow K 6) (* (pow m 2) (- 1 l)))) (* 1/384 (* (pow K 4) (- 1 l)))))))) l)>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (- 1 l)>
#<alt (- (+ 1 (* -1/8 (* (pow K 2) (* (pow m 2) (- 1 l))))) l)>
#<alt (- (+ 1 (* (pow K 2) (+ (* -1/8 (* (pow m 2) (- 1 l))) (* 1/384 (* (pow K 2) (* (pow m 4) (- 1 l))))))) l)>
#<alt (- (+ 1 (* (pow K 2) (+ (* -1/8 (* (pow m 2) (- 1 l))) (* (pow K 2) (+ (* -1/46080 (* (pow K 2) (* (pow m 6) (- 1 l)))) (* 1/384 (* (pow m 4) (- 1 l)))))))) l)>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* (cos (* 1/2 (* K m))) (- 1 l))>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>
#<alt (* 1/2 K)>

Calls

51 calls:

Time	Variable		Point	Expression
3.0ms	m	@	inf	(* (* m m) -1/4)
1.0ms	l	@	0	(* (+ (- 0 l) 1) (cos (* m (* 1/2 K))))
0.0ms	m	@	0	(* (+ (- 0 l) 1) (cos (* m (* 1/2 K))))
0.0ms	K	@	0	(* (+ (- 0 l) 1) (cos (* m (* 1/2 K))))
0.0ms	m	@	0	(* (* m m) -1/4)

rewrite203.0ms (1.7%)

Memory

1.9MiB live, 398.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 662×	`accelerator-lowering-fma.f32`
4 662×	`accelerator-lowering-fma.f64`
2 374×	`-lowering-.f32`
2 374×	`-lowering-.f64`
1 416×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	62
1	74	60
2	445	58
3	7096	58
0	9012	58

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 495

Calls

Call 1

Inputs
(exp (* (* m m) -1/4))
(* (* m m) -1/4)
(* m m)
(exp (- 0 l))
(- 0 l)
(exp (* n (* n -1/4)))
(* n (* n -1/4))
(* n -1/4)
(+ (- 0 l) 1)
(cos (* m (* 1/2 K)))
(* m (* 1/2 K))
(* (+ (- 0 l) 1) (cos (* m (* 1/2 K))))
(* 1/2 K)

Outputs
(exp.f64 (.f64 m (.f64 m #s(literal -1/4 binary64))))
(exp.f64 (.f64 (log.f64 (exp.f64 m)) (.f64 m #s(literal -1/4 binary64))))
(exp.f64 (.f64 (log.f64 (exp.f64 #s(literal -1/4 binary64))) (.f64 m m)))
(exp.f64 (.f64 (log.f64 (exp.f64 (.f64 (*.f64 m m) #s(literal -1/8 binary64)))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 m) #s(literal -1/4 binary64))) m))
(exp.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 #s(literal -1/4 binary64)) m)) m))
(exp.f64 (.f64 (log.f64 (.f64 (exp.f64 (.f64 m m)) (exp.f64 (.f64 m m)))) #s(literal -1/8 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 (.f64 m #s(literal -1/4 binary64)))) m))
(pow.f64 (exp.f64 (*.f64 m m)) #s(literal -1/4 binary64))
(pow.f64 (exp.f64 m) (*.f64 m #s(literal -1/4 binary64)))
(pow.f64 (exp.f64 m) (.f64 (.f64 m #s(literal -1/8 binary64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal -1/4 binary64)) (*.f64 m m))
(pow.f64 (exp.f64 (.f64 (.f64 m m) #s(literal -1/8 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (exp.f64 m) #s(literal -1/4 binary64)) m)
(pow.f64 (pow.f64 (exp.f64 #s(literal -1/4 binary64)) m) m)
(pow.f64 (pow.f64 (exp.f64 #s(literal -1/4 binary64)) m) (log.f64 (exp.f64 m)))
(pow.f64 (.f64 (exp.f64 (.f64 m m)) (exp.f64 (*.f64 m m))) #s(literal -1/8 binary64))
(pow.f64 (exp.f64 (*.f64 m #s(literal -1/4 binary64))) m)
(pow.f64 (pow.f64 (exp.f64 #s(literal -1/4 binary64)) (exp.f64 (log.f64 m))) (exp.f64 (log.f64 m)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 m) #s(literal -1/4 binary64)) (pow.f64 m #s(literal 1/2 binary64))) (pow.f64 m #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal -1/4 binary64)) m) (pow.f64 m #s(literal 1/2 binary64))) (pow.f64 m #s(literal 1/2 binary64)))
(pow.f64 (pow.f64 (exp.f64 (*.f64 m #s(literal -1/4 binary64))) (pow.f64 m #s(literal 1/2 binary64))) (pow.f64 m #s(literal 1/2 binary64)))
(.f64 (exp.f64 (.f64 (.f64 m m) #s(literal -1/8 binary64))) (exp.f64 (.f64 (*.f64 m m) #s(literal -1/8 binary64))))
(.f64 (pow.f64 (exp.f64 m) (/.f64 (.f64 m #s(literal -1/4 binary64)) #s(literal 2 binary64))) (pow.f64 (exp.f64 m) (/.f64 (*.f64 m #s(literal -1/4 binary64)) #s(literal 2 binary64))))
(.f64 (pow.f64 (exp.f64 #s(literal -1/4 binary64)) (/.f64 (.f64 m m) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1/4 binary64)) (/.f64 (*.f64 m m) #s(literal 2 binary64))))
(*.f64 (pow.f64 (pow.f64 (exp.f64 m) (/.f64 m #s(literal 2 binary64))) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 (exp.f64 m) (/.f64 m #s(literal 2 binary64))) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (exp.f64 (.f64 (.f64 m m) #s(literal -1/16 binary64))) #s(literal 2 binary64)) (pow.f64 (exp.f64 (.f64 (*.f64 m m) #s(literal -1/16 binary64))) #s(literal 2 binary64)))
(.f64 m (.f64 m #s(literal -1/4 binary64)))
(.f64 (.f64 m m) #s(literal -1/4 binary64))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
(.f64 (.f64 m #s(literal -1/4 binary64)) m)
(log.f64 (exp.f64 (*.f64 m m)))
(+.f64 (log.f64 (pow.f64 (exp.f64 m) (/.f64 m #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 m) (/.f64 m #s(literal 2 binary64)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 m)))
(exp.f64 (.f64 (log.f64 (.f64 m m)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 m))) #s(literal 2 binary64)))
(pow.f64 m #s(literal 2 binary64))
(pow.f64 (*.f64 m m) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 m)) #s(literal 2 binary64))
(*.f64 m m)
(*.f64 m (log.f64 (exp.f64 m)))
(*.f64 m (pow.f64 (log.f64 (exp.f64 m)) #s(literal 1 binary64)))
(*.f64 (exp.f64 (log.f64 m)) (exp.f64 (log.f64 m)))
(*.f64 (pow.f64 (pow.f64 m #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 m #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (exp.f64 (log.f64 m)) #s(literal 1 binary64)) (pow.f64 (exp.f64 (log.f64 m)) #s(literal 1 binary64)))
(exp.f64 l)
(exp.f64 (*.f64 (log.f64 (exp.f64 l)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 l)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1 binary64))) l))
(exp.f64 (*.f64 (log.f64 (exp.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64)))))
(exp.f64 (*.f64 (log.f64 (exp.f64 (fma.f64 l l #s(literal 0 binary64)))) (/.f64 #s(literal 1 binary64) l)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) l))
(neg.f64 (/.f64 #s(literal -1 binary64) (exp.f64 l)))
(/.f64 #s(literal 1 binary64) (exp.f64 l))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (exp.f64 l))))
(/.f64 (exp.f64 l) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 l)))
(/.f64 (-.f64 #s(literal 0 binary64) (exp.f64 l)) #s(literal -1 binary64))
(pow.f64 (exp.f64 l) #s(literal 1 binary64))
(pow.f64 (exp.f64 l) #s(literal -1 binary64))
(pow.f64 (exp.f64 l) (/.f64 l l))
(pow.f64 (exp.f64 l) (*.f64 (fma.f64 l l #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64)))))
(pow.f64 (exp.f64 l) (/.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64))))
(pow.f64 (exp.f64 #s(literal 1 binary64)) l)
(pow.f64 (exp.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64))))
(pow.f64 (exp.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64))) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (fma.f64 l l #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) l))
(pow.f64 (exp.f64 #s(literal -1 binary64)) l)
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (exp.f64 l))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal 1 binary64)) l)
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (fma.f64 l l #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) l))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) #s(literal -1 binary64)) l)
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) l)) (fma.f64 l l #s(literal 0 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64)))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (pow.f64 l #s(literal 3/2 binary64))) (*.f64 (pow.f64 l #s(literal 3/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64)))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (pow.f64 l #s(literal 3/2 binary64))) (/.f64 (pow.f64 l #s(literal 3/2 binary64)) (fma.f64 l l #s(literal 0 binary64))))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (/.f64 (pow.f64 l #s(literal 3/2 binary64)) l)) (/.f64 (pow.f64 l #s(literal 3/2 binary64)) l))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (/.f64 l l)) l)
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (/.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)) (*.f64 l (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (/.f64 (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) l))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (/.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)))) l)
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (/.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (/.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)))) l)
(pow.f64 (pow.f64 (exp.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64))))
(pow.f64 (pow.f64 (exp.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 l l #s(literal 0 binary64)))
(pow.f64 (pow.f64 (exp.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)))) l)
(pow.f64 (pow.f64 (exp.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)) #s(literal 0 binary64)))) (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)))
(pow.f64 (pow.f64 (exp.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 l (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)))
(pow.f64 (pow.f64 (exp.f64 (fma.f64 l l #s(literal 0 binary64))) l) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64))))
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(pow.f64 (pow.f64 (exp.f64 (fma.f64 l l #s(literal 0 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) l))
(pow.f64 (pow.f64 (exp.f64 (fma.f64 l l #s(literal 0 binary64))) (fma.f64 l l #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))))
(pow.f64 (pow.f64 (exp.f64 (fma.f64 l l #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64)))) l)
(pow.f64 (pow.f64 (exp.f64 (fma.f64 l l #s(literal 0 binary64))) (/.f64 l l)) (/.f64 #s(literal 1 binary64) l))
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l
(+.f64 #s(literal 0 binary64) l)
(+.f64 l #s(literal 0 binary64))
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(fma.f64 l (*.f64 (fma.f64 l l #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64)))) #s(literal 0 binary64))
(fma.f64 l (/.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64))) #s(literal 0 binary64))
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(fma.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64))) (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(fma.f64 #s(literal -1 binary64) (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(fma.f64 (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) #s(literal 1 binary64) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(fma.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (fma.f64 l l #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) l) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(fma.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) #s(literal -1 binary64)) l (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(fma.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 l l #s(literal 0 binary64))) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(neg.f64 (.f64 (+.f64 l #s(literal -1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K)))))
(neg.f64 (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (+.f64 l #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 l (+.f64 l #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 l #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l l #s(literal -1 binary64)))))
(/.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (/.f64 #s(literal 1 binary64) (+.f64 l #s(literal 1 binary64))))
(/.f64 (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l l #s(literal -1 binary64))) (+.f64 l #s(literal -1 binary64)))
(/.f64 (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64))) (fma.f64 l (+.f64 l #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l l #s(literal -1 binary64)))) (+.f64 l #s(literal 1 binary64)))
(/.f64 (neg.f64 (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64)))) (+.f64 (fma.f64 l l #s(literal -1 binary64)) l))
(/.f64 (+.f64 (pow.f64 (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) #s(literal 3 binary64)) (pow.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) #s(literal 3 binary64))) (fma.f64 (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 m (.f64 #s(literal 1/2 binary64) K)))))) (.f64 (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K)))))))
(/.f64 (+.f64 (pow.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) #s(literal 3 binary64)) (pow.f64 (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) #s(literal 3 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 m (.f64 #s(literal 1/2 binary64) K)))))) (-.f64 (.f64 (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))))) (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))))))))
(/.f64 (-.f64 (.f64 (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 m (.f64 #s(literal 1/2 binary64) K))))))) (-.f64 (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))))
(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 m (.f64 #s(literal 1/2 binary64) K)))))) (.f64 (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))))) (-.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (.f64 l (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))))))
(/.f64 (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal -1 binary64))) (+.f64 (fma.f64 l l #s(literal -1 binary64)) l))
(/.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (-.f64 #s(literal 0 binary64) (.f64 (fma.f64 l l #s(literal 1 binary64)) (+.f64 l #s(literal -1 binary64))))) (fma.f64 l l #s(literal 1 binary64)))
(/.f64 (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l l #s(literal 1 binary64))) (+.f64 l #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal -1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K)))) (+.f64 (fma.f64 l l #s(literal -1 binary64)) l))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 (fma.f64 l l #s(literal 1 binary64)) (+.f64 l #s(literal -1 binary64)))) (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))) (fma.f64 l l #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 l l #s(literal 1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K)))) (+.f64 l #s(literal 1 binary64)))
(pow.f64 (/.f64 (fma.f64 l (+.f64 l #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 l #s(literal -1 binary64)) (.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l l #s(literal -1 binary64)))) #s(literal -1 binary64))
(.f64 (+.f64 l #s(literal 1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (+.f64 l #s(literal 1 binary64)))
(.f64 (fma.f64 l l #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 l #s(literal -1 binary64))) (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))))
(.f64 (fma.f64 l l #s(literal -1 binary64)) (/.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (+.f64 l #s(literal -1 binary64))))
(.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 l (+.f64 l #s(literal 1 binary64)) #s(literal 1 binary64))) (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))))
(.f64 (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64)) (/.f64 (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (+.f64 l #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (fma.f64 l l #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 l #s(literal -1 binary64))))
(.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 l (+.f64 l #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (fma.f64 l l #s(literal -1 binary64))) (fma.f64 l l #s(literal -1 binary64))) (+.f64 l #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (fma.f64 l l #s(literal -1 binary64))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal -1 binary64))) (fma.f64 l (+.f64 l #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64))) (fma.f64 l (.f64 l (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))) (.f64 (+.f64 l #s(literal 1 binary64)) (fma.f64 l l #s(literal 1 binary64))))) (fma.f64 (+.f64 l #s(literal 1 binary64)) (fma.f64 l (+.f64 l #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 l l #s(literal 0 binary64)) (fma.f64 l l #s(literal 0 binary64)) #s(literal 0 binary64))))
(.f64 (/.f64 (.f64 (cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K))) (fma.f64 l (fma.f64 l l #s(literal 0 binary64)) #s(literal 1 binary64))) (*.f64 (fma.f64 l (+.f64 l #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 (fma.f64 l l #s(literal -1 binary64)) l))) (+.f64 (fma.f64 l l #s(literal -1 binary64)) l))
(*.f64 #s(literal 1/2 binary64) K)
(*.f64 K #s(literal 1/2 binary64))

simplify470.0ms (3.8%)

Memory

-6.7MiB live, 798.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 228×	`accelerator-lowering-fma.f32`
13 228×	`accelerator-lowering-fma.f64`
5 456×	`-lowering-.f32`
5 456×	`-lowering-.f64`
2 896×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	162	1470
1	439	1320
2	1451	1296
3	3733	1296
4	5476	1296
0	8479	1255

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
1
(+ 1 (* -1/4 (pow m 2)))
(+ 1 (* (pow m 2) (- (* 1/32 (pow m 2)) 1/4)))
(+ 1 (* (pow m 2) (- (* (pow m 2) (+ 1/32 (* -1/384 (pow m 2)))) 1/4)))
(exp (* -1/4 (pow m 2)))
(exp (* -1/4 (pow m 2)))
(exp (* -1/4 (pow m 2)))
(exp (* -1/4 (pow m 2)))
(exp (* -1/4 (pow m 2)))
(exp (* -1/4 (pow m 2)))
(exp (* -1/4 (pow m 2)))
(exp (* -1/4 (pow m 2)))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(* -1/4 (pow m 2))
(pow m 2)
(pow m 2)
(pow m 2)
(pow m 2)
(pow m 2)
(pow m 2)
(pow m 2)
(pow m 2)
(pow m 2)
(pow m 2)
(pow m 2)
(pow m 2)
1
(+ 1 (* -1 l))
(+ 1 (* l (- (* 1/2 l) 1)))
(+ 1 (* l (- (* l (+ 1/2 (* -1/6 l))) 1)))
(exp (neg l))
(exp (neg l))
(exp (neg l))
(exp (neg l))
(exp (* -1 l))
(exp (* -1 l))
(exp (* -1 l))
(exp (* -1 l))
(* -1 l)
(* -1 l)
(* -1 l)
(* -1 l)
(* -1 l)
(* -1 l)
(* -1 l)
(* -1 l)
(* -1 l)
(* -1 l)
(* -1 l)
(* -1 l)
1
(+ 1 (* -1/4 (pow n 2)))
(+ 1 (* (pow n 2) (- (* 1/32 (pow n 2)) 1/4)))
(+ 1 (* (pow n 2) (- (* (pow n 2) (+ 1/32 (* -1/384 (pow n 2)))) 1/4)))
(exp (* -1/4 (pow n 2)))
(exp (* -1/4 (pow n 2)))
(exp (* -1/4 (pow n 2)))
(exp (* -1/4 (pow n 2)))
(exp (* -1/4 (pow n 2)))
(exp (* -1/4 (pow n 2)))
(exp (* -1/4 (pow n 2)))
(exp (* -1/4 (pow n 2)))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 (pow n 2))
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
(* -1/4 n)
1
(+ 1 (* -1 l))
(+ 1 (* -1 l))
(+ 1 (* -1 l))
(* -1 l)
(* l (- (/ 1 l) 1))
(* l (- (/ 1 l) 1))
(* l (- (/ 1 l) 1))
(* -1 l)
(* -1 (* l (- 1 (/ 1 l))))
(* -1 (* l (- 1 (/ 1 l))))
(* -1 (* l (- 1 (/ 1 l))))
1
(+ 1 (* -1/8 (* (pow K 2) (pow m 2))))
(+ 1 (* (pow m 2) (+ (* -1/8 (pow K 2)) (* 1/384 (* (pow K 4) (pow m 2))))))
(+ 1 (* (pow m 2) (+ (* -1/8 (pow K 2)) (* (pow m 2) (+ (* -1/46080 (* (pow K 6) (pow m 2))) (* 1/384 (pow K 4)))))))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
1
(+ 1 (* -1/8 (* (pow K 2) (pow m 2))))
(+ 1 (* (pow K 2) (+ (* -1/8 (pow m 2)) (* 1/384 (* (pow K 2) (pow m 4))))))
(+ 1 (* (pow K 2) (+ (* -1/8 (pow m 2)) (* (pow K 2) (+ (* -1/46080 (* (pow K 2) (pow m 6))) (* 1/384 (pow m 4)))))))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(cos (* 1/2 (* K m)))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(* 1/2 (* K m))
(cos (* 1/2 (* K m)))
(+ (cos (* 1/2 (* K m))) (* -1 (* l (cos (* 1/2 (* K m))))))
(+ (cos (* 1/2 (* K m))) (* -1 (* l (cos (* 1/2 (* K m))))))
(+ (cos (* 1/2 (* K m))) (* -1 (* l (cos (* 1/2 (* K m))))))
(* -1 (* l (cos (* 1/2 (* K m)))))
(* l (+ (* -1 (cos (* 1/2 (* K m)))) (/ (cos (* 1/2 (* K m))) l)))
(* l (+ (* -1 (cos (* 1/2 (* K m)))) (/ (cos (* 1/2 (* K m))) l)))
(* l (+ (* -1 (cos (* 1/2 (* K m)))) (/ (cos (* 1/2 (* K m))) l)))
(* -1 (* l (cos (* 1/2 (* K m)))))
(* -1 (* l (+ (cos (* 1/2 (* K m))) (* -1 (/ (cos (* 1/2 (* K m))) l)))))
(* -1 (* l (+ (cos (* 1/2 (* K m))) (* -1 (/ (cos (* 1/2 (* K m))) l)))))
(* -1 (* l (+ (cos (* 1/2 (* K m))) (* -1 (/ (cos (* 1/2 (* K m))) l)))))
(- 1 l)
(- (+ 1 (* -1/8 (* (pow K 2) (* (pow m 2) (- 1 l))))) l)
(- (+ 1 (* (pow m 2) (+ (* -1/8 (* (pow K 2) (- 1 l))) (* 1/384 (* (pow K 4) (* (pow m 2) (- 1 l))))))) l)
(- (+ 1 (* (pow m 2) (+ (* -1/8 (* (pow K 2) (- 1 l))) (* (pow m 2) (+ (* -1/46080 (* (pow K 6) (* (pow m 2) (- 1 l)))) (* 1/384 (* (pow K 4) (- 1 l)))))))) l)
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(- 1 l)
(- (+ 1 (* -1/8 (* (pow K 2) (* (pow m 2) (- 1 l))))) l)
(- (+ 1 (* (pow K 2) (+ (* -1/8 (* (pow m 2) (- 1 l))) (* 1/384 (* (pow K 2) (* (pow m 4) (- 1 l))))))) l)
(- (+ 1 (* (pow K 2) (+ (* -1/8 (* (pow m 2) (- 1 l))) (* (pow K 2) (+ (* -1/46080 (* (pow K 2) (* (pow m 6) (- 1 l)))) (* 1/384 (* (pow m 4) (- 1 l)))))))) l)
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* (cos (* 1/2 (* K m))) (- 1 l))
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)
(* 1/2 K)

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow m 2)))
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(+ 1 (* (pow m 2) (- (* 1/32 (pow m 2)) 1/4)))
(fma.f64 m (.f64 m (fma.f64 m (.f64 m #s(literal 1/32 binary64)) #s(literal -1/4 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow m 2) (- (* (pow m 2) (+ 1/32 (* -1/384 (pow m 2)))) 1/4)))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(exp (* -1/4 (pow m 2)))
(exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 m m)))
(exp (* -1/4 (pow m 2)))
(exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 m m)))
(exp (* -1/4 (pow m 2)))
(exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 m m)))
(exp (* -1/4 (pow m 2)))
(exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 m m)))
(exp (* -1/4 (pow m 2)))
(exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 m m)))
(exp (* -1/4 (pow m 2)))
(exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 m m)))
(exp (* -1/4 (pow m 2)))
(exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 m m)))
(exp (* -1/4 (pow m 2)))
(exp.f64 (.f64 #s(literal -1/4 binary64) (.f64 m m)))
(* -1/4 (pow m 2))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
(* -1/4 (pow m 2))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
(* -1/4 (pow m 2))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
(* -1/4 (pow m 2))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
(* -1/4 (pow m 2))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
(* -1/4 (pow m 2))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
(* -1/4 (pow m 2))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
(* -1/4 (pow m 2))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
(* -1/4 (pow m 2))
(.f64 #s(literal -1/4 binary64) (.f64 m m))
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(*.f64 #s(literal 1/2 binary64) K)

eval96.0ms (0.8%)

Memory: 30.2MiB live, 214.7MiB allocated
Compiler: Compiled 13 996 to 1 518 computations (89.2% saved)

prune135.0ms (1.1%)

Memory

-1.3MiB live, 276.4MiB allocated

Pruning

26 alts after pruning (23 fresh and 3 done)

	Pruned	Kept	Total
New	818	12	830
Fresh	6	11	17
Picked	2	3	5
Done	0	0	0
Total	826	26	852

Accuracy

99.4%

Counts

852 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
	8.3%	(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
	9.0%	(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
	9.0%	(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
	8.5%	(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
	11.1%	(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
	10.8%	(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
	8.4%	(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
	8.4%	(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
	8.3%	(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
	34.4%	(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 l)))
	8.7%	(-.f64 #s(literal 1 binary64) l)
	7.6%	(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (+.f64 n m) (-.f64 n m)) (.f64 #s(literal 1/2 binary64) K)) (-.f64 n m)) M)))
	31.7%	(.f64 (cos.f64 (.f64 M (fma.f64 (.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (.f64 (*.f64 n n) #s(literal -1/4 binary64))))
	50.9%	(.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
	46.9%	(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 n n))))
	51.2%	(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 m m))))
	27.1%	(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
✓	55.8%	(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
✓	51.3%	(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
	36.0%	(exp.f64 (neg.f64 l))
	27.8%	(exp.f64 l)
	8.6%	(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))
	8.3%	(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
	8.3%	(cos.f64 (.f64 M (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 m K) M) #s(literal -1 binary64))))
	8.9%	(cos.f64 M)
✓	8.9%	#s(literal 1 binary64)

Compiler

Compiled 1 245 to 506 computations (59.4% saved)

regimes109.0ms (0.9%)

Memory

-6.4MiB live, 163.5MiB allocated

Counts

58 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)
(exp.f64 l)
(exp.f64 (neg.f64 l))
(exp.f64 (-.f64 #s(literal 0 binary64) l))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
(*.f64 (cos.f64 M) (-.f64 #s(literal 1 binary64) l))
(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
(cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M))
(.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 l)))
(cos.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 m m))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 n n))))
(.f64 (-.f64 #s(literal 1 binary64) l) (cos.f64 (.f64 n (*.f64 #s(literal 1/2 binary64) K))))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l)))
(cos.f64 (.f64 M (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 m K) M) #s(literal -1 binary64))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M)))
(.f64 (fma.f64 n (.f64 n (.f64 #s(literal -1/8 binary64) (.f64 K K))) #s(literal 1 binary64)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (+.f64 n m) (-.f64 n m)) (.f64 #s(literal 1/2 binary64) K)) (-.f64 n m)) M)))
(*.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 m K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 m (.f64 m #s(literal -1/4 binary64)))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 (.f64 n n) #s(literal -1/4 binary64))))
(.f64 (cos.f64 (.f64 M (fma.f64 (*.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (.f64 M (fma.f64 (.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (.f64 (*.f64 n n) #s(literal -1/4 binary64))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (*.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 (-.f64 (neg.f64 (.f64 m (.f64 m #s(literal 1/4 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 (.f64 n (.f64 n #s(literal 1/4 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 (.f64 n (.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) (/.f64 (fma.f64 m #s(literal -1/2 binary64) M) n) (fma.f64 m #s(literal -1/2 binary64) M)) n))))) (-.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 (.f64 n (.f64 n (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (.f64 (fma.f64 m #s(literal -1/2 binary64) M) (fma.f64 m #s(literal -1/2 binary64) M)) (.f64 n n)) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) n)))))) (-.f64 l (fabs.f64 (-.f64 m n))))))
(*.f64 (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 (fma.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) K #s(literal 0 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 (/.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 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 K (fma.f64 m #s(literal 1/2 binary64) #s(literal 0 binary64)) #s(literal 0 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 (.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 (.f64 (/.f64 K (/.f64 #s(literal 2 binary64) (fma.f64 m (.f64 m m) (.f64 n (.f64 n n))))) (/.f64 #s(literal 1 binary64) (fma.f64 n (-.f64 n m) (.f64 m 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))))))

Outputs
(*.f64 (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:

22.0ms	n
18.0ms	M
18.0ms	K
17.0ms	l
16.0ms	m

Results

Accuracy	Segments	Branch
98.1%	1	`K`
98.1%	1	`m`
98.1%	1	`n`
98.1%	1	`M`
98.1%	1	`l`
98.1%	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)

regimes98.0ms (0.8%)

Memory

-0.6MiB live, 155.2MiB allocated

Counts

52 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)
(exp.f64 l)
(exp.f64 (neg.f64 l))
(exp.f64 (-.f64 #s(literal 0 binary64) l))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
(*.f64 (cos.f64 M) (-.f64 #s(literal 1 binary64) l))
(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
(cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M))
(.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 l)))
(cos.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 m m))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 n n))))
(.f64 (-.f64 #s(literal 1 binary64) l) (cos.f64 (.f64 n (*.f64 #s(literal 1/2 binary64) K))))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l)))
(cos.f64 (.f64 M (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 m K) M) #s(literal -1 binary64))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M)))
(.f64 (fma.f64 n (.f64 n (.f64 #s(literal -1/8 binary64) (.f64 K K))) #s(literal 1 binary64)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (+.f64 n m) (-.f64 n m)) (.f64 #s(literal 1/2 binary64) K)) (-.f64 n m)) M)))
(*.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 m K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 m (.f64 m #s(literal -1/4 binary64)))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 (.f64 n n) #s(literal -1/4 binary64))))
(.f64 (cos.f64 (.f64 M (fma.f64 (*.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (.f64 M (fma.f64 (.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (.f64 (*.f64 n n) #s(literal -1/4 binary64))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (*.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 (-.f64 (neg.f64 (.f64 m (.f64 m #s(literal 1/4 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 (.f64 n (.f64 n #s(literal 1/4 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 (.f64 n (.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) (/.f64 (fma.f64 m #s(literal -1/2 binary64) M) n) (fma.f64 m #s(literal -1/2 binary64) M)) n))))) (-.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 (.f64 n (.f64 n (+.f64 #s(literal 1/4 binary64) (+.f64 (/.f64 (.f64 (fma.f64 m #s(literal -1/2 binary64) M) (fma.f64 m #s(literal -1/2 binary64) M)) (.f64 n n)) (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) n)))))) (-.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 (*.f64 n (*.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) (/.f64 (fma.f64 m #s(literal -1/2 binary64) M) n) (fma.f64 m #s(literal -1/2 binary64) M)) n))))) (-.f64 l (fabs.f64 (-.f64 m n))))))

(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l)))

Calls

6 calls:

18.0ms	K
18.0ms	n
16.0ms	M
15.0ms	m
15.0ms	l

Results

Accuracy	Segments	Branch
93.6%	3	`K`
93.2%	3	`m`
87.8%	1	`n`
97.0%	3	`M`
87.8%	1	`l`
97.4%	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)

regimes31.0ms (0.3%)

Memory

13.6MiB live, 51.0MiB allocated

Counts

50 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)
(exp.f64 l)
(exp.f64 (neg.f64 l))
(exp.f64 (-.f64 #s(literal 0 binary64) l))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
(*.f64 (cos.f64 M) (-.f64 #s(literal 1 binary64) l))
(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
(cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M))
(.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 l)))
(cos.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 m m))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 n n))))
(.f64 (-.f64 #s(literal 1 binary64) l) (cos.f64 (.f64 n (*.f64 #s(literal 1/2 binary64) K))))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l)))
(cos.f64 (.f64 M (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 m K) M) #s(literal -1 binary64))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M)))
(.f64 (fma.f64 n (.f64 n (.f64 #s(literal -1/8 binary64) (.f64 K K))) #s(literal 1 binary64)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (-.f64 (/.f64 (.f64 (.f64 (+.f64 n m) (-.f64 n m)) (.f64 #s(literal 1/2 binary64) K)) (-.f64 n m)) M)))
(*.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 M) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 m K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (*.f64 n K))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 m (.f64 m #s(literal -1/4 binary64)))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (.f64 (.f64 n n) #s(literal -1/4 binary64))))
(.f64 (cos.f64 (.f64 M (fma.f64 (*.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(.f64 (cos.f64 (.f64 M (fma.f64 (.f64 (+.f64 n m) K) (/.f64 #s(literal 1/2 binary64) M) #s(literal -1 binary64)))) (exp.f64 (.f64 (*.f64 n n) #s(literal -1/4 binary64))))
(.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (*.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 (-.f64 (neg.f64 (.f64 m (.f64 m #s(literal 1/4 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 (.f64 n (.f64 n #s(literal 1/4 binary64)))) (-.f64 l (fabs.f64 (-.f64 m n))))))

Outputs

(*.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M))))

(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l)))

(*.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M))))

Calls

2 calls:

15.0ms

14.0ms

(*.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
97.0%	3	`M`
87.8%	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 40 to 26 computations (35% saved)

regimes87.0ms (0.7%)

Memory

-8.1MiB live, 73.5MiB allocated

Counts

31 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)
(exp.f64 l)
(exp.f64 (neg.f64 l))
(exp.f64 (-.f64 #s(literal 0 binary64) l))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
(*.f64 (cos.f64 M) (-.f64 #s(literal 1 binary64) l))
(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
(cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M))
(.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 l)))
(cos.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 m m))))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 n n))))
(.f64 (-.f64 #s(literal 1 binary64) l) (cos.f64 (.f64 n (*.f64 #s(literal 1/2 binary64) K))))
(.f64 (+.f64 (-.f64 #s(literal 0 binary64) l) #s(literal 1 binary64)) (cos.f64 (.f64 m (*.f64 #s(literal 1/2 binary64) K))))

Outputs

(exp.f64 (*.f64 (*.f64 m m) #s(literal -1/4 binary64)))

(*.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M))))

(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (*.f64 #s(literal 1/4 binary64) (*.f64 n n))))

Calls

6 calls:

28.0ms	M
18.0ms	(.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))))))
10.0ms	n
10.0ms	K
10.0ms	m

Results

Accuracy	Segments	Branch
83.1%	4	`n`
59.9%	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))))))`
75.1%	3	`l`
84.0%	3	`m`
55.8%	1	`K`
82.1%	6	`M`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes12.0ms (0.1%)

Memory

-15.1MiB live, 22.5MiB allocated

Counts

28 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)
(exp.f64 l)
(exp.f64 (neg.f64 l))
(exp.f64 (-.f64 #s(literal 0 binary64) l))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
(*.f64 (cos.f64 M) (-.f64 #s(literal 1 binary64) l))
(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
(cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M))
(.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 l)))
(cos.f64 (-.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) K) (+.f64 n m) #s(literal 0 binary64)) M))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 m m))))

Outputs
(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
(.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))))
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
83.8%	3	`m`

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes18.0ms (0.1%)

Memory

-7.9MiB live, 30.0MiB allocated

Counts

24 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)
(exp.f64 l)
(exp.f64 (neg.f64 l))
(exp.f64 (-.f64 #s(literal 0 binary64) l))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
(*.f64 (cos.f64 M) (-.f64 #s(literal 1 binary64) l))
(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
(cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 m K)) M))

Outputs
(exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64)))
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))

Calls

2 calls:

8.0ms	m
8.0ms	n

Results

Accuracy	Segments	Branch
78.1%	2	`n`
78.1%	2	`m`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes31.0ms (0.3%)

Memory

20.2MiB live, 57.9MiB allocated

Counts

22 → 3

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)
(exp.f64 l)
(exp.f64 (neg.f64 l))
(exp.f64 (-.f64 #s(literal 0 binary64) l))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
(*.f64 (cos.f64 M) (-.f64 #s(literal 1 binary64) l))
(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))

Outputs
(exp.f64 l)
(exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))
(exp.f64 (neg.f64 l))

Calls

4 calls:

9.0ms	M
7.0ms	m
7.0ms	n
7.0ms	l

Results

Accuracy	Segments	Branch
70.7%	3	`l`
51.3%	1	`M`
64.5%	3	`n`
51.3%	1	`m`

Compiler

Compiled 24 to 20 computations (16.7% saved)

regimes46.0ms (0.4%)

Memory

-9.4MiB live, 71.1MiB allocated

Counts

21 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)
(exp.f64 l)
(exp.f64 (neg.f64 l))
(exp.f64 (-.f64 #s(literal 0 binary64) l))
(exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) l))
(*.f64 (cos.f64 M) (-.f64 #s(literal 1 binary64) l))
(cos.f64 (.f64 m (.f64 #s(literal 1/2 binary64) K)))
(cos.f64 (.f64 n (.f64 #s(literal 1/2 binary64) K)))

Outputs
(exp.f64 l)
(exp.f64 (neg.f64 l))

Calls

6 calls:

10.0ms	n
8.0ms	M
7.0ms	m
7.0ms	K
7.0ms	l

Results

Accuracy	Segments	Branch
39.4%	2	`M`
39.4%	2	`m`
36.0%	1	`K`
36.0%	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))))))`
36.0%	1	`n`
52.1%	2	`l`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes33.0ms (0.3%)

Memory

-2.7MiB live, 74.2MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)
(exp.f64 l)

Outputs
(exp.f64 l)

Calls

6 calls:

6.0ms	m
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))))))
5.0ms	n
5.0ms	M
5.0ms	K

Results

Accuracy	Segments	Branch
27.8%	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))))))`
27.8%	1	`n`
27.8%	1	`K`
27.8%	1	`m`
27.8%	1	`M`
27.8%	1	`l`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes36.0ms (0.3%)

Memory

7.8MiB live, 52.2MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 M M) (fma.f64 M (.f64 M #s(literal 25/24 binary64)) #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 K K) (.f64 (*.f64 m m) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) l) #s(literal 0 binary64))
(fma.f64 M (.f64 M (fma.f64 (.f64 M M) (fma.f64 (*.f64 M M) #s(literal -331/720 binary64) #s(literal 25/24 binary64)) #s(literal -3/2 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 m m) (fma.f64 (.f64 m m) (fma.f64 (*.f64 m m) #s(literal -1/384 binary64) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 n n) (fma.f64 (.f64 n n) (fma.f64 #s(literal -1/384 binary64) (*.f64 n n) #s(literal 1/32 binary64)) #s(literal -1/4 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 K K) (.f64 (-.f64 #s(literal 1 binary64) l) (fma.f64 m (.f64 m #s(literal -1/8 binary64)) (.f64 (.f64 K K) (.f64 #s(literal 1/384 binary64) (.f64 (.f64 m m) (*.f64 m m)))))) (-.f64 #s(literal 1 binary64) l))
(cos.f64 M)

Outputs
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))

Calls

6 calls:

11.0ms	m
5.0ms	n
5.0ms	l
5.0ms	K
5.0ms	M

Results

Accuracy	Segments	Branch
11.1%	1	`l`
11.1%	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))))))`
11.1%	1	`m`
11.1%	1	`M`
11.1%	1	`K`
11.1%	1	`n`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes17.0ms (0.1%)

Memory

-4.0MiB live, 34.9MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))

Outputs
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))

Calls

6 calls:

4.0ms	n
3.0ms	K
3.0ms	M
3.0ms	m
3.0ms	l

Results

Accuracy	Segments	Branch
10.8%	1	`l`
10.8%	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))))))`
10.8%	1	`n`
10.8%	1	`m`
10.8%	1	`M`
10.8%	1	`K`

Compiler

Compiled 64 to 46 computations (28.1% saved)

regimes16.0ms (0.1%)

Memory

-6.4MiB live, 32.5MiB allocated

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) l)
(fma.f64 #s(literal -1/4 binary64) (*.f64 m m) #s(literal 1 binary64))
(fma.f64 #s(literal -1/4 binary64) (*.f64 n n) #s(literal 1 binary64))
(fma.f64 M (*.f64 M #s(literal -3/2 binary64)) #s(literal 1 binary64))

Outputs
#s(literal 1 binary64)

Calls

6 calls:

3.0ms	l
2.0ms	K
2.0ms	m
2.0ms	M
2.0ms	n

Results

Accuracy	Segments	Branch
8.9%	1	`l`
8.9%	1	`n`
8.9%	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))))))`
8.9%	1	`m`
8.9%	1	`K`
8.9%	1	`M`

Compiler

Compiled 64 to 46 computations (28.1% saved)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.0	0.09134039913951365

Compiler

Compiled 37 to 29 computations (21.6% saved)

bsearch31.0ms (0.3%)

Memory

14.2MiB live, 52.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	predicate-same
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	0.34685409963157204	66.78244588389622
19.0ms	-118872.56344129314	-2224.0348328041614

Samples

20.0ms	155×	0	valid
1.0ms	5×	1	valid

Compiler

Compiled 397 to 289 computations (27.2% saved)

Precisions

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

ival-sub: 3.0ms (18.3% of total)

ival-mult: 3.0ms (18.3% of total)

ival-div: 2.0ms (12.2% of total)

ival-pow2: 2.0ms (12.2% of total)

ival-cos: 2.0ms (12.2% of total)

ival-add: 1.0ms (6.1% of total)

ival-exp: 1.0ms (6.1% of total)

ival-neg: 1.0ms (6.1% of total)

ival-fabs: 1.0ms (6.1% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

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

bsearch31.0ms (0.3%)

Memory

10.2MiB live, 51.8MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	predicate-same
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	-5.221989563753256e-308	1.1608221308147955e-295
18.0ms	-281.56788293484317	-69.80627199975508

Samples

20.0ms	151×	0	valid
3.0ms	9×	1	valid

Compiler

Compiled 317 to 261 computations (17.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-sub: 6.0ms (35.3% of total)

ival-div: 2.0ms (11.8% of total)

ival-mult: 2.0ms (11.8% of total)

ival-pow2: 2.0ms (11.8% of total)

ival-add: 1.0ms (5.9% of total)

ival-exp: 1.0ms (5.9% of total)

ival-neg: 1.0ms (5.9% of total)

ival-cos: 1.0ms (5.9% of total)

ival-fabs: 1.0ms (5.9% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

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

bsearch40.0ms (0.3%)

Memory

-5.6MiB live, 71.1MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	predicate-same
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	-5.221989563753256e-308	1.1608221308147955e-295
17.0ms	-281.56788293484317	-69.80627199975508

Samples

25.0ms	195×	0	valid
4.0ms	13×	1	valid

Compiler

Compiled 375 to 315 computations (16% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-sub: 5.0ms (22.6% of total)

ival-exp: 4.0ms (18% of total)

ival-div: 3.0ms (13.5% of total)

ival-mult: 3.0ms (13.5% of total)

ival-pow2: 2.0ms (9% of total)

ival-cos: 2.0ms (9% of total)

ival-add: 1.0ms (4.5% of total)

adjust: 1.0ms (4.5% of total)

ival-neg: 1.0ms (4.5% of total)

ival-fabs: 1.0ms (4.5% of total)

exact: 0.0ms (0% of total)

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

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

bsearch24.0ms (0.2%)

Memory

8.0MiB live, 45.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
22.0ms	-69.80627199975508	-0.33015608886952463

Samples

11.0ms	95×	0	valid
5.0ms	16×	1	valid
0.0ms	1×	2	valid

Compiler

Compiled 205 to 169 computations (17.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 3.0ms (24.5% of total)

ival-div: 2.0ms (16.3% of total)

ival-mult: 2.0ms (16.3% of total)

adjust: 1.0ms (8.2% of total)

ival-exp: 1.0ms (8.2% of total)

ival-pow2: 1.0ms (8.2% of total)

ival-cos: 1.0ms (8.2% of total)

ival-neg: 1.0ms (8.2% of total)

ival-add: 1.0ms (8.2% of total)

ival-fabs: 1.0ms (8.2% of total)

exact: 0.0ms (0% of total)

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

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

bsearch51.0ms (0.4%)

Memory

7.1MiB live, 87.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
20.0ms	3.641124181716655e-20	7.046325090921548e-17
25.0ms	-7.751311213438375e+38	-6.035166694499595e+32

Samples

33.0ms	260×	0	valid
3.0ms	12×	1	valid

Compiler

Compiled 385 to 326 computations (15.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-sub: 6.0ms (21.8% of total)

ival-div: 6.0ms (21.8% of total)

ival-mult: 3.0ms (10.9% of total)

ival-pow2: 3.0ms (10.9% of total)

ival-add: 2.0ms (7.3% of total)

ival-exp: 2.0ms (7.3% of total)

ival-cos: 2.0ms (7.3% of total)

adjust: 1.0ms (3.6% of total)

ival-fabs: 1.0ms (3.6% of total)

ival-neg: 1.0ms (3.6% of total)

exact: 0.0ms (0% of total)

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

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

bsearch17.0ms (0.1%)

Memory

-27.3MiB live, 10.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
16.0ms	7.046325090921548e-17	1.1631585166382972e-10

Samples

11.0ms	1×	1	valid
4.0ms	31×	0	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-pow2: 11.0ms (81.5% of total)

ival-sub: 1.0ms (7.4% of total)

adjust: 0.0ms (0% of total)

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

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

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

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

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

ival-mult: 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)

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

simplify58.0ms (0.5%)

Memory

3.5MiB live, 41.8MiB allocated

Algorithm

1×	egg-herbie

Rules

264×	`distribute-lft-neg-in_binary64`
180×	`neg-mul-1_binary64`
166×	`neg-sub0_binary64`
146×	`sub-neg_binary64`
120×	`+-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	263
1	159	263
2	221	263
3	273	260
4	336	260
5	389	260
6	449	260
7	529	260
8	616	260
9	689	260
10	751	260
11	809	260
12	856	260
13	920	260
14	980	260
15	1013	260
16	1021	260

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (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 0 binary64)) (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) (/.f64 (fma.f64 m #s(literal -1/2 binary64) M) n) (fma.f64 m #s(literal -1/2 binary64) M)) n))))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l))))
(if (<=.f64 M #s(literal -2450 binary64)) (.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M)))) (if (<=.f64 M #s(literal 20 binary64)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m)) l))) (.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M))))))
(if (<=.f64 m #s(literal -70 binary64)) (exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64))) (if (<=.f64 m #s(literal 1930258305619341/96512915280967053581473992690523770832804036027976092508745841039385957511899636693935577250212251899331606800230413394637016647999665010865694713564271216355093681467326336557610944624945266886348613585697529348641399137222620343503047635864810732050328281646899590278784472758879901186078227762530329829839567060992 binary64)) (.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 n n))))))
(if (<=.f64 m #s(literal -70 binary64)) (exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64))) (if (<=.f64 m #s(literal 1930258305619341/48256457640483526790736996345261885416402018013988046254372920519692978755949818346967788625106125949665803400115206697318508323999832505432847356782135608177546840733663168278805472312472633443174306792848764674320699568611310171751523817932405366025164140823449795139392236379439950593039113881265164914919783530496 binary64)) (.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M)))) (exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))))
(if (<=.f64 m #s(literal -55 binary64)) (exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64))) (exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64)))))
(if (<=.f64 l #s(literal -610000000000000027329269893955584 binary64)) (exp.f64 l) (if (<=.f64 l #s(literal 1419768672255617/20282409603651670423947251286016 binary64)) (exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64)))) (exp.f64 (neg.f64 l))))
(if (<=.f64 l #s(literal 2028240960365167/20282409603651670423947251286016 binary64)) (exp.f64 l) (exp.f64 (neg.f64 l)))
(exp.f64 l)
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(*.f64 (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 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)))))
(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 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (-.f64 (neg.f64 (.f64 n (.f64 n (-.f64 #s(literal 1/4 binary64) (/.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) (/.f64 (fma.f64 m #s(literal -1/2 binary64) M) n) (fma.f64 m #s(literal -1/2 binary64) M)) n))))) (-.f64 l (fabs.f64 (-.f64 m n)))))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 n m) (+.f64 n m)) l))))
(if (<=.f64 (.f64 (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)))) (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M))) #s(literal 0 binary64)) (.f64 (cos.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) #s(literal 2 binary64)) M)) (exp.f64 (+.f64 (.f64 n (.f64 n (-.f64 (/.f64 (fma.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) m #s(literal 0 binary64)) M) (/.f64 (fma.f64 m #s(literal -1/2 binary64) M) n) (fma.f64 m #s(literal -1/2 binary64) M)) n) #s(literal 1/4 binary64)))) (-.f64 (fabs.f64 (-.f64 m n)) l)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 m n) (+.f64 m n)) l))))
(if (<=.f64 M #s(literal -2450 binary64)) (.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M)))) (if (<=.f64 M #s(literal 20 binary64)) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 n m) (+.f64 n m)) l))) (.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M))))))
(if (<=.f64 M #s(literal -2450 binary64)) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))) (if (<=.f64 M #s(literal 20 binary64)) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (fma.f64 #s(literal 1/4 binary64) (.f64 (+.f64 m n) (+.f64 m n)) l))) (exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 M M)))))
(if (<=.f64 m #s(literal -70 binary64)) (exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64))) (if (<=.f64 m #s(literal 1930258305619341/96512915280967053581473992690523770832804036027976092508745841039385957511899636693935577250212251899331606800230413394637016647999665010865694713564271216355093681467326336557610944624945266886348613585697529348641399137222620343503047635864810732050328281646899590278784472758879901186078227762530329829839567060992 binary64)) (.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M)))) (exp.f64 (-.f64 (fabs.f64 (-.f64 n m)) (.f64 #s(literal 1/4 binary64) (.f64 n n))))))
(if (<=.f64 m #s(literal -70 binary64)) (exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64))) (if (<=.f64 m #s(literal 1930258305619341/96512915280967053581473992690523770832804036027976092508745841039385957511899636693935577250212251899331606800230413394637016647999665010865694713564271216355093681467326336557610944624945266886348613585697529348641399137222620343503047635864810732050328281646899590278784472758879901186078227762530329829839567060992 binary64)) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))) (exp.f64 (-.f64 (fabs.f64 (-.f64 m n)) (.f64 #s(literal 1/4 binary64) (*.f64 n n))))))
(if (<=.f64 m #s(literal -70 binary64)) (exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64))) (if (<=.f64 m #s(literal 1930258305619341/48256457640483526790736996345261885416402018013988046254372920519692978755949818346967788625106125949665803400115206697318508323999832505432847356782135608177546840733663168278805472312472633443174306792848764674320699568611310171751523817932405366025164140823449795139392236379439950593039113881265164914919783530496 binary64)) (.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M)))) (exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64))))))
(if (<=.f64 m #s(literal -70 binary64)) (exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64))) (if (<=.f64 m #s(literal 1930258305619341/48256457640483526790736996345261885416402018013988046254372920519692978755949818346967788625106125949665803400115206697318508323999832505432847356782135608177546840733663168278805472312472633443174306792848764674320699568611310171751523817932405366025164140823449795139392236379439950593039113881265164914919783530496 binary64)) (exp.f64 (-.f64 #s(literal 0 binary64) (.f64 M M))) (exp.f64 (.f64 n (*.f64 n #s(literal -1/4 binary64))))))
(if (<=.f64 m #s(literal -55 binary64)) (exp.f64 (.f64 (.f64 m m) #s(literal -1/4 binary64))) (exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64)))))
(if (<=.f64 l #s(literal -610000000000000027329269893955584 binary64)) (exp.f64 l) (if (<=.f64 l #s(literal 1419768672255617/20282409603651670423947251286016 binary64)) (exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64)))) (exp.f64 (neg.f64 l))))
(if (<=.f64 l #s(literal -610000000000000027329269893955584 binary64)) (exp.f64 l) (if (<=.f64 l #s(literal 1419768672255617/20282409603651670423947251286016 binary64)) (exp.f64 (.f64 n (.f64 n #s(literal -1/4 binary64)))) (exp.f64 (-.f64 #s(literal 0 binary64) l))))
(if (<=.f64 l #s(literal 2028240960365167/20282409603651670423947251286016 binary64)) (exp.f64 l) (exp.f64 (neg.f64 l)))
(if (<=.f64 l #s(literal 2028240960365167/20282409603651670423947251286016 binary64)) (exp.f64 l) (exp.f64 (-.f64 #s(literal 0 binary64) l)))
(exp.f64 l)
(fma.f64 l (fma.f64 l (fma.f64 l #s(literal -1/6 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 l (fma.f64 l #s(literal 1/2 binary64) #s(literal -1 binary64)) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness1.2s (10%)

Memory

4.2MiB live, 1 084.2MiB allocated

Rules

13 686×	`accelerator-lowering-fma.f32`
13 686×	`accelerator-lowering-fma.f64`
13 228×	`accelerator-lowering-fma.f32`
13 228×	`accelerator-lowering-fma.f64`
10 890×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	978	12249
1	3100	11805
2	7237	11805
0	8664	11362
0	791	8019
1	2389	7510
2	7522	7510
0	8859	7162
0	405	3302
1	1220	3243
2	3733	3220
0	8309	3092
0	162	1470
1	439	1320
2	1451	1296
3	3733	1296
4	5476	1296
0	8479	1255
0	21	62
1	74	60
2	445	58
3	7096	58
0	9012	58

Stop Event

1×	fuel
1×	iter limit
1×	node 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 1 466 to 944 computations (35.6% saved)

preprocess81.0ms (0.7%)

Memory: 18.9MiB live, 216.1MiB allocated
Remove: (sort m n)
Compiler: Compiled 718 to 304 computations (57.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	77
1	47	75
2	87	75
3	133	75
4	218	75
5	262	75
6	317	75
7	367	75
8	406	75
9	410	75
0	410	75

Iter	Nodes	Cost
0	21	77
1	47	75
2	87	75
3	133	75
4	218	75
5	262	75
6	317	75
7	367	75
8	406	75
9	410	75
0	410	75

analyze4.0ms (0%)

sample1.6s (13.2%)

preprocess409.0ms (3.3%)

explain530.0ms (4.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify633.0ms (5.2%)

localize164.0ms (1.3%)

series18.0ms (0.1%)

rewrite648.0ms (5.3%)

simplify449.0ms (3.7%)

eval82.0ms (0.7%)

prune92.0ms (0.8%)

simplify284.0ms (2.3%)

localize362.0ms (3%)

series63.0ms (0.5%)

rewrite383.0ms (3.1%)

simplify629.0ms (5.1%)

eval326.0ms (2.7%)

prune230.0ms (1.9%)

simplify274.0ms (2.2%)

localize237.0ms (1.9%)

series72.0ms (0.6%)

rewrite524.0ms (4.3%)

simplify617.0ms (5%)

eval218.0ms (1.8%)

prune249.0ms (2%)

simplify18.0ms (0.2%)

localize84.0ms (0.7%)

series11.0ms (0.1%)

rewrite203.0ms (1.7%)

simplify470.0ms (3.8%)

eval96.0ms (0.8%)

prune135.0ms (1.1%)

regimes109.0ms (0.9%)

regimes98.0ms (0.8%)

regimes31.0ms (0.3%)

regimes87.0ms (0.7%)

regimes12.0ms (0.1%)

regimes18.0ms (0.1%)

regimes31.0ms (0.3%)

regimes46.0ms (0.4%)

regimes33.0ms (0.3%)

regimes36.0ms (0.3%)

regimes17.0ms (0.1%)

regimes16.0ms (0.1%)

bsearch1.0ms (0%)

bsearch31.0ms (0.3%)

bsearch31.0ms (0.3%)

bsearch40.0ms (0.3%)

bsearch24.0ms (0.2%)

bsearch51.0ms (0.4%)

bsearch17.0ms (0.1%)

simplify58.0ms (0.5%)

soundness1.2s (10%)

preprocess81.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	77
1	47	75
2	87	75
3	133	75
4	218	75
5	262	75
6	317	75
7	367	75
8	406	75
9	410	75
0	410	75