Metrics for Lanczos kernel

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze22.0ms (0.1%)

Memory

-6.0MiB live, 32.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0%	100%	0%	0%	0%	0
0%	0%	0%	100%	0%	0%	0%	1
50%	0%	0%	100%	0%	0%	0%	2
50%	0%	0%	100%	0%	0%	0%	3
75%	0%	0%	100%	0%	0%	0%	4
75%	0%	0%	100%	0%	0%	0%	5
87.5%	0%	0%	100%	0%	0%	0%	6
87.5%	0%	0%	100%	0%	0%	0%	7
93.7%	0%	0%	100%	0%	0%	0%	8
93.7%	0%	0%	100%	0%	0%	0%	9
96.9%	0%	0%	100%	0%	0%	0%	10
96.9%	0%	0%	100%	0%	0%	0%	11
98.4%	0%	0%	100%	0%	0%	0%	12

Compiler

Compiled 37 to 21 computations (43.2% saved)

sample1.7s (11.8%)

Memory

26.5MiB live, 1 820.3MiB allocated

Samples

1.3s

8 256×

valid

Precisions

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

ival-sin: 245.0ms (23.6% of total)

ival-mult: 198.0ms (19.1% of total)

ival-<=: 188.0ms (18.1% of total)

const: 176.0ms (17% of total)

ival-div: 120.0ms (11.6% of total)

ival-pi: 79.0ms (7.6% of total)

ival-and: 21.0ms (2% of total)

exact: 7.0ms (0.7% of total)

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

Bogosity

explain120.0ms (0.8%)

Memory

3.7MiB live, 221.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
2	-	1	(0.8471904397010803 4.7153167724609375)	`(sin.f32 (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`(PI.f32)`
0	-	0	-	`(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))`
0	-	0	-	`(.f32 (.f32 x (PI.f32)) tau)`
0	-	0	-	`(*.f32 x (PI.f32))`
0	-	0	-	`(sin.f32 (*.f32 x (PI.f32)))`
0	-	0	-	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
0	-	0	-	`tau`
0	-	0	-	`(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sin.f32`	`(sin.f32 (.f32 (.f32 x (PI.f32)) tau))`	cancellation	1	1

Confusion

	Predicted +	Predicted -
+	1	2
-	0	253

Precision

1.0

Recall

0.3333333333333333

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	1	1
-	0	0	253

Precision?

1.0

Recall?

0.6666666666666666

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

47.0ms

512×

valid

Compiler

Compiled 151 to 34 computations (77.5% saved)

Precisions

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

ival-sin: 12.0ms (36.1% of total)

ival-mult: 10.0ms (30.1% of total)

ival-div: 6.0ms (18% of total)

ival-pi: 4.0ms (12% of total)

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

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

preprocess75.0ms (0.5%)

Memory

-12.8MiB live, 64.3MiB allocated

Algorithm

1×	egg-herbie

Rules

1 192×	`neg-sub0`
1 146×	`neg-mul-1`
868×	`distribute-frac-neg`
794×	`associate-l`
772×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	123
1	88	123
2	415	107
3	2253	107
4	4724	107
5	6828	107
6	7824	107
0	10	21
0	18	21
1	31	21
2	88	21
3	296	21
4	699	21
5	1082	21
6	1115	21
7	1115	21
0	1115	21

Stop Event

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

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Outputs

(*.f32 (/.f32 (sin.f32 (*.f32 (*.f32 x (PI.f32)) tau)) (*.f32 (*.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))

(*.f32 (sin.f32 (*.f32 x (*.f32 (PI.f32) tau))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (*.f32 x (*.f32 (PI.f32) (*.f32 (PI.f32) tau))))))

Symmetry

(abs tau)

(abs x)

Compiler

Compiled 23 to 10 computations (56.5% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify24.0ms (0.2%)

Memory

12.6MiB live, 51.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f32 (.f32 x (PI.f32)) tau)
cost-diff	0	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
cost-diff	0	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Rules

598×	`times-frac`
578×	`lower-*.f64`
572×	`lower-*.f32`
540×	`lower-/.f64`
536×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	62
0	18	62
1	31	62
2	88	62
3	296	62
4	699	62
5	1082	62
6	1115	62
7	1115	62
0	1115	62

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
(.f32 (.f32 x (PI.f32)) tau)
(*.f32 x (PI.f32))
x
(PI.f32)
tau
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(sin.f32 (*.f32 x (PI.f32)))

Outputs
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))))
(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))
(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
(.f32 (.f32 x (PI.f32)) tau)
(.f32 x (.f32 (PI.f32) tau))
(*.f32 x (PI.f32))
x
(PI.f32)
tau
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(sin.f32 (*.f32 x (PI.f32)))

localize66.0ms (0.5%)

Memory

8.7MiB live, 49.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.33984375	(*.f32 x (PI.f32))
accuracy	0.3875440802111938	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.4170112793053261	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.4489250488422101	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))

Samples

21.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sin: 6.0ms (42.4% of total)

ival-mult: 4.0ms (28.3% of total)

ival-div: 3.0ms (21.2% of total)

ival-pi: 1.0ms (7.1% of total)

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

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

series58.0ms (0.4%)

Memory

6.8MiB live, 45.3MiB allocated

Counts

6 → 120

Calls

Call 1

Inputs
#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())
#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6)))))))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
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#s(alt (* tau (* x (PI))) (taylor inf tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor inf tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor inf tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2)))) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4)))))) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4))))))) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor 0 x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor 0 x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor 0 x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor 0 x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor -inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor -inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor -inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor -inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())

Calls

30 calls:

Time	Variable		Point	Expression
32.0ms	x	@	-inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
4.0ms	x	@	0	(/ (sin (* x (PI))) (* x (PI)))
3.0ms	tau	@	inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
2.0ms	x	@	0	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
2.0ms	x	@	inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))

simplify349.0ms (2.4%)

Memory

-15.8MiB live, 468.0MiB allocated

Algorithm

1×	egg-herbie

Rules

16 966×	`lower-fma.f64`
16 966×	`lower-fma.f32`
6 828×	`lower-+.f64`
6 828×	`lower-+.f32`
6 246×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	1582
1	620	1562
2	2413	1538
3	4145	1538
4	4880	1538
5	5560	1538
6	5950	1538
7	5981	1538
8	5981	1538
0	8826	1486

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
1
(+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 4)))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 6) (* (pow x 2) (pow (PI) 6)))) (* 1/120 (* (pow tau 4) (pow (PI) 4))))))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
1
(+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))
(+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4)))))))
(+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4))))))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(* tau (* x (PI)))
(* x (+ (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* 1/120 (* (pow tau 5) (* (pow x 2) (pow (PI) 5))))))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 7) (* (pow x 2) (pow (PI) 7)))) (* 1/120 (* (pow tau 5) (pow (PI) 5)))))))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))
(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))
(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
1
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4)))))))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(fma.f32 x (.f32 x (fma.f32 (.f32 x x) (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (fma.f32 #s(literal -1/720 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 tau tau)) (fma.f32 #s(literal -1/5040 binary32) (pow.f32 tau #s(literal 6 binary32)) #s(literal -1/5040 binary32))))) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))))) #s(literal 1 binary32))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 tau tau) (.f32 (sin.f32 (.f32 x (PI.f32))) (fma.f32 (.f32 (.f32 tau tau) #s(literal 1/120 binary32)) (.f32 (.f32 x x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 tau (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (sin.f32 (.f32 x (PI.f32))) (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/5040 binary32)) (.f32 (pow.f32 x #s(literal 5 binary32)) (pow.f32 (PI.f32) #s(literal 5 binary32))) (.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x x))) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
1
#s(literal 1 binary32)
(+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))
(fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (*.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 4)))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (*.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 6) (* (pow x 2) (pow (PI) 6)))) (* 1/120 (* (pow tau 4) (pow (PI) 4))))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (pow.f32 tau #s(literal 6 binary32)) (.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32))) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32))))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
1
#s(literal 1 binary32)
(+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))
(fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (*.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))
(+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4)))))))
(fma.f32 (.f32 tau tau) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (.f32 (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 (.f32 x x) (*.f32 x x))))) #s(literal 1 binary32))
(+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4))))))))
(fma.f32 (.f32 tau tau) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (fma.f32 (.f32 tau tau) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (pow.f32 x #s(literal 6 binary32))) #s(literal -1/5040 binary32)) (.f32 (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 (.f32 x x) (.f32 x x)))))) #s(literal 1 binary32))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* x (+ (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))
(.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (*.f32 tau (PI.f32))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* 1/120 (* (pow tau 5) (* (pow x 2) (pow (PI) 5))))))))
(.f32 x (fma.f32 (.f32 x x) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (.f32 (.f32 x (.f32 x (pow.f32 (PI.f32) #s(literal 5 binary32)))) (.f32 #s(literal 1/120 binary32) (pow.f32 tau #s(literal 5 binary32))))) (.f32 tau (PI.f32))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 7) (* (pow x 2) (pow (PI) 7)))) (* 1/120 (* (pow tau 5) (pow (PI) 5)))))))))
(.f32 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/5040 binary32) (.f32 (pow.f32 tau #s(literal 7 binary32)) (.f32 x (.f32 x (pow.f32 (PI.f32) #s(literal 7 binary32))))) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 tau #s(literal 5 binary32))))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))))) (*.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))
(.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) x)) (*.f32 x (PI.f32))))
(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))
(.f32 tau (fma.f32 x (PI.f32) (.f32 (.f32 tau tau) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (.f32 tau tau) (.f32 (pow.f32 x #s(literal 5 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) #s(literal 1/120 binary32))))))))
(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))
(.f32 tau (fma.f32 (.f32 tau tau) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 (.f32 tau tau) (fma.f32 (.f32 (pow.f32 (PI.f32) #s(literal 7 binary32)) (pow.f32 x #s(literal 7 binary32))) (.f32 (.f32 tau tau) #s(literal -1/5040 binary32)) (.f32 (pow.f32 x #s(literal 5 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) #s(literal 1/120 binary32)))))) (*.f32 x (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
1
#s(literal 1 binary32)
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))))
(fma.f32 (.f32 x x) (fma.f32 x (.f32 x (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4)))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))

rewrite192.0ms (1.3%)

Memory

-12.7MiB live, 377.7MiB allocated

Rules

4 760×	`lower-*.f64`
4 754×	`lower-*.f32`
3 316×	`lower-/.f64`
3 312×	`lower-/.f32`
1 604×	`frac-times`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53

Stop Event

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

Counts

6 → 670

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
(.f32 (.f32 x (PI.f32)) tau)
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(*.f32 x (PI.f32))

Outputs
(neg.f32 (.f32 (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))))
(neg.f32 (.f32 (neg.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (*.f32 x tau)))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (*.f32 x tau))))))
(neg.f32 (/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))))
(neg.f32 (/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (neg.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (*.f32 x (PI.f32)))))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
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(.f32 (.f32 x (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (.f32 x (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (PI.f32)) #s(literal 1 binary32)))
(*.f32 (neg.f32 (neg.f32 x)) (PI.f32))
(*.f32 (neg.f32 (neg.f32 (PI.f32))) x)
(.f32 (.f32 #s(literal 1 binary32) (*.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1 binary32)) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 2/9 binary32))) (pow.f32 (PI.f32) #s(literal 1/9 binary32)))
(.f32 (.f32 (*.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(.f32 (.f32 (*.f32 x (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(.f32 (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))

eval121.0ms (0.8%)

Memory: 13.8MiB live, 249.5MiB allocated
Compiler: Compiled 24 386 to 2 296 computations (90.6% saved)

prune189.0ms (1.3%)

Memory

31.8MiB live, 385.4MiB allocated

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	984	29	1 013
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	985	29	1 014

Accuracy

99.6%

Counts

1 014 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.2%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (PI.f32)))) (*.f32 (PI.f32) tau))
	68.2%	(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
	96.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (.f32 (.f32 (PI.f32) tau) (PI.f32)))
	97.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) (neg.f32 (*.f32 x (PI.f32)))))
	96.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) #s(literal -1 binary32)) (.f32 x (.f32 (neg.f32 x) (/.f32 (.f32 (PI.f32) tau) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))))
▶	97.1%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
	97.4%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	95.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 tau (cbrt.f32 (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32))))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (*.f32 x (sqrt.f32 (PI.f32)))))))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	70.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
▶	97.4%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
	97.3%	(.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))))
	79.7%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	84.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	79.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	63.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	96.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
▶	62.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 400 to 774 computations (44.7% saved)

simplify152.0ms (1%)

Memory

-26.6MiB live, 97.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x))
cost-diff	192	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
cost-diff	352	(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau))
cost-diff	0	(.f32 (.f32 x tau) (PI.f32))
cost-diff	0	(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
cost-diff	0	(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
cost-diff	0	(.f32 x (.f32 tau (PI.f32)))
cost-diff	0	(sin.f32 (.f32 x (.f32 tau (PI.f32))))
cost-diff	0	(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
cost-diff	0	(*.f32 x (PI.f32))
cost-diff	0	(sin.f32 (*.f32 x (PI.f32)))
cost-diff	0	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))

Rules

2 088×	`lower-*.f64`
2 050×	`lower-*.f32`
1 456×	`associate-*r/`
1 386×	`times-frac`
1 318×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	387
0	78	385
1	152	383
2	361	383
3	1257	383
4	3513	383
5	3572	383
6	3574	383
7	3574	383
8	4207	383
9	4257	383
10	4257	383
11	4257	383
12	4755	383
13	4806	383
14	4806	383
0	4806	383

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
x
(PI.f32)
(.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(*.f32 x tau)
tau
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(literal 1 binary32)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(.f32 x (.f32 tau (PI.f32)))
x
(*.f32 tau (PI.f32))
tau
(PI.f32)
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
(.f32 (.f32 x x) tau)
(*.f32 x x)
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
(.f32 (.f32 x tau) (PI.f32))
(*.f32 x tau)
x
tau
(PI.f32)
(.f32 (.f32 x (PI.f32)) tau)
(*.f32 x (PI.f32))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(sin.f32 (*.f32 x (PI.f32)))
(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(PI.f32)
(*.f32 x tau)
x
tau
(/.f32 (sin.f32 (*.f32 x (PI.f32))) x)
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
(/.f32 #s(literal 1 binary32) tau)
#s(literal 1 binary32)
(.f32 (PI.f32) (.f32 x (PI.f32)))

Outputs
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 x (*.f32 x (PI.f32))))))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
x
(PI.f32)
(.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
(.f32 (PI.f32) (.f32 x tau))
(.f32 x (.f32 (PI.f32) tau))
(*.f32 x tau)
tau
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(literal 1 binary32)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
(.f32 x (.f32 tau (PI.f32)))
(.f32 x (.f32 (PI.f32) tau))
x
(*.f32 tau (PI.f32))
(*.f32 (PI.f32) tau)
tau
(PI.f32)
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 x (*.f32 x (PI.f32))))))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
(.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))))
(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
(.f32 (PI.f32) (.f32 x (*.f32 x tau)))
(.f32 (.f32 x x) tau)
(.f32 x (.f32 x tau))
(*.f32 x x)
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))))))
(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))
(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
(.f32 (.f32 x tau) (PI.f32))
(.f32 x (.f32 (PI.f32) tau))
(*.f32 x tau)
x
tau
(PI.f32)
(.f32 (.f32 x (PI.f32)) tau)
(.f32 x (.f32 (PI.f32) tau))
(*.f32 x (PI.f32))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(sin.f32 (*.f32 x (PI.f32)))
(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))))))
(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau))
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x tau)))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) x)
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
(.f32 (PI.f32) (.f32 x tau))
(.f32 x (.f32 (PI.f32) tau))
(PI.f32)
(*.f32 x tau)
x
tau
(/.f32 (sin.f32 (*.f32 x (PI.f32))) x)
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
(/.f32 #s(literal 1 binary32) tau)
#s(literal 1 binary32)
(.f32 (PI.f32) (.f32 x (PI.f32)))

localize138.0ms (1%)

Memory

39.1MiB live, 224.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.356132519536884	(.f32 (PI.f32) (.f32 x (PI.f32)))
accuracy	0.37890625	(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau))
accuracy	0.3875440802111938	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.4333000488422101	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
accuracy	0.34994125976844204	(.f32 (.f32 x tau) (PI.f32))
accuracy	0.3875440802111938	(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
accuracy	0.4170112793053261	(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.4489250488422101	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.3671875	(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
accuracy	0.3875440802111938	(sin.f32 (.f32 x (.f32 tau (PI.f32))))
accuracy	0.40462875976844204	(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
accuracy	0.4137687988422101	(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
accuracy	11.957966200324464	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
accuracy	0.34994125976844204	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.35775375976844204	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
accuracy	0.3875440802111938	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.4137687988422101	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))

Samples

78.0ms

256×

valid

Compiler

Compiled 365 to 39 computations (89.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-mult: 31.0ms (49.7% of total)

ival-sin: 19.0ms (30.5% of total)

ival-div: 11.0ms (17.6% of total)

ival-pi: 1.0ms (1.6% of total)

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

exact: 0.0ms (0% of total)

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

series53.0ms (0.4%)

Memory

-22.0MiB live, 59.5MiB allocated

Counts

23 → 504

Calls

Call 1

Inputs
#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 x (PI.f32))) (patch (sin.f32 (.f32 x (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())
#s(alt #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32)) (patch #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))) (patch #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))) #<representation binary32>) () ())
#s(alt (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))) (patch (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (patch (sin.f32 (.f32 x (.f32 tau (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 x (.f32 tau (PI.f32))) (patch (.f32 x (.f32 tau (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (patch (sin.f32 (.f32 (.f32 x tau) (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 x tau) (PI.f32)) (patch (.f32 (.f32 x tau) (PI.f32)) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (patch (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) #<representation binary32>) () ())
#s(alt (/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (.f32 x (PI.f32)))) (patch (/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (patch (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (.f32 x tau)) (patch (.f32 (PI.f32) (.f32 x tau)) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (patch (.f32 (.f32 (.f32 x x) tau) (PI.f32)) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (patch (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6)))))))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
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#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (.f32 x tau)) (patch (.f32 (PI.f32) (.f32 x tau)) #<representation binary32>) () ())) ())
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#s(alt (* tau (* x (PI))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 x tau)) (patch (.f32 (PI.f32) (.f32 x tau)) #<representation binary32>) () ())) ())
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#s(alt (* tau (* (pow x 2) (PI))) (taylor 0 x) (#s(alt (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (patch (.f32 (.f32 (.f32 x x) tau) (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (PI))) (taylor 0 x) (#s(alt (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (patch (.f32 (.f32 (.f32 x x) tau) (PI.f32)) #<representation binary32>) () ())) ())
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#s(alt (* tau (* (pow x 2) (PI))) (taylor inf x) (#s(alt (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (patch (.f32 (.f32 (.f32 x x) tau) (PI.f32)) #<representation binary32>) () ())) ())
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#s(alt (* tau (* (pow x 2) (PI))) (taylor inf x) (#s(alt (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (patch (.f32 (.f32 (.f32 x x) tau) (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (PI))) (taylor inf x) (#s(alt (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (patch (.f32 (.f32 (.f32 x x) tau) (PI.f32)) #<representation binary32>) () ())) ())
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#s(alt (* tau (* (pow x 2) (PI))) (taylor -inf x) (#s(alt (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (patch (.f32 (.f32 (.f32 x x) tau) (PI.f32)) #<representation binary32>) () ())) ())
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#s(alt (* tau (* (pow x 2) (PI))) (taylor -inf tau) (#s(alt (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (patch (.f32 (.f32 (.f32 x x) tau) (PI.f32)) #<representation binary32>) () ())) ())
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#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (patch (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (patch (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (patch (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (patch (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (patch (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #<representation binary32>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2)))) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4)))))) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4))))))) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
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#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor 0 x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor 0 x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor 0 x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor 0 x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (pow (PI) 2)) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())

Calls

126 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau))
1.0ms	tau	@	0	(/ (sin (* x (PI))) (* x (* (PI) (* (PI) (* x tau)))))
1.0ms	x	@	0	(* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau))
1.0ms	tau	@	-inf	(* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau))
1.0ms	x	@	inf	(* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau))

simplify676.0ms (4.7%)

Memory

-269.6MiB live, 631.2MiB allocated

Algorithm

1×	egg-herbie

Rules

22 998×	`lower-fma.f64`
22 998×	`lower-fma.f32`
7 622×	`lower-+.f64`
7 622×	`lower-+.f32`
6 936×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	353	7746
1	1176	7578
2	4481	7362
0	8501	7127

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 504

Calls

Call 1

Inputs
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1 (* tau (* x (PI))))
(/ (+ (* -1/6 (/ (* (pow x 2) (PI)) tau)) (/ 1 (* tau (PI)))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (/ (PI) tau)) (* 1/120 (/ (* (pow x 2) (pow (PI) 3)) tau)))) (/ 1 (* tau (PI)))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (/ (PI) tau)) (* (pow x 2) (+ (* -1/5040 (/ (* (pow x 2) (pow (PI) 5)) tau)) (* 1/120 (/ (pow (PI) 3) tau)))))) (/ 1 (* tau (PI)))) x)
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(* x (PI))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
(* tau (* (pow x 2) (pow (PI) 2)))
1
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4)))))))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (fma.f32 #s(literal -1/720 binary32) (fma.f32 tau tau (.f32 (.f32 tau tau) (.f32 tau tau))) (fma.f32 #s(literal -1/5040 binary32) (pow.f32 tau #s(literal 6 binary32)) #s(literal -1/5040 binary32)))) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 tau tau) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 tau tau) (.f32 (sin.f32 (.f32 x (PI.f32))) (fma.f32 (.f32 (.f32 tau tau) #s(literal 1/120 binary32)) (.f32 x (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 tau (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (sin.f32 (.f32 x (PI.f32))) (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/5040 binary32)) (.f32 (pow.f32 x #s(literal 5 binary32)) (pow.f32 (PI.f32) #s(literal 5 binary32))) (.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x x))) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 tau (.f32 x (PI.f32))))
(/ (+ (* -1/6 (/ (* (pow x 2) (PI)) tau)) (/ 1 (* tau (PI)))) x)
(/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32)))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (/ (PI) tau)) (* 1/120 (/ (* (pow x 2) (pow (PI) 3)) tau)))) (/ 1 (* tau (PI)))) x)
(/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32)))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (/ (PI) tau)) (* (pow x 2) (+ (* -1/5040 (/ (* (pow x 2) (pow (PI) 5)) tau)) (* 1/120 (/ (pow (PI) 3) tau)))))) (/ 1 (* tau (PI)))) x)
(/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (/.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) tau) #s(literal -1/5040 binary32)) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) tau)) (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32)))) x)
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(* x (PI))
(*.f32 x (PI.f32))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(.f32 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 5 binary32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
(.f32 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 7 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 5 binary32)))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))))) (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
1
#s(literal 1 binary32)
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
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(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 tau (.f32 x (*.f32 x (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
1
#s(literal 1 binary32)
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4)))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))

rewrite239.0ms (1.6%)

Memory

13.5MiB live, 402.0MiB allocated

Rules

4 232×	`lower-*.f64`
4 194×	`lower-*.f32`
3 934×	`lower-/.f64`
3 922×	`lower-/.f32`
1 500×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	284
0	78	280
1	230	280
2	1269	262
3	7138	262
0	8042	262

Stop Event

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

Counts

23 → 1 768

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(.f32 x (.f32 tau (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
(.f32 (.f32 x tau) (PI.f32))
(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau))
(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(.f32 (PI.f32) (.f32 x (PI.f32)))

Outputs
(neg.f32 (neg.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x)))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (neg.f32 x))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (*.f32 x tau)))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))))
(neg.f32 (.f32 (/.f32 #s(literal -1 binary32) tau) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))))))
(neg.f32 (.f32 #s(literal 1 binary32) (neg.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))))))
(neg.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) (neg.f32 x)))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau))))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (neg.f32 x))))
(neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))))
(neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (neg.f32 x))) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))
(neg.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) (neg.f32 x))))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32)))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(neg.f32 (/.f32 #s(literal -1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))))
(neg.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 x (PI.f32))))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (neg.f32 x)))) (.f32 (PI.f32) (*.f32 x tau))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (neg.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x)))) (neg.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (/.f32 (.f32 x (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))) x))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 x (PI.f32)))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))) tau)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) tau) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 x (*.f32 x (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))))))
(/.f32 #s(literal 1 binary32) (/.f32 tau (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (.f32 x (PI.f32)) (*.f32 x (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 x (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x tau) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (*.f32 x (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x)) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x)) (neg.f32 (.f32 tau (.f32 (PI.f32) (*.f32 (PI.f32) (neg.f32 x))))))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x)) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) (neg.f32 x))) (neg.f32 tau)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x tau))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
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(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) (neg.f32 x))) #s(literal 1 binary32)))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (/.f32 #s(literal 1 binary32) (PI.f32))))
(neg.f32 (.f32 #s(literal 1 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) (neg.f32 x)))))
(neg.f32 (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (neg.f32 x)) (PI.f32)))
(neg.f32 (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) x) (neg.f32 (PI.f32))))
(neg.f32 (/.f32 #s(literal -1 binary32) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (neg.f32 x))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 (PI.f32) (neg.f32 x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) (neg.f32 x))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (PI.f32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (sqrt.f32 (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (cbrt.f32 (PI.f32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #s(literal 1 binary32))
(/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) x) (PI.f32))
(/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) x) (neg.f32 (neg.f32 (PI.f32))))
(/.f32 #s(literal -1 binary32) (/.f32 (.f32 (PI.f32) (neg.f32 x)) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (neg.f32 x)))
(/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)) x)
(/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (neg.f32 (PI.f32))) (neg.f32 x))
(/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (neg.f32 x)) (neg.f32 (PI.f32)))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (cbrt.f32 (PI.f32)))
(/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 x (sin.f32 (*.f32 x (PI.f32)))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 x (cbrt.f32 (PI.f32))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (sqrt.f32 (PI.f32))) (.f32 x (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (sqrt.f32 (PI.f32))))) (neg.f32 (sqrt.f32 (PI.f32))))
(/.f32 (neg.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))))) (neg.f32 (cbrt.f32 (PI.f32))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) #s(literal 1 binary32)) (neg.f32 (PI.f32)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) #s(literal 1 binary32)) x)
(/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32))))) (sqrt.f32 (PI.f32)))
(/.f32 (.f32 #s(literal 1 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))))) (cbrt.f32 (PI.f32)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (/.f32 #s(literal 1 binary32) x)) (cbrt.f32 (PI.f32)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) x)) (sqrt.f32 (PI.f32)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) #s(literal 1 binary32)) (cbrt.f32 (PI.f32)))
(/.f32 (.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 (neg.f32 x) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 x (cbrt.f32 (PI.f32))))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 x (sqrt.f32 (PI.f32))))) (sqrt.f32 (PI.f32)))
(.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))
(.f32 #s(literal 1 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))) #s(literal 1 binary32))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 #s(literal -1 binary32) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) (neg.f32 x))))
(.f32 (neg.f32 (sin.f32 (.f32 x (PI.f32)))) (/.f32 #s(literal -1 binary32) (*.f32 x (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (sin.f32 (*.f32 x (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (pow.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (*.f32 x (PI.f32)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (/.f32 #s(literal 1 binary32) x))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 x)) (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) x))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (/.f32 #s(literal 1 binary32) (*.f32 x (cbrt.f32 (PI.f32)))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (cbrt.f32 (PI.f32)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (*.f32 x (sqrt.f32 (PI.f32)))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (sqrt.f32 (PI.f32)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (sqrt.f32 (PI.f32))))
(.f32 (/.f32 #s(literal -1 binary32) (.f32 x (PI.f32))) (neg.f32 (sin.f32 (*.f32 x (PI.f32)))))
(.f32 (pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) #s(literal -1/2 binary32)) (pow.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32)))) #s(literal -1/2 binary32)))
(neg.f32 (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))
(-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (PI.f32)))))
(/.f32 (.f32 (PI.f32) (.f32 x (PI.f32))) #s(literal 1 binary32))
(/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))) #s(literal -1 binary32))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(.f32 (PI.f32) (.f32 x (PI.f32)))
(.f32 (.f32 x (PI.f32)) (PI.f32))
(.f32 (.f32 x (PI.f32)) (neg.f32 (neg.f32 (PI.f32))))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 (.f32 (PI.f32) (*.f32 x (PI.f32))) #s(literal 1 binary32))
(.f32 #s(literal -1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (neg.f32 x))))
(.f32 (cbrt.f32 (PI.f32)) (.f32 (*.f32 x (PI.f32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (*.f32 x (PI.f32)) (cbrt.f32 (PI.f32))))
(.f32 (.f32 (PI.f32) (PI.f32)) x)
(.f32 (sqrt.f32 (PI.f32)) (.f32 (*.f32 x (PI.f32)) (sqrt.f32 (PI.f32))))
(.f32 (.f32 (PI.f32) (neg.f32 x)) (neg.f32 (PI.f32)))
(.f32 (neg.f32 (PI.f32)) (.f32 (PI.f32) (neg.f32 x)))
(.f32 (.f32 (*.f32 x (PI.f32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 x (PI.f32)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 x (PI.f32)) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (neg.f32 (neg.f32 (PI.f32))) (.f32 x (PI.f32)))

eval219.0ms (1.5%)

Memory: 49.8MiB live, 423.5MiB allocated
Compiler: Compiled 64 911 to 3 363 computations (94.8% saved)

prune689.0ms (4.7%)

Memory

-4.6MiB live, 937.8MiB allocated

Pruning

50 alts after pruning (48 fresh and 2 done)

	Pruned	Kept	Total
New	2 660	32	2 692
Fresh	8	16	24
Picked	3	2	5
Done	0	0	0
Total	2 671	50	2 721

Accuracy

99.7%

Counts

2 721 → 50

Alt Table

Click to see full alt table

Status	Accuracy	Program
	68.1%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 x tau) #s(literal 2 binary32))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
	68.2%	(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
	68.1%	(/.f32 (.f32 (/.f32 (.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (/.f32 #s(literal 1 binary32) x)) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
	96.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (.f32 (.f32 (PI.f32) tau) (PI.f32)))
	97.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) (neg.f32 (*.f32 x (PI.f32)))))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
	96.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) #s(literal -1 binary32)) (.f32 x (.f32 (neg.f32 x) (/.f32 (.f32 (PI.f32) tau) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))))
▶	97.3%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))
	97.0%	(/.f32 (.f32 (.f32 (sin.f32 (/.f32 (.f32 x (PI.f32)) (/.f32 #s(literal 1 binary32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (.f32 x (PI.f32))))
	96.7%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (.f32 x (PI.f32))))
	84.4%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
▶	97.4%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	63.4%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (.f32 x (PI.f32))))
	78.1%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
▶	62.5%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	97.1%	(.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 x (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	95.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 tau (cbrt.f32 (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (*.f32 x (sqrt.f32 (PI.f32)))))))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	70.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	84.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	84.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	70.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x)))))) (neg.f32 (sin.f32 (.f32 x (PI.f32)))))
▶	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (.f32 (PI.f32) tau) (.f32 x (PI.f32))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
	84.7%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	97.3%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	95.9%	(.f32 (exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	79.7%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	90.3%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	84.6%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	84.1%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	79.1%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	96.8%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
	63.4%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	97.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
✓	96.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
▶	84.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	70.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
✓	62.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 2 506 to 1 415 computations (43.5% saved)

simplify379.0ms (2.6%)

Memory

42.0MiB live, 129.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32))))
cost-diff	0	(/.f32 #s(literal 1 binary32) x)
cost-diff	192	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))
cost-diff	352	(.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32)))))
cost-diff	0	(.f32 (PI.f32) (.f32 x tau))
cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))
cost-diff	0	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
cost-diff	0	(.f32 x (.f32 tau (PI.f32)))
cost-diff	0	(sin.f32 (.f32 x (.f32 tau (PI.f32))))
cost-diff	0	(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
cost-diff	0	(*.f32 (PI.f32) (PI.f32))
cost-diff	0	(.f32 x (.f32 (PI.f32) (PI.f32)))
cost-diff	0	#s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))
cost-diff	0	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
cost-diff	0	(.f32 (PI.f32) (.f32 x tau))
cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))

Rules

4 012×	`lower-*.f64`
3 966×	`lower-*.f32`
2 644×	`associate-*r/`
1 732×	`associate-r`
1 502×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	528
0	97	512
1	201	506
2	535	506
3	1988	501
4	2231	501
5	2241	501
6	2253	501
7	2258	501
8	2266	501
9	3903	501
10	3904	501
11	3904	501
12	4041	501
13	4041	501
14	4437	501
15	4461	501
16	4461	501
17	5002	501
18	5002	501
19	5002	501
20	5006	501
21	5006	501
22	5006	501
23	6479	501
24	6870	501
25	6870	501
26	6882	501
27	6882	501
28	6914	501
0	6914	496

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(PI.f32)
(*.f32 x tau)
x
tau
(*.f32 x (PI.f32))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau)))
(sin.f32 (*.f32 x (PI.f32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))
(.f32 x (.f32 (PI.f32) (PI.f32)))
x
(*.f32 (PI.f32) (PI.f32))
(PI.f32)
(.f32 (PI.f32) (.f32 x (PI.f32)))
(*.f32 x (PI.f32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(.f32 x (.f32 tau (PI.f32)))
x
(*.f32 tau (PI.f32))
tau
(PI.f32)
(/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))
#s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32))))
(.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))
(fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32))
(.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))
(*.f32 (PI.f32) (PI.f32))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(*.f32 x x)
#s(literal -1/6 binary32)
(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
(.f32 (.f32 x x) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(PI.f32)
(*.f32 x tau)
x
tau
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
(.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))
(.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32)))))
(/.f32 #s(literal 1 binary32) x)
#s(literal 1 binary32)
x
(.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32))))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
(PI.f32)
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(*.f32 x tau)
tau
(*.f32 (PI.f32) tau)

Outputs
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) x)))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 (PI.f32) x))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(PI.f32)
(*.f32 x tau)
x
tau
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (*.f32 x tau)))
(sin.f32 (*.f32 x (PI.f32)))
(sin.f32 (*.f32 (PI.f32) x))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) x)))
#s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))
#s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x)))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(.f32 (PI.f32) (.f32 (PI.f32) x))
x
(*.f32 (PI.f32) (PI.f32))
(PI.f32)
(.f32 (PI.f32) (.f32 x (PI.f32)))
(.f32 (PI.f32) (.f32 (PI.f32) x))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 (PI.f32) (fma.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (PI.f32) (.f32 x x)))) x)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (*.f32 (PI.f32) x)))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 (PI.f32) (fma.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (PI.f32) (.f32 x x)))) x)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (*.f32 (PI.f32) x))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 x (.f32 tau (PI.f32)))
(.f32 (PI.f32) (.f32 x tau))
x
(*.f32 tau (PI.f32))
(*.f32 (PI.f32) tau)
tau
(PI.f32)
(/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))
(/.f32 #s(approx (sin (* x (PI))) (.f32 (PI.f32) (fma.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (PI.f32) (.f32 x x)))) x))) (.f32 (.f32 x tau) (.f32 (PI.f32) (*.f32 (PI.f32) x))))
#s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32))))
#s(approx (sin (* x (PI))) (.f32 (PI.f32) (fma.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (PI.f32) (*.f32 x x)))) x)))
(.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))
(.f32 (PI.f32) (fma.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (PI.f32) (*.f32 x x)))) x))
(fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32))
(fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 x x))) (PI.f32))
(.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))
(*.f32 (PI.f32) (PI.f32))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(*.f32 x x)
#s(literal -1/6 binary32)
(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
(.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) x)))
(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
(.f32 (PI.f32) (.f32 x (*.f32 x tau)))
(.f32 (.f32 x x) tau)
(.f32 x (.f32 x tau))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) x)))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 (PI.f32) x)))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(PI.f32)
(*.f32 x tau)
x
tau
(sin.f32 (*.f32 x (PI.f32)))
(sin.f32 (*.f32 (PI.f32) x))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) x)))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau)))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) x)))))
(.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32)))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 x x))))
(/.f32 #s(literal 1 binary32) x)
#s(literal 1 binary32)
x
(.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))
(sin.f32 (*.f32 x (PI.f32)))
(sin.f32 (*.f32 (PI.f32) x))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(PI.f32)
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 (PI.f32) x))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(*.f32 x tau)
tau
(*.f32 (PI.f32) tau)

localize362.0ms (2.5%)

Memory

-22.5MiB live, 244.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.33984375	(*.f32 x (PI.f32))
accuracy	0.349941259768442	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.38754408021119385	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.40529252930532605	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))
accuracy	0.349941259768442	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.35775375976844204	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
accuracy	0.38754408021119385	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.42453007814753607	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
accuracy	0.4137687988422101	(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
accuracy	0.41796875	(.f32 (.f32 x x) #s(literal -1/6 binary32))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	4.46038070697027	#s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32))))
accuracy	0.356132519536884	(.f32 (PI.f32) (.f32 x (PI.f32)))
accuracy	0.4333000488422101	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	11.622782297165104	#s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))
accuracy	0.33984375	(*.f32 x (PI.f32))
accuracy	0.349941259768442	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.38754408021119385	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.4287300293053261	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))

Samples

267.0ms

256×

valid

Compiler

Compiled 438 to 51 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 161.0ms

ival-mult: 128.0ms (79.5% of total)

ival-div: 14.0ms (8.7% of total)

ival-sin: 13.0ms (8.1% of total)

const: 4.0ms (2.5% of total)

ival-pi: 1.0ms (0.6% of total)

ival-add: 1.0ms (0.6% of total)

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

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

exact: 0.0ms (0% of total)

series51.0ms (0.4%)

Memory

10.6MiB live, 47.0MiB allocated

Counts

23 → 456

Calls

Call 1

Inputs
#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (patch (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (.f32 x tau)) (patch (.f32 (PI.f32) (.f32 x tau)) #<representation binary32>) () ())
#s(alt (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32)))) (patch (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (patch #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 x (.f32 (PI.f32) (PI.f32))) (patch (.f32 x (.f32 (PI.f32) (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (PI.f32)) (patch (.f32 (PI.f32) (PI.f32)) #<representation binary32>) () ())
#s(alt #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))) (patch #s(approx ( (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))) #<representation binary32>) () ())
#s(alt (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))) (patch (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (patch (sin.f32 (.f32 x (.f32 tau (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 x (.f32 tau (PI.f32))) (patch (.f32 x (.f32 tau (PI.f32))) #<representation binary32>) () ())
#s(alt (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (patch (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #<representation binary32>) () ())
#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())
#s(alt (/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (.f32 (PI.f32) tau)) (patch (/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (.f32 (PI.f32) tau)) #<representation binary32>) () ())
#s(alt (/.f32 #s(literal 1 binary32) x) (patch (/.f32 #s(literal 1 binary32) x) #<representation binary32>) () ())
#s(alt (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (.f32 x (PI.f32))) (patch (.f32 (PI.f32) (.f32 x (PI.f32))) #<representation binary32>) () ())
#s(alt #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (patch #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6)))))))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())) ())
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#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor inf x) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor -inf x) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor -inf x) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor -inf x) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor -inf x) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (* (PI) (sin (* x (PI)))))) (taylor 0 tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))) (* x (* (PI) (sin (* x (PI))))))) (taylor 0 tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* x (* (PI) (sin (* x (PI))))) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))))))) (taylor 0 tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* x (* (PI) (sin (* x (PI))))) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (* (pow (PI) 7) (sin (* x (PI))))))) (* 1/120 (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI)))))))))))) (taylor 0 tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor inf tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor inf tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor inf tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor inf tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor -inf tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor -inf tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor -inf tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (taylor -inf tau) (#s(alt (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (* tau (PI)) (taylor 0 x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (* -1/6 (* (pow tau 3) (pow (PI) 3)))))) (taylor 0 x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (* 1/36 (* (pow tau 3) (pow (PI) 5)))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (+ (* 1/36 (* (pow tau 3) (pow (PI) 5))) (* (pow x 2) (+ (* -1/720 (* (pow tau 3) (pow (PI) 7))) (+ (* -1/720 (* (pow tau 5) (pow (PI) 7))) (+ (* -1/5040 (* tau (pow (PI) 7))) (* -1/5040 (* (pow tau 7) (pow (PI) 7))))))))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor inf x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor inf x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor inf x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor inf x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor -inf x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor -inf x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor -inf x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor -inf x) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* tau (sin (* x (PI)))) x) (taylor 0 tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* -1/6 (* (pow tau 2) (* x (* (pow (PI) 2) (sin (* x (PI))))))) (/ (sin (* x (PI))) x))) (taylor 0 tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* (pow tau 2) (+ (* -1/6 (* x (* (pow (PI) 2) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 4) (sin (* x (PI))))))))) (/ (sin (* x (PI))) x))) (taylor 0 tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* (pow tau 2) (+ (* -1/6 (* x (* (pow (PI) 2) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 6) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 4) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) x))) (taylor 0 tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor inf tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor inf tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor inf tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor inf tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor -inf tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor -inf tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor -inf tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI))) (taylor -inf tau) (#s(alt (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) #<representation binary32>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (.f32 (PI.f32) tau)) (patch (/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (.f32 (PI.f32) tau)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))) (taylor 0 x) (#s(alt (/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (.f32 (PI.f32) tau)) (patch (/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (.f32 (PI.f32) tau)) #<representation binary32>) () ())) ())
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#s(alt (* tau (* x (pow (PI) 2))) (taylor 0 x) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())) ())

Calls

114 calls:

Time	Variable		Point	Expression
7.0ms	x	@	inf	(* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))))
1.0ms	tau	@	0	(* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))))
1.0ms	x	@	0	(* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))))
1.0ms	x	@	-inf	(/ (sin (* (PI) (* x tau))) (* x (PI)))
1.0ms	tau	@	inf	(* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))))

simplify686.0ms (4.7%)

Memory

-4.3MiB live, 401.0MiB allocated

Algorithm

1×	egg-herbie

Rules

18 578×	`lower-fma.f64`
18 578×	`lower-fma.f32`
7 796×	`lower-*.f64`
7 796×	`lower-*.f32`
5 128×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	436	7698
1	1496	7470
2	5781	7192
0	8049	6951

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 454

Calls

Call 1

Inputs
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
tau
(+ tau (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 2)))))
(+ tau (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 2))) (* 1/120 (* (pow tau 5) (* (pow x 2) (pow (PI) 4)))))))
(+ tau (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 2))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 7) (* (pow x 2) (pow (PI) 6)))) (* 1/120 (* (pow tau 5) (pow (PI) 4))))))))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
tau
(* tau (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))))
(* tau (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4))))))))
(* tau (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4)))))))))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(/ (sin (* tau (* x (PI)))) (* x (PI)))
(* tau (* x (PI)))
(* x (+ (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* 1/120 (* (pow tau 5) (* (pow x 2) (pow (PI) 5))))))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 7) (* (pow x 2) (pow (PI) 7)))) (* 1/120 (* (pow tau 5) (pow (PI) 5)))))))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))
(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))
(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(* x (pow (PI) 2))
(* x (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 4))) (* -1/6 (pow (PI) 4)))) (pow (PI) 2)))
(* x (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 4))) (+ (* -1/6 (pow (PI) 4)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 6))) (+ (* 1/120 (pow (PI) 6)) (* 1/36 (* (pow tau 2) (pow (PI) 6))))))))) (pow (PI) 2)))
(* x (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 4))) (+ (* -1/6 (pow (PI) 4)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 6))) (+ (* 1/120 (pow (PI) 6)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 6))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 8))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 8))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 8))) (* -1/5040 (pow (PI) 8))))))))))))) (pow (PI) 2)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(* (PI) (sin (* x (PI))))
(+ (* -1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 3) (sin (* x (PI))))))) (* (PI) (sin (* x (PI)))))
(+ (* (PI) (sin (* x (PI)))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 3) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 5) (sin (* x (PI))))))))))
(+ (* (PI) (sin (* x (PI)))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 3) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 7) (sin (* x (PI))))))) (* 1/120 (* (pow x 4) (* (pow (PI) 5) (sin (* x (PI)))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau x))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(* tau (* x (PI)))
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1
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
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(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(* (pow x 2) (+ (* tau (pow (PI) 2)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 4))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 4))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 6))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 6))) (+ (* 1/36 (* (pow tau 3) (pow (PI) 6))) (* (pow x 2) (+ (* -1/720 (* (pow tau 3) (pow (PI) 8))) (+ (* -1/720 (* (pow tau 5) (pow (PI) 8))) (+ (* -1/5040 (* tau (pow (PI) 8))) (* -1/5040 (* (pow tau 7) (pow (PI) 8))))))))))))))))
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(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(* tau (* x (* (PI) (sin (* x (PI))))))
(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))) (* x (* (PI) (sin (* x (PI)))))))
(* tau (+ (* x (* (PI) (sin (* x (PI))))) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI)))))))))))
(* tau (+ (* x (* (PI) (sin (* x (PI))))) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (* (pow (PI) 7) (sin (* x (PI))))))) (* 1/120 (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))))))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
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(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(* tau (PI))
(+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (* -1/6 (* (pow tau 3) (pow (PI) 3))))))
(+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (* 1/36 (* (pow tau 3) (pow (PI) 5))))))))))
(+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (+ (* 1/36 (* (pow tau 3) (pow (PI) 5))) (* (pow x 2) (+ (* -1/720 (* (pow tau 3) (pow (PI) 7))) (+ (* -1/720 (* (pow tau 5) (pow (PI) 7))) (+ (* -1/5040 (* tau (pow (PI) 7))) (* -1/5040 (* (pow tau 7) (pow (PI) 7)))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* tau (sin (* x (PI)))) x)
(* tau (+ (* -1/6 (* (pow tau 2) (* x (* (pow (PI) 2) (sin (* x (PI))))))) (/ (sin (* x (PI))) x)))
(* tau (+ (* (pow tau 2) (+ (* -1/6 (* x (* (pow (PI) 2) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 4) (sin (* x (PI))))))))) (/ (sin (* x (PI))) x)))
(* tau (+ (* (pow tau 2) (+ (* -1/6 (* x (* (pow (PI) 2) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 6) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 4) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) x)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(* tau (* x (PI)))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (* -1/6 (* (pow tau 3) (pow (PI) 3)))))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (* 1/36 (* (pow tau 3) (pow (PI) 5)))))))))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (+ (* 1/36 (* (pow tau 3) (pow (PI) 5))) (* (pow x 2) (+ (* -1/720 (* (pow tau 3) (pow (PI) 7))) (+ (* -1/720 (* (pow tau 5) (pow (PI) 7))) (+ (* -1/5040 (* tau (pow (PI) 7))) (* -1/5040 (* (pow tau 7) (pow (PI) 7))))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(* tau (sin (* x (PI))))
(* tau (+ (sin (* x (PI))) (* -1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))))))
(* tau (+ (sin (* x (PI))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI)))))))))))
(* tau (+ (sin (* x (PI))) (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 6) (sin (* x (PI))))))) (* 1/120 (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI)))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
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(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
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(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (PI))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
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(sin (* x (PI)))
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(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))

Outputs
1
#s(literal 1 binary32)
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tau
(+ tau (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 2)))))
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(+ tau (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 2))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 7) (* (pow x 2) (pow (PI) 6)))) (* 1/120 (* (pow tau 5) (pow (PI) 4))))))))
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tau
(* tau (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))))
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(* tau (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4)))))))))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))
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(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))
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1
#s(literal 1 binary32)
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(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
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(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))

rewrite375.0ms (2.6%)

Memory

-47.1MiB live, 335.2MiB allocated

Rules

4 868×	`lower-*.f64`
4 822×	`lower-*.f32`
4 100×	`lower-/.f64`
4 086×	`lower-/.f32`
4 084×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	57	338
0	97	326
1	317	324
2	2044	312
0	8298	312

Stop Event

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

Counts

23 → 1 439

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32)))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32))))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(*.f32 (PI.f32) (PI.f32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(.f32 x (.f32 tau (PI.f32)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32)))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(literal 1 binary32) x)
(.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (*.f32 x (PI.f32))))
(*.f32 x (PI.f32))
(.f32 (PI.f32) (.f32 x (PI.f32)))
#s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32))))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))

Outputs
(neg.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 x (.f32 (PI.f32) x))) (neg.f32 (*.f32 (PI.f32) tau))))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (neg.f32 x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (*.f32 (PI.f32) tau)))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (*.f32 (PI.f32) x))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau))))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 x)) (/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) x)) (.f32 (PI.f32) tau))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (neg.f32 x))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau)))))
(neg.f32 (.f32 (/.f32 #s(literal -1 binary32) x) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau))))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (*.f32 (PI.f32) x))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 x (.f32 (PI.f32) x))) (neg.f32 (*.f32 (PI.f32) tau))))
(-.f32 #s(literal 0 binary32) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))))
(-.f32 (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
(-.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 (.f32 (PI.f32) tau))) (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 x (.f32 (PI.f32) x))) (neg.f32 (.f32 (PI.f32) tau))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x)))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 x (*.f32 (PI.f32) tau))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (.f32 (PI.f32) x) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (*.f32 (PI.f32) x)))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 (PI.f32) x))) (*.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (*.f32 (PI.f32) x))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (.f32 (neg.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x))))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (.f32 (.f32 (PI.f32) (neg.f32 x)) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (*.f32 (PI.f32) x))))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (neg.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 (PI.f32) x))) (*.f32 (PI.f32) (neg.f32 x)))))
(/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) x)) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 (PI.f32) x))))
(/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) tau))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (*.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) x) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (*.f32 (PI.f32) tau))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 x (.f32 (PI.f32) tau)) (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (*.f32 (PI.f32) (neg.f32 x)))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (neg.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (.f32 (.f32 (PI.f32) (neg.f32 x)) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (.f32 (neg.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (PI.f32)))
(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (.f32 (PI.f32) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x)) (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x)) (neg.f32 (neg.f32 (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) tau) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) x))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32)) (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x))))))
(/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 (PI.f32) x)))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (PI.f32) x)) (sin.f32 (*.f32 (PI.f32) x))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (*.f32 (PI.f32) x))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (PI.f32) (neg.f32 x))) (neg.f32 (sin.f32 (*.f32 (PI.f32) x)))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (neg.f32 (.f32 x (.f32 (PI.f32) tau)))) (neg.f32 (sin.f32 (*.f32 (PI.f32) x)))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (neg.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))) (neg.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) (neg.f32 x)) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 (PI.f32) x)))) (neg.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 (*.f32 (PI.f32) x))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 (*.f32 (PI.f32) x))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x)))
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(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 x))) (neg.f32 (PI.f32)))
(/.f32 (neg.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))))) (neg.f32 (.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))))
(/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 x (sin.f32 (*.f32 (PI.f32) x))))
(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (PI.f32)) x)
(/.f32 (neg.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x) (sin.f32 (.f32 (PI.f32) x)))) (neg.f32 (PI.f32)))
(/.f32 (neg.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (PI.f32))) (neg.f32 x))
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) x)) (sin.f32 (*.f32 (PI.f32) x)))
(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (*.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)))
(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) x)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 #s(literal 1 binary32) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))
(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))
(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) #s(literal 1 binary32))
(.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))))
(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x) (sin.f32 (*.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (*.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) x))
(neg.f32 (*.f32 (PI.f32) (neg.f32 x)))
(exp.f32 (-.f32 (log.f32 (PI.f32)) (*.f32 (log.f32 x) #s(literal -1 binary32))))
(-.f32 #s(literal 0 binary32) (*.f32 (PI.f32) (neg.f32 x)))
(/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))
(/.f32 (*.f32 (PI.f32) x) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(/.f32 (*.f32 (PI.f32) (neg.f32 x)) #s(literal -1 binary32))
(/.f32 (neg.f32 (PI.f32)) (/.f32 #s(literal -1 binary32) x))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(*.f32 x (neg.f32 (neg.f32 (PI.f32))))
(.f32 (.f32 (PI.f32) x) #s(literal 1 binary32))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))
(.f32 #s(literal -1 binary32) (.f32 (PI.f32) (neg.f32 x)))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) x))
(*.f32 (neg.f32 x) (neg.f32 (PI.f32)))
(*.f32 (neg.f32 (PI.f32)) (neg.f32 x))
(.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(*.f32 (neg.f32 (neg.f32 (PI.f32))) x)
(neg.f32 (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))
(-.f32 #s(literal 0 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (*.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (PI.f32) (.f32 (PI.f32) x)) #s(literal 1 binary32))
(/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))) #s(literal -1 binary32))
(.f32 (PI.f32) (.f32 (PI.f32) x))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(.f32 x (neg.f32 (.f32 (PI.f32) (neg.f32 (PI.f32)))))
(.f32 (.f32 (PI.f32) x) (PI.f32))
(.f32 (.f32 (PI.f32) x) (neg.f32 (neg.f32 (PI.f32))))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) x)))
(.f32 (.f32 (PI.f32) (PI.f32)) x)
(.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) #s(literal 1 binary32))
(.f32 #s(literal -1 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (neg.f32 x))))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) (*.f32 (PI.f32) x)))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 (PI.f32) x)))
(.f32 (.f32 (PI.f32) (neg.f32 x)) (neg.f32 (PI.f32)))
(.f32 (neg.f32 x) (.f32 (PI.f32) (neg.f32 (PI.f32))))
(.f32 (neg.f32 (PI.f32)) (.f32 (PI.f32) (neg.f32 x)))
(.f32 (.f32 (PI.f32) (neg.f32 (PI.f32))) (neg.f32 x))
(.f32 (.f32 (*.f32 (PI.f32) x) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (neg.f32 (neg.f32 (PI.f32))) (.f32 (PI.f32) x))
(.f32 (neg.f32 (.f32 (PI.f32) (neg.f32 (PI.f32)))) x)
(neg.f32 (neg.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))))
(-.f32 #s(literal 0 binary32) (neg.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))))
(/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) #s(literal 1 binary32))
(/.f32 (neg.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))) #s(literal -1 binary32))
#s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))
(.f32 #s(literal 1 binary32) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))))
(.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) #s(literal 1 binary32))
(.f32 #s(literal -1 binary32) (neg.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))))
(/.f32 (*.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) x))
(.f32 x (.f32 x #s(literal -1/6 binary32)))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(.f32 #s(literal -1/6 binary32) (.f32 x x))
(.f32 (.f32 x #s(literal -1/6 binary32)) x)
(/.f32 (.f32 (PI.f32) (.f32 (PI.f32) x)) (/.f32 #s(literal 1 binary32) tau))
(/.f32 (.f32 (PI.f32) (.f32 (PI.f32) tau)) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (.f32 (PI.f32) (PI.f32)) tau) (/.f32 #s(literal 1 binary32) x))
(.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))
(.f32 x (.f32 (*.f32 (PI.f32) tau) (PI.f32)))
(.f32 tau (.f32 (PI.f32) (*.f32 (PI.f32) x)))
(.f32 (.f32 x tau) (*.f32 (PI.f32) (PI.f32)))
(.f32 (.f32 x (*.f32 (PI.f32) tau)) (PI.f32))
(.f32 (.f32 (PI.f32) x) (*.f32 (PI.f32) tau))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau))))
(.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 x tau))
(.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) tau)
(.f32 (.f32 (PI.f32) tau) (*.f32 (PI.f32) x))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (.f32 (PI.f32) tau))))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 x (.f32 (PI.f32) tau))))
(.f32 (.f32 (PI.f32) (*.f32 (PI.f32) tau)) x)
(.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) tau) x)

eval333.0ms (2.3%)

Memory: 4.3MiB live, 500.9MiB allocated
Compiler: Compiled 59 148 to 3 171 computations (94.6% saved)

prune656.0ms (4.5%)

Memory

-11.3MiB live, 950.7MiB allocated

Pruning

78 alts after pruning (72 fresh and 6 done)

	Pruned	Kept	Total
New	2 387	40	2 427
Fresh	11	32	43
Picked	0	5	5
Done	1	1	2
Total	2 399	78	2 477

Accuracy

99.7%

Counts

2 477 → 78

Alt Table

Click to see full alt table

Status	Accuracy	Program
	68.1%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 x tau) #s(literal 2 binary32))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
	62.5%	(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
	62.6%	(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
	68.0%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	68.2%	(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
	96.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (.f32 (.f32 (PI.f32) tau) (PI.f32)))
	97.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) (neg.f32 (*.f32 x (PI.f32)))))
▶	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
✓	97.3%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))
	78.4%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))))) (*.f32 (PI.f32) tau))
	62.6%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
	79.0%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 tau (.f32 (fma.f32 (.f32 (.f32 x (.f32 tau tau)) x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (sin.f32 (.f32 x (PI.f32))))))) (*.f32 (PI.f32) tau))
	96.7%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (.f32 x (PI.f32))))
	84.4%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
	96.7%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	97.2%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 x (.f32 (PI.f32) tau)) (PI.f32))))
✓	97.4%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	78.6%	(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
	62.4%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
	78.1%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
	62.5%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
	62.5%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
✓	62.5%	(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
	97.0%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))))
	76.6%	(-.f32 (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	97.1%	(.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 x (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	96.9%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
	95.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 tau (cbrt.f32 (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (*.f32 x (sqrt.f32 (PI.f32)))))))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	70.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
▶	84.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	84.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	70.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
▶	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x)))))) (neg.f32 (sin.f32 (.f32 x (PI.f32)))))
✓	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (.f32 (PI.f32) tau) (.f32 x (PI.f32))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
	62.5%	(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
	62.6%	(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
	84.7%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	62.6%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
	97.2%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (*.f32 (PI.f32) x))))
	97.0%	(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	95.9%	(.f32 (exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	79.7%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	90.3%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	84.6%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	84.1%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) (.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
▶	79.1%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	63.4%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.8%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
	84.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (PI.f32)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	84.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau))))))
	84.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))))))
	84.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (neg.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))))) (.f32 (.f32 x tau) (.f32 (PI.f32) (*.f32 (PI.f32) (neg.f32 x))))))
	84.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	84.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
	84.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))))))
	84.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	84.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	84.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	84.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	84.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	97.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	97.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
✓	84.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
▶	70.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	78.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	63.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	78.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	84.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (neg.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
✓	62.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 4 152 to 2 267 computations (45.4% saved)

simplify139.0ms (1%)

Memory

25.1MiB live, 217.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f32 (*.f32 x (PI.f32)))
cost-diff	0	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (*.f32 x (PI.f32))))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
cost-diff	192	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
cost-diff	0	(.f32 (.f32 x tau) (PI.f32))
cost-diff	0	(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
cost-diff	0	(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
cost-diff	0	(.f32 x (.f32 tau (PI.f32)))
cost-diff	0	(sin.f32 (.f32 x (.f32 tau (PI.f32))))
cost-diff	0	(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
cost-diff	0	(.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))
cost-diff	0	(*.f32 x x)
cost-diff	0	(fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))
cost-diff	0	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
cost-diff	0	(.f32 (PI.f32) (.f32 x tau))
cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))

Rules

3 454×	`lower-*.f64`
3 404×	`lower-*.f32`
2 398×	`lower-fma.f64`
2 392×	`lower-fma.f32`
1 950×	`associate-*r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	541
0	114	529
1	244	527
2	689	527
3	2494	523
4	2846	523
5	3050	523
6	3495	523
7	4104	523
8	4752	523
9	7323	523
10	7592	523
11	7789	523
12	7976	523
0	8036	519

Stop Event

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

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(PI.f32)
(*.f32 x tau)
x
tau
(.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))
(*.f32 x x)
x
(.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))
(*.f32 (PI.f32) (PI.f32))
(PI.f32)
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
#s(literal -1/6 binary32)
(*.f32 tau tau)
tau
#s(literal 1 binary32)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(.f32 x (.f32 tau (PI.f32)))
x
(*.f32 tau (PI.f32))
tau
(PI.f32)
(/.f32 #s(approx (sin (* x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))
#s(approx (sin (* x (PI))) (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
(.f32 (.f32 x x) tau)
(*.f32 x x)
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
(.f32 (.f32 x tau) (PI.f32))
(*.f32 x tau)
x
tau
(PI.f32)
(.f32 (.f32 x (PI.f32)) tau)
(*.f32 x (PI.f32))
(/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))
#s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32))))
(.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))
(fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32))
(.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))
(*.f32 (PI.f32) (PI.f32))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(*.f32 x x)
#s(literal -1/6 binary32)
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (*.f32 x (PI.f32))))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
x
(PI.f32)
(.f32 x (.f32 x (PI.f32)))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(*.f32 x tau)
tau
(*.f32 (PI.f32) tau)

Outputs
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x (.f32 x tau))))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x (.f32 x tau)))))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(PI.f32)
(*.f32 x tau)
x
tau
(.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(.f32 (PI.f32) (.f32 (PI.f32) (.f32 x (.f32 x tau))))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(.f32 x (.f32 tau (*.f32 (PI.f32) (PI.f32))))
(sin.f32 (*.f32 x (PI.f32)))
(sin.f32 (*.f32 (PI.f32) x))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))
(fma.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32))
(*.f32 x x)
x
(.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))
(.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (*.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))
(*.f32 (PI.f32) (PI.f32))
(PI.f32)
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(fma.f32 tau (*.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))
#s(literal -1/6 binary32)
(*.f32 tau tau)
tau
#s(literal 1 binary32)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x (*.f32 x tau))))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x (*.f32 x tau)))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 x (.f32 tau (PI.f32)))
(.f32 (PI.f32) (.f32 x tau))
x
(*.f32 tau (PI.f32))
(*.f32 (PI.f32) tau)
tau
(PI.f32)
(/.f32 #s(approx (sin (* x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))
(/.f32 #s(approx (sin (* x (PI))) (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x (*.f32 x tau)))))
#s(approx (sin (* x (PI))) (*.f32 x (PI.f32)))
#s(approx (sin (* x (PI))) (*.f32 (PI.f32) x))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
(.f32 (PI.f32) (.f32 (PI.f32) (.f32 x (.f32 x tau))))
(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
(.f32 (PI.f32) (.f32 x (*.f32 x tau)))
(.f32 (.f32 x x) tau)
(.f32 x (.f32 x tau))
(*.f32 x x)
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 (PI.f32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 (.f32 x x) #s(literal -1/6 binary32))) x)))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x (*.f32 x tau)))))
(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))
(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (.f32 x tau) (PI.f32))
(.f32 (PI.f32) (.f32 x tau))
(*.f32 x tau)
x
tau
(PI.f32)
(.f32 (.f32 x (PI.f32)) tau)
(.f32 (PI.f32) (.f32 x tau))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
(/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))
(/.f32 #s(approx (sin (* x (PI))) (.f32 (PI.f32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 (.f32 x x) #s(literal -1/6 binary32))) x))) (.f32 (PI.f32) x))
#s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32))))
#s(approx (sin (* x (PI))) (.f32 (PI.f32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 (*.f32 x x) #s(literal -1/6 binary32))) x)))
(.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))
(.f32 (PI.f32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 (*.f32 x x) #s(literal -1/6 binary32))) x))
(fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32))
(fma.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (PI.f32))
(.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))
(*.f32 (PI.f32) (PI.f32))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(*.f32 x x)
#s(literal -1/6 binary32)
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x (.f32 x tau))))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 x x))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (*.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (*.f32 x x)))
(sin.f32 (*.f32 x (PI.f32)))
(sin.f32 (*.f32 (PI.f32) x))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
x
(PI.f32)
(.f32 x (.f32 x (PI.f32)))
(.f32 (PI.f32) (.f32 x x))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
(*.f32 x tau)
tau
(*.f32 (PI.f32) tau)

localize217.0ms (1.5%)

Memory

-13.0MiB live, 312.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.34603500976844204	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (*.f32 x (PI.f32))))
accuracy	0.34994125976844204	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.3875440802111938	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.40529252930532605	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
accuracy	0.41796875	(.f32 (.f32 x x) #s(literal -1/6 binary32))
accuracy	0.4489250488422101	(/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	4.46038070697027	#s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32))))
accuracy	0.3875440802111938	(sin.f32 (.f32 x (.f32 tau (PI.f32))))
accuracy	0.40462875976844204	(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
accuracy	0.4137687988422101	(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
accuracy	9.176681278854982	#s(approx (sin (* x (PI))) (*.f32 x (PI.f32)))
accuracy	0.33984375	(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
accuracy	0.41015625	(.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	6.67352153691147	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
accuracy	0.35775375976844204	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
accuracy	0.3875440802111938	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.3912887695368841	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
accuracy	0.4576950195368841	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))

Samples

126.0ms

256×

valid

Compiler

Compiled 450 to 56 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 106.0ms

ival-mult: 52.0ms (49% of total)

ival-add: 18.0ms (17% of total)

ival-sin: 16.0ms (15.1% of total)

ival-div: 13.0ms (12.3% of total)

const: 5.0ms (4.7% of total)

ival-pi: 1.0ms (0.9% of total)

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

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

exact: 0.0ms (0% of total)

series44.0ms (0.3%)

Memory

-7.8MiB live, 71.7MiB allocated

Counts

28 → 540

Calls

Call 1

Inputs
#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (patch (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (.f32 x tau)) (patch (.f32 (PI.f32) (.f32 x tau)) #<representation binary32>) () ())
#s(alt #s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))) (patch #s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)) (patch (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (.f32 x x) (patch (.f32 x x) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (patch (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #<representation binary32>) () ())
#s(alt #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))) (patch #s(approx ( (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))) #<representation binary32>) () ())
#s(alt (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))) (patch (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (patch (sin.f32 (.f32 x (.f32 tau (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 x (.f32 tau (PI.f32))) (patch (.f32 x (.f32 tau (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (patch (sin.f32 (.f32 (.f32 x tau) (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 x tau) (PI.f32)) (patch (.f32 (.f32 x tau) (PI.f32)) #<representation binary32>) () ())
#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) tau)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) tau)) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 x (PI.f32))) (patch (sin.f32 (.f32 x (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (patch (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (PI.f32)) (patch (.f32 (PI.f32) (PI.f32)) #<representation binary32>) () ())
#s(alt (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) (patch (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #<representation binary32>) () ())
#s(alt #s(approx (sin (* x (PI))) (.f32 x (PI.f32))) (patch #s(approx (sin ( x (PI))) (*.f32 x (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (patch (.f32 (.f32 (.f32 x x) tau) (PI.f32)) #<representation binary32>) () ())
#s(alt #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (patch #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) #<representation binary32>) () ())
#s(alt (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))) (patch (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6)))))))))))))) (taylor 0 x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ 1 (* x (PI))) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #<representation binary32>) () ())) ())
#s(alt (/ (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (PI)))) (/ 1 (PI))) x) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #<representation binary32>) () ())) ())
#s(alt (/ (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (PI))) (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 3)))))) (/ 1 (PI))) x) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #<representation binary32>) () ())) ())
#s(alt (/ (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (PI))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 6) (* (pow x 2) (pow (PI) 5)))) (* 1/120 (* (pow tau 4) (pow (PI) 3))))))) (/ 1 (PI))) x) (taylor 0 x) (#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #<representation binary32>) () ())) ())
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#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
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#s(alt (* -1/6 (pow x 2)) (taylor 0 x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())

Calls

135 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(* (/ (sin (* (* x tau) (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
1.0ms	tau	@	inf	(+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1)
1.0ms	tau	@	-inf	(/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau)))))
1.0ms	x	@	0	(+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1)
1.0ms	x	@	inf	(/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau)))))

simplify401.0ms (2.8%)

Memory

11.1MiB live, 683.8MiB allocated

Algorithm

1×	egg-herbie

Rules

20 628×	`lower-fma.f64`
20 628×	`lower-fma.f32`
6 910×	`lower-*.f64`
6 910×	`lower-*.f32`
5 594×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	355	8162
1	1143	7960
2	4346	7728
3	7900	7728
0	8151	7440

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 540

Calls

Call 1

Inputs
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1 (* x (PI)))
(/ (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (PI)))) (/ 1 (PI))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (PI))) (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 3)))))) (/ 1 (PI))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (PI))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 6) (* (pow x 2) (pow (PI) 5)))) (* 1/120 (* (pow tau 4) (pow (PI) 3))))))) (/ 1 (PI))) x)
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1 (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (PI)))) (/ 1 (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* 1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))))) (/ 1 (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (pow (PI) 5)))) (* 1/120 (* (pow x 3) (pow (PI) 3))))))) (/ 1 (* x (PI))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(* tau (* x (PI)))
(* x (+ (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* 1/120 (* (pow tau 5) (* (pow x 2) (pow (PI) 5))))))))
(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 7) (* (pow x 2) (pow (PI) 7)))) (* 1/120 (* (pow tau 5) (pow (PI) 5)))))))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))
(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))
(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
1
(+ 1 (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6))))
(+ 1 (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6))))
(+ 1 (* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6))))
(* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))
(* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))
(* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))
(* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))
(* (pow x 2) (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)))
(* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))
(* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))
(* (pow x 2) (+ (* (pow (PI) 2) (- (* -1/6 (pow tau 2)) 1/6)) (/ 1 (pow x 2))))
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))
(+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))
(+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2)))))
(* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))
(* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))
(* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))
(* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))
(* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))
(* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))
(* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))
(* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (+ (* -1/6 (/ (* (pow x 2) (pow (PI) 2)) (pow tau 2))) (/ 1 (pow tau 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1/6 (pow (PI) 2))
(+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))
(+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))
(+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))
(* -1/6 (* (pow tau 2) (pow (PI) 2)))
(* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))
(* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))
(* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))
(* -1/6 (* (pow tau 2) (pow (PI) 2)))
(* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))
(* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))
(* (pow tau 2) (+ (* -1/6 (/ (pow (PI) 2) (pow tau 2))) (* -1/6 (pow (PI) 2))))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
1
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (sin (* x (PI))) (* x (PI)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(* tau (PI))
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(+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (* 1/36 (* (pow tau 3) (pow (PI) 5))))))))))
(+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 3))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 5))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 5))) (+ (* 1/36 (* (pow tau 3) (pow (PI) 5))) (* (pow x 2) (+ (* -1/720 (* (pow tau 3) (pow (PI) 7))) (+ (* -1/720 (* (pow tau 5) (pow (PI) 7))) (+ (* -1/5040 (* tau (pow (PI) 7))) (* -1/5040 (* (pow tau 7) (pow (PI) 7)))))))))))))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* tau (sin (* x (PI)))) x)
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(* tau (+ (* (pow tau 2) (+ (* -1/6 (* x (* (pow (PI) 2) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 6) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 4) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) x)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (pow x 2) (PI)))
(/ 1 x)
(/ (+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2)))) x)
(/ (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4)))))) x)
(/ (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4))))))) x)
(/ (sin (* x (PI))) (* (pow x 2) (PI)))
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(/ (sin (* x (PI))) (* (pow x 2) (PI)))
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(sin (* x (PI)))
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(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
-1/6
(- (* -1/6 (pow tau 2)) 1/6)
(- (* -1/6 (pow tau 2)) 1/6)
(- (* -1/6 (pow tau 2)) 1/6)
(* -1/6 (pow tau 2))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(* -1/6 (pow tau 2))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(* x (PI))
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1
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(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32))))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32)))))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (fma.f32 #s(literal -1/720 binary32) (fma.f32 tau tau (.f32 (.f32 tau tau) (.f32 tau tau))) (fma.f32 #s(literal -1/5040 binary32) (pow.f32 tau #s(literal 6 binary32)) #s(literal -1/5040 binary32)))) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32))))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (*.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 tau tau) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 tau tau) (.f32 (sin.f32 (.f32 x (PI.f32))) (fma.f32 x (.f32 (PI.f32) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 x (.f32 x x)))) (.f32 (.f32 tau tau) #s(literal 1/120 binary32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 tau tau) (fma.f32 (.f32 tau tau) (.f32 (sin.f32 (.f32 x (PI.f32))) (fma.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 1/120 binary32)) (.f32 (.f32 (pow.f32 x #s(literal 5 binary32)) (pow.f32 (PI.f32) #s(literal 5 binary32))) (.f32 (.f32 tau tau) #s(literal -1/5040 binary32))))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ 1 (* x (PI)))
(/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))
(/ (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (PI)))) (/ 1 (PI))) x)
(/.f32 (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (PI))) (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 3)))))) (/ 1 (PI))) x)
(/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (PI))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 6) (* (pow x 2) (pow (PI) 5)))) (* 1/120 (* (pow tau 4) (pow (PI) 3))))))) (/ 1 (PI))) x)
(/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/5040 binary32) (.f32 (pow.f32 tau #s(literal 6 binary32)) (.f32 x (.f32 x (pow.f32 (PI.f32) #s(literal 5 binary32))))) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (*.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ 1 (* x (PI)))
(/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))
(+ (* -1/6 (* (pow tau 2) (* x (PI)))) (/ 1 (* x (PI))))
(fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (PI))) (* 1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))))) (/ 1 (* x (PI))))
(fma.f32 (.f32 tau tau) (fma.f32 x (.f32 (PI.f32) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 x (.f32 x x)))) (.f32 (.f32 tau tau) #s(literal 1/120 binary32)))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))
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(fma.f32 (.f32 tau tau) (fma.f32 (.f32 tau tau) (fma.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 1/120 binary32)) (.f32 (.f32 (pow.f32 x #s(literal 5 binary32)) (pow.f32 (PI.f32) #s(literal 5 binary32))) (.f32 (.f32 tau tau) #s(literal -1/5040 binary32)))) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* x (+ (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))
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(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* 1/120 (* (pow tau 5) (* (pow x 2) (pow (PI) 5))))))))
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(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 7) (* (pow x 2) (pow (PI) 7)))) (* 1/120 (* (pow tau 5) (pow (PI) 5)))))))))
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(sin (* tau (* x (PI))))
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(sin (* tau (* x (PI))))
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(sin (* tau (* x (PI))))
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(sin (* tau (* x (PI))))
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(sin (* tau (* x (PI))))
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(sin (* tau (* x (PI))))
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(* tau (* x (PI)))
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(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))
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(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))
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(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))
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(sin (* tau (* x (PI))))
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(sin (* tau (* x (PI))))
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(sin (* tau (* x (PI))))
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(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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(* tau (* x (PI)))
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1
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(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(* tau (* x (pow (PI) 2)))
(.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
-1/6
#s(literal -1/6 binary32)
(- (* -1/6 (pow tau 2)) 1/6)
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(- (* -1/6 (pow tau 2)) 1/6)
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(- (* -1/6 (pow tau 2)) 1/6)
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(* -1/6 (pow tau 2))
(.f32 #s(literal -1/6 binary32) (.f32 tau tau))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(* -1/6 (pow tau 2))
(.f32 #s(literal -1/6 binary32) (.f32 tau tau))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(* -1 (* (pow tau 2) (+ 1/6 (* 1/6 (/ 1 (pow tau 2))))))
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(.f32 x (fma.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (*.f32 (PI.f32) (PI.f32)) (PI.f32)))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(.f32 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 5 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 (PI.f32) #s(literal -1/6 binary32)))) (PI.f32)))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
(.f32 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 7 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 5 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 (PI.f32) #s(literal -1/6 binary32)))) (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* tau (* (pow x 2) (PI)))
(.f32 (PI.f32) (.f32 (*.f32 x x) tau))
(* x (PI))
(*.f32 x (PI.f32))
(* x (+ (PI) (* -1/6 (* (pow x 2) (pow (PI) 3)))))
(.f32 x (fma.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (*.f32 (PI.f32) (PI.f32)) (PI.f32)))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* 1/120 (* (pow x 2) (pow (PI) 5)))))))
(.f32 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 5 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 (PI.f32) #s(literal -1/6 binary32)))) (PI.f32)))
(* x (+ (PI) (* (pow x 2) (+ (* -1/6 (pow (PI) 3)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 7))) (* 1/120 (pow (PI) 5))))))))
(.f32 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 7 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 5 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 (PI.f32) #s(literal -1/6 binary32)))) (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
(sin (* x (PI)))
(sin.f32 (*.f32 x (PI.f32)))
1
#s(literal 1 binary32)
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4)))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(* -1/6 (pow x 2))
(.f32 (.f32 x x) #s(literal -1/6 binary32))

rewrite315.0ms (2.2%)

Memory

5.7MiB live, 530.5MiB allocated

Rules

5 374×	`lower-/.f64`
5 362×	`lower-/.f32`
4 442×	`lower-*.f64`
4 392×	`lower-*.f32`
3 782×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	387
0	114	381
1	384	361
2	2490	361
0	8177	359

Stop Event

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

Counts

28 → 1 514

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
(.f32 (PI.f32) (.f32 x tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))
(*.f32 x x)
(.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32)))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(.f32 x (.f32 tau (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
(.f32 (.f32 x tau) (PI.f32))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (*.f32 x (PI.f32))))
(sin.f32 (*.f32 x (PI.f32)))
(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
(*.f32 (PI.f32) (PI.f32))
(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
#s(approx (sin (* x (PI))) (*.f32 x (PI.f32)))
(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
#s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32))))
(/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32)))
(.f32 (.f32 x x) #s(literal -1/6 binary32))

Outputs
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x x)))) (*.f32 tau (neg.f32 (PI.f32)))))
(neg.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (neg.f32 (.f32 (PI.f32) (.f32 x x)))) (*.f32 (PI.f32) tau)))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (.f32 x x)))) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (.f32 x x)))) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))) #s(literal -1 binary32))
(pow.f32 (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x)))) #s(literal -1 binary32))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 tau (neg.f32 (PI.f32)))) (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x x)))) (.f32 tau (neg.f32 (PI.f32)))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) x) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (.f32 x x)))) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))
(/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x)))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (.f32 x x)))) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (*.f32 (PI.f32) x))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x)))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x)))
(/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (/.f32 (.f32 (PI.f32) (.f32 x tau)) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) x)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 tau (.f32 (PI.f32) (.f32 x x))) (neg.f32 (PI.f32))) (.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x tau))) (.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) tau)) (.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))))
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(/.f32 (neg.f32 (neg.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x))) (neg.f32 (neg.f32 (PI.f32))))
(/.f32 (neg.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (PI.f32))) (neg.f32 x))
(/.f32 (neg.f32 (/.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))) (neg.f32 (cbrt.f32 (PI.f32))))
(/.f32 (neg.f32 (/.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sqrt.f32 (PI.f32)))) (neg.f32 (sqrt.f32 (PI.f32))))
(.f32 #s(literal 1 binary32) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (.f32 (PI.f32) x)))
(.f32 (/.f32 #s(literal 1 binary32) x) (pow.f32 (/.f32 (PI.f32) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32))))) #s(literal -1 binary32)))
(.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))
(.f32 #s(literal -1 binary32) (/.f32 #s(literal 1 binary32) (neg.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32))))))))
(.f32 (neg.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (neg.f32 x))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) (pow.f32 (/.f32 #s(literal 1 binary32) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32))))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 (.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))
(.f32 (neg.f32 (neg.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))
(.f32 (neg.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x)) (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (PI.f32)) (/.f32 #s(literal 1 binary32) x))
(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x))
(.f32 (/.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))))
(.f32 (/.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(/.f32 (*.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) x))
(.f32 x (.f32 x #s(literal -1/6 binary32)))
(.f32 (.f32 x x) #s(literal -1/6 binary32))
(.f32 #s(literal -1/6 binary32) (.f32 x x))
(.f32 (.f32 x #s(literal -1/6 binary32)) x)

eval331.0ms (2.3%)

Memory: 18.8MiB live, 394.3MiB allocated
Compiler: Compiled 60 797 to 3 502 computations (94.2% saved)

prune819.0ms (5.6%)

Memory

24.0MiB live, 1 269.5MiB allocated

Pruning

105 alts after pruning (98 fresh and 7 done)

	Pruned	Kept	Total
New	2 192	52	2 244
Fresh	21	46	67
Picked	2	3	5
Done	2	4	6
Total	2 217	105	2 322

Accuracy

99.7%

Counts

2 322 → 105

Alt Table

Click to see full alt table

Status	Accuracy	Program
	68.1%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 x tau) #s(literal 2 binary32))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
	62.5%	(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
	68.0%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	68.2%	(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
	84.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) x))
	84.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (*.f32 x tau)))
	97.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) (neg.f32 (*.f32 x (PI.f32)))))
✓	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
	84.6%	(/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
✓	97.3%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))
	79.0%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 tau (.f32 (fma.f32 (.f32 (.f32 x (.f32 tau tau)) x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (sin.f32 (.f32 x (PI.f32))))))) (*.f32 (PI.f32) tau))
	96.7%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (.f32 x (PI.f32))))
	96.7%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	97.2%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 x (.f32 (PI.f32) tau)) (PI.f32))))
✓	97.4%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	84.2%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))
	84.7%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (.f32 x tau)) (/.f32 (.f32 (PI.f32) x) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))))))
	84.5%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) tau))
	70.1%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
	78.6%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
	84.5%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))))
	97.0%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))))
	76.6%	(-.f32 (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	84.7%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (.f32 x tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	97.3%	(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
	97.1%	(.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 x (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	84.4%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
	84.1%	(.f32 (/.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	84.1%	(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	95.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 tau (cbrt.f32 (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	70.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	84.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (/.f32 (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) x)) (PI.f32)))) (*.f32 x (PI.f32))))
	84.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x #s(literal -1/6 binary32)) x) (PI.f32)))) (.f32 x (PI.f32))))
	84.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) tau)))) (sin.f32 (.f32 x (PI.f32))))
	84.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (*.f32 (PI.f32) (PI.f32)) (PI.f32)))))
✓	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
	62.5%	(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
	78.5%	(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	63.5%	(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	79.0%	(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	84.7%	(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	97.2%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (*.f32 (PI.f32) x))))
	84.5%	(.f32 (.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	96.7%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (.f32 x x))))) (pow.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(literal -1 binary32))) (sin.f32 (*.f32 x (PI.f32))))
	84.3%	(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x))))))
	97.0%	(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	84.6%	(.f32 (.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (*.f32 x tau)))))
	97.1%	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 x x))) (*.f32 (PI.f32) tau)))
	84.3%	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x))))))
	95.9%	(.f32 (exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	82.8%	(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	79.3%	(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	63.7%	(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
	79.6%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
	84.1%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 tau tau) (fma.f32 x (.f32 (PI.f32) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 x (.f32 x x)))) (.f32 (.f32 tau tau) #s(literal 1/120 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))
	83.9%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
	90.3%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	84.6%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
	84.2%	(.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x))))))
	84.1%	#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32))))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32)))))) #s(literal 1 binary32)))
	79.1%	#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
	63.4%	#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	79.1%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
	84.1%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) (.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
✓	79.1%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	69.2%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
	63.7%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	69.2%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
	78.5%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
	63.7%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	4.6%	#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
	96.8%	#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
	84.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (PI.f32)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	84.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau))))))
	84.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))))))
	84.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (neg.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))))) (.f32 (.f32 x tau) (.f32 (PI.f32) (*.f32 (PI.f32) (neg.f32 x))))))
	84.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
	84.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))))))
	70.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 #s(approx (sin (* x (PI))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
	84.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	84.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	84.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	84.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	84.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	70.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	97.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	97.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
✓	70.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	70.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x x)) tau)))))
	70.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) (*.f32 x tau))))))
	68.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	78.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	63.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	68.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	78.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
	70.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (PI))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
	84.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (neg.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
✓	62.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 7 149 to 2 249 computations (68.5% saved)

regimes229.0ms (1.6%)

Memory

19.1MiB live, 378.0MiB allocated

Counts

154 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))))) (*.f32 (PI.f32) tau))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (PI))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) (*.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x x)) tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 #s(approx (sin (* x (PI))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
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(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
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(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 x (.f32 (PI.f32) tau)) (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x)))))) (neg.f32 (sin.f32 (.f32 x (PI.f32)))))
(.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (*.f32 (PI.f32) x))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 x x))) (*.f32 (PI.f32) tau)))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (PI.f32)))) (*.f32 (PI.f32) tau))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) (neg.f32 (*.f32 x (PI.f32)))))
(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 x (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (.f32 (.f32 (PI.f32) tau) (PI.f32)))
(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 x tau) #s(literal 2 binary32))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) #s(literal -1 binary32)) (.f32 x (.f32 (neg.f32 x) (/.f32 (.f32 (PI.f32) tau) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))))
(/.f32 (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 (.f32 (.f32 (sin.f32 (/.f32 (.f32 x (PI.f32)) (/.f32 #s(literal 1 binary32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 (.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (/.f32 #s(literal 1 binary32) x)) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(/.f32 (.f32 (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (.f32 x (PI.f32))))
(-.f32 (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (.f32 x x))))) (pow.f32 (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) #s(literal -1 binary32))) (sin.f32 (*.f32 x (PI.f32))))
(.f32 (exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 tau (cbrt.f32 (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (*.f32 x (sqrt.f32 (PI.f32)))))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32))))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (.f32 x (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Outputs
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))

Calls

4 calls:

71.0ms	tau
63.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
45.0ms	x
43.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`tau`
97.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
97.7%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes142.0ms (1%)

Memory

26.2MiB live, 295.0MiB allocated

Counts

120 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
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(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (.f32 x tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (*.f32 x tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (/.f32 (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) x)) (PI.f32)))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) x)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (.f32 (PI.f32) tau) (.f32 x (PI.f32))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (.f32 (PI.f32) x) (.f32 (PI.f32) tau)))) (sin.f32 (.f32 x (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 x (.f32 (PI.f32) tau)) (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x)))))) (neg.f32 (sin.f32 (.f32 x (PI.f32)))))
(.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (*.f32 (PI.f32) x))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 x x))) (*.f32 (PI.f32) tau)))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x x)))))

Outputs
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))

Calls

4 calls:

36.0ms	x
34.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
33.0ms	tau
33.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
97.4%	1	`x`
97.4%	1	`tau`
97.4%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
97.4%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes121.0ms (0.8%)

Memory

-22.4MiB live, 272.8MiB allocated

Counts

104 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
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(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (.f32 x tau)) (/.f32 (.f32 (PI.f32) x) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (.f32 x tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (*.f32 x tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (/.f32 (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) x)) (PI.f32)))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))

Outputs

#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (*.f32 (sin.f32 (*.f32 (*.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 (PI.f32) (*.f32 (*.f32 (*.f32 x x) tau) (PI.f32))))))

Calls

4 calls:

33.0ms	tau
28.0ms	x
27.0ms	(*.f32 x (PI.f32))
26.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
97.0%	1	`x`
97.0%	1	`tau`
97.0%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
97.0%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes113.0ms (0.8%)

Memory

1.0MiB live, 198.4MiB allocated

Counts

102 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))))) (*.f32 (PI.f32) tau))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
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#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (/.f32 (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) x)) (PI.f32)))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))

Outputs

#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (*.f32 (sin.f32 (*.f32 x (*.f32 tau (PI.f32)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 (*.f32 (PI.f32) (PI.f32)) (*.f32 x (*.f32 x tau))))))

Calls

4 calls:

28.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
28.0ms	x
27.0ms	tau
26.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
97.0%	1	`x`
97.0%	1	`(*.f32 x (PI.f32))`
97.0%	1	`tau`
97.0%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes131.0ms (0.9%)

Memory

15.2MiB live, 168.5MiB allocated

Counts

101 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))))) (*.f32 (PI.f32) tau))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (PI))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) (*.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x x)) tau)))))
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#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))

Outputs

#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (*.f32 (sin.f32 (*.f32 x (*.f32 tau (PI.f32)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 (PI.f32) (*.f32 (*.f32 (*.f32 x x) tau) (PI.f32))))))

Calls

4 calls:

36.0ms	(*.f32 x (PI.f32))
35.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
28.0ms	x
27.0ms	tau

Results

Accuracy	Segments	Branch
96.9%	1	`x`
96.9%	1	`tau`
96.9%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
96.9%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes123.0ms (0.8%)

Memory

-25.2MiB live, 208.4MiB allocated

Counts

100 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))))) (*.f32 (PI.f32) tau))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (PI))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) (*.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x x)) tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 #s(approx (sin (* x (PI))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) tau))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 x (.f32 x (/.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau))))))
(.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x))))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x))))))
(.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (*.f32 (PI.f32) (PI.f32)) (PI.f32)))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 tau (.f32 (fma.f32 (.f32 (.f32 x (.f32 tau tau)) x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (sin.f32 (.f32 x (PI.f32))))))) (*.f32 (PI.f32) tau))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (neg.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (.f32 (PI.f32) (neg.f32 x))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (neg.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))))) (.f32 (.f32 x tau) (.f32 (PI.f32) (*.f32 (PI.f32) (neg.f32 x))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) (.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32))))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))))))
(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (PI.f32)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x #s(literal -1/6 binary32)) x) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (*.f32 x tau)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) x))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 tau tau) (fma.f32 x (.f32 (PI.f32) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 x (.f32 x x)))) (.f32 (.f32 tau tau) #s(literal 1/120 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (.f32 x tau)) (/.f32 (.f32 (PI.f32) x) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (.f32 x tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (*.f32 x tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (/.f32 (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) x)) (PI.f32)))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))

Outputs

(*.f32 #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (*.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (*.f32 #s(literal 1/120 binary32) (*.f32 x (*.f32 x (*.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32)))) x)) (sin.f32 (*.f32 (PI.f32) (*.f32 x tau))))

Calls

4 calls:

36.0ms	tau
28.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
27.0ms	(*.f32 x (PI.f32))
25.0ms	x

Results

Accuracy	Segments	Branch
90.3%	1	`x`
90.3%	1	`(*.f32 x (PI.f32))`
90.3%	1	`tau`
90.3%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes111.0ms (0.8%)

Memory

3.1MiB live, 156.3MiB allocated

Counts

98 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
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#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) (.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32))))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))))))
(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32))) (PI.f32)))) (PI.f32)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x #s(literal -1/6 binary32)) x) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (*.f32 x tau)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) x))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 tau tau) (fma.f32 x (.f32 (PI.f32) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 x (.f32 x x)))) (.f32 (.f32 tau tau) #s(literal 1/120 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (.f32 x tau)) (/.f32 (.f32 (PI.f32) x) #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32)))) (PI.f32)))))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (PI.f32)) (.f32 x tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32))))) (.f32 (PI.f32) (*.f32 x tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (PI.f32)))) x) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))))
(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) x)) (/.f32 #s(literal 1 binary32) tau)) (.f32 (PI.f32) (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (/.f32 (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) x)) (PI.f32)))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 (.f32 (PI.f32) tau) (/.f32 #s(literal 1 binary32) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))

Outputs

(*.f32 (/.f32 (sin.f32 (*.f32 (*.f32 x (PI.f32)) tau)) (*.f32 (*.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (*.f32 (PI.f32) (PI.f32)) (*.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))

Calls

4 calls:

29.0ms	x
26.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
26.0ms	(*.f32 x (PI.f32))
24.0ms	tau

Results

Accuracy	Segments	Branch
85.2%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
85.2%	1	`tau`
85.2%	1	`x`
85.2%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes64.0ms (0.4%)

Memory

4.8MiB live, 82.3MiB allocated

Counts

52 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))))) (*.f32 (PI.f32) tau))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (PI))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) (*.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x x)) tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 #s(approx (sin (* x (PI))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))

Outputs

(*.f32 (/.f32 (sin.f32 (*.f32 (*.f32 x tau) (PI.f32))) (*.f32 (*.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (*.f32 (PI.f32) (PI.f32)) (*.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))

Calls

4 calls:

15.0ms	x
14.0ms	tau
13.0ms	(*.f32 x (PI.f32))
13.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
84.6%	1	`tau`
84.6%	1	`x`
84.6%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
84.6%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes65.0ms (0.4%)

Memory

12.7MiB live, 118.5MiB allocated

Counts

51 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))))) (*.f32 (PI.f32) tau))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (PI))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) (*.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x x)) tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 #s(approx (sin (* x (PI))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Outputs

(*.f32 #s(approx (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (*.f32 x x) (*.f32 #s(literal -1/6 binary32) (*.f32 tau (*.f32 tau (*.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Calls

4 calls:

15.0ms	tau
15.0ms	x
13.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
13.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
79.7%	1	`x`
79.7%	1	`(*.f32 x (PI.f32))`
79.7%	1	`tau`
79.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes72.0ms (0.5%)

Memory

11.0MiB live, 90.0MiB allocated

Counts

50 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))))) (*.f32 (PI.f32) tau))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (PI))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) x) (*.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) (*.f32 x x)) tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (.f32 #s(approx (sin (* x (PI))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 tau (.f32 (PI.f32) (*.f32 x x)))))))

Outputs

(*.f32 #s(approx (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (*.f32 (PI.f32) (*.f32 #s(literal -1/6 binary32) (*.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))

Calls

4 calls:

26.0ms	tau
18.0ms	x
13.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
13.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
79.6%	1	`x`
79.6%	1	`(*.f32 x (PI.f32))`
79.6%	1	`tau`
79.6%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes57.0ms (0.4%)

Memory

4.2MiB live, 76.8MiB allocated

Counts

43 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))))) (*.f32 (PI.f32) tau))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 x (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 tau (.f32 tau tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (PI.f32))))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32)))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (* x tau) (PI))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau))) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* x (PI)))) (/.f32 #s(literal 1 binary32) x)) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (*.f32 (PI.f32) tau))

Outputs

(*.f32 #s(approx (/ (sin (* (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (*.f32 x x) (*.f32 #s(literal -1/6 binary32) (*.f32 tau (*.f32 tau (*.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin (* x (PI))) (*.f32 x (fma.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) (PI.f32))) (*.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (*.f32 x (PI.f32))))

Calls

4 calls:

17.0ms	tau
15.0ms	x
11.0ms	(*.f32 x (PI.f32))
11.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
79.3%	1	`x`
79.3%	1	`(*.f32 x (PI.f32))`
79.3%	1	`tau`
79.3%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes49.0ms (0.3%)

Memory

-0.5MiB live, 52.4MiB allocated

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 #s(approx (sin ( x (* tau (PI)))) (.f32 x (.f32 tau (PI.f32)))) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (*.f32 x x) tau) (PI.f32))))))

Outputs

#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (*.f32 (*.f32 (PI.f32) (*.f32 (PI.f32) (*.f32 x x))) (fma.f32 (*.f32 tau tau) (*.f32 (*.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (*.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))

Calls

4 calls:

26.0ms	tau
7.0ms	x
7.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
7.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
79.1%	1	`x`
79.1%	1	`tau`
79.1%	1	`(*.f32 x (PI.f32))`
79.1%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes33.0ms (0.2%)

Memory

0.3MiB live, 37.7MiB allocated

Counts

24 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) x))) #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (*.f32 (PI.f32) x))
(/.f32 (/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) x)
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(approx ( (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 (PI.f32) (.f32 (PI.f32) x))) (*.f32 (PI.f32) (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(/.f32 (.f32 (/.f32 #s(literal 1 binary32) x) #s(approx ( (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI)))) (.f32 x (.f32 tau (PI.f32))))) (*.f32 (PI.f32) tau))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (/.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 #s(literal 1 binary32) x))) (.f32 (PI.f32) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 #s(approx (sin (* x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32)) (.f32 x x)) #s(literal 1 binary32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (*.f32 (PI.f32) x) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (fma.f32 (.f32 x x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) #s(literal -1/6 binary32))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (.f32 (PI.f32) tau))

Outputs

#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (*.f32 x (*.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (fma.f32 tau (*.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))

Calls

4 calls:

11.0ms	tau
7.0ms	(*.f32 x (PI.f32))
7.0ms	x
7.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
79.1%	1	`x`
79.1%	1	`tau`
79.1%	1	`(*.f32 x (PI.f32))`
79.1%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes15.0ms (0.1%)

Memory

18.6MiB live, 18.6MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (* (PI) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))

Outputs

#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (*.f32 x x) (*.f32 (*.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))

Calls

4 calls:

4.0ms	tau
4.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
4.0ms	(*.f32 x (PI.f32))
3.0ms	x

Results

Accuracy	Segments	Branch
79.1%	1	`tau`
79.1%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
79.1%	1	`x`
79.1%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes19.0ms (0.1%)

Memory

-19.6MiB live, 17.7MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) x)) (/ 1 tau)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (PI.f32) (.f32 x (PI.f32))))

Outputs

#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (*.f32 x x) #s(approx (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (*.f32 #s(literal -1/6 binary32) (*.f32 tau (*.f32 tau (*.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))

Calls

4 calls:

9.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
3.0ms	(*.f32 x (PI.f32))
3.0ms	tau
3.0ms	x

Results

Accuracy	Segments	Branch
69.2%	1	`tau`
69.2%	1	`x`
69.2%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
69.2%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes9.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))))))

Outputs

#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (*.f32 (PI.f32) (PI.f32)) (*.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))

Calls

4 calls:

2.0ms	tau
2.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
2.0ms	(*.f32 x (PI.f32))
2.0ms	x

Results

Accuracy	Segments	Branch
63.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
63.7%	1	`tau`
63.7%	1	`x`
63.7%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes6.0ms (0%)

Memory

12.4MiB live, 12.4MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Outputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Calls

4 calls:

1.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
1.0ms	x
1.0ms	(*.f32 x (PI.f32))
1.0ms	tau

Results

Accuracy	Segments	Branch
62.6%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
62.6%	1	`x`
62.6%	1	`(*.f32 x (PI.f32))`
62.6%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

simplify36.0ms (0.2%)

Memory

-22.7MiB live, 15.6MiB allocated

Algorithm

1×	egg-herbie

Rules

88×	`*-commutative_binary32`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	144	660
1	193	660

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Outputs
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 tau (.f32 x x)))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 tau (.f32 x x))))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (PI.f32) (*.f32 x tau))))
(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* (PI) (* x tau))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (/.f32 (PI.f32) tau) (/.f32 (.f32 #s(literal 1/120 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) tau)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau))) x)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (sin.f32 (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx (/ (sin (* (PI) (* x tau))) (* x (* (PI) (* (PI) (* x tau))))) (fma.f32 (.f32 (PI.f32) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) x (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x tau) (PI))) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 #s(approx (sin ( x (PI))) (.f32 x (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)))) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x x))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) #s(literal -1/36 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau (PI.f32)) (PI.f32))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (* x (PI)))) (sin (* (PI) (* x tau)))) (* (PI) tau)) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 tau (.f32 (PI.f32) tau) (PI.f32))))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ 1 x) (* (sin (* x (PI))) (/ (sin (* (PI) (* x tau))) (* x (PI))))) (* (PI) tau)) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

soundness2.7s (18.9%)

Memory

-35.9MiB live, 1 576.9MiB allocated

Rules

22 998×	`lower-fma.f64`
22 998×	`lower-fma.f32`
20 628×	`lower-fma.f64`
20 628×	`lower-fma.f32`
18 578×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	355	8162
1	1143	7960
2	4346	7728
3	7900	7728
0	8151	7440
0	196	1582
1	620	1562
2	2413	1538
3	4145	1538
4	4880	1538
5	5560	1538
6	5950	1538
7	5981	1538
8	5981	1538
0	8826	1486
0	353	7746
1	1176	7578
2	4481	7362
0	8501	7127
0	64	387
0	114	381
1	384	361
2	2490	361
0	8177	359
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53
0	44	284
0	78	280
1	230	280
2	1269	262
3	7138	262
0	8042	262
0	436	7698
1	1496	7470
2	5781	7192
0	8049	6951

Stop Event

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

Compiler

Compiled 1 019 to 425 computations (58.3% saved)

preprocess175.0ms (1.2%)

Memory

-7.7MiB live, 241.1MiB allocated

Remove

(abs x)

(abs tau)

Compiler

Compiled 1 972 to 768 computations (61.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze22.0ms (0.1%)

sample1.7s (11.8%)

explain120.0ms (0.8%)

preprocess75.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify24.0ms (0.2%)

localize66.0ms (0.5%)

series58.0ms (0.4%)

simplify349.0ms (2.4%)

rewrite192.0ms (1.3%)

eval121.0ms (0.8%)

prune189.0ms (1.3%)

simplify152.0ms (1%)

localize138.0ms (1%)

series53.0ms (0.4%)

simplify676.0ms (4.7%)

rewrite239.0ms (1.6%)

eval219.0ms (1.5%)

prune689.0ms (4.7%)

simplify379.0ms (2.6%)

localize362.0ms (2.5%)

series51.0ms (0.4%)

simplify686.0ms (4.7%)

rewrite375.0ms (2.6%)

eval333.0ms (2.3%)

prune656.0ms (4.5%)

simplify139.0ms (1%)

localize217.0ms (1.5%)

series44.0ms (0.3%)

simplify401.0ms (2.8%)

rewrite315.0ms (2.2%)

eval331.0ms (2.3%)

prune819.0ms (5.6%)

regimes229.0ms (1.6%)

regimes142.0ms (1%)

regimes121.0ms (0.8%)

regimes113.0ms (0.8%)

regimes131.0ms (0.9%)

regimes123.0ms (0.8%)

regimes111.0ms (0.8%)

regimes64.0ms (0.4%)

regimes65.0ms (0.4%)

regimes72.0ms (0.5%)

regimes57.0ms (0.4%)

regimes49.0ms (0.3%)

regimes33.0ms (0.2%)

regimes15.0ms (0.1%)

regimes19.0ms (0.1%)

regimes9.0ms (0.1%)

regimes6.0ms (0%)

simplify36.0ms (0.2%)

soundness2.7s (18.9%)

preprocess175.0ms (1.2%)

end0.0ms (0%)

Profiling