Metrics for Lanczos kernel

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze30.0ms (0.3%)

Memory

-28.7MiB live, 17.4MiB 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)

sample1.9s (16.4%)

Memory

47.4MiB live, 1 668.0MiB allocated

Samples

1.4s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-sin: 333.0ms (29.8% of total)

ival-div: 256.0ms (22.9% of total)

ival-mult: 157.0ms (14.1% of total)

const: 150.0ms (13.4% of total)

ival-pi: 97.0ms (8.7% of total)

ival-<=: 96.0ms (8.6% of total)

ival-and: 20.0ms (1.8% of total)

exact: 7.0ms (0.6% of total)

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

Bogosity

explain174.0ms (1.5%)

Memory

-17.8MiB live, 263.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
1	-	1	(0.9765286445617676 1.0308988094329834)	`(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`

Confusion

	Predicted +	Predicted -
+	0	3
-	0	253

Precision

0/0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	1	2
-	0	0	253

Precision?

1.0

Recall?

0.3333333333333333

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

74.0ms

512×

valid

Compiler

Compiled 151 to 34 computations (77.5% saved)

Precisions

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

ival-sin: 27.0ms (44.4% of total)

ival-div: 22.0ms (36.2% of total)

ival-mult: 8.0ms (13.2% of total)

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

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

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

preprocess71.0ms (0.6%)

Memory

27.2MiB live, 65.1MiB 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 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (*.f32 (*.f32 (*.f32 x x) tau) (*.f32 (PI.f32) (PI.f32)))) (sin.f32 (*.f32 tau (*.f32 (PI.f32) x))))

Symmetry

(abs tau)

(abs x)

Compiler

Compiled 23 to 10 computations (56.5% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.8%	(.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)

simplify33.0ms (0.3%)

Memory

-4.2MiB live, 33.8MiB 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 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 x x) tau) (.f32 (PI.f32) (PI.f32)))) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))
(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(.f32 (.f32 x (PI.f32)) tau)
(.f32 tau (.f32 (PI.f32) x))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
x
(PI.f32)
tau
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(sin.f32 (*.f32 x (PI.f32)))
(sin.f32 (*.f32 (PI.f32) x))

localize46.0ms (0.4%)

Memory

-27.9MiB live, 58.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3674688180802656	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.39357377930532605	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.4091987793053261	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

Samples

32.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

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

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

ival-sin: 6.0ms (25.2% of total)

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

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

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

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

series51.0ms (0.4%)

Memory

16.1MiB live, 54.1MiB 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 (/ (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 1 (taylor 0 tau) (#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 (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))) (taylor 0 tau) (#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 (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4))))))) (taylor 0 tau) (#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 (+ 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)))))))) (taylor 0 tau) (#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 (* tau (* x (PI))) (taylor 0 tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI)))) (taylor 0 tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* 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)))))))) (taylor 0 tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* 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))))))))) (taylor 0 tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) 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 (.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>) () ())) ())
#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)))) (* tau (* x (PI)))) (taylor inf tau) (#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 (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor inf tau) (#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 (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor inf tau) (#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 (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor inf tau) (#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 (* tau (* x (PI)))) (taylor inf tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor inf tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor inf tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor inf tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.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>) () ())) ())
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#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)))) (* tau (* x (PI)))) (taylor -inf x) (#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 (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor -inf x) (#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 (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor -inf x) (#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 (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor -inf x) (#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 (* tau (* x (PI)))) (taylor -inf x) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor -inf x) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor -inf x) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor -inf x) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf x) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf x) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf x) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf x) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<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 -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

6 calls:

Time	Variable		Point	Expression
26.0ms	x	@	inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
7.0ms	x	@	-inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
5.0ms	tau	@	-inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
4.0ms	tau	@	inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
3.0ms	x	@	0	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))

simplify310.0ms (2.7%)

Memory

3.4MiB live, 282.4MiB 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	2407	1538
3	4137	1538
4	4871	1538
5	5550	1538
6	5940	1538
7	5971	1538
8	5971	1538
0	8816	1486

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

rewrite203.0ms (1.8%)

Memory

10.2MiB live, 247.3MiB 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
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (neg.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (neg.f32 (PI.f32)) x)) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) x))
(.f32 (.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (neg.f32 tau)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (neg.f32 (PI.f32)) x)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (neg.f32 x)) (/.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (PI.f32))))
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(neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)))
(.f32 (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))
(.f32 (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(.f32 (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) x) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(.f32 (.f32 (*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) x) (pow.f32 (PI.f32) #s(literal 2/9 binary32))) (pow.f32 (PI.f32) #s(literal 1/9 binary32)))
(.f32 (.f32 (*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) x) #s(literal 1 binary32)) (cbrt.f32 (PI.f32)))
(.f32 (.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) x)) (cbrt.f32 (PI.f32)))
(*.f32 (neg.f32 (neg.f32 (PI.f32))) x)
(*.f32 (neg.f32 (neg.f32 x)) (PI.f32))
(.f32 (.f32 (sqrt.f32 (PI.f32)) x) (/.f32 (sqrt.f32 (PI.f32)) #s(literal 1 binary32)))
(.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (cbrt.f32 (PI.f32)) x) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) x) (/.f32 (cbrt.f32 (PI.f32)) #s(literal 1 binary32)))
(.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) x) (cbrt.f32 (PI.f32)))
(*.f32 (neg.f32 (PI.f32)) (neg.f32 x))
(*.f32 (neg.f32 x) (neg.f32 (PI.f32)))
(.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 (sqrt.f32 (PI.f32))) (*.f32 (sqrt.f32 (PI.f32)) x)))
(.f32 #s(literal -1 binary32) (.f32 (neg.f32 (PI.f32)) x))
(.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (PI.f32)) x) #s(literal 1 binary32)))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) x))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (/.f32 (.f32 (cbrt.f32 (PI.f32)) x) #s(literal 1 binary32)))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))
(.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (*.f32 (sqrt.f32 (PI.f32)) x)))
(.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (*.f32 (cbrt.f32 (PI.f32)) x)))
(.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) x))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))
(.f32 (.f32 (PI.f32) x) #s(literal 1 binary32))
(*.f32 (PI.f32) (/.f32 x #s(literal 1 binary32)))
(*.f32 (PI.f32) (neg.f32 (neg.f32 x)))
(*.f32 (PI.f32) x)
(*.f32 x (/.f32 (PI.f32) #s(literal 1 binary32)))
(*.f32 x (neg.f32 (neg.f32 (PI.f32))))
(*.f32 x (PI.f32))
(/.f32 (*.f32 (neg.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) x) #s(literal 1 binary32))
(-.f32 #s(literal 0 binary32) (*.f32 (neg.f32 (PI.f32)) x))
(pow.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)) #s(literal -1 binary32))
(neg.f32 (*.f32 (neg.f32 (PI.f32)) x))

eval166.0ms (1.4%)

Memory: -14.8MiB live, 204.2MiB allocated
Compiler: Compiled 24 386 to 2 303 computations (90.6% saved)

prune278.0ms (2.4%)

Memory

-39.8MiB live, 321.6MiB allocated

Pruning

34 alts after pruning (34 fresh and 0 done)

	Pruned	Kept	Total
New	979	34	1 013
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	980	34	1 014

Accuracy

99.7%

Counts

1 014 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	96.9%	(/.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (PI.f32)) (neg.f32 x))
▶	66.9%	(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
	97.6%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (PI.f32) x))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) (neg.f32 tau)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
	97.6%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
▶	97.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	66.9%	(/.f32 (.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))) #s(literal 2 binary32))
	97.0%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) tau)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) x))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))
	97.1%	(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))))
	97.5%	(/.f32 #s(literal -1 binary32) (.f32 (/.f32 (.f32 (neg.f32 (PI.f32)) x) (sin.f32 (.f32 (PI.f32) x))) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))))
	97.1%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.0%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))))
	96.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	95.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))))
	85.5%	(.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 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	71.2%	(.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)))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 (cbrt.f32 (PI.f32)) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (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) x)) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))))
▶	97.1%	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))))
	97.1%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
	97.2%	(.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
	80.1%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	97.7%	(neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x))))
	84.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32)))
	79.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	64.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
	97.4%	#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 x (.f32 tau (.f32 (PI.f32) x))))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))))
▶	64.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 652 to 878 computations (46.9% saved)

simplify112.0ms (1%)

Memory

17.8MiB live, 92.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))
cost-diff	0	(cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32))))
cost-diff	0	(-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (*.f32 (PI.f32) (fma.f32 tau x x))))
cost-diff	0	(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
cost-diff	0	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
cost-diff	0	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x)
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x)))
cost-diff	192	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
cost-diff	0	(.f32 tau (.f32 (PI.f32) x))
cost-diff	0	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
cost-diff	0	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
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 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))
cost-diff	128	(neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x))))
cost-diff	192	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x)))

Rules

3 462×	`lower-/.f64`
3 454×	`lower-*.f64`
3 450×	`lower-/.f32`
3 428×	`lower-*.f32`
1 838×	`lower-neg.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	381
0	71	385
1	168	385
2	564	379
3	2389	379
4	4860	379
0	8303	379

Stop Event

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

Calls

Call 1

Inputs
(neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x))
(sin.f32 (*.f32 (PI.f32) x))
(*.f32 (PI.f32) x)
(PI.f32)
x
(*.f32 (neg.f32 (PI.f32)) x)
(neg.f32 (PI.f32))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(.f32 tau (.f32 (PI.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)
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(.f32 tau (.f32 (PI.f32) x))
tau
(*.f32 (PI.f32) x)
(PI.f32)
x
(.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))
(.f32 (.f32 (PI.f32) x) (PI.f32))
(*.f32 tau x)
(sin.f32 (*.f32 (PI.f32) x))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x)
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(.f32 tau (.f32 (PI.f32) x))
tau
(*.f32 (PI.f32) x)
(PI.f32)
x
(sin.f32 (*.f32 (PI.f32) x))
(.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))
(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
(-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (*.f32 (PI.f32) (fma.f32 tau x x))))
(cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32))))
(.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))
(*.f32 (PI.f32) x)
(PI.f32)
x
(-.f32 tau #s(literal 1 binary32))
tau
#s(literal 1 binary32)
(cos.f32 (*.f32 (PI.f32) (fma.f32 tau x x)))
(*.f32 (PI.f32) (fma.f32 tau x x))
(fma.f32 tau x x)
(.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32))
(.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))
(.f32 (.f32 (PI.f32) x) (PI.f32))
(*.f32 tau x)
#s(literal 2 binary32)

Outputs
(neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) (sin.f32 (.f32 tau (.f32 x (PI.f32)))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x)))
(.f32 (sin.f32 (.f32 (neg.f32 (PI.f32)) x)) (/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (sin.f32 (.f32 (neg.f32 (PI.f32)) x)) (/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (*.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (neg.f32 (PI.f32)) x))
(sin.f32 (*.f32 (PI.f32) x))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(PI.f32)
x
(*.f32 (neg.f32 (PI.f32)) x)
(neg.f32 (PI.f32))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin.f32 (.f32 tau (.f32 x (PI.f32))))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (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)
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) (sin.f32 (.f32 tau (.f32 x (PI.f32)))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin.f32 (.f32 tau (.f32 x (PI.f32))))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
tau
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(PI.f32)
x
(.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))
(.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))
(.f32 (.f32 (PI.f32) x) (PI.f32))
(.f32 (.f32 x (PI.f32)) (PI.f32))
(*.f32 tau x)
(sin.f32 (*.f32 (PI.f32) x))
(sin.f32 (*.f32 x (PI.f32)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) (sin.f32 (.f32 tau (.f32 x (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) x) (sin.f32 (.f32 x (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x)
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) x)
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin.f32 (.f32 tau (.f32 x (PI.f32))))
(.f32 tau (.f32 (PI.f32) x))
(.f32 tau (.f32 x (PI.f32)))
tau
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(PI.f32)
x
(sin.f32 (*.f32 (PI.f32) x))
(sin.f32 (*.f32 x (PI.f32)))
(.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))
(.f32 (.f32 (*.f32 x (PI.f32)) (PI.f32)) tau)
(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 (.f32 #s(literal 2 binary32) x) x) (.f32 (.f32 (PI.f32) (PI.f32)) tau)))
(-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (*.f32 (PI.f32) (fma.f32 tau x x))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32))))
(cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))
(.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))
(.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)
(*.f32 (PI.f32) x)
(*.f32 x (PI.f32))
(PI.f32)
x
(-.f32 tau #s(literal 1 binary32))
tau
#s(literal 1 binary32)
(cos.f32 (*.f32 (PI.f32) (fma.f32 tau x x)))
(cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32)))
(*.f32 (PI.f32) (fma.f32 tau x x))
(*.f32 (fma.f32 tau x x) (PI.f32))
(fma.f32 tau x x)
(.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32))
(.f32 (.f32 (.f32 #s(literal 2 binary32) x) x) (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
(.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))
(.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))
(.f32 (.f32 (PI.f32) x) (PI.f32))
(.f32 (.f32 x (PI.f32)) (PI.f32))
(*.f32 tau x)
#s(literal 2 binary32)

localize137.0ms (1.2%)

Memory

-0.3MiB live, 165.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.359375	(*.f32 (PI.f32) x)
accuracy	0.4111900879159782	(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
accuracy	0.4248237793053261	(.f32 (.f32 (PI.f32) x) (PI.f32))
accuracy	10.176071618189527	(-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (*.f32 (PI.f32) (fma.f32 tau x x))))
accuracy	0.33984375	(.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))
accuracy	0.359375	(*.f32 (PI.f32) x)
accuracy	0.3674688180802656	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.4059562988422102	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
accuracy	0.3674688180802656	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.39681625976844204	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))
accuracy	0.4225387695368841	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
accuracy	0.4248237793053261	(.f32 (.f32 (PI.f32) x) (PI.f32))
accuracy	11.511971425197743	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
accuracy	0.359375	(*.f32 (PI.f32) x)
accuracy	0.3674688180802656	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.39357377930532605	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x))
accuracy	0.4394913086106522	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x)))

Samples

88.0ms

256×

valid

Compiler

Compiled 386 to 42 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-mult: 21.0ms (32.2% of total)

ival-sin: 12.0ms (18.4% of total)

ival-div: 11.0ms (16.9% of total)

ival-cos: 11.0ms (16.9% of total)

ival-pi: 5.0ms (7.7% of total)

ival-sub: 2.0ms (3.1% of total)

ival-neg: 2.0ms (3.1% of total)

ival-add: 1.0ms (1.5% of total)

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

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

exact: 0.0ms (0% of total)

series71.0ms (0.6%)

Memory

-1.6MiB live, 78.0MiB allocated

Counts

19 → 420

Calls

Call 1

Inputs
#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x))) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x))) #<representation binary32>) () ())
#s(alt (neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))) (patch (neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (patch (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) #<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 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x))) (patch (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (patch (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (patch (sin.f32 (.f32 tau (.f32 (PI.f32) x))) #<representation binary32>) () ())
#s(alt (.f32 tau (.f32 (PI.f32) x)) (patch (.f32 tau (.f32 (PI.f32) x)) #<representation binary32>) () ())
#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32))) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (patch (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (patch (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) #<representation binary32>) () ())
#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32))) #<representation binary32>) () ())
#s(alt (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (patch (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) #<representation binary32>) () ())
#s(alt (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (patch (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32))) (patch (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) x) (patch (.f32 (PI.f32) x) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (PI.f32) x) (PI.f32)) (patch (.f32 (.f32 (PI.f32) x) (PI.f32)) #<representation binary32>) () ())
#s(alt (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)) (patch (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)) #<representation binary32>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	x	@	0	((/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x))) (neg (/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x)))) (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (* (neg (PI)) x)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (cos (* (* (PI) x) (- tau 1))) (* (* (PI) x) (- tau 1)) (* (PI) x) (* (* (PI) x) (PI)) (* (* tau (* (PI) x)) (PI)))
12.0ms	tau	@	-inf	((/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x))) (neg (/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x)))) (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (* (neg (PI)) x)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (cos (* (* (PI) x) (- tau 1))) (* (* (PI) x) (- tau 1)) (* (PI) x) (* (* (PI) x) (PI)) (* (* tau (* (PI) x)) (PI)))
7.0ms	x	@	-inf	((/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x))) (neg (/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x)))) (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (* (neg (PI)) x)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (cos (* (* (PI) x) (- tau 1))) (* (* (PI) x) (- tau 1)) (* (PI) x) (* (* (PI) x) (PI)) (* (* tau (* (PI) x)) (PI)))
6.0ms	tau	@	inf	((/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x))) (neg (/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x)))) (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (* (neg (PI)) x)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (cos (* (* (PI) x) (- tau 1))) (* (* (PI) x) (- tau 1)) (* (PI) x) (* (* (PI) x) (PI)) (* (* tau (* (PI) x)) (PI)))
6.0ms	x	@	inf	((/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x))) (neg (/ (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (* tau (* (PI) x)))) (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (* (neg (PI)) x)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (cos (* (* (PI) x) (- tau 1))) (* (* (PI) x) (- tau 1)) (* (PI) x) (* (* (PI) x) (PI)) (* (* tau (* (PI) x)) (PI)))

simplify207.0ms (1.8%)

Memory

0.1MiB live, 191.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 170×	`lower-fma.f64`
9 170×	`lower-fma.f32`
5 826×	`lower-*.f64`
5 826×	`lower-*.f32`
4 526×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	658	8156
1	2232	7803
2	5363	7520
0	8143	7282

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(* -1 (/ (sin (* x (PI))) (* x (PI))))
(+ (* -1 (/ (sin (* x (PI))) (* x (PI)))) (* 1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))))
(+ (* -1 (/ (sin (* x (PI))) (* x (PI)))) (* (pow tau 2) (+ (* -1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))) (* 1/6 (* x (* (PI) (sin (* x (PI)))))))))
(+ (* -1 (/ (sin (* x (PI))) (* x (PI)))) (* (pow tau 2) (+ (* 1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* 1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))))))))
(/ (sin (* x (PI))) (* x (PI)))
(- (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (* -1 (/ (sin (* x (PI))) (* x (PI)))))
(- (* (pow tau 2) (- (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))) (* 1/6 (* x (* (PI) (sin (* x (PI)))))))) (* -1 (/ (sin (* x (PI))) (* x (PI)))))
(- (* (pow tau 2) (- (* (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)))))))) (* 1/6 (* x (* (PI) (sin (* x (PI)))))))) (* -1 (/ (sin (* x (PI))) (* x (PI)))))
(* -1 (* tau (sin (* x (PI)))))
(* tau (+ (* -1 (sin (* x (PI)))) (* 1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))))))
(* tau (+ (* -1 (sin (* x (PI)))) (* (pow tau 2) (+ (* -1/120 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI))))))) (* 1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI))))))))))
(* tau (+ (* -1 (sin (* x (PI)))) (* (pow tau 2) (+ (* 1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/120 (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI)))))) (* 1/5040 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 6) (sin (* x (PI)))))))))))))
(/ (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 (* 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))))
(/ 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))))
(* 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)))))))))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(/ (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))))
(* tau (* (PI) (sin (* x (PI)))))
(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 3) (sin (* x (PI))))))) (* (PI) (sin (* x (PI))))))
(* tau (+ (* (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)))))))))))
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(+ (* 1/2 (/ (- (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))) (* tau (pow (PI) 2)))) (* (pow x 2) (+ (* 1/2 (* (pow x 2) (- (* -1/720 (/ (* (pow (PI) 4) (pow (- tau 1) 6)) tau)) (* -1/720 (/ (* (pow (PI) 4) (pow (+ 1 tau) 6)) tau))))) (* 1/2 (- (* 1/24 (/ (* (pow (PI) 2) (pow (- tau 1) 4)) tau)) (* 1/24 (/ (* (pow (PI) 2) (pow (+ 1 tau) 4)) tau)))))))
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(* (pow x 2) (- (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))))
(* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))))
(* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (+ (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* (pow x 2) (- (* -1/720 (* (pow (PI) 6) (pow (- tau 1) 6))) (* -1/720 (* (pow (PI) 6) (pow (+ 1 tau) 6)))))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))))
(* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (+ (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* (pow x 2) (- (+ (* -1/720 (* (pow (PI) 6) (pow (- tau 1) 6))) (* (pow x 2) (- (* 1/40320 (* (pow (PI) 8) (pow (- tau 1) 8))) (* 1/40320 (* (pow (PI) 8) (pow (+ 1 tau) 8)))))) (* -1/720 (* (pow (PI) 6) (pow (+ 1 tau) 6)))))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))))
1
(+ 1 (* -1/2 (* (pow x 2) (* (pow (PI) 2) (pow (- tau 1) 2)))))
(+ 1 (* (pow x 2) (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* 1/24 (* (pow x 2) (* (pow (PI) 4) (pow (- tau 1) 4)))))))
(+ 1 (* (pow x 2) (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (* (pow (PI) 6) (pow (- tau 1) 6)))) (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))))))))
(* x (* (PI) (- tau 1)))
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(* x (PI))
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(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* tau (* x (pow (PI) 2)))
(* -1 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (* (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 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI))))
(* -1 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI))))
(* -1 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI))))
(* -1 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (PI))))
(* -1 (/ (sin (* x (PI))) (* x (PI))))
(* -1 (/ (sin (* x (PI))) (* x (PI))))
(* -1 (/ (sin (* x (PI))) (* x (PI))))
(* -1 (/ (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))))
(/ (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))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
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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)))) x)
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)
(/ (sin (* tau (* x (PI)))) x)
(/ (sin (* tau (* x (PI)))) x)
(/ (sin (* tau (* x (PI)))) x)
(/ (sin (* tau (* x (PI)))) x)
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x)))))
(cos (* x (* (PI) (- tau 1))))
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(cos (* x (* (PI) (- tau 1))))
(* x (* (PI) (- tau 1)))
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(* 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 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (* (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)))) (* 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))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* 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)))) x)
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) x)
(/ (sin (* tau (* x (PI)))) x)
(/ (sin (* tau (* x (PI)))) x)
(/ (sin (* tau (* x (PI)))) x)
(/ (sin (* tau (* x (PI)))) x)
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
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(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
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(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(cos (* x (* (PI) (- tau 1))))
(cos (* x (* (PI) (- tau 1))))
(cos (* x (* (PI) (- tau 1))))
(cos (* x (* (PI) (- tau 1))))
(* x (* (PI) (- tau 1)))
(* x (* (PI) (- tau 1)))
(* x (* (PI) (- tau 1)))
(* x (* (PI) (- tau 1)))
(* x (PI))
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(* x (PI))
(* x (PI))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* x (pow (PI) 2))
(* 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 (/ (sin (* x (PI))) (* x (PI))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x))
(+ (* -1 (/ (sin (* x (PI))) (* x (PI)))) (* 1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))))
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(+ (* -1 (/ (sin (* x (PI))) (* x (PI)))) (* (pow tau 2) (+ (* -1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))) (* 1/6 (* x (* (PI) (sin (* x (PI)))))))))
(fma.f32 (fma.f32 (.f32 #s(literal 1/6 binary32) x) (.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (.f32 (.f32 #s(literal -1/120 binary32) (.f32 tau tau)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 x x) x)))) (.f32 tau tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)))
(+ (* -1 (/ (sin (* x (PI))) (* x (PI)))) (* (pow tau 2) (+ (* 1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* 1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))))))))
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(/ (sin (* x (PI))) (* x (PI)))
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(- (* (pow tau 2) (- (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))) (* 1/6 (* x (* (PI) (sin (* x (PI)))))))) (* -1 (/ (sin (* x (PI))) (* x (PI)))))
(fma.f32 (fma.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau tau)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 x x) x)) (.f32 (.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) #s(literal -1/6 binary32))) (.f32 tau tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(- (* (pow tau 2) (- (* (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)))))))) (* 1/6 (* x (* (PI) (sin (* x (PI)))))))) (* -1 (/ (sin (* x (PI))) (* x (PI)))))
(fma.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) x) (.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (.f32 (fma.f32 (.f32 #s(literal 1/120 binary32) (.f32 (.f32 x x) x)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 #s(literal -1/5040 binary32) (.f32 tau tau)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) (sin.f32 (.f32 (PI.f32) x))) (pow.f32 x #s(literal 5 binary32))))) (.f32 tau tau))) (.f32 tau tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))
(* -1 (* tau (sin (* x (PI)))))
(.f32 (neg.f32 tau) (sin.f32 (.f32 (PI.f32) x)))
(* tau (+ (* -1 (sin (* x (PI)))) (* 1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))))))
(.f32 (-.f32 (.f32 (.f32 #s(literal 1/6 binary32) (.f32 tau tau)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 x x))) (sin.f32 (.f32 (PI.f32) x))) tau)
(* tau (+ (* -1 (sin (* x (PI)))) (* (pow tau 2) (+ (* -1/120 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI))))))) (* 1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI))))))))))
(.f32 (-.f32 (.f32 (fma.f32 (.f32 #s(literal 1/6 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 #s(literal -1/120 binary32) (.f32 tau tau)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (sin.f32 (.f32 (PI.f32) x))) (pow.f32 x #s(literal 4 binary32))))) (.f32 tau tau)) (sin.f32 (*.f32 (PI.f32) x))) tau)
(* tau (+ (* -1 (sin (* x (PI)))) (* (pow tau 2) (+ (* 1/6 (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/120 (* (pow x 4) (* (pow (PI) 4) (sin (* x (PI)))))) (* 1/5040 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 6) (sin (* x (PI)))))))))))))
(.f32 (-.f32 (.f32 (fma.f32 (.f32 #s(literal 1/6 binary32) (.f32 x x)) (.f32 (.f32 (PI.f32) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (fma.f32 (.f32 #s(literal 1/5040 binary32) (.f32 tau tau)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (sin.f32 (.f32 (PI.f32) x))) (pow.f32 x #s(literal 6 binary32))) (.f32 (.f32 #s(literal -1/120 binary32) (pow.f32 x #s(literal 4 binary32))) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (sin.f32 (.f32 (PI.f32) x))))) (.f32 tau tau))) (.f32 tau tau)) (sin.f32 (.f32 (PI.f32) x))) tau)
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))
(+ (* (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))))
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(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x)
(/ (sin (* tau (* x (PI)))) x)
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x)
(/ (sin (* tau (* x (PI)))) x)
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x)
(/ (sin (* tau (* x (PI)))) x)
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x)
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))
(cos (* x (* (PI) (- tau 1))))
(cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))
(* x (* (PI) (- tau 1)))
(.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)
(* x (* (PI) (- tau 1)))
(.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)
(* x (* (PI) (- tau 1)))
(.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)
(* x (* (PI) (- tau 1)))
(.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)
(* x (PI))
(*.f32 (PI.f32) x)
(* x (PI))
(*.f32 (PI.f32) x)
(* x (PI))
(*.f32 (PI.f32) x)
(* x (PI))
(*.f32 (PI.f32) x)
(* x (pow (PI) 2))
(.f32 (.f32 (PI.f32) (PI.f32)) x)
(* x (pow (PI) 2))
(.f32 (.f32 (PI.f32) (PI.f32)) x)
(* x (pow (PI) 2))
(.f32 (.f32 (PI.f32) (PI.f32)) x)
(* x (pow (PI) 2))
(.f32 (.f32 (PI.f32) (PI.f32)) x)
(* tau (* x (pow (PI) 2)))
(.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) x) tau)
(* tau (* x (pow (PI) 2)))
(.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) x) tau)
(* tau (* x (pow (PI) 2)))
(.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) x) tau)
(* tau (* x (pow (PI) 2)))
(.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) x) tau)

rewrite255.0ms (2.2%)

Memory

25.4MiB live, 255.9MiB allocated

Rules

6 042×	`lower-/.f64`
6 030×	`lower-/.f32`
3 626×	`lower-*.f64`
3 600×	`lower-*.f32`
2 132×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	257
0	71	261
1	299	255
2	2176	241
0	8190	241

Stop Event

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

Counts

19 → 1 494

Calls

Call 1

Inputs
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x)))
(neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(.f32 tau (.f32 (PI.f32) x))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x)
(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
(-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (*.f32 (PI.f32) (fma.f32 tau x x))))
(cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32))))
(.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))
(*.f32 (PI.f32) x)
(.f32 (.f32 (PI.f32) x) (PI.f32))
(.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))

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

eval291.0ms (2.5%)

Memory: 38.2MiB live, 335.8MiB allocated
Compiler: Compiled 67 755 to 3 722 computations (94.5% saved)

prune470.0ms (4.1%)

Memory

-5.1MiB live, 630.1MiB allocated

Pruning

58 alts after pruning (57 fresh and 1 done)

	Pruned	Kept	Total
New	2 369	41	2 410
Fresh	13	16	29
Picked	4	1	5
Done	0	0	0
Total	2 386	58	2 444

Accuracy

99.9%

Counts

2 444 → 58

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.9%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 x (PI.f32)) (PI.f32))) (.f32 #s(literal 2 binary32) (*.f32 tau x)))
	97.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) x) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	64.3%	(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) (PI.f32))) (.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 (.f32 x (PI.f32)) (PI.f32)) tau)) x)) (.f32 (.f32 #s(literal 2 binary32) (.f32 tau x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))))) (.f32 (.f32 #s(literal 2 binary32) (.f32 tau x)) (.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 (.f32 x (PI.f32)) (PI.f32)) tau)) x)))
	66.9%	(/.f32 (-.f32 (cos.f32 (fma.f32 (.f32 tau (PI.f32)) x (.f32 (neg.f32 (PI.f32)) x))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
	66.8%	(/.f32 (-.f32 (cos.f32 (/.f32 (fma.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))) (pow.f32 (.f32 (neg.f32 (PI.f32)) x) #s(literal 3 binary32))) (fma.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 tau (.f32 x (PI.f32))) (-.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 (neg.f32 (PI.f32)) x)))))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
	66.9%	(/.f32 (-.f32 (cos.f32 (/.f32 (.f32 (fma.f32 tau tau #s(literal -1 binary32)) (.f32 x (PI.f32))) (+.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
	66.9%	(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 tau x)) #s(literal 2 binary32)))
	51.7%	(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) (fma.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
	33.4%	(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) #s(literal 1 binary32)) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
▶	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 (.f32 (*.f32 x (PI.f32)) (PI.f32)) tau))
	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
	66.9%	(/.f32 (.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))) #s(literal 2 binary32))
	97.0%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) tau)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) x))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))
	97.4%	(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (PI.f32)) x))
	97.2%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32)))
	97.6%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x)))
	63.7%	(/.f32 #s(approx (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 x x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
	63.9%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	97.5%	(/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) (/.f32 (.f32 tau (.f32 x (PI.f32))) (sin.f32 (.f32 tau (*.f32 x (PI.f32)))))))
	97.1%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.0%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))))
	95.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))))
▶	85.5%	(.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 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	71.2%	(.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)))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (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 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
▶	66.9%	(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
	97.3%	(.f32 (.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (PI.f32)) x))) (sin.f32 (*.f32 (PI.f32) x)))
	97.4%	(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))))
	97.3%	(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (sin.f32 (*.f32 x (PI.f32)))))
▶	97.1%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
	97.2%	(.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
	85.0%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (fma.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau tau)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) x))) (.f32 tau tau) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (.f32 (PI.f32) x)))
	80.0%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (*.f32 (PI.f32) x)))
	79.9%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 (PI.f32) x)))
	96.9%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (sin.f32 (*.f32 (PI.f32) x)))
	64.9%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x)))
	96.3%	(.f32 #s(literal -1 binary32) (/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) (fma.f32 (-.f32 tau #s(literal 1 binary32)) x (fma.f32 tau x x))) #s(literal 1/2 binary32))) (sin.f32 (.f32 (.f32 (PI.f32) (-.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) x) (fma.f32 tau x x))) #s(literal 1/2 binary32)))) (.f32 (.f32 (.f32 tau (*.f32 x (PI.f32))) x) (PI.f32))))
	96.4%	(.f32 #s(literal -2 binary32) (/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) (fma.f32 (-.f32 tau #s(literal 1 binary32)) x (fma.f32 tau x x))) #s(literal 1/2 binary32))) (sin.f32 (.f32 (.f32 (PI.f32) (-.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) x) (fma.f32 tau x x))) #s(literal 1/2 binary32)))) (.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 (.f32 x (PI.f32)) (PI.f32)) tau)) x)))
	97.3%	(neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 (.f32 tau (PI.f32)) x))) (.f32 tau (*.f32 (PI.f32) x))))
	85.4%	(neg.f32 (/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) (* (neg (PI)) x)) (fma.f32 (.f32 #s(literal 1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)) #s(literal -1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x))))
	78.3%	(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (-.f32 (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau))) (.f32 x x)) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 (PI.f32) x))))
	63.9%	(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
	64.9%	(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (neg.f32 tau) (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x))))
	63.8%	#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau)) #s(literal 1/2 binary32)))
▶	6.3%	#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
	79.4%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	64.8%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
	84.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32)))
	79.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
✓	64.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 3 116 to 1 691 computations (45.7% saved)

simplify131.0ms (1.1%)

Memory

3.6MiB live, 152.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(.f32 (.f32 tau (*.f32 x (PI.f32))) x)
cost-diff	0	(.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))
cost-diff	0	(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32)))
cost-diff	0	(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
cost-diff	0	(*.f32 (PI.f32) x)
cost-diff	0	(sin.f32 (*.f32 (PI.f32) x))
cost-diff	0	(neg.f32 (sin.f32 (*.f32 (PI.f32) x)))
cost-diff	128	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
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	0	(.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 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
cost-diff	0	#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
cost-diff	0	(sin.f32 (*.f32 x (PI.f32)))
cost-diff	0	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (*.f32 x (PI.f32)))))
cost-diff	192	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))

Rules

9 436×	`lower-fma.f64`
9 432×	`lower-fma.f32`
3 968×	`lower-*.f64`
3 930×	`lower-*.f32`
3 696×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	410
0	109	408
1	234	408
2	622	408
3	2607	408
4	4682	408
0	8262	408

Stop Event

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

Calls

Call 1

Inputs
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (*.f32 x (PI.f32)))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(sin.f32 (*.f32 x (PI.f32)))
(*.f32 x (PI.f32))
x
(PI.f32)
(sin.f32 (.f32 tau (.f32 x (PI.f32))))
(.f32 tau (.f32 x (PI.f32)))
tau
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
#s(literal 0 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 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.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
#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
(fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
(.f32 (.f32 #s(literal -1/6 binary32) x) x)
(*.f32 #s(literal -1/6 binary32) x)
#s(literal -1/6 binary32)
(*.f32 (PI.f32) (PI.f32))
#s(literal 1 binary32)
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
(neg.f32 (sin.f32 (*.f32 (PI.f32) x)))
(sin.f32 (*.f32 (PI.f32) x))
(*.f32 (PI.f32) x)
(PI.f32)
x
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(.f32 tau (.f32 (PI.f32) x))
tau
(.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))
(.f32 (.f32 (PI.f32) x) x)
(*.f32 (neg.f32 tau) (PI.f32))
(neg.f32 tau)
(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32)))
#s(literal 1/2 binary32)
(.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))
(.f32 (.f32 tau (*.f32 x (PI.f32))) x)
(.f32 tau (.f32 x (PI.f32)))
tau
(*.f32 x (PI.f32))
x
(PI.f32)
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))
(.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)
(*.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32))
(-.f32 tau #s(literal 1 binary32))
#s(literal 1 binary32)
(cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32)))
(*.f32 (fma.f32 tau x x) (PI.f32))
(fma.f32 tau x x)

Outputs
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) (.f32 x x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (*.f32 x (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (*.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/.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)
x
(PI.f32)
(sin.f32 (.f32 tau (.f32 x (PI.f32))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
tau
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
#s(literal 0 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 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))
(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(.f32 (.f32 x (PI.f32)) tau)
(.f32 tau (.f32 (PI.f32) x))
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
x
(PI.f32)
tau
#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32)))
(fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
(fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))
(.f32 (.f32 #s(literal -1/6 binary32) x) x)
(*.f32 #s(literal -1/6 binary32) x)
#s(literal -1/6 binary32)
(*.f32 (PI.f32) (PI.f32))
#s(literal 1 binary32)
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) (.f32 x x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))
(neg.f32 (sin.f32 (*.f32 (PI.f32) x)))
(sin.f32 (*.f32 (PI.f32) x))
(*.f32 (PI.f32) x)
(PI.f32)
x
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (neg.f32 (PI.f32)) (PI.f32)) (.f32 (.f32 x x) tau)))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(.f32 tau (.f32 (PI.f32) x))
tau
(.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))
(.f32 (.f32 (neg.f32 (PI.f32)) (PI.f32)) (.f32 (.f32 x x) tau))
(.f32 (.f32 (PI.f32) x) x)
(*.f32 (neg.f32 tau) (PI.f32))
(neg.f32 tau)
(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
(.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) (.f32 x x))))
(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32)))
(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) (.f32 x x)))
#s(literal 1/2 binary32)
(.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))
(.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) (.f32 x x))
(.f32 (.f32 tau (*.f32 x (PI.f32))) x)
(.f32 (.f32 (*.f32 (PI.f32) x) x) tau)
(.f32 tau (.f32 x (PI.f32)))
(.f32 tau (.f32 (PI.f32) x))
tau
(*.f32 x (PI.f32))
(*.f32 (PI.f32) x)
x
(PI.f32)
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))
(.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)
(*.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32))
(-.f32 tau #s(literal 1 binary32))
#s(literal 1 binary32)
(cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32)))
(*.f32 (fma.f32 tau x x) (PI.f32))
(fma.f32 tau x x)

localize192.0ms (1.7%)

Memory

21.4MiB live, 296.6MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3984375	(.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))
accuracy	0.44273378907376815	(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
accuracy	10.176071618189527	(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
accuracy	0.3674688180802656	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.390625	(.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))
accuracy	0.39681625976844204	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))))
accuracy	0.4225387695368841	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
accuracy	0.3674688180802656	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.4091987793053261	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	4.427938075790228	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
accuracy	29.982374435491185	#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3674688180802656	(sin.f32 (.f32 tau (.f32 x (PI.f32))))
accuracy	0.39357377930532605	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.4394913086106522	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))

Samples

143.0ms

256×

valid

Compiler

Compiled 395 to 59 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 111.0ms

ival-mult: 40.0ms (36% of total)

ival-sin: 40.0ms (36% of total)

ival-cos: 11.0ms (9.9% of total)

ival-div: 8.0ms (7.2% of total)

const: 4.0ms (3.6% of total)

ival-sub: 3.0ms (2.7% of total)

ival-add: 2.0ms (1.8% of total)

ival-neg: 2.0ms (1.8% 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)

series61.0ms (0.5%)

Memory

-13.7MiB live, 104.3MiB allocated

Counts

25 → 492

Calls

Call 1

Inputs
#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32)))) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (patch (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (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 (sin.f32 (.f32 x (PI.f32))) (patch (sin.f32 (.f32 x (PI.f32))) #<representation binary32>) () ())
#s(alt #s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32)) (patch #s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32)) #<representation binary32>) () ())
#s(alt (.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 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))) (patch (.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 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))) #<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 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))))) (patch (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))))) #<representation binary32>) () ())
#s(alt (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (patch (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 (PI.f32) x)) (patch (sin.f32 (.f32 (PI.f32) x)) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) x) (patch (.f32 (PI.f32) x) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))))) (patch (.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))))) #<representation binary32>) () ())
#s(alt (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (patch (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32)) (patch (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32)) #<representation binary32>) () ())
#s(alt (.f32 (.f32 tau (.f32 x (PI.f32))) x) (patch (.f32 (.f32 tau (.f32 x (PI.f32))) x) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (patch (sin.f32 (.f32 tau (.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))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (PI.f32)) (patch (.f32 (PI.f32) (PI.f32)) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))) (patch (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))) (patch (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (patch (sin.f32 (.f32 tau (.f32 (PI.f32) x))) #<representation binary32>) () ())
#s(alt (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (patch (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) #<representation binary32>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	tau	@	0	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (neg (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI))))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (* (PI) x) (* (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI))))) (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (* (* (* tau (* x (PI))) x) (PI)) (* (* tau (* x (PI))) x) (sin (* tau (* x (PI)))) (* x (PI)) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (* (* (* (PI) x) x) (* (neg tau) (PI))) (sin (* tau (* (PI) x))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI)))))
9.0ms	x	@	inf	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (neg (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI))))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (* (PI) x) (* (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI))))) (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (* (* (* tau (* x (PI))) x) (PI)) (* (* tau (* x (PI))) x) (sin (* tau (* x (PI)))) (* x (PI)) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (* (* (* (PI) x) x) (* (neg tau) (PI))) (sin (* tau (* (PI) x))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI)))))
5.0ms	x	@	-inf	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (neg (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI))))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (* (PI) x) (* (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI))))) (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (* (* (* tau (* x (PI))) x) (PI)) (* (* tau (* x (PI))) x) (sin (* tau (* x (PI)))) (* x (PI)) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (* (* (* (PI) x) x) (* (neg tau) (PI))) (sin (* tau (* (PI) x))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI)))))
5.0ms	tau	@	inf	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (neg (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI))))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (* (PI) x) (* (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI))))) (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (* (* (* tau (* x (PI))) x) (PI)) (* (* tau (* x (PI))) x) (sin (* tau (* x (PI)))) (* x (PI)) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (* (* (* (PI) x) x) (* (neg tau) (PI))) (sin (* tau (* (PI) x))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI)))))
5.0ms	tau	@	-inf	((/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (neg (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI))))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (* (PI) x) (* (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI))))) (/ 1/2 (* (* (* tau (* x (PI))) x) (PI))) (* (* (* tau (* x (PI))) x) (PI)) (* (* tau (* x (PI))) x) (sin (* tau (* x (PI)))) (* x (PI)) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (* (* (* (PI) x) x) (* (neg tau) (PI))) (sin (* tau (* (PI) x))) (- (cos (* (* (- tau 1) (PI)) x)) (cos (* (+ (* tau x) x) (PI)))))

simplify273.0ms (2.4%)

Memory

2.7MiB live, 273.1MiB allocated

Algorithm

1×	egg-herbie

Rules

15 152×	`lower-fma.f64`
15 152×	`lower-fma.f32`
8 736×	`lower-*.f64`
8 736×	`lower-*.f32`
3 160×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	540	8555
1	1767	8233
2	6566	7957
0	8309	7702

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

Inputs
(/ (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))))
(* 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))))))))))))
(* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(/ (+ (* 1/2 (* tau (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))) (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2))))) tau)
(/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (* tau (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))) (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))))) tau)
(/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI))))) (* tau (+ (* 1/2 (* tau (- (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* -1/6 (* x (* (PI) (sin (* -1 (* x (PI)))))))))) (* 1/2 (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))))))) tau)
(/ (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))))
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))))))))
(* 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)))))))))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(/ (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))))
(* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(/ (+ (* 1/2 (* tau (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))) (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2))))) tau)
(/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (* tau (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))) (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))))) tau)
(/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI))))) (* tau (+ (* 1/2 (* tau (- (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* -1/6 (* x (* (PI) (sin (* -1 (* x (PI)))))))))) (* 1/2 (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))))))) tau)
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1/2 (* 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) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (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)))))))))
(/ -1 (* x (PI)))
(- (* 1/6 (* (pow tau 2) (* x (PI)))) (/ 1 (* x (PI))))
(- (* (pow tau 2) (+ (* -1/120 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* 1/6 (* x (PI))))) (/ 1 (* x (PI))))
(- (* (pow tau 2) (+ (* 1/6 (* x (PI))) (* (pow tau 2) (+ (* -1/120 (* (pow x 3) (pow (PI) 3))) (* 1/5040 (* (pow tau 2) (* (pow x 5) (pow (PI) 5)))))))) (/ 1 (* x (PI))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* 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)))))))))
(- (cos (* -1 (* x (PI)))) (cos (* x (PI))))
(- (+ (cos (* -1 (* x (PI)))) (* tau (- (* x (* (PI) (sin (* x (PI))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI))))
(- (+ (cos (* -1 (* x (PI)))) (* tau (- (+ (* tau (- (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* x (PI)))))))) (* x (* (PI) (sin (* x (PI)))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI))))
(- (+ (cos (* -1 (* x (PI)))) (* tau (- (+ (* tau (- (+ (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* tau (- (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI)))))))))) (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* x (PI)))))))) (* x (* (PI) (sin (* x (PI)))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* 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))))
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(* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2)))))
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(* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (+ (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* (pow x 2) (- (+ (* -1/720 (* (pow (PI) 6) (pow (- tau 1) 6))) (* (pow x 2) (- (* 1/40320 (* (pow (PI) 8) (pow (- tau 1) 8))) (* 1/40320 (* (pow (PI) 8) (pow (+ 1 tau) 8)))))) (* -1/720 (* (pow (PI) 6) (pow (+ 1 tau) 6)))))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 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)))) (* 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 (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* 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)))) (* 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))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* 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))))
(* -1 (sin (* x (PI))))
(* -1 (sin (* x (PI))))
(* -1 (sin (* x (PI))))
(* -1 (sin (* x (PI))))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1/2 (* 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) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* x (PI))
(* x (PI))
(* 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 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (+ x (* tau x)))))
(/ (* (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)))) (* 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 (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(/ (sin (* x (PI))) (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* 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)))) (* 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))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* x (PI)))
(* tau (* 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))))
(* -1 (sin (* x (PI))))
(* -1 (sin (* x (PI))))
(* -1 (sin (* x (PI))))
(* -1 (sin (* x (PI))))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(sin (* x (PI)))
(* x (PI))
(* x (PI))
(* x (PI))
(* x (PI))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/ 1/2 (* 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) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(* tau (* (pow x 2) (PI)))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(* x (PI))
(* x (PI))
(* 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 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(sin (* tau (* x (PI))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))

Outputs
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))
(+ (* (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 (fma.f32 (.f32 (.f32 tau tau) #s(literal 1/120 binary32)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 x x) x)) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (PI.f32)) (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(+ (* (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 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (PI.f32)) (sin.f32 (.f32 (PI.f32) x)) (.f32 (fma.f32 (.f32 (.f32 #s(literal 1/120 binary32) (.f32 x x)) x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 #s(literal -1/5040 binary32) (.f32 tau tau)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) (sin.f32 (.f32 (PI.f32) x))) (pow.f32 x #s(literal 5 binary32))))) (.f32 tau tau))) (.f32 tau tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))
(* tau (sin (* x (PI))))
(.f32 tau (sin.f32 (.f32 (PI.f32) x)))
(* tau (+ (sin (* x (PI))) (* -1/6 (* (pow tau 2) (* (pow x 2) (* (pow (PI) 2) (sin (* x (PI)))))))))
(.f32 (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 x x)) (sin.f32 (*.f32 (PI.f32) x))) tau)
(* 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)))))))))))
(.f32 (fma.f32 (fma.f32 (.f32 (.f32 tau tau) #s(literal 1/120 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 x x) (.f32 x x))) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (PI.f32) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))))) (.f32 tau tau) (sin.f32 (*.f32 (PI.f32) x))) tau)
(* 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))))))))))))
(.f32 (fma.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 (.f32 (.f32 #s(literal 1/120 binary32) (.f32 (.f32 x x) (.f32 x x))) (sin.f32 (.f32 (PI.f32) x))) (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (.f32 #s(literal -1/5040 binary32) (.f32 tau tau)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (sin.f32 (.f32 (PI.f32) x))) (pow.f32 x #s(literal 6 binary32))))) (.f32 tau tau))) (.f32 tau tau) (sin.f32 (.f32 (PI.f32) x))) tau)
(* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
#s(literal 0 binary32)
(/ (+ (* 1/2 (* tau (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))) (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2))))) tau)
(/.f32 (fma.f32 (.f32 tau #s(literal 1/2 binary32)) (+.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x))) #s(literal 0 binary32)) tau)
(/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (* tau (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))) (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))))) tau)
(/.f32 (fma.f32 (.f32 tau #s(literal 1/2 binary32)) (fma.f32 #s(literal 0 binary32) tau (+.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))) #s(literal 0 binary32)) tau)
(/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI))))) (* tau (+ (* 1/2 (* tau (- (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* -1/6 (* x (* (PI) (sin (* -1 (* x (PI)))))))))) (* 1/2 (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))))))) tau)
(/.f32 (fma.f32 (fma.f32 (fma.f32 (.f32 (.f32 #s(literal 1/2 binary32) tau) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) x) (+.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x)))) #s(literal 0 binary32)) tau (.f32 (+.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x))) #s(literal 1/2 binary32))) tau #s(literal 0 binary32)) tau)
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))
(+ (* (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 (fma.f32 (.f32 (.f32 tau tau) #s(literal 1/120 binary32)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 x x) x)) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (PI.f32)) (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(+ (* (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 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (PI.f32)) (sin.f32 (.f32 (PI.f32) x)) (.f32 (fma.f32 (.f32 (.f32 #s(literal 1/120 binary32) (.f32 x x)) x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 #s(literal -1/5040 binary32) (.f32 tau tau)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) (sin.f32 (.f32 (PI.f32) x))) (pow.f32 x #s(literal 5 binary32))))) (.f32 tau tau))) (.f32 tau tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))
1
#s(literal 1 binary32)
(+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))
(fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (*.f32 tau (PI.f32)) tau) (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)))))))
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(sin.f32 (*.f32 (PI.f32) x))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.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 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.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 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.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 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32))))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(* tau (* x (PI)))
(.f32 tau (.f32 (PI.f32) x))
(* tau (* x (PI)))
(.f32 tau (.f32 (PI.f32) x))
(* tau (* x (PI)))
(.f32 tau (.f32 (PI.f32) x))
(* tau (* x (PI)))
(.f32 tau (.f32 (PI.f32) x))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.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 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.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 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.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 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32))))
(* -1 (sin (* x (PI))))
(sin.f32 (*.f32 (neg.f32 (PI.f32)) x))
(* -1 (sin (* x (PI))))
(sin.f32 (*.f32 (neg.f32 (PI.f32)) x))
(* -1 (sin (* x (PI))))
(sin.f32 (*.f32 (neg.f32 (PI.f32)) x))
(* -1 (sin (* x (PI))))
(sin.f32 (*.f32 (neg.f32 (PI.f32)) x))
(sin (* x (PI)))
(sin.f32 (*.f32 (PI.f32) x))
(sin (* x (PI)))
(sin.f32 (*.f32 (PI.f32) x))
(sin (* x (PI)))
(sin.f32 (*.f32 (PI.f32) x))
(sin (* x (PI)))
(sin.f32 (*.f32 (PI.f32) x))
(* x (PI))
(*.f32 (PI.f32) x)
(* x (PI))
(*.f32 (PI.f32) x)
(* x (PI))
(*.f32 (PI.f32) x)
(* x (PI))
(*.f32 (PI.f32) x)
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(* 1/2 (/ (- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2)))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))) #s(literal 1/2 binary32))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32))))
(/ 1/2 (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))
(* tau (* (pow x 2) (PI)))
(.f32 (.f32 (*.f32 x x) (PI.f32)) tau)
(* tau (* (pow x 2) (PI)))
(.f32 (.f32 (*.f32 x x) (PI.f32)) tau)
(* tau (* (pow x 2) (PI)))
(.f32 (.f32 (*.f32 x x) (PI.f32)) tau)
(* tau (* (pow x 2) (PI)))
(.f32 (.f32 (*.f32 x x) (PI.f32)) tau)
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(* x (PI))
(*.f32 (PI.f32) x)
(* x (PI))
(*.f32 (PI.f32) x)
(* x (PI))
(*.f32 (PI.f32) x)
(* x (PI))
(*.f32 (PI.f32) x)
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (neg.f32 tau) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x)))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (neg.f32 tau) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x)))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (neg.f32 tau) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x)))
(* -1 (/ (sin (* tau (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (neg.f32 tau) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x)))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (neg.f32 tau) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (neg.f32 tau) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (neg.f32 tau) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x))
(* -1 (* tau (* (pow x 2) (pow (PI) 2))))
(.f32 (neg.f32 tau) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(- (cos (* x (* (PI) (- tau 1)))) (cos (* (PI) (- (* tau x) (* -1 x)))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))

rewrite297.0ms (2.6%)

Memory

40.4MiB live, 344.4MiB allocated

Rules

5 516×	`lower-/.f64`
5 506×	`lower-/.f32`
4 034×	`lower-*.f64`
3 996×	`lower-*.f32`
3 138×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	303
0	109	301
1	386	301
2	2311	283
0	8443	281

Stop Event

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

Counts

25 → 1 007

Calls

Call 1

Inputs
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (*.f32 x (PI.f32)))))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(sin.f32 (*.f32 x (PI.f32)))
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 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 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.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 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
(neg.f32 (sin.f32 (*.f32 (PI.f32) x)))
(sin.f32 (*.f32 (PI.f32) x))
(*.f32 (PI.f32) x)
(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
(/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32)))
(.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))
(.f32 (.f32 tau (*.f32 x (PI.f32))) x)
(sin.f32 (.f32 tau (.f32 x (PI.f32))))
(*.f32 x (PI.f32))
#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
(*.f32 (PI.f32) (PI.f32))
(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))))
(.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))
(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))

Outputs
(.f32 (pow.f32 (/.f32 (.f32 tau x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)) (pow.f32 (/.f32 (PI.f32) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (.f32 tau x) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) #s(literal -1 binary32)) (pow.f32 (/.f32 (PI.f32) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 tau (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)) (pow.f32 (/.f32 (.f32 (PI.f32) x) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (.f32 (PI.f32) x) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) #s(literal -1 binary32)) (pow.f32 (/.f32 tau (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (.f32 tau (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) #s(literal -1 binary32)) (pow.f32 (/.f32 x (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 x (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)) (pow.f32 (/.f32 (.f32 tau (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)) (pow.f32 (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) #s(literal -1 binary32)) (pow.f32 (/.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32))) (pow.f32 (/.f32 x (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 tau x)) (pow.f32 (/.f32 (PI.f32) (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) (PI.f32)) (.f32 x x))) #s(literal -1 binary32)) (sin.f32 (*.f32 (PI.f32) x)))
(.f32 (/.f32 #s(literal 1 binary32) x) (pow.f32 (/.f32 (.f32 tau (PI.f32)) (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) tau) (pow.f32 (/.f32 (.f32 (PI.f32) x) (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 tau (PI.f32))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 tau x)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (PI.f32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau))
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(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))))
(-.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (neg.f32 (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))) (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (fma.f32 tau x x) (PI.f32)))))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (neg.f32 (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32)))))))
(-.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))))) (+.f32 (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))) (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)))) (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (fma.f32 tau x x) (PI.f32)))))) (+.f32 (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))) (cos.f32 (.f32 (*.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)))))
(-.f32 (/.f32 (pow.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) #s(literal 3 binary32)) (fma.f32 (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))) (+.f32 (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))) (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))) (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))))))) (/.f32 (pow.f32 (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))) #s(literal 3 binary32)) (fma.f32 (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))) (+.f32 (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))) (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))) (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (*.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x))))))))
(-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))
(fma.f32 #s(literal -1 binary32) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))) (cos.f32 (.f32 (*.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)))
(pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32))))) #s(literal -1 binary32))
(+.f32 (neg.f32 (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))) (cos.f32 (.f32 (*.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)))
(+.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (neg.f32 (cos.f32 (*.f32 (fma.f32 tau x x) (PI.f32)))))

eval473.0ms (4.1%)

Memory: -118.4MiB live, 391.8MiB allocated
Compiler: Compiled 52 810 to 3 044 computations (94.2% saved)

prune492.0ms (4.3%)

Memory

26.3MiB live, 878.4MiB allocated

Pruning

85 alts after pruning (80 fresh and 5 done)

	Pruned	Kept	Total
New	1 646	49	1 695
Fresh	21	31	52
Picked	1	4	5
Done	0	1	1
Total	1 668	85	1 753

Accuracy

99.9%

Counts

1 753 → 85

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) x) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	85.1%	(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (PI.f32))) x)
	85.0%	(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau x)) (PI.f32))
	85.1%	(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) x) (.f32 tau (PI.f32)))
	66.9%	(/.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))))) (.f32 (.f32 (*.f32 (PI.f32) x) x) tau)) (PI.f32))
	64.3%	(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (.f32 (.f32 (PI.f32) x) (PI.f32))) (.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau)) x)) (.f32 (.f32 #s(literal 2 binary32) (.f32 tau x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))))) (.f32 (.f32 #s(literal 2 binary32) (.f32 tau x)) (.f32 (.f32 #s(literal 2 binary32) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau)) x)))
	66.9%	(/.f32 (-.f32 (cos.f32 (fma.f32 (.f32 tau (PI.f32)) x (.f32 (neg.f32 (PI.f32)) x))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
	66.8%	(/.f32 (-.f32 (cos.f32 (/.f32 (fma.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))) (pow.f32 (.f32 (neg.f32 (PI.f32)) x) #s(literal 3 binary32))) (fma.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 tau (.f32 x (PI.f32))) (-.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 (neg.f32 (PI.f32)) x)))))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
	66.9%	(/.f32 (-.f32 (cos.f32 (/.f32 (.f32 (fma.f32 tau tau #s(literal -1 binary32)) (.f32 x (PI.f32))) (+.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
	66.9%	(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 tau x)) #s(literal 2 binary32)))
	51.7%	(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) (fma.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
	33.4%	(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) #s(literal 1 binary32)) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
▶	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
✓	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
	85.1%	(/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)) (.f32 x x) (PI.f32)) x)) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
	66.9%	(/.f32 (.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))) #s(literal 2 binary32))
	97.0%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) tau)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) x))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))
	97.4%	(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (PI.f32)) x))
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) x) tau) (PI.f32)))
▶	97.6%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x)))
▶	85.4%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
	71.2%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
	78.3%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (+.f32 tau (.f32 (.f32 tau tau) tau))) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 x (PI.f32))))
	64.9%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 x (PI.f32))))
	85.1%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) x) (/.f32 (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))) tau)))
	85.2%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))))
	84.7%	(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau x))))
	97.5%	(/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))))
	97.1%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	85.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	84.9%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (PI.f32))) x) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	85.1%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (.f32 tau (PI.f32))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	85.3%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau) (.f32 (PI.f32) x)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	84.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	95.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))) (*.f32 x (PI.f32))))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	84.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	84.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
	84.9%	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau x)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (PI.f32)))
	84.9%	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 tau (PI.f32))))
	97.2%	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (neg.f32 tau) (PI.f32))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (*.f32 (PI.f32) x) x)))
	79.2%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (.f32 tau tau) tau) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	79.6%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 (PI.f32) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	85.1%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	84.9%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (PI.f32)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	66.9%	(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 (.f32 tau x) x) (PI.f32)) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
✓	66.9%	(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
	85.1%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (/.f32 #s(literal 1 binary32) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	85.4%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	97.3%	(.f32 (.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (PI.f32)) x))) (sin.f32 (*.f32 (PI.f32) x)))
	85.3%	(.f32 (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) (.f32 tau (*.f32 (PI.f32) x))))
	85.4%	(.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 tau (*.f32 (PI.f32) x))))
	85.3%	(.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32)))))
	97.4%	(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))))
	97.3%	(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (sin.f32 (*.f32 x (PI.f32)))))
	97.1%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) x) (PI.f32)) (neg.f32 tau))))
✓	97.1%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
	80.0%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #s(approx (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (fma.f32 (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32)) x (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) x)))))
	84.8%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #s(approx (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (/.f32 (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 x x) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 tau tau))) #s(literal -1/120 binary32) (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32))) (.f32 x x) (/.f32 #s(literal -1 binary32) (PI.f32))) x)))
	97.2%	(.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
	84.7%	(.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)) (.f32 x x) (PI.f32)) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (*.f32 (neg.f32 tau) (PI.f32)))))
	71.0%	(.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (*.f32 (neg.f32 tau) (PI.f32)))))
	84.4%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	80.0%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 tau (PI.f32)) tau) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
▶	65.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	85.0%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (fma.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau tau)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) x))) (.f32 tau tau) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (.f32 (PI.f32) x)))
	80.0%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (*.f32 (PI.f32) x)))
	79.9%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 (PI.f32) x)))
	96.9%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (sin.f32 (*.f32 (PI.f32) x)))
	96.2%	(.f32 #s(literal -1 binary32) (/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) (fma.f32 (-.f32 tau #s(literal 1 binary32)) x (fma.f32 tau x x))) #s(literal 1/2 binary32))) (sin.f32 (.f32 (.f32 (PI.f32) (-.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) x) (fma.f32 tau x x))) #s(literal 1/2 binary32)))) (.f32 (.f32 (.f32 (*.f32 (PI.f32) x) x) tau) (PI.f32))))
	97.3%	(neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 (.f32 tau (PI.f32)) x))) (.f32 tau (*.f32 (PI.f32) x))))
	63.9%	(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
✓	6.3%	#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
	79.4%	#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 (.f32 #s(literal -1/6 binary32) tau) tau #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	96.7%	#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))))
	64.8%	#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
▶	84.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32)))
	79.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
✓	64.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 4 616 to 2 559 computations (44.6% saved)

simplify135.0ms (1.2%)

Memory

4.4MiB live, 157.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f32 (*.f32 (PI.f32) x))
cost-diff	0	(/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))
cost-diff	192	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
cost-diff	0	(fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (*.f32 x x)))
cost-diff	0	(fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32)))
cost-diff	320	(fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))
cost-diff	0	(fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
cost-diff	0	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
cost-diff	0	(.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (*.f32 x (PI.f32)))))
cost-diff	0	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
cost-diff	0	(fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
cost-diff	0	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
cost-diff	0	#s(approx (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32))
cost-diff	0	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
cost-diff	0	(sin.f32 (.f32 tau (.f32 x (PI.f32))))
cost-diff	0	(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
cost-diff	0	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x)))
cost-diff	128	(.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x))

Rules

4 396×	`lower-fma.f64`
4 384×	`lower-fma.f32`
4 330×	`lower-*.f64`
4 290×	`lower-*.f32`
2 356×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	585
0	101	587
1	226	574
2	646	560
3	2362	560
4	5814	560
0	8201	554

Stop Event

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

Calls

Call 1

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

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

localize190.0ms (1.7%)

Memory

19.5MiB live, 285.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.359375	(*.f32 (PI.f32) x)
accuracy	0.3674688180802656	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.375	(/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))
accuracy	0.4629288086106522	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
accuracy	0.492851269536884	(fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	1.58496250072115	(pow.f32 (PI.f32) #s(literal 4 binary32))
accuracy	4.853242528911046	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32)))
accuracy	0.3674688180802656	(sin.f32 (.f32 tau (.f32 x (PI.f32))))
accuracy	0.4394913086106522	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	4.427938075790228	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
accuracy	0.3203125	(*.f32 #s(literal -1/6 binary32) x)
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	4.427938075790228	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
accuracy	11.220349930483764	#s(approx (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3674688180802656	(sin.f32 (.f32 tau (.f32 x (PI.f32))))
accuracy	0.40234375	(.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x))
accuracy	0.4111900879159782	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x)))

Samples

134.0ms

256×

valid

Compiler

Compiled 508 to 56 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-mult: 42.0ms (38.2% of total)

ival-pow: 25.0ms (22.8% of total)

ival-sin: 16.0ms (14.6% of total)

ival-div: 10.0ms (9.1% of total)

const: 9.0ms (8.2% of total)

ival-add: 6.0ms (5.5% of total)

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

ival-neg: 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)

series107.0ms (0.9%)

Memory

-29.4MiB live, 95.8MiB allocated

Counts

25 → 444

Calls

Call 1

Inputs
#s(alt (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x)) (patch (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x)) #<representation binary32>) () ())
#s(alt (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x))) (patch (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x))) #<representation binary32>) () ())
#s(alt (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (patch (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (patch (sin.f32 (.f32 tau (.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))) (patch (.f32 #s(approx (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))) #<representation binary32>) () ())
#s(alt #s(approx (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (patch #s(approx (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) (patch (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32)))) (patch (/.f32 (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32)))) #<representation binary32>) () ())
#s(alt (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (patch (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (*.f32 x (PI.f32))))) #<representation binary32>) () ())
#s(alt (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau))) (patch (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau))) #<representation binary32>) () ())
#s(alt #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32))) (patch #s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())
#s(alt (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32)) (patch (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (patch (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) #<representation binary32>) () ())
#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) #<representation binary32>) () ())
#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #<representation binary32>) () ())
#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (patch (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 (PI.f32) x)) (patch (sin.f32 (.f32 (PI.f32) x)) #<representation binary32>) () ())
#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) (PI.f32)) (patch (.f32 (PI.f32) (PI.f32)) #<representation binary32>) () ())
#s(alt (.f32 #s(literal -1/6 binary32) x) (patch (.f32 #s(literal -1/6 binary32) x) #<representation binary32>) () ())
#s(alt (pow.f32 (PI.f32) #s(literal 4 binary32)) (patch (pow.f32 (PI.f32) #s(literal 4 binary32)) #<representation binary32>) () ())
#s(alt (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (patch (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (patch (sin.f32 (.f32 tau (.f32 (PI.f32) x))) #<representation binary32>) () ())
#s(alt (.f32 (PI.f32) x) (patch (.f32 (PI.f32) x) #<representation binary32>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
57.0ms	tau	@	inf	((* (* tau (* (neg (PI)) x)) (* (neg (PI)) x)) (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (* tau (* (neg (PI)) x)) (* (neg (PI)) x))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (sin (* tau (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (PI)) (sin (* (PI) x)) (* x (PI)) (* (PI) (PI)) (* -1/6 x) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (sin (* tau (* (PI) x))) (* (PI) x))
7.0ms	x	@	inf	((* (* tau (* (neg (PI)) x)) (* (neg (PI)) x)) (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (* tau (* (neg (PI)) x)) (* (neg (PI)) x))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (sin (* tau (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (PI)) (sin (* (PI) x)) (* x (PI)) (* (PI) (PI)) (* -1/6 x) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (sin (* tau (* (PI) x))) (* (PI) x))
5.0ms	x	@	-inf	((* (* tau (* (neg (PI)) x)) (* (neg (PI)) x)) (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (* tau (* (neg (PI)) x)) (* (neg (PI)) x))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (sin (* tau (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (PI)) (sin (* (PI) x)) (* x (PI)) (* (PI) (PI)) (* -1/6 x) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (sin (* tau (* (PI) x))) (* (PI) x))
4.0ms	tau	@	-inf	((* (* tau (* (neg (PI)) x)) (* (neg (PI)) x)) (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (* tau (* (neg (PI)) x)) (* (neg (PI)) x))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (sin (* tau (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (PI)) (sin (* (PI) x)) (* x (PI)) (* (PI) (PI)) (* -1/6 x) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (sin (* tau (* (PI) x))) (* (PI) x))
4.0ms	tau	@	0	((* (* tau (* (neg (PI)) x)) (* (neg (PI)) x)) (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* (* tau (* (neg (PI)) x)) (* (neg (PI)) x))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (sin (* tau (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) (PI)) (sin (* (PI) x)) (* x (PI)) (* (PI) (PI)) (* -1/6 x) (pow (PI) 4) (+ (* (* tau tau) (* tau tau)) 1) (sin (* tau (* (PI) x))) (* (PI) x))

simplify207.0ms (1.8%)

Memory

41.1MiB live, 343.2MiB allocated

Algorithm

1×	egg-herbie

Rules

15 780×	`lower-fma.f64`
15 780×	`lower-fma.f32`
8 370×	`lower-*.f64`
8 370×	`lower-*.f32`
3 296×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	474	8546
1	1635	8246
2	6201	7952
0	8005	7588

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 443

Calls

Call 1

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

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

rewrite246.0ms (2.1%)

Memory

-8.8MiB live, 471.7MiB allocated

Rules

5 266×	`lower-/.f64`
5 258×	`lower-/.f32`
5 244×	`lower-fma.f64`
5 232×	`lower-fma.f32`
4 290×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	405
0	101	402
1	374	382
2	2644	373
0	8866	364

Stop Event

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

Counts

25 → 1 075

Calls

Call 1

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

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

eval250.0ms (2.2%)

Memory: 24.1MiB live, 450.6MiB allocated
Compiler: Compiled 56 939 to 3 166 computations (94.4% saved)

prune538.0ms (4.7%)

Memory

2.3MiB live, 933.1MiB allocated

Pruning

98 alts after pruning (92 fresh and 6 done)

	Pruned	Kept	Total
New	1 737	50	1 787
Fresh	33	42	75
Picked	4	1	5
Done	0	5	5
Total	1 774	98	1 872

Accuracy

99.9%

Counts

1 872 → 98

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.9%	(/.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 (PI.f32) #s(literal 2 binary32))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
	97.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) x) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	85.1%	(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (PI.f32) tau)) x)
	85.0%	(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)) (PI.f32))
	66.9%	(/.f32 (/.f32 (.f32 #s(literal 1/2 binary32) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32))))) (.f32 (.f32 (*.f32 (PI.f32) x) x) tau)) (PI.f32))
	65.1%	(/.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (.f32 (PI.f32) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (.f32 (PI.f32) #s(literal 2 binary32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) x))
	66.9%	(/.f32 (-.f32 (cos.f32 (fma.f32 (.f32 tau (PI.f32)) x (.f32 (neg.f32 (PI.f32)) x))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
	66.8%	(/.f32 (-.f32 (cos.f32 (/.f32 (fma.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 tau (.f32 x (PI.f32)))) (.f32 tau (.f32 x (PI.f32))) (pow.f32 (.f32 (neg.f32 (PI.f32)) x) #s(literal 3 binary32))) (fma.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 tau (.f32 x (PI.f32))) (-.f32 (.f32 (.f32 x (PI.f32)) (.f32 x (PI.f32))) (.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 (neg.f32 (PI.f32)) x)))))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
	66.9%	(/.f32 (-.f32 (cos.f32 (/.f32 (.f32 (fma.f32 tau tau #s(literal -1 binary32)) (.f32 x (PI.f32))) (+.f32 #s(literal 1 binary32) tau))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
	66.9%	(/.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 tau x)) #s(literal 2 binary32)))
	66.9%	(/.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 (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32)) x) #s(literal 2 binary32)))
	51.7%	(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) (fma.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
	33.4%	(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) #s(literal 1 binary32)) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
✓	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
✓	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
	85.0%	(/.f32 (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)) (PI.f32)) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) x))
	66.9%	(/.f32 (.f32 (-.f32 (cos.f32 (.f32 (.f32 (PI.f32) x) (-.f32 tau #s(literal 1 binary32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))) #s(literal 2 binary32))
	97.0%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) tau)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) x))
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) x) tau) (PI.f32)))
	97.6%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 x (PI.f32)) tau) (.f32 x (PI.f32))))
	96.8%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))) tau))
	96.9%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) #s(approx (* (* tau (* (neg (PI)) x)) (* (neg (PI)) x)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) tau) x) x)))
	85.1%	(/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) (PI)) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
	85.4%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
	85.4%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 x x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
	84.9%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))) (.f32 tau (.f32 x (PI.f32))))
	79.1%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) #s(approx (sin ( tau (* x (PI)))) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (.f32 x x) tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (PI.f32) tau)) x))) (.f32 tau (*.f32 x (PI.f32))))
	85.4%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
	71.2%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
	78.3%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau)) (.f32 x x) (.f32 (PI.f32) tau)) x)) (.f32 tau (.f32 x (PI.f32))))
	64.9%	(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (sin.f32 (.f32 (PI.f32) x)) tau)) (.f32 tau (.f32 x (PI.f32))))
	97.5%	(/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))))
	97.1%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sqrt.f32 (PI.f32))) (.f32 (sqrt.f32 (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	85.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	85.1%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (.f32 tau (PI.f32))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	84.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	84.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	84.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x tau)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (PI.f32)))
	84.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 (PI.f32) tau)))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32)))))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	84.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32)) x)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	97.2%	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (neg.f32 tau) (PI.f32))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (*.f32 (PI.f32) x) x)))
	84.9%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (PI.f32)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	97.3%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32)) x)) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau))))
	85.3%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau))))
	84.9%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) tau)))
	66.9%	(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 (.f32 tau x) x) (PI.f32)) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
✓	66.9%	(.f32 (/.f32 #s(literal 1/2 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (-.f32 (cos.f32 (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (PI.f32)) x)) (cos.f32 (.f32 (fma.f32 tau x x) (PI.f32)))))
	85.4%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	85.4%	(.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 (*.f32 x (PI.f32)) tau)))
	97.4%	(.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32)) x)))
	97.3%	(.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (*.f32 x (PI.f32)) tau) (PI.f32)) x))))
	97.4%	(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))))
	97.1%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) x) (PI.f32)) (neg.f32 tau))))
✓	97.1%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
	80.0%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #s(approx (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (fma.f32 (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32)) x (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) x)))))
	84.8%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #s(approx (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (/.f32 (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 x x) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 tau tau))) #s(literal -1/120 binary32) (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32))) (.f32 x x) (/.f32 #s(literal -1 binary32) (PI.f32))) x)))
	84.7%	(.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)) (.f32 x x) (PI.f32)) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (*.f32 (neg.f32 tau) (PI.f32)))))
	71.0%	(.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (*.f32 (neg.f32 tau) (PI.f32)))))
	84.4%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	80.0%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 tau (PI.f32)) tau) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	80.0%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	65.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
	65.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
	65.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (pow.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) #s(literal 2/3 binary32)) #s(literal 1 binary32))))
	65.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
	65.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
	65.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
	65.1%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (.f32 #s(literal -1/6 binary32) x)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (*.f32 x x) #s(literal -1 binary32)))))
	65.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))))))
	65.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
	4.6%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
	85.0%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (fma.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau tau)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) x))) (.f32 tau tau) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (.f32 (PI.f32) x)))
	80.0%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (*.f32 (PI.f32) x)))
	79.9%	(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 (PI.f32) x)))
	96.2%	(.f32 #s(literal -1 binary32) (/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) (fma.f32 (-.f32 tau #s(literal 1 binary32)) x (fma.f32 tau x x))) #s(literal 1/2 binary32))) (sin.f32 (.f32 (.f32 (PI.f32) (-.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) x) (fma.f32 tau x x))) #s(literal 1/2 binary32)))) (.f32 (.f32 (.f32 (*.f32 (PI.f32) x) x) tau) (PI.f32))))
	97.3%	(neg.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)) (sin.f32 (.f32 (.f32 tau (PI.f32)) x))) (.f32 tau (*.f32 (PI.f32) x))))
	63.9%	(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
✓	6.3%	#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
	79.4%	#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
	64.8%	#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
	96.7%	#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))))
	84.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(approx (+ (* (* tau tau) (* tau tau)) 1) (.f32 (.f32 tau tau) (.f32 tau tau))) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (*.f32 x x) #s(literal 1 binary32)))
	84.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
	84.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))
	84.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
	84.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (*.f32 tau tau)))))) x) x #s(literal 1 binary32)))
	79.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	83.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))))
	84.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (.f32 x x)) #s(literal 1 binary32)))
	13.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (.f32 (.f32 (.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (.f32 tau tau) #s(literal 1/36 binary32)) (.f32 tau tau) #s(literal 1/120 binary32)) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 x x)) (*.f32 x x))))
	13.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (.f32 (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) #s(literal 1/120 binary32)) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (.f32 x x) (*.f32 x x)))))
✓	64.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 7 106 to 2 138 computations (69.9% saved)

regimes268.0ms (2.3%)

Memory

-60.2MiB live, 375.5MiB allocated

Counts

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

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))))

Calls

4 calls:

64.0ms	(*.f32 x (PI.f32))
58.0ms	x
58.0ms	(.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))))
47.0ms	tau

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`tau`
97.8%	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))))`
97.8%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes152.0ms (1.3%)

Memory

4.7MiB live, 357.3MiB allocated

Counts

131 → 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 (.f32 #s(literal -1/6 binary32) tau) tau #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 tau (PI.f32)) tau) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau)) #s(literal 1/2 binary32)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau)) (.f32 x x) (.f32 (PI.f32) tau)) x)) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (+.f32 tau (.f32 (.f32 tau tau) tau))) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 x (PI.f32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (-.f32 (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau))) (.f32 x x)) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (.f32 #s(literal -1/6 binary32) x)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (*.f32 x x) #s(literal -1 binary32)))))
(/.f32 #s(approx (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 x x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (*.f32 tau tau)))))) x) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (.f32 x x)) #s(literal 1 binary32)))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 (PI.f32) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (.f32 tau tau) tau) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) #s(approx (sin ( tau (* x (PI)))) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (.f32 x x) tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (PI.f32) tau)) x))) (.f32 tau (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 x (PI.f32))))
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(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32)) x)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) #s(approx (* (* tau (* (neg (PI)) x)) (* (neg (PI)) x)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) tau) x) x)))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32)))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))) tau))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 x (PI.f32)) tau) (.f32 x (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) x) tau) (PI.f32)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)))
(.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32)))))
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) x) (PI.f32)) (neg.f32 tau))))
(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (.f32 (neg.f32 tau) (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (.f32 (neg.f32 (PI.f32)) x)))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 tau (.f32 (neg.f32 (PI.f32)) x)) (PI.f32)) x))
(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))) (sin.f32 (*.f32 x (PI.f32)))))
(.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (*.f32 x (PI.f32)) tau) (PI.f32)) x))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32)) x)) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (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)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32)))))

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

Calls

4 calls:

39.0ms	tau
36.0ms	(.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))))
35.0ms	(*.f32 x (PI.f32))
34.0ms	x

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`tau`
97.6%	1	`(*.f32 x (PI.f32))`
97.6%	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)

regimes215.0ms (1.9%)

Memory

-8.6MiB live, 200.2MiB allocated

Counts

115 → 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 (.f32 #s(literal -1/6 binary32) tau) tau #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 tau (PI.f32)) tau) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau)) #s(literal 1/2 binary32)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau)) (.f32 x x) (.f32 (PI.f32) tau)) x)) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (+.f32 tau (.f32 (.f32 tau tau) tau))) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 x (PI.f32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (-.f32 (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau))) (.f32 x x)) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (.f32 #s(literal -1/6 binary32) x)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (*.f32 x x) #s(literal -1 binary32)))))
(/.f32 #s(approx (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 x x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (*.f32 tau tau)))))) x) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (.f32 x x)) #s(literal 1 binary32)))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 (PI.f32) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (.f32 tau tau) tau) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) #s(approx (sin ( tau (* x (PI)))) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (.f32 x x) tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (PI.f32) tau)) x))) (.f32 tau (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (sin.f32 (.f32 (PI.f32) x)) tau)) (.f32 tau (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (pow.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) #s(literal 2/3 binary32)) #s(literal 1 binary32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (neg.f32 tau) (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x))))
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(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) #s(approx (* (* tau (* (neg (PI)) x)) (* (neg (PI)) x)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) tau) x) x)))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32)))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (PI.f32))) tau))

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

Calls

4 calls:

83.0ms	tau
62.0ms	(*.f32 x (PI.f32))
34.0ms	x
30.0ms	(.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
97.5%	1	`x`
97.5%	1	`(*.f32 x (PI.f32))`
97.5%	1	`tau`
97.5%	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)

regimes218.0ms (1.9%)

Memory

-3.4MiB live, 155.0MiB allocated

Counts

109 → 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 (.f32 #s(literal -1/6 binary32) tau) tau #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 tau (PI.f32)) tau) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau)) #s(literal 1/2 binary32)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau)) (.f32 x x) (.f32 (PI.f32) tau)) x)) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (+.f32 tau (.f32 (.f32 tau tau) tau))) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 x (PI.f32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (-.f32 (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau))) (.f32 x x)) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (.f32 #s(literal -1/6 binary32) x)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (*.f32 x x) #s(literal -1 binary32)))))
(/.f32 #s(approx (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 x x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (*.f32 tau tau)))))) x) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (.f32 x x)) #s(literal 1 binary32)))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 (PI.f32) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (.f32 tau tau) tau) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) #s(approx (sin ( tau (* x (PI)))) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (.f32 x x) tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (PI.f32) tau)) x))) (.f32 tau (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (sin.f32 (.f32 (PI.f32) x)) tau)) (.f32 tau (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (pow.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) #s(literal 2/3 binary32)) #s(literal 1 binary32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (neg.f32 tau) (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x))))
(.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 (PI))) #s(literal 1 binary32)) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (.f32 (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) #s(literal 1/120 binary32)) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (.f32 x x) (*.f32 x x)))))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (*.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (.f32 (.f32 (.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (.f32 tau tau) #s(literal 1/36 binary32)) (.f32 tau tau) #s(literal 1/120 binary32)) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 x x)) (*.f32 x x))))
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #s(approx (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (fma.f32 (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32)) x (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) x)))))
(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) #s(literal 1 binary32)) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
(.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (*.f32 (neg.f32 tau) (PI.f32)))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 (*.f32 x (PI.f32)) tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #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 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 x x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (*.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (sin.f32 (*.f32 (PI.f32) x)))
(neg.f32 (/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) (* (neg (PI)) x)) (fma.f32 (.f32 #s(literal 1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)) #s(literal -1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32)))))
(.f32 (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau))))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 tau (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau x)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 (PI.f32) tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x tau)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (PI.f32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau) (.f32 (PI.f32) x)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (.f32 tau (PI.f32))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (PI.f32))) x) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) x) (.f32 tau (PI.f32)))
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau x)) (PI.f32))
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (PI.f32))) x)
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)) (PI.f32))
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (PI.f32) tau)) x)
(/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) (PI)) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (/.f32 #s(literal 1 binary32) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) tau)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))))
(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (PI.f32)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau x))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) x) (/.f32 (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))) tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(approx (+ (* (* tau tau) (* tau tau)) 1) (.f32 (.f32 tau tau) (.f32 tau tau))) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32)))
(.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)) (.f32 x x) (PI.f32)) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (*.f32 (neg.f32 tau) (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)) (.f32 x x) (PI.f32)) x)) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)) (PI.f32)) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) x))
(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) (fma.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (fma.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau tau)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) x))) (.f32 tau tau) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (.f32 (PI.f32) x)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #s(approx (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (/.f32 (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 x x) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 tau tau))) #s(literal -1/120 binary32) (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32))) (.f32 x x) (/.f32 #s(literal -1 binary32) (PI.f32))) x)))
#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 x (.f32 tau (.f32 (PI.f32) x))))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) x) (.f32 (PI.f32) (PI.f32)))))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 tau (.f32 x x)) (.f32 (PI.f32) (PI.f32))))) (sin.f32 (*.f32 (PI.f32) x)))
(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 tau (.f32 x (PI.f32))) x) (PI.f32))))
(.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32)) x)))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 tau x))) (sin.f32 (.f32 (PI.f32) x)))

Outputs

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

Calls

4 calls:

60.0ms	(*.f32 x (PI.f32))
48.0ms	tau
44.0ms	(.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	x

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)

regimes157.0ms (1.4%)

Memory

45.4MiB live, 117.2MiB 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
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(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau) (.f32 (PI.f32) x)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (.f32 tau (PI.f32))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (PI.f32))) x) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) x) (.f32 tau (PI.f32)))
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau x)) (PI.f32))
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (PI.f32))) x)
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 x tau)) (PI.f32))
(/.f32 (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (PI.f32) tau)) x)
(/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) (PI)) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (/.f32 #s(literal 1 binary32) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) tau)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))))
(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (PI.f32)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau x))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) x) (/.f32 (.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))) tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(approx (+ (* (* tau tau) (* tau tau)) 1) (.f32 (.f32 tau tau) (.f32 tau tau))) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) #s(literal 1/120 binary32) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x))) (.f32 x x) #s(literal 1 binary32)))
(.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)) (.f32 x x) (PI.f32)) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (*.f32 (neg.f32 tau) (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 (.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(approx (sin ( x (PI))) (.f32 (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)) (.f32 x x) (PI.f32)) x)) (.f32 x (PI.f32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)) (PI.f32)) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) x))
(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) (fma.f32 (.f32 #s(literal -1/2 binary32) (.f32 x x)) (.f32 (.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (fma.f32 (.f32 #s(literal 1/120 binary32) (.f32 tau tau)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) x))) (.f32 tau tau) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (.f32 (PI.f32) x)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #s(approx (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (/.f32 (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 x x) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 tau tau))) #s(literal -1/120 binary32) (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32))) (.f32 x x) (/.f32 #s(literal -1 binary32) (PI.f32))) x)))

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 (*.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))

Calls

4 calls:

56.0ms	(*.f32 x (PI.f32))
45.0ms	x
26.0ms	tau
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
85.5%	1	`tau`
85.5%	1	`x`
85.5%	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))))`
85.5%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes129.0ms (1.1%)

Memory

-33.3MiB live, 84.5MiB allocated

Counts

59 → 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 (.f32 #s(literal -1/6 binary32) tau) tau #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 tau (PI.f32)) tau) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau)) #s(literal 1/2 binary32)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau)) (.f32 x x) (.f32 (PI.f32) tau)) x)) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (+.f32 tau (.f32 (.f32 tau tau) tau))) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 x (PI.f32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (-.f32 (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau))) (.f32 x x)) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (.f32 #s(literal -1/6 binary32) x)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (*.f32 x x) #s(literal -1 binary32)))))
(/.f32 #s(approx (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 x x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (*.f32 tau tau)))))) x) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (.f32 x x)) #s(literal 1 binary32)))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 (PI.f32) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (.f32 tau tau) tau) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) #s(approx (sin ( tau (* x (PI)))) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (.f32 x x) tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (PI.f32) tau)) x))) (.f32 tau (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (sin.f32 (.f32 (PI.f32) x)) tau)) (.f32 tau (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (pow.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) #s(literal 2/3 binary32)) #s(literal 1 binary32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (neg.f32 tau) (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x))))
(.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 (PI))) #s(literal 1 binary32)) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (.f32 (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) #s(literal 1/120 binary32)) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (.f32 x x) (*.f32 x x)))))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (*.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (.f32 (.f32 (.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (.f32 tau tau) #s(literal 1/36 binary32)) (.f32 tau tau) #s(literal 1/120 binary32)) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 x x)) (*.f32 x x))))
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #s(approx (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (fma.f32 (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32)) x (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) x)))))
(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) #s(literal 1 binary32)) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
(.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (*.f32 (neg.f32 tau) (PI.f32)))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))) (.f32 (*.f32 x (PI.f32)) tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

30.0ms	(*.f32 x (PI.f32))
16.0ms	x
16.0ms	tau
15.0ms	(.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
85.4%	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))))`
85.4%	1	`x`
85.4%	1	`(*.f32 x (PI.f32))`
85.4%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes117.0ms (1%)

Memory

34.5MiB live, 107.2MiB allocated

Counts

53 → 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 (.f32 #s(literal -1/6 binary32) tau) tau #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 tau (PI.f32)) tau) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau)) #s(literal 1/2 binary32)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau)) (.f32 x x) (.f32 (PI.f32) tau)) x)) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (+.f32 tau (.f32 (.f32 tau tau) tau))) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 x (PI.f32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (-.f32 (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau))) (.f32 x x)) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (.f32 #s(literal -1/6 binary32) x)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (*.f32 x x) #s(literal -1 binary32)))))
(/.f32 #s(approx (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 x x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (*.f32 tau tau)))))) x) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))) (.f32 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (.f32 x x)) #s(literal 1 binary32)))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 x x) x)) (.f32 (PI.f32) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (.f32 tau tau) tau) (PI.f32)) (.f32 (PI.f32) (PI.f32))) (.f32 tau (PI.f32))) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))) #s(approx (sin ( tau (* x (PI)))) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (.f32 x x) tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (PI.f32) tau)) x))) (.f32 tau (*.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (.f32 tau tau)))))) (*.f32 x x) #s(literal 1 binary32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (sin.f32 (.f32 (PI.f32) x)) tau)) (.f32 tau (.f32 x (PI.f32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (pow.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) #s(literal 2/3 binary32)) #s(literal 1 binary32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (neg.f32 tau) (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x))))
(.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 (PI))) #s(literal 1 binary32)) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) #s(literal 1 binary32))) (sin.f32 (.f32 tau (.f32 x (PI.f32))))) (.f32 tau (.f32 x (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (.f32 (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) #s(literal 1/120 binary32)) (.f32 (.f32 tau tau) (.f32 tau tau))) (.f32 (.f32 x x) (*.f32 x x)))))
(.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* (* (* (PI) x) (PI)) (* tau x))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) x) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)))) (sin.f32 (*.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* (* (pow (PI) 4) (+ (* (+ (* (* tau tau) (* tau tau)) 1) 1/120) (* 1/36 (* tau tau)))) (* x x))) (* x x)) 1) (.f32 (.f32 (.f32 (fma.f32 (fma.f32 #s(literal 1/120 binary32) (.f32 tau tau) #s(literal 1/36 binary32)) (.f32 tau tau) #s(literal 1/120 binary32)) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 x x)) (*.f32 x x))))
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) #s(approx (/ (sin (* tau (* (PI) x))) (* (* (* (PI) x) x) (* (neg tau) (PI)))) (fma.f32 (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32)) x (/.f32 #s(literal -1 binary32) (.f32 (PI.f32) x)))))
(/.f32 (-.f32 #s(approx (cos (* (* (PI) x) (- tau 1))) #s(literal 1 binary32)) (cos.f32 (.f32 (PI.f32) (fma.f32 tau x x)))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 tau x)) #s(literal 2 binary32)))
(.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) x) (*.f32 (neg.f32 tau) (PI.f32)))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Outputs

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

Calls

4 calls:

52.0ms	tau
34.0ms	x
14.0ms	(*.f32 x (PI.f32))
14.0ms	(.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
84.8%	1	`x`
84.8%	1	`(*.f32 x (PI.f32))`
84.8%	1	`tau`
84.8%	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 (0.4%)

Memory

-29.5MiB live, 60.2MiB 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 (.f32 #s(literal -1/6 binary32) tau) tau #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 tau (PI.f32)) tau) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau)) #s(literal 1/2 binary32)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau)) (.f32 x x) (.f32 (PI.f32) tau)) x)) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (+.f32 tau (.f32 (.f32 tau tau) tau))) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 x (PI.f32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (-.f32 (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau))) (.f32 x x)) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (.f32 #s(literal -1/6 binary32) x)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (*.f32 x x) #s(literal -1 binary32)))))
(/.f32 #s(approx (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 x x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (PI.f32)) (fma.f32 #s(literal 1/120 binary32) (fma.f32 (.f32 tau tau) (.f32 tau tau) #s(literal 1 binary32)) (.f32 #s(literal 1/36 binary32) (*.f32 tau tau)))))) x) x #s(literal 1 binary32)))

Outputs

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

Calls

4 calls:

20.0ms	tau
12.0ms	(*.f32 x (PI.f32))
8.0ms	x
8.0ms	(.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
84.8%	1	`tau`
84.8%	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))))`
84.8%	1	`x`
84.8%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes40.0ms (0.3%)

Memory

-3.5MiB live, 34.7MiB allocated

Counts

25 → 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 (.f32 #s(literal -1/6 binary32) tau) tau #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 tau (PI.f32)) tau) (PI.f32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) (.f32 (/.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau)) #s(literal 1/2 binary32)))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau)) (.f32 x x) (.f32 (PI.f32) tau)) x)) (.f32 tau (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (.f32 (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (+.f32 tau (.f32 (.f32 tau tau) tau))) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 x (PI.f32))))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (-.f32 (.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (fma.f32 (.f32 tau tau) tau tau))) (.f32 x x)) (.f32 tau (PI.f32))) x)) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) (.f32 #s(literal -1/6 binary32) x)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (*.f32 x x) #s(literal -1 binary32)))))
(/.f32 #s(approx (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (.f32 (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))) (-.f32 (-.f32 tau #s(literal 1 binary32)) (-.f32 tau #s(literal -1 binary32))))) (.f32 x x))) (.f32 (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (*.f32 tau x)) #s(literal 2 binary32)))

Outputs

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

Calls

4 calls:

17.0ms	tau
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))
7.0ms	x

Results

Accuracy	Segments	Branch
80.0%	1	`tau`
80.0%	1	`x`
80.0%	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))))`
80.0%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes57.0ms (0.5%)

Memory

0.6MiB live, 37.0MiB allocated

Counts

17 → 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* x (PI))) (* x (PI))) (sin (* tau (* x (PI))))) (* tau (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 (.f32 #s(literal -1/6 binary32) tau) tau #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) x)) (PI)) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) x)) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
(neg.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) (* (neg (PI)) x)) (sin (* tau (* (PI) x)))) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 #s(literal -1/6 binary32) x) x) #s(literal 1 binary32))))))

Outputs

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

Calls

4 calls:

40.0ms	x
5.0ms	(.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))))
5.0ms	tau
5.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
79.4%	1	`x`
79.4%	1	`(*.f32 x (PI.f32))`
79.4%	1	`tau`
79.4%	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))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes15.0ms (0.1%)

Memory

17.5MiB live, 17.5MiB 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (*.f32 #s(literal -1/6 binary32) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (+.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

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	tau
4.0ms	(*.f32 x (PI.f32))
4.0ms	x

Results

Accuracy	Segments	Branch
65.2%	1	`x`
65.2%	1	`tau`
65.2%	1	`(*.f32 x (PI.f32))`
65.2%	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))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes10.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

5 → 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(approx (+ (* (* (* -1/6 x) x) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) x) x))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 (*.f32 (PI.f32) (PI.f32)) x)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
65.2%	1	`tau`
65.2%	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))))`
65.2%	1	`x`
65.2%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes30.0ms (0.3%)

Memory

-34.2MiB live, 12.6MiB allocated

Accuracy

Total -19.4b remaining (-168.3%)

Threshold costs -19.4b (-168.3%)

Counts

3 → 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 (/ (- (cos (* (* (PI) x) (- tau 1))) (cos (* (PI) (+ (* tau x) x)))) (* (* (* (* (PI) x) (PI)) (* tau x)) 2)) #s(literal 0 binary32))

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

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

Calls

4 calls:

24.0ms	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
64.0%	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))))`
64.0%	1	`tau`
64.0%	1	`x`
64.0%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

simplify8.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	90	473
1	134	473

Stop Event

1×

saturated

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

soundness1.5s (13.1%)

Memory

28.1MiB live, 1 208.6MiB allocated

Rules

16 966×	`lower-fma.f64`
16 966×	`lower-fma.f32`
15 780×	`lower-fma.f64`
15 780×	`lower-fma.f32`
15 152×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	540	8555
1	1767	8233
2	6566	7957
0	8309	7702
0	196	1582
1	620	1562
2	2407	1538
3	4137	1538
4	4871	1538
5	5550	1538
6	5940	1538
7	5971	1538
8	5971	1538
0	8816	1486
0	56	405
0	101	402
1	374	382
2	2644	373
0	8866	364
0	42	257
0	71	261
1	299	255
2	2176	241
0	8190	241
0	65	303
0	109	301
1	386	301
2	2311	283
0	8443	281
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53
0	474	8546
1	1635	8246
2	6201	7952
0	8005	7588

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

Compiler

Compiled 806 to 336 computations (58.3% saved)

preprocess126.0ms (1.1%)

Memory

-14.3MiB live, 222.8MiB allocated

Remove

(abs x)

(abs tau)

Compiler

Compiled 1 830 to 668 computations (63.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze30.0ms (0.3%)

sample1.9s (16.4%)

explain174.0ms (1.5%)

preprocess71.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify33.0ms (0.3%)

localize46.0ms (0.4%)

series51.0ms (0.4%)

simplify310.0ms (2.7%)

rewrite203.0ms (1.8%)

eval166.0ms (1.4%)

prune278.0ms (2.4%)

simplify112.0ms (1%)

localize137.0ms (1.2%)

series71.0ms (0.6%)

simplify207.0ms (1.8%)

rewrite255.0ms (2.2%)

eval291.0ms (2.5%)

prune470.0ms (4.1%)

simplify131.0ms (1.1%)

localize192.0ms (1.7%)

series61.0ms (0.5%)

simplify273.0ms (2.4%)

rewrite297.0ms (2.6%)

eval473.0ms (4.1%)

prune492.0ms (4.3%)

simplify135.0ms (1.2%)

localize190.0ms (1.7%)

series107.0ms (0.9%)

simplify207.0ms (1.8%)

rewrite246.0ms (2.1%)

eval250.0ms (2.2%)

prune538.0ms (4.7%)

regimes268.0ms (2.3%)

regimes152.0ms (1.3%)

regimes215.0ms (1.9%)

regimes218.0ms (1.9%)

regimes157.0ms (1.4%)

regimes129.0ms (1.1%)

regimes117.0ms (1%)

regimes49.0ms (0.4%)

regimes40.0ms (0.3%)

regimes57.0ms (0.5%)

regimes15.0ms (0.1%)

regimes10.0ms (0.1%)

regimes30.0ms (0.3%)

simplify8.0ms (0.1%)

soundness1.5s (13.1%)

preprocess126.0ms (1.1%)

end0.0ms (0%)

Profiling