Metrics for Lanczos kernel

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated

analyze21.0ms (0.2%)

Memory

24.8MiB live, 63.1MiB 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)

sample1.8s (17.8%)

Memory

20.6MiB live, 2 269.5MiB allocated

Samples

1.4s

8 256×

valid

Precisions

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

ival-mult: 254.0ms (22.3% of total)

const: 199.0ms (17.5% of total)

ival-sinu: 150.0ms (13.2% of total)

ival-sin: 145.0ms (12.7% of total)

ival-div: 137.0ms (12% of total)

ival-<=: 113.0ms (9.9% of total)

ival-pi: 110.0ms (9.6% of total)

ival-and: 21.0ms (1.8% of total)

exact: 8.0ms (0.7% of total)

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

Bogosity

explain163.0ms (1.6%)

Memory

15.9MiB live, 175.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
1	-	1	(0.9861630201339722 2.1064319610595703)	`(sin.f32 (*.f32 x (PI.f32)))`
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	-	`(sin.f32 (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`(*.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	5
-	0	251

Precision

0/0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	5
-	0	0	251

Precision?

0/0

Recall?

0.0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0.0

Samples

66.0ms

512×

valid

Compiler

Compiled 149 to 34 computations (77.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 30.0ms (57.1% of total)

ival-sinu: 7.0ms (13.3% of total)

ival-sin: 7.0ms (13.3% of total)

ival-div: 6.0ms (11.4% of total)

ival-pi: 2.0ms (3.8% of total)

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

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

preprocess112.0ms (1.1%)

Memory

-16.8MiB live, 108.0MiB 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 tau (*.f32 (PI.f32) x))) (*.f32 (*.f32 (PI.f32) x) (PI.f32))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (*.f32 tau x)))

Symmetry

(abs tau)

(abs x)

Compiler

Compiled 21 to 10 computations (52.4% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.6MiB live, 1.6MiB 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 21 to 10 computations (52.4% saved)

simplify22.0ms (0.2%)

Memory

-4.0MiB live, 34.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
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)) (/.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 tau (.f32 (PI.f32) x))) (.f32 (.f32 (PI.f32) x) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))

localize37.0ms (0.4%)

Memory

-11.7MiB live, 65.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.3125	(.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))))
accuracy	0.34375	(*.f32 x (PI.f32))
accuracy	0.4137687988422102	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42710878907376815	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

Samples

26.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 4.0ms (25.8% of total)

ival-div: 3.0ms (19.4% of total)

ival-sinu: 3.0ms (19.4% of total)

ival-sin: 3.0ms (19.4% of total)

ival-pi: 1.0ms (6.5% of total)

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

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

series31.0ms (0.3%)

Memory

35.9MiB live, 72.6MiB 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>) () ())) ())
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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)))) (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
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)))
5.0ms	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)))
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)))
4.0ms	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)))

simplify232.0ms (2.3%)

Memory

-26.7MiB live, 286.6MiB 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 (pow.f32 (PI.f32) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32))) (.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 (pow.f32 tau #s(literal 4 binary32)) (.f32 (sin.f32 (.f32 (PI.f32) x)) (fma.f32 (.f32 (pow.f32 x #s(literal 3 binary32)) #s(literal 1/120 binary32)) (pow.f32 (PI.f32) #s(literal 3 binary32)) (.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)))))) (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))))
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)) (pow.f32 x #s(literal 4 binary32))))) (.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 (pow.f32 tau #s(literal 4 binary32)) (fma.f32 (.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1/120 binary32)) (pow.f32 (PI.f32) #s(literal 4 binary32)) (.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))))) (fma.f32 (.f32 tau (.f32 (.f32 x x) tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #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 (pow.f32 x #s(literal 3 binary32)) (.f32 tau tau)) (.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)) #s(literal -1/6 binary32)) (*.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))))))))
(fma.f32 (pow.f32 tau #s(literal 3 binary32)) (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 #s(literal -1/6 binary32) (pow.f32 (PI.f32) #s(literal 3 binary32))) (pow.f32 x #s(literal 3 binary32)))) (.f32 tau (*.f32 (PI.f32) x)))
(* 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)))))))))
(fma.f32 (pow.f32 tau #s(literal 3 binary32)) (fma.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (PI.f32) #s(literal 3 binary32))) (pow.f32 x #s(literal 3 binary32)) (.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 (.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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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 (.f32 #s(literal 1/36 binary32) tau) tau (fma.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1/120 binary32) #s(literal 1/120 binary32)))) (.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) (fma.f32 tau tau (pow.f32 tau #s(literal 4 binary32))) #s(literal -1/5040 binary32)))) (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (.f32 #s(literal 1/36 binary32) tau) tau (fma.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1/120 binary32) #s(literal 1/120 binary32))))) (.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 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1/120 binary32)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) x) x) (.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 4 binary32)) #s(literal 1/120 binary32)) (pow.f32 (PI.f32) #s(literal 4 binary32)) (.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 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))))
(fma.f32 (.f32 tau x) (PI.f32) (.f32 (.f32 (pow.f32 tau #s(literal 3 binary32)) #s(literal -1/6 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)) (pow.f32 x #s(literal 3 binary32)))))
(* 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))))))))
(fma.f32 (.f32 tau x) (PI.f32) (.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 #s(literal -1/6 binary32) (pow.f32 (PI.f32) #s(literal 3 binary32))) (pow.f32 tau #s(literal 3 binary32)))) (pow.f32 x #s(literal 3 binary32))))
(* 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)))))))))
(fma.f32 (.f32 tau x) (PI.f32) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (PI.f32) #s(literal 3 binary32))) (pow.f32 tau #s(literal 3 binary32)) (.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))) (pow.f32 x #s(literal 3 binary32))))
(* 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 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau 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)

rewrite395.0ms (3.9%)

Memory

-210.8MiB live, 293.4MiB 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
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eval96.0ms (0.9%)

Memory: 8.8MiB live, 251.1MiB allocated
Compiler: Compiled 24 307 to 2 341 computations (90.4% saved)

prune70.0ms (0.7%)

Memory

-13.5MiB live, 189.4MiB allocated

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	980	33	1 013
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	981	33	1 014

Accuracy

99.8%

Counts

1 014 → 33

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.4%	(/.f32 (.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 tau (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) x)
	97.8%	(/.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))
	97.7%	(/.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))
	97.5%	(/.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)))
▶	98.0%	(/.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)))
	97.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) (neg.f32 tau)))
	97.6%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) x) (*.f32 (neg.f32 (PI.f32)) x)))
	97.4%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
	97.3%	(.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)))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) x)))))
	95.9%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (cbrt.f32 (PI.f32))))
▶	97.8%	(.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))))
	96.0%	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) tau) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (.f32 (sqrt.f32 (PI.f32)) x)))) (*.f32 x (PI.f32))))
	96.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (cbrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))) (cbrt.f32 (cbrt.f32 (PI.f32))))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (*.f32 (cbrt.f32 (PI.f32)) x)))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (cbrt.f32 (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) x) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) (/.f32 #s(literal 1 binary32) x)))
	73.2%	(.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)))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.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))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (/.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x))) (PI.f32)))
	97.9%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x)))
	97.4%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32))))
	97.6%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 (*.f32 (neg.f32 x) tau) (PI.f32))))
	66.2%	#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)))
	67.0%	#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)))
	97.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau x))))
▶	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 448 to 836 computations (42.3% saved)

simplify88.0ms (0.9%)

Memory

11.8MiB live, 129.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau))
cost-diff	0	(/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
cost-diff	704	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.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 tau (.f32 (PI.f32) x)))
cost-diff	0	(/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (*.f32 (neg.f32 (PI.f32)) x))
cost-diff	128	(.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))))
cost-diff	0	(.f32 (.f32 tau (PI.f32)) x)
cost-diff	0	(sin.f32 (.f32 (.f32 tau (PI.f32)) x))
cost-diff	0	(/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
cost-diff	0	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
cost-diff	0	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (*.f32 (PI.f32) x)))
cost-diff	0	(/.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)))

Rules

3 082×	`lower-*.f64`
3 062×	`lower-*.f32`
2 580×	`lower-fma.f64`
2 580×	`lower-fma.f32`
2 052×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	344
0	73	322
1	165	322
2	409	322
3	2238	322
4	4589	322
5	7050	322
6	7995	322
0	8016	322

Stop Event

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

Calls

Call 1

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

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

localize107.0ms (1%)

Memory

3.3MiB live, 247.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.34375	(*.f32 (PI.f32) x)
accuracy	0.34375	(*.f32 x (PI.f32))
accuracy	0.4137687988422102	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42710878907376815	(/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.34375	(*.f32 (neg.f32 (PI.f32)) x)
accuracy	0.34375	(*.f32 (PI.f32) x)
accuracy	0.42710878907376815	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.4381637695368841	(.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))))
accuracy	0.328125	(*.f32 tau (PI.f32))
accuracy	0.34375	(*.f32 x (PI.f32))
accuracy	0.4137687988422102	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42710878907376815	(/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	10.818006556956254	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
accuracy	0.3294525390737681	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
accuracy	0.34375	(*.f32 (PI.f32) x)
accuracy	0.35546875	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (*.f32 (PI.f32) x)))
accuracy	0.42320253907376804	(/.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)))

Samples

81.0ms

256×

valid

Compiler

Compiled 344 to 36 computations (89.5% saved)

Precisions

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

ival-mult: 22.0ms (33.8% of total)

ival-div: 14.0ms (21.5% of total)

ival-sin: 14.0ms (21.5% of total)

ival-neg: 9.0ms (13.8% of total)

ival-sinu: 3.0ms (4.6% of total)

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

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

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

exact: 0.0ms (0% of total)

series42.0ms (0.4%)

Memory

-21.9MiB live, 97.9MiB allocated

Counts

21 → 432

Calls

Call 1

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

Outputs
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (/.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))) (patch (/.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))) #<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 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (patch (/.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))) #<representation binary32>) () ())) ())
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#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 (/ (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>) () ())) ())
#s(alt (* -1 (* x (PI))) (taylor -inf x) (#s(alt (.f32 (neg.f32 (PI.f32)) x) (patch (.f32 (neg.f32 (PI.f32)) x) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (PI))) (taylor -inf x) (#s(alt (.f32 (neg.f32 (PI.f32)) x) (patch (.f32 (neg.f32 (PI.f32)) x) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (PI))) (taylor -inf x) (#s(alt (.f32 (neg.f32 (PI.f32)) x) (patch (.f32 (neg.f32 (PI.f32)) x) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (PI))) (taylor -inf x) (#s(alt (.f32 (neg.f32 (PI.f32)) x) (patch (.f32 (neg.f32 (PI.f32)) x) #<representation binary32>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (sin (* (* tau (PI)) x)) (* (* tau (PI)) x) (* (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (neg (sin (* (PI) x)))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ 1 (/ 1 (* (PI) x))) (* (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (PI) x) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* tau (PI)) (* (neg (PI)) x))
5.0ms	x	@	inf	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (sin (* (* tau (PI)) x)) (* (* tau (PI)) x) (* (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (neg (sin (* (PI) x)))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ 1 (/ 1 (* (PI) x))) (* (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (PI) x) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* tau (PI)) (* (neg (PI)) x))
4.0ms	tau	@	0	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (sin (* (* tau (PI)) x)) (* (* tau (PI)) x) (* (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (neg (sin (* (PI) x)))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ 1 (/ 1 (* (PI) x))) (* (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (PI) x) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* tau (PI)) (* (neg (PI)) x))
4.0ms	tau	@	-inf	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (sin (* (* tau (PI)) x)) (* (* tau (PI)) x) (* (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (neg (sin (* (PI) x)))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ 1 (/ 1 (* (PI) x))) (* (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (PI) x) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* tau (PI)) (* (neg (PI)) x))
4.0ms	tau	@	inf	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* tau (PI)) x)) (* (* x (PI)) tau)) (sin (* (* tau (PI)) x)) (* (* tau (PI)) x) (* (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (neg (sin (* (PI) x)))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ 1 (/ 1 (* (PI) x))) (* (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (* x (PI)) tau)) (sin (* (/ 1 (/ 1 (* (PI) x))) tau)) (* (PI) x) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* tau (PI)) (* (neg (PI)) x))

simplify215.0ms (2.1%)

Memory

13.5MiB live, 365.0MiB allocated

Algorithm

1×	egg-herbie

Rules

20 394×	`lower-fma.f64`
20 394×	`lower-fma.f32`
6 604×	`lower-*.f64`
6 604×	`lower-*.f32`
5 640×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	334	6954
1	1110	6818
2	4341	6664
3	7968	6664
0	8027	6437

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 430

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

rewrite185.0ms (1.8%)

Memory

-16.3MiB live, 347.1MiB allocated

Rules

3 446×	`lower-*.f64`
3 426×	`lower-*.f32`
3 076×	`lower-/.f64`
3 062×	`lower-/.f32`
1 706×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	250
0	73	232
1	267	232
2	1287	220
3	6173	220
0	8441	220

Stop Event

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

Counts

21 → 1 551

Calls

Call 1

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

Outputs
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eval255.0ms (2.5%)

Memory: 34.6MiB live, 686.1MiB allocated
Compiler: Compiled 69 966 to 4 304 computations (93.8% saved)

prune146.0ms (1.4%)

Memory

-11.7MiB live, 402.6MiB allocated

Pruning

39 alts after pruning (36 fresh and 3 done)

	Pruned	Kept	Total
New	2 784	23	2 807
Fresh	15	13	28
Picked	2	3	5
Done	0	0	0
Total	2 801	39	2 840

Accuracy

99.9%

Counts

2 840 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (.f32 (PI.f32) tau) x))) x) (.f32 (.f32 (*.f32 (PI.f32) tau) x) (PI.f32)))
	96.1%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (.f32 (/.f32 (.f32 (.f32 (PI.f32) tau) x) (sin.f32 (.f32 (*.f32 (PI.f32) tau) x))) (cbrt.f32 (PI.f32))))
	97.4%	(/.f32 (.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 tau (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) x)
	97.7%	(/.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))
	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x)) (sin.f32 (.f32 (.f32 (PI.f32) tau) x))) (*.f32 x (PI.f32)))
	32.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (fma.f32 #s(literal 0 binary32) (neg.f32 x) (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
✓	98.0%	(/.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)))
	97.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) (neg.f32 tau)))
	97.9%	(/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (/.f32 (.f32 (.f32 (PI.f32) tau) x) (sin.f32 (.f32 x (PI.f32)))) (*.f32 x (PI.f32))))
	67.0%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))
▶	97.6%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (PI.f32))) x) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) tau) (.f32 x (.f32 (neg.f32 (PI.f32)) (.f32 x (PI.f32))))) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) x)))))
✓	97.8%	(.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))))
	95.9%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (exp.f32 (.f32 (log.f32 (pow.f32 (.f32 x (PI.f32)) #s(literal -2 binary32))) #s(literal -1/2 binary32))))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (neg.f32 (PI.f32)) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.0%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	73.1%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (.f32 (PI.f32) tau) x) (PI.f32))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x))
	97.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) tau)))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 x (PI.f32)) x)))
▶	98.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (PI.f32) tau) x)))
	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (.f32 (sqrt.f32 (PI.f32)) x)))) (*.f32 x (PI.f32))))
	96.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (cbrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))) (cbrt.f32 (cbrt.f32 (PI.f32))))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (cbrt.f32 (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) x) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) (/.f32 #s(literal 1 binary32) x)))
	73.2%	(.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)))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	95.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))) (.f32 x (PI.f32))))
	73.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.9%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x)))
	66.9%	(.f32 (/.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) #s(literal 1 binary32)) (.f32 (neg.f32 (PI.f32)) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	66.9%	(.f32 #s(approx (/ (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) x)) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
	67.0%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
▶	96.8%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 x x))))
▶	66.2%	#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)))
✓	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 602 to 979 computations (38.9% saved)

simplify145.0ms (1.4%)

Memory

3.6MiB live, 191.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

12 162×	`lower-fma.f64`
12 158×	`lower-fma.f32`
4 842×	`lower-*.f64`
4 812×	`lower-*.f32`
2 250×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	431
0	95	429
1	224	429
2	561	429
3	1781	429
4	4063	429
5	7376	429
0	8138	429

Stop Event

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

Calls

Call 1

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

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

localize143.0ms (1.4%)

Memory

11.3MiB live, 278.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.328125	(*.f32 (PI.f32) tau)
accuracy	0.34375	(*.f32 (PI.f32) x)
accuracy	0.42710878907376815	(/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x))
accuracy	0.4381637695368841	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (PI.f32))) x) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
accuracy	0.34375	(*.f32 (PI.f32) x)
accuracy	0.36556625976844204	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x)))
accuracy	0.3828125	(.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))
accuracy	0.39291000976844204	(/.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	0.34765625	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 x x))
accuracy	0.3600387695368841	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (*.f32 (PI.f32) (PI.f32))))
accuracy	0.44501879884221013	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 x x)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	5.763007819378079	#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)))
accuracy	17.95938207676469	(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))
accuracy	26.137415673917033	(fma.f32 tau tau #s(literal 1 binary32))
accuracy	0.3294525390737681	(/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (*.f32 x (PI.f32)))
accuracy	0.33984375	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (PI.f32) tau) x))
accuracy	0.34375	(*.f32 x (PI.f32))
accuracy	0.40853500976844204	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (PI.f32) tau) x)))

Samples

101.0ms

256×

valid

Compiler

Compiled 399 to 48 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-mult: 34.0ms (41.4% of total)

ival-div: 20.0ms (24.3% of total)

ival-sin: 10.0ms (12.2% of total)

ival-neg: 7.0ms (8.5% of total)

const: 4.0ms (4.9% of total)

ival-sinu: 4.0ms (4.9% of total)

ival-add: 2.0ms (2.4% of total)

ival-pi: 1.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series63.0ms (0.6%)

Memory

39.6MiB live, 77.3MiB allocated

Counts

27 → 552

Calls

Call 1

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

Outputs
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) 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 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) 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 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) 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 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x))) #<representation binary32>) () ())) ())
#s(alt tau (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* tau (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* tau (+ 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 (PI.f32) tau) x)) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* tau (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4))))))))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (patch (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) #<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 (PI.f32) tau) x)) (patch (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) #<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 (PI.f32) tau) x)) (patch (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) #<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 (PI.f32) tau) x)) (patch (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 (PI.f32) tau) x) (patch (.f32 (.f32 (PI.f32) tau) x) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 (PI.f32) tau) x) (patch (.f32 (.f32 (PI.f32) tau) x) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 (PI.f32) tau) x) (patch (.f32 (.f32 (PI.f32) tau) x) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 (PI.f32) tau) x) (patch (.f32 (.f32 (PI.f32) tau) x) #<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 (.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))) (patch #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))) #<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 (.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))) (patch #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))) #<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 (.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))) (patch #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))) #<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 (.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))) (patch #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))) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2)))) (taylor 0 tau) (#s(alt (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)) (patch (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)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2))))) (taylor 0 tau) (#s(alt (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)) (patch (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)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2))))) (taylor 0 tau) (#s(alt (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)) (patch (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)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))) (* -1/6 (* (pow x 2) (pow (PI) 2))))) (taylor 0 tau) (#s(alt (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)) (patch (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)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow (PI) 2)) (taylor 0 tau) (#s(alt (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (patch (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (patch (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (patch (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (patch (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) #<representation binary32>) () ())) ())
#s(alt 1 (taylor 0 tau) (#s(alt (fma.f32 tau tau #s(literal 1 binary32)) (patch (fma.f32 tau tau #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (pow tau 2)) (taylor 0 tau) (#s(alt (fma.f32 tau tau #s(literal 1 binary32)) (patch (fma.f32 tau tau #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (pow tau 2)) (taylor 0 tau) (#s(alt (fma.f32 tau tau #s(literal 1 binary32)) (patch (fma.f32 tau tau #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (pow tau 2)) (taylor 0 tau) (#s(alt (fma.f32 tau tau #s(literal 1 binary32)) (patch (fma.f32 tau tau #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt #s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)))) (patch #s(approx (/ ( (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.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 #s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)))) (patch #s(approx (/ ( (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.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 #s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)))) (patch #s(approx (/ ( (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.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 #s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)))) (patch #s(approx (/ ( (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 x x)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.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 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.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 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.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 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x))) (patch (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* tau (pow (PI) 2))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* tau (pow (PI) 2))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* tau (pow (PI) 2))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* tau (pow (PI) 2))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (patch (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) #<representation binary32>) () ())) ())
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#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 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) (patch (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) #<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 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) (patch (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) #<representation binary32>) () ())) ())
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#s(alt (* tau (+ (* (pow tau 2) (+ (* -1/6 (* x (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (pow (PI) 7)))) (* 1/120 (* (pow x 3) (pow (PI) 5))))))) (/ (PI) x))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) (patch (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (pow (PI) 2))) (taylor 0 tau) (#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 0 tau) (#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 0 tau) (#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 0 tau) (#s(alt (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)) (patch (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)) #<representation binary32>) () ())) ())
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#s(alt (* tau (PI)) (taylor 0 tau) (#s(alt (.f32 (PI.f32) tau) (patch (.f32 (PI.f32) tau) #<representation binary32>) () ())) ())
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#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>) () ())) ())
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#s(alt (/ (sin (* tau (* x (PI)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) (patch (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) (patch (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) (patch (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) #<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>) () ())) ())
#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
13.0ms	tau	@	inf	((* (/ (sin (* (* (PI) tau) x)) (* x (PI))) (/ (sin (* x (PI))) (* (* (PI) tau) x))) (/ (sin (* (* (PI) tau) x)) (* x (PI))) (sin (* (* (PI) tau) x)) (* (* (PI) tau) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (/ (sin (* tau (* (PI) x))) (* x x))) (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (sin (* (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) (sin (* tau (* (PI) x))) (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (* (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (neg (sin (* (PI) x)))) (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (* x (PI)) (/ (sin (* x (PI))) (* (* (PI) tau) x)) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* x x)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (* (PI) tau))
7.0ms	x	@	inf	((* (/ (sin (* (* (PI) tau) x)) (* x (PI))) (/ (sin (* x (PI))) (* (* (PI) tau) x))) (/ (sin (* (* (PI) tau) x)) (* x (PI))) (sin (* (* (PI) tau) x)) (* (* (PI) tau) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (/ (sin (* tau (* (PI) x))) (* x x))) (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (sin (* (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) (sin (* tau (* (PI) x))) (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (* (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (neg (sin (* (PI) x)))) (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (* x (PI)) (/ (sin (* x (PI))) (* (* (PI) tau) x)) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* x x)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (* (PI) tau))
7.0ms	tau	@	-inf	((* (/ (sin (* (* (PI) tau) x)) (* x (PI))) (/ (sin (* x (PI))) (* (* (PI) tau) x))) (/ (sin (* (* (PI) tau) x)) (* x (PI))) (sin (* (* (PI) tau) x)) (* (* (PI) tau) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (/ (sin (* tau (* (PI) x))) (* x x))) (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (sin (* (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) (sin (* tau (* (PI) x))) (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (* (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (neg (sin (* (PI) x)))) (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (* x (PI)) (/ (sin (* x (PI))) (* (* (PI) tau) x)) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* x x)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (* (PI) tau))
6.0ms	x	@	-inf	((* (/ (sin (* (* (PI) tau) x)) (* x (PI))) (/ (sin (* x (PI))) (* (* (PI) tau) x))) (/ (sin (* (* (PI) tau) x)) (* x (PI))) (sin (* (* (PI) tau) x)) (* (* (PI) tau) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (/ (sin (* tau (* (PI) x))) (* x x))) (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (sin (* (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) (sin (* tau (* (PI) x))) (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (* (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (neg (sin (* (PI) x)))) (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (* x (PI)) (/ (sin (* x (PI))) (* (* (PI) tau) x)) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* x x)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (* (PI) tau))
6.0ms	tau	@	0	((* (/ (sin (* (* (PI) tau) x)) (* x (PI))) (/ (sin (* x (PI))) (* (* (PI) tau) x))) (/ (sin (* (* (PI) tau) x)) (* x (PI))) (sin (* (* (PI) tau) x)) (* (* (PI) tau) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (/ (sin (* tau (* (PI) x))) (* x x))) (/ (sin (* (PI) x)) (* tau (* (PI) (PI)))) (sin (* (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) (sin (* tau (* (PI) x))) (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (* (/ (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) x) (neg (sin (* (PI) x)))) (/ (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (/ (sin (* (* (PI) tau) x)) (* (* (PI) tau) x)) (* x (PI)) (/ (sin (* x (PI))) (* (* (PI) tau) x)) (* (PI) (PI)) (/ (sin (* tau (* (PI) x))) (* x x)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (* (PI) tau))

simplify264.0ms (2.6%)

Memory

2.7MiB live, 274.7MiB allocated

Algorithm

1×	egg-herbie

Rules

22 966×	`lower-fma.f64`
22 966×	`lower-fma.f32`
9 098×	`lower-*.f64`
9 098×	`lower-*.f32`
5 320×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	486	9044
1	1622	8750
2	6049	8516
0	8684	8210

Stop Event

1×	iter limit
1×	node limit

Counts

552 → 550

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

rewrite201.0ms (2%)

Memory

16.3MiB live, 283.1MiB allocated

Rules

5 216×	`lower-/.f64`
5 198×	`lower-/.f32`
3 964×	`lower-*.f64`
3 934×	`lower-*.f32`
2 126×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	340
0	95	338
1	376	338
2	2321	322
0	8463	320

Stop Event

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

Counts

27 → 3 294

Calls

Call 1

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

Outputs
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eval429.0ms (4.2%)

Memory: 21.0MiB live, 736.0MiB allocated
Compiler: Compiled 104 820 to 5 723 computations (94.5% saved)

prune254.0ms (2.5%)

Memory

5.6MiB live, 530.5MiB allocated

Pruning

71 alts after pruning (67 fresh and 4 done)

	Pruned	Kept	Total
New	4 272	51	4 323
Fresh	15	16	31
Picked	2	3	5
Done	2	1	3
Total	4 291	71	4 362

Accuracy

99.9%

Counts

4 362 → 71

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.7%	(/.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) x) (PI.f32))
	97.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (.f32 (PI.f32) tau) x))) x) (.f32 (.f32 (*.f32 (PI.f32) tau) x) (PI.f32)))
▶	98.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (*.f32 x (PI.f32)))
	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 tau (PI.f32))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (*.f32 x (PI.f32))))
	32.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (fma.f32 #s(literal 0 binary32) (neg.f32 x) (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
	96.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (.f32 tau (PI.f32))))))
✓	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)))
	73.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	97.1%	(/.f32 (.f32 (.f32 (pow.f32 x #s(literal -2 binary32)) (sin.f32 (.f32 x (.f32 tau (PI.f32))))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
	97.9%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (.f32 tau (PI.f32))) (.f32 (neg.f32 (PI.f32)) x)))
	97.4%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) (.f32 (neg.f32 tau) (.f32 x (PI.f32)))))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x x) (.f32 (neg.f32 tau) (.f32 (PI.f32) (PI.f32)))))
	96.9%	(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32))))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (neg.f32 x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) tau) x)))
	66.9%	(/.f32 (.f32 #s(approx (/ (sin ( tau (* (PI) x))) x) (.f32 tau (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	67.0%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))
	65.9%	(/.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)))
	97.0%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 tau (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) x)) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (PI.f32))) x) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
✓	97.6%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (PI.f32))) x) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	73.0%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (PI.f32))) x) (neg.f32 #s(approx (sin ( (PI) x)) (*.f32 (PI.f32) x))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) x)))))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.0%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	73.1%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	96.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) tau) x)))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (.f32 (PI.f32) tau) x) (PI.f32))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x))
	97.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) tau)))
	96.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))) (.f32 (.f32 (PI.f32) tau) x)))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))))
	73.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) #s(approx (/ (sin (* x (PI))) (* (* (PI) tau) x)) (/.f32 #s(literal 1 binary32) tau)))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (cbrt.f32 (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) x) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))))
	73.2%	(.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)))
▶	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (PI.f32) tau) x)))
	73.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 (.f32 (neg.f32 (PI.f32)) tau) (.f32 x (PI.f32))) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	97.8%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 (neg.f32 (PI.f32)) x) (.f32 x (.f32 tau (PI.f32))))) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	28.1%	(.f32 (/.f32 #s(approx (/ (/ (sin ( (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (fma.f32 (.f32 (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32)) x) x (/.f32 #s(literal -1 binary32) (PI.f32)))) x) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
	66.9%	(.f32 (/.f32 #s(approx (/ (/ (sin ( (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (/.f32 #s(literal -1 binary32) (PI.f32))) x) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
	66.9%	(.f32 (/.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) #s(literal 1 binary32)) (.f32 (neg.f32 (PI.f32)) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	97.4%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (PI.f32))) (sin.f32 (.f32 x (.f32 tau (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (PI.f32)))))
	67.0%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
✓	96.8%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 x x))))
	72.9%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x))))
	72.9%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 #s(approx (/ (sin ( (PI) x)) (* tau (* (PI) (PI)))) (/.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x))))
▶	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (*.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)))) (*.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
	7.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (pow.f32 tau #s(literal 4 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (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)))
	66.2%	#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 (neg.f32 (PI.f32)) (neg.f32 (PI.f32))) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#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)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal 1 binary32) (.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)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (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)))
	7.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 tau tau))) (/.f32 (pow.f32 tau #s(literal 4 binary32)) (-.f32 #s(literal 1 binary32) (.f32 tau tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
▶	7.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (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)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (*.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) x #s(literal 1 binary32)))
	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) (.f32 tau tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	6.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 x (PI.f32)) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32)) #s(literal 1 binary32)))
	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) tau) tau)) (*.f32 x x) #s(literal 1 binary32)))
	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) #s(literal 1 binary32)))
	40.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 x (PI.f32)) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
▶	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
	4.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x))))
✓	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 2 816 to 1 845 computations (34.5% saved)

simplify173.0ms (1.7%)

Memory

1.4MiB live, 168.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f32 x (PI.f32))
cost-diff	0	(.f32 (.f32 x (PI.f32)) tau)
cost-diff	0	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
cost-diff	0	(fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (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))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (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)))
cost-diff	64	(.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)))
cost-diff	160	(*.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32))))
cost-diff	0	(*.f32 (PI.f32) (PI.f32))
cost-diff	0	(fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (.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 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (.f32 x x) #s(literal 1 binary32)))
cost-diff	320	(fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (*.f32 tau tau)))
cost-diff	0	(.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x)
cost-diff	0	(fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))
cost-diff	0	#s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32)))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
cost-diff	0	(.f32 x (.f32 tau (PI.f32)))
cost-diff	0	(sin.f32 (.f32 x (.f32 tau (PI.f32))))
cost-diff	0	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (*.f32 x (PI.f32)))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))

Rules

17 234×	`lower-fma.f64`
17 224×	`lower-fma.f32`
5 838×	`lower-*.f64`
5 806×	`lower-*.f32`
2 224×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	487
0	97	487
1	191	468
2	513	468
3	1920	468
4	5465	468
5	6322	468
6	7876	468
0	8030	460

Stop Event

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

Calls

Call 1

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

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

localize132.0ms (1.3%)

Memory

28.1MiB live, 209.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.328125	(*.f32 tau (PI.f32))
accuracy	0.34375	(*.f32 x (PI.f32))
accuracy	0.4137687988422102	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42710878907376815	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	5.763007819378079	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (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)))
accuracy	20.553392873004118	(fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (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))
accuracy	29.648142511195413	(fma.f32 tau tau #s(literal -1 binary32))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	5.763007819378079	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (.f32 x x) #s(literal 1 binary32)))
accuracy	20.55991299613453	(fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (.f32 x x) #s(literal 1 binary32))
accuracy	24.77641014427914	(fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (*.f32 tau tau)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	5.763007819378079	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
accuracy	10.757409774396331	#s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32)))
accuracy	17.637111200102282	(fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))
accuracy	0.328125	(*.f32 tau (PI.f32))
accuracy	0.34375	(*.f32 x (PI.f32))
accuracy	0.3896675293053261	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (*.f32 x (PI.f32)))
accuracy	0.42710878907376815	(/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32))))

Samples

96.0ms

256×

valid

Compiler

Compiled 415 to 49 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-mult: 40.0ms (51.6% of total)

ival-div: 9.0ms (11.6% of total)

ival-add: 7.0ms (9% of total)

ival-sin: 7.0ms (9% of total)

ival-sinu: 5.0ms (6.4% of total)

const: 4.0ms (5.2% of total)

ival-pow: 3.0ms (3.9% of total)

ival-pi: 1.0ms (1.3% of total)

ival-sub: 1.0ms (1.3% of total)

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

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

exact: 0.0ms (0% of total)

series60.0ms (0.6%)

Memory

1.6MiB live, 75.7MiB allocated

Counts

25 → 468

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
10.0ms	x	@	-inf	((* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (/ (* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (* x (PI))) (sin (* x (* tau (PI)))) (* x (* tau (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (* (* (* (PI) (PI)) -1/6) x) (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* x x)) 1) (* (PI) (PI)) (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* x (PI)) (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (* tau (PI)) (+ (* tau tau) -1) (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI))))
5.0ms	tau	@	-inf	((* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (/ (* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (* x (PI))) (sin (* x (* tau (PI)))) (* x (* tau (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (* (* (* (PI) (PI)) -1/6) x) (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* x x)) 1) (* (PI) (PI)) (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* x (PI)) (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (* tau (PI)) (+ (* tau tau) -1) (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI))))
5.0ms	x	@	inf	((* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (/ (* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (* x (PI))) (sin (* x (* tau (PI)))) (* x (* tau (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (* (* (* (PI) (PI)) -1/6) x) (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* x x)) 1) (* (PI) (PI)) (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* x (PI)) (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (* tau (PI)) (+ (* tau tau) -1) (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI))))
5.0ms	tau	@	inf	((* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (/ (* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (* x (PI))) (sin (* x (* tau (PI)))) (* x (* tau (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (* (* (* (PI) (PI)) -1/6) x) (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* x x)) 1) (* (PI) (PI)) (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* x (PI)) (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (* tau (PI)) (+ (* tau tau) -1) (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI))))
4.0ms	tau	@	0	((* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (/ (* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (* x (PI))) (sin (* x (* tau (PI)))) (* x (* tau (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (* (* (* (PI) (PI)) -1/6) x) (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (* x x)) 1) (* (PI) (PI)) (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (* (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* x (PI)) (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (* tau (PI)) (+ (* tau tau) -1) (/ (sin (* (* x (PI)) tau)) (* (* tau (PI)) x)) (/ (sin (* x (PI))) (* x (PI))))

simplify229.0ms (2.2%)

Memory

-0.0MiB live, 273.0MiB allocated

Algorithm

1×	egg-herbie

Rules

18 552×	`lower-fma.f64`
18 552×	`lower-fma.f32`
6 658×	`lower-*.f64`
6 658×	`lower-*.f32`
5 244×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	303	7544
1	983	7098
2	3723	6948
3	7523	6948
0	8426	6589

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 468

Calls

Call 1

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

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

rewrite302.0ms (3%)

Memory

-16.7MiB live, 313.2MiB allocated

Rules

5 472×	`lower-fma.f64`
5 464×	`lower-fma.f32`
4 348×	`lower-/.f64`
4 340×	`lower-/.f32`
4 010×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	393
0	97	379
1	348	354
2	2388	335
0	8181	317

Stop Event

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

Counts

25 → 1 557

Calls

Call 1

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

Outputs
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eval332.0ms (3.3%)

Memory: -28.2MiB live, 428.6MiB allocated
Compiler: Compiled 55 787 to 4 508 computations (91.9% saved)

prune332.0ms (3.3%)

Memory

12.3MiB live, 365.0MiB allocated

Pruning

86 alts after pruning (77 fresh and 9 done)

	Pruned	Kept	Total
New	2 227	32	2 259
Fresh	17	45	62
Picked	0	5	5
Done	0	4	4
Total	2 244	86	2 330

Accuracy

99.9%

Counts

2 330 → 86

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.7%	(/.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) x) (PI.f32))
	97.5%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 (.f32 (PI.f32) tau) x))) x) (.f32 (.f32 (*.f32 (PI.f32) tau) x) (PI.f32)))
	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (PI.f32) tau)) (sin.f32 (.f32 (PI.f32) x))) (.f32 x (*.f32 (PI.f32) x)))
	97.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (.f32 tau (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (PI.f32)))
	96.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x)))) (.f32 x (PI.f32)))
	96.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x)))
✓	98.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (*.f32 x (PI.f32)))
	32.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (fma.f32 #s(literal 0 binary32) (neg.f32 x) (.f32 x (PI.f32)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
	96.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (.f32 tau (PI.f32))))))
✓	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)))
	73.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	97.1%	(/.f32 (.f32 (.f32 (pow.f32 x #s(literal -2 binary32)) (sin.f32 (.f32 x (.f32 tau (PI.f32))))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (*.f32 (PI.f32) (PI.f32)) tau))
	97.9%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 (PI.f32) tau) x) (.f32 (neg.f32 (PI.f32)) x)))
	97.4%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)))) (.f32 (.f32 (PI.f32) x) (.f32 (neg.f32 tau) (.f32 (PI.f32) x))))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (.f32 x x) (.f32 (neg.f32 tau) (.f32 (PI.f32) (PI.f32)))))
	96.9%	(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32))))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (neg.f32 x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) tau) x)))
	66.9%	(/.f32 (.f32 #s(approx (/ (sin ( tau (* (PI) x))) x) (.f32 tau (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	67.0%	(/.f32 #s(approx (* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 x (PI.f32)))
	67.0%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))
	65.9%	(/.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)))
✓	97.6%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (PI.f32))) x) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	73.0%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (PI.f32))) x) (neg.f32 #s(approx (sin ( (PI) x)) (*.f32 (PI.f32) x))))
	97.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 (PI.f32) x)))))
	97.4%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (*.f32 (PI.f32) tau) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) x))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 tau (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.0%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	73.1%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 (.f32 (PI.f32) tau) x) (PI.f32))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x))
	97.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) tau)))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))))
	73.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 x (PI.f32))) #s(approx (/ (sin (* x (PI))) (* (* (PI) tau) x)) (/.f32 #s(literal 1 binary32) tau)))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (cbrt.f32 (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) x) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))))
	73.2%	(.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)))
✓	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	73.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (PI.f32) tau) x)))
	73.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 (.f32 (neg.f32 (PI.f32)) tau) (.f32 x (PI.f32))) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	97.8%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 (neg.f32 (PI.f32)) x) (.f32 x (.f32 tau (PI.f32))))) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	28.1%	(.f32 (/.f32 #s(approx (/ (/ (sin ( (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (fma.f32 (.f32 (.f32 (.f32 (.f32 tau (PI.f32)) tau) #s(literal 1/6 binary32)) x) x (/.f32 #s(literal -1 binary32) (PI.f32)))) x) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
	66.9%	(.f32 (/.f32 #s(approx (/ (/ (sin ( (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (/.f32 #s(literal -1 binary32) (PI.f32))) x) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
	66.9%	(.f32 (/.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) #s(literal 1 binary32)) (.f32 (neg.f32 (PI.f32)) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
	97.4%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (PI.f32))) (sin.f32 (.f32 x (.f32 tau (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (PI.f32)))))
✓	96.8%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 x x))))
	72.9%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x))))
	72.9%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 #s(approx (/ (sin ( (PI) x)) (* tau (* (PI) (PI)))) (/.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x))))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (.f32 tau tau) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	2.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (PI.f32) #s(literal 2 binary32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
✓	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (*.f32 x x) #s(literal 1 binary32)))
	6.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
	7.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)) (.f32 (pow.f32 (.f32 (PI.f32) tau) #s(literal 2 binary32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	7.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (-.f32 (pow.f32 tau #s(literal 6 binary32)) #s(literal -1 binary32))) (fma.f32 #s(literal -1 binary32) (fma.f32 tau tau #s(literal -1 binary32)) (pow.f32 tau #s(literal 4 binary32)))) (.f32 x x) #s(literal 1 binary32)))
	7.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (pow.f32 tau #s(literal 4 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (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)))
	66.2%	#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)))
	66.2%	#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)) x) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal 1 binary32) (.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)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (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)))
	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (-.f32 (.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)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
	7.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (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)))
✓	7.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (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)))
	7.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (.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)))
	7.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (fma.f32 tau tau #s(literal -1 binary32)) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	7.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (-.f32 tau #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal -1/6 binary32)) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (*.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal 1 binary32) (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)))
	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) (.f32 tau tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx ( (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (.f32 tau tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)))
	6.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 x (PI.f32)) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32)) #s(literal 1 binary32)))
	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) tau) tau)) (*.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) #s(literal 1 binary32)))
	41.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) (sqrt.f32 (PI.f32))) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
✓	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
	66.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (PI.f32) (*.f32 x x)) #s(literal 1 binary32))))
	67.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))))
	4.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (PI.f32)))))
✓	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 4 553 to 1 727 computations (62.1% saved)

regimes216.0ms (2.1%)

Memory

12.0MiB live, 199.8MiB allocated

Counts

140 → 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 (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (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)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (PI.f32) (*.f32 x x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.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 #s(approx (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (.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 #s(approx (+ ( tau tau) 1) #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)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) 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 (.f32 #s(approx ( (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (.f32 tau tau)) (.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 #s(approx (+ ( tau tau) 1) (.f32 tau tau)) (.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 x (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 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 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.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 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (fma.f32 tau tau #s(literal 1 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 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 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 (fma.f32 tau tau #s(literal 1 binary32)) (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 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (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 tau tau #s(literal 1 binary32)) x) (.f32 (.f32 (.f32 (PI.f32) (PI.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 (* (* 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 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 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (neg.f32 (PI.f32)) (neg.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 #s(literal 1 binary32) (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 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32))) #s(literal 1 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 (fma.f32 #s(literal 1 binary32) (.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 (* 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)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #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 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.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 (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.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 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 #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 (.f32 tau tau) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #s(literal 1 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 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (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)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #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))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(/.f32 #s(approx (* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 x (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 x (PI.f32)) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 x (PI.f32)) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)))) (*.f32 x x) #s(literal 1 binary32)))
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(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) tau) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (.f32 tau (PI.f32))))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x)))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x)))) (.f32 x (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (*.f32 (cbrt.f32 (PI.f32)) x)))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (exp.f32 (.f32 (log.f32 (pow.f32 (.f32 x (PI.f32)) #s(literal -2 binary32))) #s(literal -1/2 binary32))))) (.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 tau (.f32 (PI.f32) x))) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (cbrt.f32 (PI.f32))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (.f32 (/.f32 (.f32 (.f32 (PI.f32) tau) x) (sin.f32 (.f32 (*.f32 (PI.f32) tau) x))) (cbrt.f32 (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (cbrt.f32 (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) x) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))))
(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))) tau)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (cbrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))) (cbrt.f32 (cbrt.f32 (PI.f32))))))

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

Calls

4 calls:

57.0ms	tau
56.0ms	(.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))))
50.0ms	x
42.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`tau`
98.0%	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))))`
98.0%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes165.0ms (1.6%)

Memory

1.4MiB live, 135.5MiB allocated

Counts

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

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

Calls

4 calls:

58.0ms	x
39.0ms	(*.f32 x (PI.f32))
38.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
26.0ms	tau

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`(*.f32 x (PI.f32))`
98.0%	1	`tau`
98.0%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes136.0ms (1.3%)

Memory

0.2MiB live, 121.0MiB allocated

Counts

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

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

Calls

4 calls:

42.0ms	x
38.0ms	(.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))))
30.0ms	(*.f32 x (PI.f32))
23.0ms	tau

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`tau`
97.9%	1	`(*.f32 x (PI.f32))`
97.9%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes169.0ms (1.7%)

Memory

-3.6MiB live, 117.3MiB allocated

Counts

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

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

Calls

4 calls:

62.0ms	(.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	x
35.0ms	tau
20.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`tau`
97.9%	1	`(*.f32 x (PI.f32))`
97.9%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes121.0ms (1.2%)

Memory

-6.2MiB live, 106.1MiB allocated

Counts

74 → 1

Calls

Call 1

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

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

Calls

4 calls:

39.0ms	(*.f32 x (PI.f32))
31.0ms	tau
19.0ms	x
19.0ms	(.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
97.8%	1	`x`
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))`
97.8%	1	`tau`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes91.0ms (0.9%)

Memory

-12.9MiB live, 196.0MiB allocated

Counts

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

Outputs
(.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)))

Calls

4 calls:

21.0ms	(.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))))
21.0ms	tau
21.0ms	(*.f32 x (PI.f32))
19.0ms	x

Results

Accuracy	Segments	Branch
73.2%	1	`x`
73.2%	1	`(*.f32 x (PI.f32))`
73.2%	1	`tau`
73.2%	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 26 to 18 computations (30.8% saved)

regimes60.0ms (0.6%)

Memory

16.9MiB live, 132.9MiB allocated

Counts

51 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (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)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (PI.f32) (*.f32 x x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.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 #s(approx (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (.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 #s(approx (+ ( tau tau) 1) #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)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) 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 (.f32 #s(approx ( (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (.f32 tau tau)) (.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 #s(approx (+ ( tau tau) 1) (.f32 tau tau)) (.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 x (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 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 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.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 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (fma.f32 tau tau #s(literal 1 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 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 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 (fma.f32 tau tau #s(literal 1 binary32)) (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 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (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 tau tau #s(literal 1 binary32)) x) (.f32 (.f32 (.f32 (PI.f32) (PI.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 (* (* 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 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 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (neg.f32 (PI.f32)) (neg.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 #s(literal 1 binary32) (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 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32))) #s(literal 1 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 (fma.f32 #s(literal 1 binary32) (.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 (* 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)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #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 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.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 (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.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 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 #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 (.f32 tau tau) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #s(literal 1 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 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (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)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #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))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(/.f32 #s(approx (* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 x (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 x (PI.f32)) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 x (PI.f32)) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)))) (*.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) #s(literal 1 binary32)) (.f32 (neg.f32 (PI.f32)) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.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)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) (sqrt.f32 (PI.f32))) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)) (.f32 (pow.f32 (.f32 (PI.f32) tau) #s(literal 2 binary32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 #s(approx (/ (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) x)) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
(.f32 (/.f32 #s(approx (/ (/ (sin ( (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (/.f32 #s(literal -1 binary32) (PI.f32))) x) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))

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

Calls

4 calls:

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))))
14.0ms	tau
14.0ms	x
14.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
73.0%	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))))`
73.0%	1	`x`
73.0%	1	`tau`
73.0%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes61.0ms (0.6%)

Memory

20.4MiB live, 137.8MiB allocated

Counts

50 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (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)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (PI.f32) (*.f32 x x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.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 #s(approx (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (.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 #s(approx (+ ( tau tau) 1) #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)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) 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 (.f32 #s(approx ( (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (.f32 tau tau)) (.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 #s(approx (+ ( tau tau) 1) (.f32 tau tau)) (.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 x (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 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 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.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 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (fma.f32 tau tau #s(literal 1 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 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 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 (fma.f32 tau tau #s(literal 1 binary32)) (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 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (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 tau tau #s(literal 1 binary32)) x) (.f32 (.f32 (.f32 (PI.f32) (PI.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 (* (* 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 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 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (neg.f32 (PI.f32)) (neg.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 #s(literal 1 binary32) (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 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32))) #s(literal 1 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 (fma.f32 #s(literal 1 binary32) (.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 (* 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)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #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 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.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 (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.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 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 #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 (.f32 tau tau) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #s(literal 1 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 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (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)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #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))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(/.f32 #s(approx (* (/ (sin (* x (* tau (PI)))) (* x (* tau (PI)))) (sin (* x (PI)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 x (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 x (PI.f32)) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 x (PI.f32)) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)))) (*.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 #s(approx (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) #s(literal 1 binary32)) (.f32 (neg.f32 (PI.f32)) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.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)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) (sqrt.f32 (PI.f32))) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)) (.f32 (pow.f32 (.f32 (PI.f32) tau) #s(literal 2 binary32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 #s(approx (/ (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) (* (neg (PI)) x)) (/.f32 (/.f32 #s(literal -1 binary32) (PI.f32)) x)) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
(.f32 (/.f32 #s(approx (/ (/ (sin ( (* (PI) tau) x)) (* (* (PI) tau) x)) (neg (PI))) (/.f32 #s(literal -1 binary32) (PI.f32))) x) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))

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

Calls

4 calls:

16.0ms	tau
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))))
13.0ms	x

Results

Accuracy	Segments	Branch
73.0%	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))))`
73.0%	1	`x`
73.0%	1	`(*.f32 x (PI.f32))`
73.0%	1	`tau`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes61.0ms (0.6%)

Memory

10.8MiB live, 168.7MiB allocated

Counts

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

Outputs

#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (*.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))))

Calls

4 calls:

17.0ms	x
15.0ms	tau
14.0ms	(*.f32 x (PI.f32))
13.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
67.1%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
67.1%	1	`tau`
67.1%	1	`x`
67.1%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes41.0ms (0.4%)

Memory

-22.4MiB live, 101.6MiB allocated

Accuracy

Total -20.1b remaining (-185.6%)

Threshold costs -20.1b (-185.6%)

Counts

34 → 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 (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* (PI) (PI)) -1/6) x) x) 1) (.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (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)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (PI.f32) (*.f32 x x)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.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 #s(approx (+ (* (* (PI) (PI)) -1/6) (* (* -1/6 (* (PI) (PI))) (* tau tau))) (.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 #s(approx (+ ( tau tau) 1) #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)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 tau tau) #s(literal -1/6 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) 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 (.f32 #s(approx ( (- (pow tau 4) 1) (/ 1 (+ (* tau tau) -1))) (.f32 tau tau)) (.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 #s(approx (+ ( tau tau) 1) (.f32 tau tau)) (.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 x (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 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 x x) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.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 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) (.f32 (fma.f32 tau tau #s(literal 1 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 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 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 (fma.f32 tau tau #s(literal 1 binary32)) (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 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (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 tau tau #s(literal 1 binary32)) x) (.f32 (.f32 (.f32 (PI.f32) (PI.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 (* (* 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 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 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (neg.f32 (PI.f32)) (neg.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 #s(literal 1 binary32) (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 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32))) #s(literal 1 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 (fma.f32 #s(literal 1 binary32) (.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 (* 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)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #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 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.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 (+.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.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 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32) (.f32 (.f32 tau tau) (.f32 #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 (.f32 tau tau) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) #s(literal 1 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 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (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)))

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

Calls

4 calls:

10.0ms	x
10.0ms	(.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))))
9.0ms	(*.f32 x (PI.f32))
9.0ms	tau

Results

Accuracy	Segments	Branch
66.2%	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))))`
66.2%	1	`tau`
66.2%	1	`x`
66.2%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify49.0ms (0.5%)

Memory

-15.8MiB live, 62.9MiB allocated

Algorithm

1×	egg-herbie

Rules

346×	`distribute-lft-neg-in-binary32-*.f32-neg.f32`
178×	`neg-mul-1-binary32-*.f32-neg.f32`
174×	`neg-sub0-binary32--.f32-neg.f32`
172×	`unsub-neg-binary32--.f32-neg.f32-+.f32`
160×	`cancel-sign-sub-binary32-+.f32-neg.f32-*.f32--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	250
1	110	250
2	137	250
3	178	246
4	231	246
5	333	246
6	452	246
7	612	246
8	775	246
9	900	246
10	1001	246
11	1059	246
12	1078	246
13	1081	246

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.9s (18.2%)

Memory

30.5MiB live, 1 235.9MiB allocated

Rules

22 966×	`lower-fma.f64`
22 966×	`lower-fma.f32`
20 394×	`lower-fma.f64`
20 394×	`lower-fma.f32`
18 552×	`lower-fma.f64`

Iterations

Useful iterations: 2 (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
0	303	7544
1	983	7098
2	3723	6948
3	7523	6948
0	8426	6589
0	54	340
0	95	338
1	376	338
2	2321	322
0	8463	320
0	41	250
0	73	232
1	267	232
2	1287	220
3	6173	220
0	8441	220
0	58	393
0	97	379
1	348	354
2	2388	335
0	8181	317
0	334	6954
1	1110	6818
2	4341	6664
3	7968	6664
0	8027	6437
0	486	9044
1	1622	8750
2	6049	8516
0	8684	8210
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	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 514 to 223 computations (56.6% saved)

preprocess91.0ms (0.9%)

Memory

-19.9MiB live, 264.3MiB allocated

Remove

(abs x)

(abs tau)

Compiler

Compiled 1 208 to 540 computations (55.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze21.0ms (0.2%)

sample1.8s (17.8%)

explain163.0ms (1.6%)

preprocess112.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify22.0ms (0.2%)

localize37.0ms (0.4%)

series31.0ms (0.3%)

simplify232.0ms (2.3%)

rewrite395.0ms (3.9%)

eval96.0ms (0.9%)

prune70.0ms (0.7%)

simplify88.0ms (0.9%)

localize107.0ms (1%)

series42.0ms (0.4%)

simplify215.0ms (2.1%)

rewrite185.0ms (1.8%)

eval255.0ms (2.5%)

prune146.0ms (1.4%)

simplify145.0ms (1.4%)

localize143.0ms (1.4%)

series63.0ms (0.6%)

simplify264.0ms (2.6%)

rewrite201.0ms (2%)

eval429.0ms (4.2%)

prune254.0ms (2.5%)

simplify173.0ms (1.7%)

localize132.0ms (1.3%)

series60.0ms (0.6%)

simplify229.0ms (2.2%)

rewrite302.0ms (3%)

eval332.0ms (3.3%)

prune332.0ms (3.3%)

regimes216.0ms (2.1%)

regimes165.0ms (1.6%)

regimes136.0ms (1.3%)

regimes169.0ms (1.7%)

regimes121.0ms (1.2%)

regimes91.0ms (0.9%)

regimes60.0ms (0.6%)

regimes61.0ms (0.6%)

regimes61.0ms (0.6%)

regimes41.0ms (0.4%)

simplify49.0ms (0.5%)

soundness1.9s (18.2%)

preprocess91.0ms (0.9%)

end0.0ms (0%)

Profiling