Metrics for Lanczos kernel

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze21.0ms (0.1%)

Memory

19.5MiB live, 64.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 37 to 21 computations (43.2% saved)

sample1.8s (11%)

Memory

19.5MiB live, 4 071.3MiB allocated

Samples

1.4s

8 256×

valid

Precisions

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

ival-sin: 324.0ms (29.7% of total)

const: 247.0ms (22.7% of total)

ival-mult: 194.0ms (17.8% of total)

ival-<=: 136.0ms (12.5% of total)

ival-div: 109.0ms (10% of total)

ival-pi: 48.0ms (4.4% of total)

ival-and: 22.0ms (2% of total)

exact: 8.0ms (0.7% of total)

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

Bogosity

explain230.0ms (1.4%)

Memory

-10.5MiB live, 479.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
1	-	1	(0.725566029548645 1.3918665647506714)	`(sin.f32 (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`(PI.f32)`
0	-	0	-	`(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))`
0	-	0	-	`(.f32 (.f32 x (PI.f32)) tau)`
0	-	0	-	`(*.f32 x (PI.f32))`
0	-	0	-	`(sin.f32 (*.f32 x (PI.f32)))`
0	-	0	-	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
0	-	0	-	`tau`
0	-	0	-	`(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`x`

Confusion

	Predicted +	Predicted -
+	0	4
-	0	252

Precision

0/0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	1	3
-	0	0	252

Precision?

1.0

Recall?

0.25

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

47.0ms

512×

valid

Compiler

Compiled 151 to 34 computations (77.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-sin: 13.0ms (42.3% of total)

ival-mult: 9.0ms (29.3% of total)

ival-div: 6.0ms (19.5% of total)

ival-pi: 2.0ms (6.5% of total)

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

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

preprocess86.0ms (0.5%)

Memory

23.4MiB live, 167.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs tau)

(abs x)

Compiler

Compiled 23 to 10 computations (56.5% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.0%	(.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))))

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify25.0ms (0.2%)

Memory

-4.7MiB live, 41.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize38.0ms (0.2%)

Memory

16.0MiB live, 58.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.3385970049616671	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3659363281475362	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42091752930532605	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

Samples

22.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

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

ival-sin: 6.0ms (40.5% of total)

ival-mult: 5.0ms (33.7% of total)

ival-div: 3.0ms (20.2% of total)

ival-pi: 1.0ms (6.7% of total)

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

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

series32.0ms (0.2%)

Memory

8.7MiB live, 51.4MiB allocated

Counts

6 → 120

Calls

Call 1

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

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

Calls

30 calls:

Time	Variable		Point	Expression
8.0ms	tau	@	inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
3.0ms	x	@	0	(/ (sin (* x (PI))) (* x (PI)))
2.0ms	x	@	0	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
2.0ms	x	@	inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
2.0ms	x	@	-inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))

simplify494.0ms (3%)

Memory

14.8MiB live, 575.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

rewrite306.0ms (1.8%)

Memory

17.2MiB live, 573.5MiB allocated

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

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

Counts

6 → 670

Calls

Call 1

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

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

eval129.0ms (0.8%)

Memory: -32.4MiB live, 244.8MiB allocated
Compiler: Compiled 24 386 to 2 296 computations (90.6% saved)

prune321.0ms (1.9%)

Memory

-28.1MiB live, 546.3MiB allocated

Pruning

37 alts after pruning (36 fresh and 1 done)

	Pruned	Kept	Total
New	977	36	1 013
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	977	37	1 014

Accuracy

99.7%

Counts

1 014 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	66.6%	(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
	66.6%	(/.f32 (.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))) #s(literal 2 binary32))
	97.3%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 x tau))))
	97.7%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 x tau)))) (*.f32 x (PI.f32)))
▶	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32)))))) tau)
	97.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	97.3%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))))
	97.1%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	97.2%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (.f32 x (cbrt.f32 (PI.f32))) tau))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	95.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
▶	97.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) x))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (sin.f32 (*.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 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
	95.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))))
	96.2%	(.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 x (cbrt.f32 (PI.f32)))))))
✓	98.0%	(.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))))
	87.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	71.6%	(.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)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) x))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (sin.f32 (*.f32 x (PI.f32))))))
	97.6%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (*.f32 x tau))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	79.5%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
	97.3%	(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	80.1%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	94.4%	(exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))) #s(literal -1 binary32)))
	85.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	96.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
▶	64.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 837 to 976 computations (46.9% saved)

simplify152.0ms (0.9%)

Memory

13.2MiB live, 144.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

2 380×	`lower-*.f64`
2 348×	`lower-*.f32`
1 772×	`associate-/r*`
1 526×	`associate-/l/`
1 488×	`associate-/l*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	389
0	78	387
1	148	387
2	332	387
3	1102	387
4	3239	387
5	3241	387
6	3243	387
7	3243	387
8	4270	387
9	4714	387
10	4911	387
11	4991	387
12	5008	387
13	5008	387
14	5369	387
15	5482	387
16	5739	387
17	5828	387
18	5828	387
0	5828	387

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

localize143.0ms (0.9%)

Memory

31.1MiB live, 321.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3828125	(/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32))))
accuracy	0.4069137695368841	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.43263627930532605	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.38900375976844204	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
accuracy	0.390625	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 x (PI.f32)))))
accuracy	0.4069137695368841	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.35546875	(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
accuracy	0.359375	(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.4020500488422101	(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
accuracy	11.298214867531112	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
accuracy	0.3385970049616671	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.42091752930532605	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.42806625976844204	(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))

Samples

86.0ms

256×

valid

Compiler

Compiled 367 to 38 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 29.0ms (41.2% of total)

ival-div: 25.0ms (35.5% of total)

ival-sin: 15.0ms (21.3% of total)

ival-pi: 1.0ms (1.4% of total)

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

exact: 0.0ms (0% of total)

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

series50.0ms (0.3%)

Memory

-15.2MiB live, 73.7MiB allocated

Counts

23 → 492

Calls

Call 1

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

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

Calls

123 calls:

Time	Variable		Point	Expression
14.0ms	x	@	0	(/ (/ 1 (* (PI) (* x tau))) x)
1.0ms	tau	@	0	(/ (/ 1 (* (PI) (* x tau))) x)
1.0ms	x	@	0	(* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))))
1.0ms	x	@	0	(/ (sin (* (PI) (* x tau))) (/ (PI) (sin (* x (PI)))))
1.0ms	x	@	-inf	(/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))

simplify428.0ms (2.6%)

Memory

38.4MiB live, 974.9MiB allocated

Algorithm

1×	egg-herbie

Rules

18 798×	`lower-fma.f64`
18 798×	`lower-fma.f32`
7 760×	`lower-*.f64`
7 760×	`lower-*.f32`
6 608×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	368	7796
1	1212	7607
2	4714	7396
0	8581	7162

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 490

Calls

Call 1

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

Outputs
1
#s(literal 1 binary32)
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))))
(fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4))))))))))
(fma.f32 (.f32 x x) (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32))))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 (PI.f32) (.f32 tau tau) (PI.f32))))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6))))))))))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32))) (.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (fma.f32 #s(literal -1/720 binary32) (fma.f32 tau tau (.f32 (.f32 tau tau) (.f32 tau tau))) (fma.f32 #s(literal -1/5040 binary32) (pow.f32 tau #s(literal 6 binary32)) #s(literal -1/5040 binary32)))))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 (PI.f32) (*.f32 tau tau) (PI.f32))))) #s(literal 1 binary32))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 tau tau) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 (.f32 tau tau) (.f32 (sin.f32 (.f32 x (PI.f32))) (fma.f32 (.f32 (.f32 tau tau) #s(literal 1/120 binary32)) (.f32 (.f32 x x) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI))))
(fma.f32 tau (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (sin.f32 (.f32 x (PI.f32))) (fma.f32 (.f32 (.f32 tau tau) #s(literal -1/5040 binary32)) (.f32 (pow.f32 x #s(literal 5 binary32)) (pow.f32 (PI.f32) #s(literal 5 binary32))) (.f32 (.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32)))))
1
#s(literal 1 binary32)
(+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2))))
(fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.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 (.f32 x x) (fma.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4)))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32))) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(/ (sin (* x (PI))) (* x (PI)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
1
#s(literal 1 binary32)
(+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2)))))
(fma.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* 1/120 (* (pow tau 4) (* (pow x 2) (pow (PI) 4)))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 6) (* (pow x 2) (pow (PI) 6)))) (* 1/120 (* (pow tau 4) (pow (PI) 4))))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) (pow.f32 (PI.f32) #s(literal 4 binary32))) (.f32 (pow.f32 tau #s(literal 6 binary32)) (.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32)))))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))
(/ (sin (* tau (* x (PI)))) (* tau (* x (PI))))
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(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
(/ 1 (* tau (* x (PI))))
(/.f32 #s(literal 1 binary32) (.f32 x (.f32 tau (PI.f32))))
x
(* x (+ 1 (* -1/6 (* (pow x 2) (pow (PI) 2)))))
(fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 x #s(literal -1/6 binary32)) x)
(* x (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* 1/120 (* (pow x 2) (pow (PI) 4)))))))
(fma.f32 (.f32 x (.f32 x x)) (fma.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 (.f32 x x) #s(literal 1/120 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) x)
(* x (+ 1 (* (pow x 2) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 6))) (* 1/120 (pow (PI) 4))))))))
(fma.f32 (.f32 x (.f32 x x)) (fma.f32 (.f32 x x) (fma.f32 x (.f32 x (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32))) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) x)
(/ (sin (* x (PI))) (PI))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
(/ (sin (* x (PI))) (PI))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
(/ (sin (* x (PI))) (PI))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
(/ (sin (* x (PI))) (PI))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
(/ (sin (* x (PI))) (PI))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
(/ (sin (* x (PI))) (PI))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
(/ (sin (* x (PI))) (PI))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
(/ (sin (* x (PI))) (PI))
(/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* x (PI))
(*.f32 x (PI.f32))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (PI)))
(.f32 x (.f32 x (*.f32 tau (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))
(/ 1 (* x (PI)))
(/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))
(/ (+ (* -1/6 (* (pow x 2) (PI))) (/ 1 (PI))) x)
(/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (PI)) (* 1/120 (* (pow x 2) (pow (PI) 3))))) (/ 1 (PI))) x)
(/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)
(/ (+ (* (pow x 2) (+ (* -1/6 (PI)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (pow (PI) 5))) (* 1/120 (pow (PI) 3)))))) (/ 1 (PI))) x)
(/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)
(/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (sin (* x (PI))) (* (pow x 2) (pow (PI) 2)))
(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ 1 x)
(/.f32 #s(literal 1 binary32) x)
(/ (+ 1 (* 1/6 (* (pow x 2) (pow (PI) 2)))) x)
(/.f32 (fma.f32 (.f32 x x) (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal 1/6 binary32)) #s(literal 1 binary32)) x)
(/ (+ 1 (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/36 (pow (PI) 4)) (* 1/120 (pow (PI) 4))))) (* -1/6 (pow (PI) 2))))) x)
(/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) #s(literal 7/360 binary32)) (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1/5040 (pow (PI) 6)) (+ (* 1/720 (pow (PI) 6)) (* 1/6 (* (pow (PI) 2) (+ (* -1/36 (pow (PI) 4)) (* 1/120 (pow (PI) 4))))))))) (+ (* -1/36 (pow (PI) 4)) (* 1/120 (pow (PI) 4))))) (* -1/6 (pow (PI) 2))))) x)
(/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (neg.f32 (fma.f32 (.f32 x x) (fma.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal 1/840 binary32) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) #s(literal -7/360 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal 1/6 binary32)))) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) #s(literal -7/360 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal 1/6 binary32))) #s(literal 1 binary32)) x)
(/ (PI) (sin (* x (PI))))
(/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32))))
(/ (PI) (sin (* x (PI))))
(/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32))))
(/ (PI) (sin (* x (PI))))
(/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32))))
(/ (PI) (sin (* x (PI))))
(/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32))))
(/ (PI) (sin (* x (PI))))
(/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32))))
(/ (PI) (sin (* x (PI))))
(/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32))))
(/ (PI) (sin (* x (PI))))
(/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32))))
(/ (PI) (sin (* x (PI))))
(/.f32 (PI.f32) (sin.f32 (*.f32 x (PI.f32))))

rewrite311.0ms (1.9%)

Memory

27.4MiB live, 591.2MiB allocated

Rules

4 006×	`lower-*.f64`
3 974×	`lower-*.f32`
3 634×	`lower-/.f64`
3 614×	`lower-/.f32`
1 366×	`lower-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	291
0	78	289
1	247	269
2	1525	269
3	7346	269
0	8303	269

Stop Event

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

Counts

23 → 1 720

Calls

Call 1

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

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

eval283.0ms (1.7%)

Memory: -33.1MiB live, 653.5MiB allocated
Compiler: Compiled 62 932 to 3 434 computations (94.5% saved)

prune755.0ms (4.5%)

Memory

-17.0MiB live, 1 230.6MiB allocated

Pruning

54 alts after pruning (52 fresh and 2 done)

	Pruned	Kept	Total
New	2 543	39	2 582
Fresh	18	13	31
Picked	4	1	5
Done	0	1	1
Total	2 565	54	2 619

Accuracy

99.7%

Counts

2 619 → 54

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.1%	(/.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32)))) x) tau)
	66.7%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 (PI.f32) (.f32 x (*.f32 x (PI.f32)))) #s(literal 2 binary32))) tau)
	97.3%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x (PI.f32)) (*.f32 (PI.f32) tau))) x)
	97.3%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) (PI.f32))
	66.6%	(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
	97.1%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) tau)
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))) tau)
	94.6%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	91.7%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
▶	86.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	71.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
▶	97.4%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
	97.4%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (neg.f32 (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	97.4%	(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))) (sin.f32 (*.f32 x (PI.f32)))))
	79.2%	(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (*.f32 tau tau) tau))) tau)) tau)
	97.3%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))))
	97.4%	(/.f32 #s(literal -1 binary32) (.f32 (/.f32 (PI.f32) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) (neg.f32 (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	97.0%	(.f32 (pow.f32 (/.f32 tau (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))))
	97.1%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.0%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))))
	78.3%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (*.f32 tau (PI.f32))))))
	64.4%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 x (.f32 x (*.f32 tau (PI.f32))))))
	97.2%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))
	96.9%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (.f32 x (cbrt.f32 (PI.f32))) tau))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 x (/.f32 #s(literal 1 binary32) (PI.f32))) tau)) (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)) x))
	96.0%	(.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 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
	95.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))))
✓	98.0%	(.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))))
	86.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (PI)) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 x #s(literal -1/6 binary32)) x)) x))
	87.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
	71.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) #s(literal 1 binary32)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (sin.f32 (*.f32 x (PI.f32))))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))))
▶	97.2%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
	97.2%	(.f32 (/.f32 #s(literal -1 binary32) (.f32 x (.f32 (PI.f32) tau))) (/.f32 #s(literal 1 binary32) (neg.f32 (.f32 x (/.f32 (PI.f32) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))))))))
	97.3%	(.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) x)) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	79.9%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) x))
	80.1%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	65.4%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)) x))
	79.5%	#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
	97.0%	#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
	65.5%	#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	85.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
▶	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	96.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	96.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	96.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 (/.f32 x (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	97.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))) tau))))
	97.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (PI.f32) tau)))))
	97.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 x (PI.f32)) (.f32 x tau))))))
✓	64.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 2 661 to 1 501 computations (43.6% saved)

simplify430.0ms (2.6%)

Memory

12.3MiB live, 193.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))
cost-diff	0	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32))))
cost-diff	192	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32)))) x)
cost-diff	192	(/.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32)))) x) tau)
cost-diff	0	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
cost-diff	0	(.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
cost-diff	160	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
cost-diff	0	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
cost-diff	352	(/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)
cost-diff	0	(.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))
cost-diff	0	(*.f32 x x)
cost-diff	0	(fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
cost-diff	0	(.f32 x (.f32 (PI.f32) tau))
cost-diff	0	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
cost-diff	0	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))
cost-diff	0	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))

Rules

10 064×	`lower-*.f64`
10 032×	`lower-*.f32`
7 108×	`times-frac`
2 158×	`associate-r`
2 014×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	483
0	91	481
1	195	481
2	502	481
3	1905	481
4	3238	481
5	3409	481
6	3662	481
7	4067	481
8	4475	481
9	4747	481
10	5733	481
11	5817	481
12	5817	481
13	5817	481
14	6212	481
15	6212	481
16	6226	481
17	6357	481
18	6482	481
19	6493	481
20	6493	481
21	6493	481
22	6493	481
23	7220	481
24	7747	481
25	7759	481
26	7767	481
27	7821	477
28	7969	477
0	11317	473

Stop Event

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

Calls

Call 1

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

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

localize210.0ms (1.3%)

Memory

22.9MiB live, 266.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.354511279305326	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32))))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.390625	(.f32 x (.f32 (PI.f32) (PI.f32)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.37337875976844204	(.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))
accuracy	0.4069137695368841	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.45150375976844204	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
accuracy	0.38900375976844204	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
accuracy	0.4069137695368841	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.43337134456313287	(fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	3.918171691077344	#s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))
accuracy	0.328125	(.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))
accuracy	0.359375	(fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	6.564288781921612	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
accuracy	0.34375	(*.f32 (PI.f32) tau)
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3643150879159781	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
accuracy	0.37337875976844204	(.f32 (PI.f32) (.f32 x (*.f32 (PI.f32) tau)))

Samples

129.0ms

256×

valid

Compiler

Compiled 436 to 51 computations (88.3% saved)

Precisions

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

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

ival-mult: 39.0ms (35.4% of total)

ival-div: 15.0ms (13.6% of total)

const: 9.0ms (8.2% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series64.0ms (0.4%)

Memory

-25.4MiB live, 64.7MiB allocated

Counts

28 → 540

Calls

Call 1

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

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

Calls

135 calls:

Time	Variable		Point	Expression
19.0ms	tau	@	0	(* (PI) (* (PI) (* x tau)))
8.0ms	tau	@	inf	(+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1)
1.0ms	tau	@	inf	(* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))
1.0ms	x	@	-inf	(/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI))))
1.0ms	x	@	0	(+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1)

simplify380.0ms (2.3%)

Memory

18.3MiB live, 540.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16 806×	`lower-fma.f64`
16 806×	`lower-fma.f32`
7 392×	`lower-*.f64`
7 392×	`lower-*.f32`
6 176×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	351	8461
1	1187	8207
2	4478	7893
0	8102	7630

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 538

Calls

Call 1

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

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

rewrite557.0ms (3.4%)

Memory

1.1MiB live, 594.7MiB allocated

Rules

5 040×	`lower-/.f64`
5 024×	`lower-/.f32`
4 318×	`lower-*.f64`
4 286×	`lower-*.f32`
3 632×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	366
0	91	364
1	348	342
2	2212	342
0	8155	340

Stop Event

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

Counts

28 → 1 824

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))) (neg.f32 x))))
(neg.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32))))) (neg.f32 tau)))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))) #s(literal -1 binary32)))
(pow.f32 (/.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) #s(literal -1 binary32))
(pow.f32 (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))) #s(literal -1 binary32))
(pow.f32 (.f32 (/.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) tau) #s(literal -1 binary32))
(-.f32 (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) #s(literal 1/2 binary32)) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) #s(literal 1/2 binary32)) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))))
(-.f32 (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) #s(literal 2 binary32))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))) (neg.f32 x))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))) (neg.f32 x))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (neg.f32 (PI.f32))))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (neg.f32 (PI.f32))))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 (neg.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32)))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (neg.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32)))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 (.f32 x tau) (neg.f32 (.f32 x (.f32 (PI.f32) (PI.f32)))))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (.f32 x tau) (neg.f32 (.f32 x (.f32 (PI.f32) (PI.f32)))))))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 (.f32 x tau))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) (PI.f32))))) (neg.f32 (.f32 x tau))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 tau (neg.f32 x))) (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) (PI.f32))))) (.f32 tau (neg.f32 x))))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 tau)) (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32))))) (neg.f32 tau)))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))))
(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (neg.f32 (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))) (neg.f32 x))))
(/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))))
(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))
(/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
(/.f32 #s(literal 1 binary32) (.f32 (/.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) tau))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))) #s(literal 1 binary32)))
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(.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/216 binary32) (.f32 (.f32 x x) (.f32 (.f32 x x) (.f32 x x)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))))
(.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/216 binary32) (.f32 (.f32 x x) (.f32 (.f32 x x) (.f32 x x)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))))))
(.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (fma.f32 x (.f32 (*.f32 x (PI.f32)) #s(literal -1/6 binary32)) (/.f32 #s(literal -1 binary32) (PI.f32)))))
(.f32 (neg.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/216 binary32) (.f32 (.f32 x x) (.f32 (.f32 x x) (.f32 x x)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))))))
(.f32 (neg.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32)))))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 x (.f32 (*.f32 x (PI.f32)) #s(literal -1/6 binary32)) (/.f32 #s(literal -1 binary32) (PI.f32))))))
(.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))))) (/.f32 #s(literal 1 binary32) (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32))))))
(/.f32 (*.f32 x tau) (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 (.f32 (.f32 x tau) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 x (.f32 (PI.f32) tau))
(.f32 (PI.f32) (.f32 x tau))
(.f32 tau (.f32 x (PI.f32)))
(.f32 (.f32 (PI.f32) tau) x)
(.f32 (.f32 x (PI.f32)) tau)
(.f32 #s(literal 1 binary32) (.f32 x (*.f32 (PI.f32) tau)))
(.f32 (.f32 x tau) (PI.f32))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) (*.f32 x tau)))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 x tau)))
(.f32 (.f32 (*.f32 x tau) #s(literal 1 binary32)) (PI.f32))
(.f32 (.f32 (*.f32 x tau) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(/.f32 (*.f32 x (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(/.f32 (.f32 (.f32 x (PI.f32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(.f32 (PI.f32) (.f32 x (PI.f32)))
(.f32 (.f32 x (PI.f32)) (PI.f32))
(.f32 (.f32 (PI.f32) (PI.f32)) x)
(.f32 #s(literal 1 binary32) (.f32 x (*.f32 (PI.f32) (PI.f32))))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) (*.f32 x (PI.f32))))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (*.f32 x (PI.f32))))
(.f32 (.f32 (*.f32 x (PI.f32)) #s(literal 1 binary32)) (PI.f32))
(.f32 (.f32 (*.f32 x (PI.f32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 x (PI.f32)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))

eval420.0ms (2.5%)

Memory: 10.9MiB live, 462.8MiB allocated
Compiler: Compiled 71 303 to 3 839 computations (94.6% saved)

prune1.4s (8.6%)

Memory

-29.8MiB live, 997.9MiB allocated

Pruning

78 alts after pruning (75 fresh and 3 done)

	Pruned	Kept	Total
New	2 705	48	2 753
Fresh	20	27	47
Picked	4	1	5
Done	0	2	2
Total	2 729	78	2 807

Accuracy

99.8%

Counts

2 807 → 78

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.1%	(/.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (PI.f32))) (/.f32 x (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) x) tau)
	94.5%	(/.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (*.f32 x (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 6 binary32)))) x) tau)
	65.0%	(/.f32 (/.f32 (-.f32 (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) #s(literal 1/2 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) #s(literal 1/2 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32))))) x) tau)
	66.7%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) x) (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))))
	97.0%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) tau) (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))))
	79.1%	(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) tau))) x) tau)
	64.6%	(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (*.f32 x tau)) x) tau)
	66.7%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32)) (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))))) tau)
	66.6%	(/.f32 (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	97.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau))))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau))))
	97.1%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) tau)
	86.5%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))) tau)
	94.6%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) #s(literal -1/5040 binary32)) (.f32 (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32))) (.f32 #s(literal -1/6 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	91.7%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	86.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	86.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32)))) x))) tau)
	71.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
▶	86.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
	71.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
	86.2%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (.f32 (fma.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) x)))) tau)
	86.2%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 x (*.f32 x (PI.f32)))))))) tau)
	86.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 x (*.f32 x (PI.f32))))) (neg.f32 x))))) tau)
	97.3%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 (PI.f32) tau)) x)))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x tau))))
	97.4%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (neg.f32 (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) (PI.f32))))) (*.f32 x tau))
▶	79.4%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	65.5%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	79.3%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	86.3%	(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 tau #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))))
	79.2%	(/.f32 #s(approx (/ (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))) tau)) tau)
▶	97.7%	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau))) #s(literal 1 binary32))))
	97.3%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))))
	86.2%	(/.f32 #s(literal 1 binary32) (/.f32 tau (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))))
	74.1%	(-.f32 (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) #s(literal 1/2 binary32)) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) #s(literal 1/2 binary32)) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))))
	97.0%	(.f32 (pow.f32 (/.f32 tau (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))))
	97.0%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))))
	78.3%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (*.f32 tau (PI.f32))))))
	97.2%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))
▶	96.9%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 x (/.f32 #s(literal 1 binary32) (PI.f32))) tau)) (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)) x))
✓	98.0%	(.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))))
	86.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (PI)) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 x #s(literal -1/6 binary32)) x)) x))
	87.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
	71.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) #s(literal 1 binary32)))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))))
	86.3%	(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) tau) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))
✓	97.2%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
	97.2%	(.f32 (/.f32 #s(literal -1 binary32) (.f32 x (.f32 (PI.f32) tau))) (/.f32 #s(literal 1 binary32) (neg.f32 (.f32 x (/.f32 (PI.f32) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))))))))
	66.7%	(.f32 (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) #s(literal 2 binary32))))
	97.2%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32)))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))
	79.9%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) x))
	80.1%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	86.2%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau))
	97.0%	#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) x #s(literal 1 binary32)))
	85.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (/.f32 (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (.f32 (PI.f32) (PI.f32))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) (-.f32 #s(literal 1/36 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (-.f32 #s(literal 1/36 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)))) (-.f32 #s(literal -1/6 binary32) (.f32 tau (*.f32 tau #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1/36 binary32) (-.f32 (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	69.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
	65.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	69.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))) (.f32 x x)) #s(literal 1 binary32)))
	79.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) #s(literal 1 binary32)))))
	96.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	96.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	96.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 (/.f32 x (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	97.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))) tau))))
	97.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 x (PI.f32)) (.f32 x tau))))))
▶	65.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	3.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
✓	64.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 3 952 to 2 261 computations (42.8% saved)

simplify565.0ms (3.4%)

Memory

60.8MiB live, 513.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
cost-diff	0	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))
cost-diff	0	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32))))
cost-diff	352	(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))))))
cost-diff	0	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
cost-diff	704	(/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))))
cost-diff	0	(.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
cost-diff	0	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
cost-diff	160	(fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32)))
cost-diff	352	(/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)
cost-diff	0	(.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))
cost-diff	0	(fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))
cost-diff	0	#s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32)))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
cost-diff	0	(/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32))))
cost-diff	160	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau))) #s(literal 1 binary32))
cost-diff	352	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau))) #s(literal 1 binary32))))
cost-diff	384	(/.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau))) #s(literal 1 binary32)))

Rules

25 082×	`lower-fma.f64`
25 074×	`lower-fma.f32`
5 220×	`lower-+.f64`
5 220×	`lower-+.f32`
5 182×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	750
0	129	726
1	268	717
2	712	706
3	3047	702
4	3880	694
5	4108	694
6	4587	694
7	5232	694
8	5964	694
9	7243	694
10	7259	694
11	7259	694
12	7259	694
13	7519	694
14	7523	694
15	7523	694
0	9819	678

Stop Event

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

Calls

Call 1

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

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

localize384.0ms (2.3%)

Memory

-39.1MiB live, 360.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.390625	(.f32 x (.f32 (PI.f32) (PI.f32)))
accuracy	0.445976269536884	(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	0.38900375976844204	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))))))
accuracy	0.4069137695368841	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.430467470097017	(fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	3.918171691077344	#s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))
accuracy	0.43337134456313287	(fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	3.918171691077344	#s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))
accuracy	6.120420587578255	#s(approx (sin (* (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (*.f32 tau (PI.f32)))))
accuracy	0.078125	(.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	6.564288781921612	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
accuracy	11.443020103142922	#s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32)))
accuracy	0.34375	(*.f32 (PI.f32) tau)
accuracy	0.359375	(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau))) #s(literal 1 binary32))))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.42091752930532605	(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))

Samples

275.0ms

256×

valid

Compiler

Compiled 567 to 64 computations (88.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 205.0ms

ival-mult: 66.0ms (32.3% of total)

ival-div: 46.0ms (22.5% of total)

ival-pi: 38.0ms (18.6% of total)

ival-sin: 31.0ms (15.2% of total)

ival-add: 20.0ms (9.8% of total)

const: 4.0ms (2% of total)

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

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

exact: 0.0ms (0% of total)

series58.0ms (0.3%)

Memory

16.9MiB live, 63.1MiB allocated

Counts

31 → 576

Calls

Call 1

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

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

Calls

144 calls:

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

simplify355.0ms (2.1%)

Memory

21.9MiB live, 350.6MiB allocated

Algorithm

1×	egg-herbie

Rules

12 748×	`lower-fma.f64`
12 748×	`lower-fma.f32`
8 874×	`lower-*.f64`
8 874×	`lower-*.f32`
2 574×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	471	10354
1	1645	10025
2	6847	9997
0	8246	9602

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 574

Calls

Call 1

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

Outputs
1
#s(literal 1 binary32)
(+ 1 (* -1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))))
(fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 (/ (* (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4)))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))) (* tau (pow (PI) 2)))) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))))
(fma.f32 (.f32 x x) (neg.f32 (fma.f32 (.f32 x x) (fma.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)) (fma.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (/.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))))) (.f32 tau (.f32 (PI.f32) (PI.f32)))))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))))) #s(literal 1 binary32))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1 (* (pow x 2) (+ (* -1 (/ (* (+ (* -1 (/ (* (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4)))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))) (* tau (pow (PI) 2)))) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))) (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4))))) (* tau (pow (PI) 2)))) (+ (* -1 (/ (* (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))) (+ (* 1/120 (* tau (pow (PI) 6))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 6))) (* 1/36 (* (pow tau 3) (pow (PI) 6)))))) (* tau (pow (PI) 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 (/ (* (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4)))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2)))) (* tau (pow (PI) 2)))) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))))) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))))
(fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (neg.f32 (fma.f32 (.f32 x x) (fma.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)) (fma.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (/.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))))) (.f32 tau (.f32 (PI.f32) (PI.f32)))))) (.f32 #s(literal 1/6 binary32) (/.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) (.f32 tau (.f32 (PI.f32) (PI.f32))))) (fma.f32 #s(literal 1/6 binary32) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (PI.f32))) (/.f32 (fma.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (fma.f32 #s(literal 1/120 binary32) (pow.f32 tau #s(literal 5 binary32)) (.f32 (.f32 tau (.f32 tau tau)) #s(literal 1/36 binary32))) (.f32 tau (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal 1/120 binary32)))) (.f32 tau (.f32 (PI.f32) (PI.f32))))) (fma.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (fma.f32 (.f32 tau tau) #s(literal -1/720 binary32) (.f32 (.f32 (.f32 tau tau) (.f32 tau tau)) #s(literal -1/720 binary32))) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (fma.f32 #s(literal -1/5040 binary32) (pow.f32 tau #s(literal 6 binary32)) #s(literal -1/5040 binary32)))))) (fma.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)) (fma.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau))) (/.f32 (.f32 #s(literal 1/6 binary32) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))))) (.f32 tau (.f32 (PI.f32) (PI.f32)))))))) (.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))
(/ (* tau (* (pow x 2) (pow (PI) 2))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))))
(/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))))
(/ (* tau (* (pow x 2) (pow (PI) 2))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))))
(/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))))
(/ (* tau (* (pow x 2) (pow (PI) 2))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))))
(/.f32 (.f32 tau (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))))
(/ (* tau (* (pow x 2) (pow (PI) 2))) (* (sin (* tau (* x (PI)))) (sin (* x (PI)))))
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tau
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(* x (+ tau (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 2))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 2))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 4))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 4))) (+ (* 1/36 (* (pow tau 3) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 3) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 5) (pow (PI) 6))) (+ (* -1/5040 (* tau (pow (PI) 6))) (* -1/5040 (* (pow tau 7) (pow (PI) 6))))))))))))))))
(.f32 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 tau (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) #s(literal 1/120 binary32)) (fma.f32 (.f32 x x) (fma.f32 #s(literal -1/5040 binary32) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (+.f32 tau (pow.f32 tau #s(literal 7 binary32)))) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) (fma.f32 (.f32 tau (.f32 tau tau)) #s(literal -1/720 binary32) (.f32 (pow.f32 tau #s(literal 5 binary32)) #s(literal -1/720 binary32))))) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (pow.f32 tau #s(literal 5 binary32)) (.f32 (.f32 tau (.f32 tau tau)) #s(literal 1/36 binary32)))))) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (*.f32 tau tau)))))) tau))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
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(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
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(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (* tau (sin (* x (PI)))) (PI))
(.f32 (sin.f32 (.f32 x (PI.f32))) (/.f32 tau (PI.f32)))
(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 2) (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (PI))))
(.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32))) (sin.f32 (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32))))
(* tau (+ (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 4) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (PI))))
(.f32 tau (fma.f32 (.f32 tau tau) (fma.f32 (.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 x x) (.f32 x x))) (.f32 (.f32 tau tau) #s(literal 1/120 binary32)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32))) (sin.f32 (.f32 x (PI.f32))))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32))))
(* tau (+ (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 4) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (PI))))
(.f32 tau (fma.f32 (.f32 tau tau) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32)))) #s(literal -1/6 binary32)) (.f32 tau (.f32 tau (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 x x) (.f32 x x))) (.f32 #s(literal -1/5040 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (pow.f32 (PI.f32) #s(literal 5 binary32))) (pow.f32 x #s(literal 6 binary32))))))))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
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(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32)))))
(/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* x (pow (PI) 2)))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32)))))
(* tau (* (pow x 2) (pow (PI) 2)))
(.f32 tau (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))))
(* (pow x 2) (+ (* tau (pow (PI) 2)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 4))) (* -1/6 (* (pow tau 3) (pow (PI) 4)))))))
(.f32 (.f32 x x) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) (.f32 tau (*.f32 (PI.f32) (PI.f32)))))
(* (pow x 2) (+ (* tau (pow (PI) 2)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 4))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 4))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 6))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 6))) (* 1/36 (* (pow tau 3) (pow (PI) 6)))))))))))
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(* (pow x 2) (+ (* tau (pow (PI) 2)) (* (pow x 2) (+ (* -1/6 (* tau (pow (PI) 4))) (+ (* -1/6 (* (pow tau 3) (pow (PI) 4))) (* (pow x 2) (+ (* 1/120 (* tau (pow (PI) 6))) (+ (* 1/120 (* (pow tau 5) (pow (PI) 6))) (+ (* 1/36 (* (pow tau 3) (pow (PI) 6))) (* (pow x 2) (+ (* -1/720 (* (pow tau 3) (pow (PI) 8))) (+ (* -1/720 (* (pow tau 5) (pow (PI) 8))) (+ (* -1/5040 (* tau (pow (PI) 8))) (* -1/5040 (* (pow tau 7) (pow (PI) 8))))))))))))))))
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(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
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(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
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(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* tau (* x (* (PI) (sin (* x (PI))))))
(.f32 (.f32 x (.f32 tau (PI.f32))) (sin.f32 (.f32 x (PI.f32))))
(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))) (* x (* (PI) (sin (* x (PI)))))))
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(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
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(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
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(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
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(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* (sin (* tau (* x (PI)))) (sin (* x (PI))))
(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* x (+ (* -1/6 (* (pow tau 3) (* (pow x 2) (pow (PI) 3)))) (* tau (PI))))
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(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* 1/120 (* (pow tau 5) (* (pow x 2) (pow (PI) 5))))))))
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(* x (+ (* tau (PI)) (* (pow x 2) (+ (* -1/6 (* (pow tau 3) (pow (PI) 3))) (* (pow x 2) (+ (* -1/5040 (* (pow tau 7) (* (pow x 2) (pow (PI) 7)))) (* 1/120 (* (pow tau 5) (pow (PI) 5)))))))))
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(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
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(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(sin (* tau (* x (PI))))
(sin.f32 (.f32 x (.f32 tau (PI.f32))))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI))))
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(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5))))))))
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(* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5)))))))))
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(sin (* tau (* x (PI))))
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(sin.f32 (.f32 x (.f32 tau (PI.f32))))
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#s(literal 1 binary32)
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(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* tau (* x (PI)))
(.f32 x (.f32 tau (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))
(* x (pow (PI) 2))
(.f32 x (.f32 (PI.f32) (PI.f32)))

rewrite459.0ms (2.8%)

Memory

-14.2MiB live, 285.5MiB allocated

Rules

4 992×	`lower-*.f64`
4 980×	`lower-fma.f64`
4 972×	`lower-fma.f32`
4 944×	`lower-*.f32`
3 778×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	588
0	129	562
1	475	529
2	3045	529
0	8676	522

Stop Event

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

Counts

31 → 1 522

Calls

Call 1

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

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

eval363.0ms (2.2%)

Memory: -11.3MiB live, 255.2MiB allocated
Compiler: Compiled 68 189 to 4 576 computations (93.3% saved)

prune1.3s (7.6%)

Memory

-109.7MiB live, 1 022.7MiB allocated

Pruning

108 alts after pruning (104 fresh and 4 done)

	Pruned	Kept	Total
New	2 219	44	2 263
Fresh	10	60	70
Picked	4	1	5
Done	0	3	3
Total	2 233	108	2 341

Accuracy

99.8%

Counts

2 341 → 108

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.1%	(/.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (PI.f32))) (/.f32 x (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) x) tau)
	94.5%	(/.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (*.f32 x (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 6 binary32)))) x) tau)
	66.7%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) x) (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))))
	97.1%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x tau)) (.f32 x (*.f32 (PI.f32) (PI.f32))))
	79.1%	(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) tau))) x) tau)
	64.6%	(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (*.f32 x tau)) x) tau)
	66.7%	(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32)) (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))))) tau)
	66.6%	(/.f32 (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	97.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (*.f32 (PI.f32) tau)))
	97.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau))))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau))))
	97.1%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) tau)
	86.2%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
	86.5%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))) (sin.f32 (.f32 x (PI.f32))))) tau)
	86.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) tau)
	94.6%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) #s(literal -1/5040 binary32)) (.f32 (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32))) (.f32 #s(literal -1/6 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	91.7%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	86.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	91.7%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 x (fma.f32 #s(literal -1/6 binary32) (PI.f32) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	71.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
✓	86.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
	86.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)))))))) tau)
	71.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
	86.2%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (.f32 (fma.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) x)))) tau)
	86.2%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 x (*.f32 x (PI.f32)))))))) tau)
	86.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 x (*.f32 x (PI.f32))))) (neg.f32 x))))) tau)
	86.3%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ 1 (/ x (+ (* (PI) (* (* x x) -1/6)) (/ 1 (PI))))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
	86.1%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ 1 (/ x (+ (* (PI) (* (* x x) -1/6)) (/ 1 (PI))))) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (PI.f32))))) (*.f32 x tau))
	97.3%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 (PI.f32) tau)) x)))
	97.4%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (neg.f32 (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	79.4%	(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32)))))) tau)
	79.4%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) x) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
	79.3%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) tau)
	79.4%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x (PI.f32)) (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	79.6%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 x (fma.f32 #s(literal -1/6 binary32) (PI.f32) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	4.7%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 x x) (PI.f32)))) x))) tau)
	69.6%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
	79.3%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
	79.2%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
	4.7%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))))) tau)
	79.1%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
	79.4%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32))))) (.f32 (PI.f32) tau)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	79.4%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 tau (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32)))))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	79.2%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) tau) tau) (PI.f32))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
	65.5%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	79.1%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (/.f32 (PI.f32) (.f32 x x)))))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	79.3%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 tau (.f32 tau tau)) (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) (/.f32 (PI.f32) (.f32 tau tau))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	79.3%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	79.2%	(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
	86.3%	(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 tau #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))))
	79.2%	(/.f32 #s(approx (/ (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))) tau)) tau)
	97.3%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))))
	85.6%	(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* x (PI)) (sin (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal 1/6 binary32)) #s(literal 1 binary32))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) #s(literal 1 binary32))))
	86.2%	(/.f32 #s(literal 1 binary32) (/.f32 tau (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))))
	79.2%	(/.f32 #s(literal 1 binary32) (/.f32 tau (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))))
	79.2%	(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* x (PI)) (sin (* x (PI)))) (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) 1)) (fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) #s(literal 1 binary32))))
	74.1%	(-.f32 (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) #s(literal 1/2 binary32)) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) #s(literal 1/2 binary32)) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))))
	97.0%	(.f32 (pow.f32 (/.f32 tau (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))))
	97.0%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))))
	78.3%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (*.f32 tau (PI.f32))))))
	97.2%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))
	94.5%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 6 binary32)))) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
	97.2%	(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 x (/.f32 #s(literal 1 binary32) (PI.f32))) tau)) (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)) x))
✓	98.0%	(.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))))
	86.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (PI)) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 x #s(literal -1/6 binary32)) x)) x))
	87.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
	71.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) #s(literal 1 binary32)))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32))))
	86.3%	(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) tau) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))
	79.1%	(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) tau) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))))
✓	97.2%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
	97.2%	(.f32 (/.f32 #s(literal -1 binary32) (.f32 x (.f32 (PI.f32) tau))) (/.f32 #s(literal 1 binary32) (neg.f32 (.f32 x (/.f32 (PI.f32) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))))))))
	65.1%	(.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (.f32 (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (.f32 (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
	66.7%	(.f32 (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) #s(literal 2 binary32))))
	97.2%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32)))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))
	78.7%	(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) tau))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
	64.6%	(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x tau)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
	79.9%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) x))
	80.1%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	79.3%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (/.f32 #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) tau))
	86.2%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau))) (/.f32 #s(literal 1 binary32) tau)))
	79.1%	(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) (/.f32 #s(literal 1 binary32) tau)))
	97.0%	#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
	97.0%	#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) x #s(literal 1 binary32)))
	85.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (/.f32 (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (.f32 (PI.f32) (PI.f32))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) (-.f32 #s(literal 1/36 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (-.f32 #s(literal 1/36 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)))) (-.f32 #s(literal -1/6 binary32) (.f32 tau (*.f32 tau #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	69.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
	69.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32)))))) #s(literal 1 binary32)))
	79.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))) (.f32 x x)) #s(literal 1 binary32)))
	79.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) #s(literal 1 binary32)))))
	96.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	96.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	96.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 (/.f32 x (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	97.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))) tau))))
	97.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 x (PI.f32)) (.f32 x tau))))))
	65.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))) (PI.f32) #s(literal 1 binary32))))
	65.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
	65.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	65.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32))))
	65.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32)))) #s(literal 1 binary32))))
	4.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))))
✓	64.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 7 264 to 2 364 computations (67.5% saved)

regimes213.0ms (1.3%)

Memory

24.2MiB live, 587.2MiB allocated

Counts

168 → 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 (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))))
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(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
(/.f32 (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(/.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (PI.f32)))) x) tau)
(/.f32 #s(literal -1 binary32) (.f32 (/.f32 (PI.f32) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) (neg.f32 (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
(.f32 (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))) #s(literal 2 binary32))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))
(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 (PI.f32) (.f32 x (*.f32 x (PI.f32)))) #s(literal 2 binary32))) tau)
(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) x) (.f32 #s(literal 2 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau)))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (/.f32 (PI.f32) (sin.f32 (.f32 x (PI.f32))))))
(/.f32 (.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))) #s(literal 2 binary32))
(.f32 (/.f32 #s(literal -1 binary32) (.f32 x (.f32 (PI.f32) tau))) (/.f32 #s(literal 1 binary32) (neg.f32 (.f32 x (/.f32 (PI.f32) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))))))))
(/.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (PI.f32))) (/.f32 x (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) x) tau)
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (sin.f32 (*.f32 x (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (sin.f32 (*.f32 x (PI.f32))))))
(.f32 (/.f32 (sin.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 x (PI.f32)))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (*.f32 (PI.f32) tau))) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 x (/.f32 #s(literal 1 binary32) (PI.f32))) tau)) (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)) x))
(/.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) #s(literal 2 binary32)) (-.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 (/.f32 x (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
(-.f32 (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) #s(literal 1/2 binary32)) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) #s(literal 1/2 binary32)) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))))
(.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (.f32 (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (.f32 (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
(/.f32 (/.f32 (-.f32 (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (neg.f32 (PI.f32))))) #s(literal 1/2 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32)))) (/.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) #s(literal 1/2 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32))))) x) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 #s(literal -1/6 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 5 binary32)) #s(literal -1/5040 binary32)) (.f32 (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (PI.f32))) (PI.f32))) (.f32 #s(literal -1/6 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(.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 x (sqrt.f32 (PI.f32))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))) (sqrt.f32 (sqrt.f32 (PI.f32)))))
(.f32 (pow.f32 (/.f32 tau (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32))))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))) #s(literal -1 binary32)))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 6 binary32)))) (/.f32 #s(literal 1 binary32) (*.f32 x tau)))
(/.f32 (/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (*.f32 x (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 6 binary32)))) x) tau)
(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (.f32 x (cbrt.f32 (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 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 x (cbrt.f32 (PI.f32)))))))
(.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 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (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))))

Calls

4 calls:

70.0ms	(*.f32 x (PI.f32))
46.0ms	tau
46.0ms	x
45.0ms	(.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
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 34 to 18 computations (47.1% saved)

regimes155.0ms (0.9%)

Memory

7.2MiB live, 368.9MiB allocated

Counts

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

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

Calls

4 calls:

55.0ms	tau
34.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
31.0ms	(*.f32 x (PI.f32))
30.0ms	x

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes135.0ms (0.8%)

Memory

-8.2MiB live, 322.1MiB allocated

Counts

109 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #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)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x tau)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (*.f32 x tau)) x) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) x #s(literal 1 binary32)))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* x (PI)) (sin (* x (PI)))) (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) 1)) (fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (*.f32 tau tau) tau))) tau)) tau)
(/.f32 #s(approx (/ (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))) tau)) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 x (.f32 x (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) #s(literal 1 binary32)))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) tau))) x) tau)
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) tau))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (-.f32 #s(literal 1/36 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)))) (-.f32 #s(literal -1/6 binary32) (.f32 tau (*.f32 tau #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 x x) (PI.f32)))) x))) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (/.f32 (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (.f32 (PI.f32) (PI.f32))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) (-.f32 #s(literal 1/36 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (/.f32 #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) tau))
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#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (PI.f32) tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))) tau))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau)))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x tau))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 (PI.f32) tau)) x)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (.f32 (PI.f32) (neg.f32 (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32)))) (sin.f32 (.f32 x (*.f32 (PI.f32) tau))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))))

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

Calls

4 calls:

41.0ms	(*.f32 x (PI.f32))
30.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
29.0ms	x
29.0ms	tau

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes119.0ms (0.7%)

Memory

20.9MiB live, 200.5MiB allocated

Counts

101 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #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)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x tau)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (*.f32 x tau)) x) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) x #s(literal 1 binary32)))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* x (PI)) (sin (* x (PI)))) (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) 1)) (fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (*.f32 tau tau) tau))) tau)) tau)
(/.f32 #s(approx (/ (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))) tau)) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 x (.f32 x (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) #s(literal 1 binary32)))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) tau))) x) tau)
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) tau))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (-.f32 #s(literal 1/36 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)))) (-.f32 #s(literal -1/6 binary32) (.f32 tau (*.f32 tau #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 x x) (PI.f32)))) x))) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (/.f32 (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (.f32 (PI.f32) (PI.f32))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) (-.f32 #s(literal 1/36 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (/.f32 #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) tau))
(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) tau) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1/36 binary32) (-.f32 (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))))) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) (/.f32 #s(literal 1 binary32) tau)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
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Outputs
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32))))

Calls

4 calls:

29.0ms	tau
29.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
28.0ms	x
28.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
97.3%	1	`x`
97.3%	1	`tau`
97.3%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
97.3%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes166.0ms (1%)

Memory

-3.6MiB live, 281.7MiB allocated

Counts

99 → 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 (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #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)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x tau)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (*.f32 x tau)) x) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) x #s(literal 1 binary32)))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* x (PI)) (sin (* x (PI)))) (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) 1)) (fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (*.f32 tau tau) tau))) tau)) tau)
(/.f32 #s(approx (/ (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))) tau)) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 x (.f32 x (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) #s(literal 1 binary32)))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) tau))) x) tau)
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) tau))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
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(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))))) tau)
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#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (/.f32 (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (.f32 (PI.f32) (PI.f32))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) (-.f32 #s(literal 1/36 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))) #s(literal 1 binary32)))
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(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1/36 binary32) (-.f32 (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))))) #s(literal 1 binary32)))
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(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (/.f32 (PI.f32) (.f32 x x)))))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) x) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32)))) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 tau (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32)))))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 x (fma.f32 #s(literal -1/6 binary32) (PI.f32) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.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 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) #s(literal 1 binary32)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ 1 (/ x (+ (* (PI) (* (* x x) -1/6)) (/ 1 (PI))))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 x (*.f32 x (PI.f32)))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ 1 (/ x (+ (* (PI) (* (* x x) -1/6)) (/ 1 (PI))))) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 x (*.f32 x (PI.f32))))) (neg.f32 x))))) tau)
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) x))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau))
(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) tau) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32)))) x))) tau)
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau))) (/.f32 #s(literal 1 binary32) tau)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (.f32 (fma.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) x)))) tau)
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 tau #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (PI)) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 x #s(literal -1/6 binary32)) x)) x))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 #s(literal 1 binary32) (/.f32 tau (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)))))))) tau)
(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* x (PI)) (sin (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal 1/6 binary32)) #s(literal 1 binary32))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 x (fma.f32 #s(literal -1/6 binary32) (PI.f32) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) (/.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)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 x (PI.f32)) (.f32 x tau))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (PI.f32) tau)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))) tau))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 tau (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) tau))))) (sin.f32 (.f32 x (PI.f32))))

Outputs

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

Calls

4 calls:

74.0ms	(.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))))
29.0ms	tau
27.0ms	x
27.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
97.3%	1	`x`
97.3%	1	`tau`
97.3%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
97.3%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes103.0ms (0.6%)

Memory

10.2MiB live, 290.5MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

25.0ms	tau
24.0ms	(.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))))
23.0ms	(*.f32 x (PI.f32))
23.0ms	x

Results

Accuracy	Segments	Branch
91.7%	1	`x`
91.7%	1	`tau`
91.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
91.7%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes98.0ms (0.6%)

Memory

21.9MiB live, 206.0MiB allocated

Counts

87 → 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 (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #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)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x tau)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (*.f32 x tau)) x) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) x #s(literal 1 binary32)))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* x (PI)) (sin (* x (PI)))) (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) 1)) (fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (*.f32 tau tau) tau))) tau)) tau)
(/.f32 #s(approx (/ (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))) tau)) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 x (.f32 x (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) #s(literal 1 binary32)))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) tau))) x) tau)
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) tau))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (-.f32 #s(literal 1/36 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)))) (-.f32 #s(literal -1/6 binary32) (.f32 tau (*.f32 tau #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 x x) (PI.f32)))) x))) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (/.f32 (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (.f32 (PI.f32) (PI.f32))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) (-.f32 #s(literal 1/36 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (/.f32 #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) tau))
(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) tau) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1/36 binary32) (-.f32 (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))))) #s(literal 1 binary32)))
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(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32))))) (.f32 (PI.f32) tau)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x (PI.f32)) (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
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(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) tau)
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(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (/.f32 (PI.f32) (.f32 x x)))))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) x) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32)))) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 tau (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32)))))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 x (fma.f32 #s(literal -1/6 binary32) (PI.f32) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.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 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) #s(literal 1 binary32)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ 1 (/ x (+ (* (PI) (* (* x x) -1/6)) (/ 1 (PI))))) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 x (*.f32 x (PI.f32)))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ 1 (/ x (+ (* (PI) (* (* x x) -1/6)) (/ 1 (PI))))) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 x (*.f32 x (PI.f32))))) (neg.f32 x))))) tau)
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) x))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau))
(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) tau) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32)))) x))) tau)
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (.f32 (sin.f32 (.f32 x (*.f32 (PI.f32) tau))) (/.f32 #s(literal 1 binary32) tau)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (.f32 (fma.f32 (PI.f32) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) x)))) tau)
(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 tau #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(approx (/ (sin ( x (PI))) (PI)) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (.f32 x #s(literal -1/6 binary32)) x)) x))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 #s(literal 1 binary32) (/.f32 tau (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)))))))) tau)
(/.f32 #s(literal 1 binary32) (/.f32 #s(approx (/ (* x (PI)) (sin (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal 1/6 binary32)) #s(literal 1 binary32))) (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)

Outputs

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

Calls

4 calls:

25.0ms	(*.f32 x (PI.f32))
23.0ms	tau
23.0ms	x
23.0ms	(.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
91.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
91.7%	1	`x`
91.7%	1	`(*.f32 x (PI.f32))`
91.7%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes107.0ms (0.6%)

Memory

-2.1MiB live, 182.4MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

30.0ms	(*.f32 x (PI.f32))
25.0ms	x
25.0ms	(.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))))
23.0ms	tau

Results

Accuracy	Segments	Branch
87.0%	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))))`
87.0%	1	`x`
87.0%	1	`(*.f32 x (PI.f32))`
87.0%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes75.0ms (0.5%)

Memory

36.0MiB live, 130.5MiB allocated

Counts

63 → 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 (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #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)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x tau)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (*.f32 x tau)) x) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) x #s(literal 1 binary32)))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* x (PI)) (sin (* x (PI)))) (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) 1)) (fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (*.f32 tau tau) tau))) tau)) tau)
(/.f32 #s(approx (/ (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))) tau)) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 x (.f32 x (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) #s(literal 1 binary32)))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) tau))) x) tau)
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) tau))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (-.f32 #s(literal 1/36 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)))) (-.f32 #s(literal -1/6 binary32) (.f32 tau (*.f32 tau #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 x x) (PI.f32)))) x))) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (/.f32 (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (.f32 (PI.f32) (PI.f32))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) (-.f32 #s(literal 1/36 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (/.f32 #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) tau))
(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) tau) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1/36 binary32) (-.f32 (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))))) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) (/.f32 #s(literal 1 binary32) tau)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32))))) (.f32 (PI.f32) tau)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x (PI.f32)) (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 #s(literal 1 binary32) (/.f32 tau (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) tau) tau) (PI.f32))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 tau (.f32 tau tau)) (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) (/.f32 (PI.f32) (.f32 tau tau))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (/.f32 (PI.f32) (.f32 x x)))))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) x) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32)))) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 tau (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32)))))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 x (fma.f32 #s(literal -1/6 binary32) (PI.f32) (.f32 #s(literal 1/120 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32))))))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 (/.f32 (sin.f32 (*.f32 x (PI.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 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) #s(literal 1 binary32)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

21.0ms	tau
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))))
16.0ms	(*.f32 x (PI.f32))
16.0ms	x

Results

Accuracy	Segments	Branch
87.0%	1	`x`
87.0%	1	`tau`
87.0%	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))))`
87.0%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes75.0ms (0.5%)

Memory

-5.2MiB live, 181.0MiB allocated

Counts

62 → 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 (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #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)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x tau)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (*.f32 x tau)) x) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) x #s(literal 1 binary32)))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
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(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 x x) (PI.f32)))) x))) tau)
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(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
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(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1/36 binary32) (-.f32 (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))))) #s(literal 1 binary32)))
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(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32))))) (.f32 (PI.f32) tau)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x (PI.f32)) (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 #s(literal 1 binary32) (/.f32 tau (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) tau) tau) (PI.f32))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 tau (.f32 tau tau)) (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) (/.f32 (PI.f32) (.f32 tau tau))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (/.f32 (PI.f32) (.f32 x x)))))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
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#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32)))) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 tau (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32)))))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
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(.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 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( x (PI))) (PI)) x) #s(literal 1 binary32)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Outputs

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

Calls

4 calls:

19.0ms	tau
18.0ms	x
18.0ms	(*.f32 x (PI.f32))
17.0ms	(.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
80.1%	1	`x`
80.1%	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))))`
80.1%	1	`(*.f32 x (PI.f32))`
80.1%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes73.0ms (0.4%)

Memory

1.2MiB live, 234.5MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

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))))
18.0ms	x
17.0ms	tau
17.0ms	(*.f32 x (PI.f32))

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes77.0ms (0.5%)

Memory

9.9MiB live, 149.0MiB allocated

Counts

55 → 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 (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) #s(approx (+ (* x (* x (* -1/6 (* (PI) (PI))))) 1) (.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #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)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))) #s(literal -1/6 binary32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x tau)) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (*.f32 x tau)) x) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (.f32 (.f32 x x) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (PI.f32) (PI.f32))))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) #s(approx ( (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6)) (.f32 tau (.f32 #s(literal -1/6 binary32) (.f32 tau (.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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) #s(approx (+ ( -1/6 (* tau tau)) -1/6) (.f32 #s(literal -1/6 binary32) (.f32 tau tau)))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (PI.f32) (.f32 (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #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 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) x #s(literal 1 binary32)))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) #s(approx (/ (/ (* x (PI)) (sin (* x (PI)))) (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) 1)) (fma.f32 #s(literal 1/6 binary32) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) (fma.f32 tau (*.f32 tau tau) tau))) tau)) tau)
(/.f32 #s(approx (/ (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))) tau)) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 x (.f32 x (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 x (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (fma.f32 tau (.f32 tau #s(literal -1/6 binary32)) #s(literal -1/6 binary32))))) #s(literal 1 binary32)))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (/.f32 #s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) tau))) x) tau)
(.f32 #s(approx (/ ( (sin (* x (* (PI) tau))) (sin (* x (PI)))) (* x (* (PI) (PI)))) (.f32 x (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) (+.f32 tau (.f32 tau (.f32 tau tau)))) tau))) (/.f32 #s(literal 1 binary32) (.f32 x tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (/.f32 (-.f32 #s(literal 1/36 binary32) (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)))) (-.f32 #s(literal -1/6 binary32) (.f32 tau (*.f32 tau #s(literal -1/6 binary32)))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) (.f32 #s(literal -1/6 binary32) (.f32 (*.f32 x x) (PI.f32)))) x))) tau)
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) x) #s(approx (/ (sin ( (PI) (* x tau))) (/ (PI) (sin (* x (PI))))) (.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (*.f32 tau (PI.f32))))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (/.f32 (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (.f32 (PI.f32) (PI.f32))) (fma.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32)) (-.f32 #s(literal 1/36 binary32) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (fma.f32 x (.f32 #s(literal -1/6 binary32) (PI.f32)) (/.f32 x (.f32 (*.f32 x x) (PI.f32))))))) tau)
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (/.f32 #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) tau))
(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) tau) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))))
(/.f32 (.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) #s(approx (sin (* (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) #s(approx (/ (+ (* -1/6 (* (* x x) (PI))) (/ 1 (PI))) x) (neg.f32 (.f32 x (fma.f32 (PI.f32) #s(literal 1/6 binary32) (/.f32 #s(literal -1 binary32) (.f32 (*.f32 x x) (PI.f32))))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (fma.f32 (.f32 #s(literal -1/216 binary32) (.f32 tau (.f32 tau tau))) (.f32 tau (.f32 tau tau)) #s(literal -1/216 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1/36 binary32) (-.f32 (.f32 (.f32 tau tau) (.f32 (.f32 tau tau) #s(literal 1/36 binary32))) (.f32 (*.f32 tau tau) #s(literal 1/36 binary32))))))) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)) (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) (/.f32 #s(literal 1 binary32) tau)))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 (.f32 tau tau) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal -1/6 binary32))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32))))) (.f32 (PI.f32) tau)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x (PI.f32)) (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 #s(literal 1 binary32) (/.f32 tau (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 tau (.f32 tau #s(literal -1/6 binary32)))) (PI.f32))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) tau) tau) (PI.f32))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32)))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))))) (.f32 x (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (/.f32 x (fma.f32 (PI.f32) (.f32 (.f32 x x) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32))))))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 tau (.f32 tau tau)) (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (.f32 (.f32 x x) (PI.f32)))) (/.f32 (PI.f32) (.f32 tau tau))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (*.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
#s(approx (/ (* (sin (* (PI) (* x tau))) (/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x #s(approx (+ ( (* (* x x) (* (PI) (* (PI) (PI)))) (* (* -1/6 (* tau tau)) tau)) (* tau (PI))) (.f32 (.f32 x x) (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (.f32 tau (/.f32 (PI.f32) (.f32 x x)))))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 (.f32 x x) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) tau) (.f32 tau (PI.f32))))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (/.f32 #s(literal 1 binary32) x) (.f32 (/.f32 #s(literal 1 binary32) x) (.f32 x (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32))))))) tau)
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* x x) (* (* (PI) (PI)) (+ (* -1/6 (* tau tau)) -1/6))) 1) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32)))) #s(literal 1 binary32))))
(/.f32 (.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 tau (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)) (.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (.f32 tau (.f32 tau (.f32 tau #s(literal -1/6 binary32)))))))))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 x x) (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)

Outputs

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

Calls

4 calls:

25.0ms	x
18.0ms	tau
18.0ms	(.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	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
79.5%	1	`x`
79.5%	1	`(*.f32 x (PI.f32))`
79.5%	1	`tau`
79.5%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes37.0ms (0.2%)

Memory

-12.9MiB live, 78.0MiB allocated

Counts

26 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

11.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
10.0ms	x
7.0ms	tau
7.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
79.5%	1	`x`
79.5%	1	`(*.f32 x (PI.f32))`
79.5%	1	`tau`
79.5%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes21.0ms (0.1%)

Memory

2.4MiB live, 47.9MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

8.0ms	tau
4.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
4.0ms	x
4.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
69.9%	1	`x`
69.9%	1	`tau`
69.9%	1	`(*.f32 x (PI.f32))`
69.9%	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 34 to 18 computations (47.1% saved)

regimes20.0ms (0.1%)

Memory

-7.2MiB live, 44.3MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

8.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
4.0ms	tau
4.0ms	(*.f32 x (PI.f32))
4.0ms	x

Results

Accuracy	Segments	Branch
69.9%	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))))`
69.9%	1	`tau`
69.9%	1	`x`
69.9%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes19.0ms (0.1%)

Memory

-3.8MiB live, 41.8MiB allocated

Counts

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

Outputs

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

Calls

4 calls:

7.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
4.0ms	tau
4.0ms	(*.f32 x (PI.f32))
4.0ms	x

Results

Accuracy	Segments	Branch
65.6%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
65.6%	1	`x`
65.6%	1	`tau`
65.6%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes10.0ms (0.1%)

Memory

27.9MiB live, 28.0MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
65.6%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
65.6%	1	`x`
65.6%	1	`tau`
65.6%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes11.0ms (0.1%)

Memory

-22.4MiB live, 23.4MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

Outputs

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

Calls

4 calls:

5.0ms	x
2.0ms	(*.f32 x (PI.f32))
2.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
2.0ms	tau

Results

Accuracy	Segments	Branch
65.6%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
65.6%	1	`x`
65.6%	1	`(*.f32 x (PI.f32))`
65.6%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes6.0ms (0%)

Memory

20.0MiB live, 20.0MiB allocated

Accuracy

Total -19.6b remaining (-173.4%)

Threshold costs -19.6b (-173.4%)

Counts

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

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

Calls

4 calls:

2.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
1.0ms	x
1.0ms	tau
1.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
64.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
64.7%	1	`x`
64.7%	1	`tau`
64.7%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

simplify18.0ms (0.1%)

Memory

-16.8MiB live, 29.7MiB allocated

Algorithm

1×	egg-herbie

Rules

124×	`*-commutative_binary32`
20×	`sub-neg_binary32`
20×	`+-commutative_binary32`
18×	`distribute-lft-neg-in_binary32`
18×	`distribute-rgt-neg-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	147	735
1	215	735
2	238	735
3	260	735
4	272	735
5	278	735
6	280	735

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.3s (14%)

Memory

69.6MiB live, 1 765.4MiB allocated

Rules

18 798×	`lower-fma.f64`
18 798×	`lower-fma.f32`
16 966×	`lower-fma.f64`
16 966×	`lower-fma.f32`
16 806×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	8461
1	1187	8207
2	4478	7893
0	8102	7630
0	196	1582
1	620	1562
2	2413	1538
3	4145	1538
4	4880	1538
5	5560	1538
6	5950	1538
7	5981	1538
8	5981	1538
0	8826	1486
0	44	291
0	78	289
1	247	269
2	1525	269
3	7346	269
0	8303	269
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53
0	368	7796
1	1212	7607
2	4714	7396
0	8581	7162
0	75	588
0	129	562
1	475	529
2	3045	529
0	8676	522
0	471	10354
1	1645	10025
2	6847	9997
0	8246	9602
0	51	366
0	91	364
1	348	342
2	2212	342
0	8155	340

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×	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×	node limit

Compiler

Compiled 1 008 to 421 computations (58.2% saved)

preprocess169.0ms (1%)

Memory

-8.0MiB live, 287.9MiB allocated

Remove

(abs x)

(abs tau)

Compiler

Compiled 1 968 to 700 computations (64.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze21.0ms (0.1%)

sample1.8s (11%)

explain230.0ms (1.4%)

preprocess86.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify25.0ms (0.2%)

localize38.0ms (0.2%)

series32.0ms (0.2%)

simplify494.0ms (3%)

rewrite306.0ms (1.8%)

eval129.0ms (0.8%)

prune321.0ms (1.9%)

simplify152.0ms (0.9%)

localize143.0ms (0.9%)

series50.0ms (0.3%)

simplify428.0ms (2.6%)

rewrite311.0ms (1.9%)

eval283.0ms (1.7%)

prune755.0ms (4.5%)

simplify430.0ms (2.6%)

localize210.0ms (1.3%)

series64.0ms (0.4%)

simplify380.0ms (2.3%)

rewrite557.0ms (3.4%)

eval420.0ms (2.5%)

prune1.4s (8.6%)

simplify565.0ms (3.4%)

localize384.0ms (2.3%)

series58.0ms (0.3%)

simplify355.0ms (2.1%)

rewrite459.0ms (2.8%)

eval363.0ms (2.2%)

prune1.3s (7.6%)

regimes213.0ms (1.3%)

regimes155.0ms (0.9%)

regimes135.0ms (0.8%)

regimes119.0ms (0.7%)

regimes166.0ms (1%)

regimes103.0ms (0.6%)

regimes98.0ms (0.6%)

regimes107.0ms (0.6%)

regimes75.0ms (0.5%)

regimes75.0ms (0.5%)

regimes73.0ms (0.4%)

regimes77.0ms (0.5%)

regimes37.0ms (0.2%)

regimes21.0ms (0.1%)

regimes20.0ms (0.1%)

regimes19.0ms (0.1%)

regimes10.0ms (0.1%)

regimes11.0ms (0.1%)

regimes6.0ms (0%)

simplify18.0ms (0.1%)

soundness2.3s (14%)

preprocess169.0ms (1%)

end0.0ms (0%)

Profiling