Metrics for Lanczos kernel

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze52.0ms (0.4%)

Memory

2.9MiB live, 43.7MiB 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)

sample2.6s (20.2%)

Memory

-216.0MiB live, 4 016.3MiB allocated

Samples

2.1s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.8s

const: 333.0ms (18.3% of total)

ival-div: 328.0ms (18% of total)

ival-mult: 323.0ms (17.7% of total)

ival-<=: 270.0ms (14.8% of total)

ival-pi: 212.0ms (11.6% of total)

ival-sinu: 165.0ms (9% of total)

ival-sin: 158.0ms (8.7% of total)

ival-and: 23.0ms (1.3% of total)

exact: 9.0ms (0.5% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain461.0ms (3.6%)

Memory

-17.2MiB live, 305.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
1	-	1	(0.7444535493850708 1.2923463582992554)	`(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	1
-	0	255

Precision

0/0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	1
-	0	0	255

Precision?

0/0

Recall?

0.0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0.0

Samples

172.0ms

512×

valid

Compiler

Compiled 149 to 34 computations (77.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 97.0ms

ival-mult: 67.0ms (69% of total)

ival-sinu: 11.0ms (11.3% of total)

ival-sin: 8.0ms (8.2% of total)

ival-div: 7.0ms (7.2% of total)

ival-pi: 2.0ms (2.1% of total)

ival-true: 1.0ms (1% of total)

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

preprocess79.0ms (0.6%)

Memory

4.2MiB live, 81.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs tau)

(abs x)

Compiler

Compiled 21 to 10 computations (52.4% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.1%	(.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 21 to 10 computations (52.4% saved)

simplify52.0ms (0.4%)

Memory

-2.9MiB live, 36.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize52.0ms (0.4%)

Memory

24.9MiB live, 65.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.33922793102896015	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3802337890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42939379884221013	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

Samples

44.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 22.0ms (59.4% of total)

ival-sinu: 7.0ms (18.9% of total)

ival-sin: 4.0ms (10.8% of total)

ival-div: 3.0ms (8.1% of total)

ival-pi: 1.0ms (2.7% of total)

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

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

series74.0ms (0.6%)

Memory

-14.2MiB live, 64.4MiB 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 (/ (sin (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* -1/6 (* (pow tau 2) (* x (* (PI) (sin (* x (PI))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* 1/120 (* (pow tau 2) (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (+ (* (pow tau 2) (+ (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 5) (* (pow (PI) 5) (sin (* x (PI))))))) (* 1/120 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))))))) (/ (sin (* x (PI))) (* x (PI)))) (taylor 0 tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt 1 (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* -1/6 (* (pow tau 2) (* (pow x 2) (pow (PI) 2))))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* 1/120 (* (pow tau 2) (* (pow x 4) (pow (PI) 4))))))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow tau 2) (+ (* -1/6 (* (pow x 2) (pow (PI) 2))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 6) (pow (PI) 6)))) (* 1/120 (* (pow x 4) (pow (PI) 4)))))))) (taylor 0 tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* -1/6 (* (pow tau 2) (* (pow x 3) (pow (PI) 3)))) (* x (PI)))) (taylor 0 tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* 1/120 (* (pow tau 2) (* (pow x 5) (pow (PI) 5)))))))) (taylor 0 tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* x (PI)) (* (pow tau 2) (+ (* -1/6 (* (pow x 3) (pow (PI) 3))) (* (pow tau 2) (+ (* -1/5040 (* (pow tau 2) (* (pow x 7) (pow (PI) 7)))) (* 1/120 (* (pow x 5) (pow (PI) 5))))))))) (taylor 0 tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf tau) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor inf tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor inf tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor inf tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor inf tau) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor inf tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor inf tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor inf tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor inf tau) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor inf tau) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
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#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (patch (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* tau (* x (PI)))) (* tau (* x (PI)))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (patch (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor -inf x) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor -inf x) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor -inf x) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (sin (* tau (* x (PI)))) (taylor -inf x) (#s(alt (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (patch (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf x) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf x) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf x) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf x) (#s(alt (.f32 (.f32 x (PI.f32)) tau) (patch (.f32 (.f32 x (PI.f32)) tau) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (patch (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor -inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor -inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor -inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor -inf x) (#s(alt (.f32 x (PI.f32)) (patch (.f32 x (PI.f32)) #<representation binary32>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
35.0ms	tau	@	inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
20.0ms	x	@	-inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
5.0ms	tau	@	-inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
4.0ms	x	@	inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
3.0ms	x	@	0	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))

simplify382.0ms (3%)

Memory

9.2MiB live, 291.0MiB 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	2407	1538
3	4137	1538
4	4871	1538
5	5550	1538
6	5940	1538
7	5971	1538
8	5971	1538
0	8816	1486

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

rewrite260.0ms (2%)

Memory

14.3MiB live, 248.8MiB allocated

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

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

Counts

6 → 670

Calls

Call 1

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

Outputs
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (neg.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (neg.f32 (PI.f32)) x)) (neg.f32 (sin.f32 (*.f32 (PI.f32) x))))
(.f32 (.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 tau (PI.f32))) (sin.f32 (*.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) x))
(.f32 (.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) #s(literal 1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) tau))
(.f32 (.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (neg.f32 tau)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (neg.f32 (PI.f32)) x)))
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(pow.f32 (/.f32 x (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))) #s(literal -1 binary32))
(pow.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) #s(literal -1 binary32))
(pow.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) #s(literal 1 binary32))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (*.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(neg.f32 (/.f32 #s(literal -1 binary32) (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x)))))
(neg.f32 (.f32 #s(literal 1 binary32) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (neg.f32 (PI.f32)) x))))
(neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (neg.f32 (PI.f32)) x)) #s(literal 1 binary32)))
(neg.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (neg.f32 (PI.f32)) x)))
(.f32 (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (pow.f32 (PI.f32) #s(literal 1/4 binary32))) (pow.f32 (PI.f32) #s(literal 1/4 binary32)))
(.f32 (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(.f32 (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))
(.f32 (.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (cbrt.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))) (cbrt.f32 (cbrt.f32 (PI.f32))))
(.f32 (.f32 (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) #s(literal 1 binary32)) (cbrt.f32 (PI.f32)))
(.f32 (.f32 #s(literal 1 binary32) (*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (cbrt.f32 (PI.f32)))
(*.f32 (neg.f32 (neg.f32 (PI.f32))) x)
(*.f32 (neg.f32 (neg.f32 x)) (PI.f32))
(.f32 (.f32 (sqrt.f32 (PI.f32)) x) (/.f32 (sqrt.f32 (PI.f32)) #s(literal 1 binary32)))
(.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))
(.f32 (.f32 (cbrt.f32 (PI.f32)) x) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))
(.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (/.f32 (cbrt.f32 (PI.f32)) #s(literal 1 binary32)))
(.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (cbrt.f32 (PI.f32)))
(*.f32 (neg.f32 (PI.f32)) (neg.f32 x))
(*.f32 (neg.f32 x) (neg.f32 (PI.f32)))
(.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (*.f32 (sqrt.f32 (PI.f32)) x)))
(.f32 #s(literal -1 binary32) (.f32 (neg.f32 (PI.f32)) x))
(.f32 (sqrt.f32 (PI.f32)) (/.f32 (.f32 (sqrt.f32 (PI.f32)) x) #s(literal 1 binary32)))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) x))
(.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (/.f32 (.f32 (cbrt.f32 (PI.f32)) x) #s(literal 1 binary32)))
(.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))
(.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (*.f32 (sqrt.f32 (PI.f32)) x)))
(.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (*.f32 (cbrt.f32 (PI.f32)) x)))
(.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) x))
(.f32 (.f32 (PI.f32) x) #s(literal 1 binary32))
(*.f32 (PI.f32) (/.f32 x #s(literal 1 binary32)))
(*.f32 (PI.f32) (neg.f32 (neg.f32 x)))
(*.f32 (PI.f32) x)
(*.f32 x (/.f32 (PI.f32) #s(literal 1 binary32)))
(*.f32 x (neg.f32 (neg.f32 (PI.f32))))
(*.f32 x (PI.f32))
(/.f32 (*.f32 (neg.f32 (PI.f32)) x) #s(literal -1 binary32))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)))
(/.f32 (*.f32 (PI.f32) x) #s(literal 1 binary32))
(-.f32 #s(literal 0 binary32) (*.f32 (neg.f32 (PI.f32)) x))
(pow.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)) #s(literal -1 binary32))
(neg.f32 (*.f32 (neg.f32 (PI.f32)) x))

eval227.0ms (1.8%)

Memory: -21.6MiB live, 218.6MiB allocated
Compiler: Compiled 24 307 to 2 341 computations (90.4% saved)

prune163.0ms (1.3%)

Memory

11.5MiB live, 213.9MiB allocated

Pruning

37 alts after pruning (37 fresh and 0 done)

	Pruned	Kept	Total
New	976	37	1 013
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	977	37	1 014

Accuracy

99.8%

Counts

1 014 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.3%	(/.f32 (.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 tau (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) x)
	96.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (cbrt.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x))))
	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (PI.f32) x))
	97.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) x))
	97.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) (neg.f32 tau)))
	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) x) (*.f32 (neg.f32 (PI.f32)) x)))
▶	97.2%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
	97.3%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))) (neg.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))))
▶	97.9%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.1%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau x)) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) x)) (PI.f32)))
	95.9%	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 tau x)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) tau) x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (.f32 (cbrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	95.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (sqrt.f32 (PI.f32)) x))) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	97.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	95.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))) (.f32 x (PI.f32))))
	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (sqrt.f32 (PI.f32)) x)))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))) (.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))))
	97.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))))
	72.6%	(.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)))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (/.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x))) (PI.f32)))
	97.8%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x)))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))))
	97.3%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 (*.f32 (neg.f32 x) tau) (PI.f32))))
	93.6%	(.f32 (exp.f32 (.f32 (log.f32 (/.f32 (.f32 tau (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) #s(literal -1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	66.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
	97.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau x))))
▶	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 628 to 942 computations (42.1% saved)

simplify93.0ms (0.7%)

Memory

-17.5MiB live, 178.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
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 (sqrt.f32 (PI.f32)) x) (*.f32 (sqrt.f32 (PI.f32)) tau)))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
cost-diff	800	(.f32 (.f32 (sqrt.f32 (PI.f32)) x) (*.f32 (sqrt.f32 (PI.f32)) tau))
cost-diff	0	(*.f32 (PI.f32) x)
cost-diff	0	(sin.f32 (*.f32 (PI.f32) x))
cost-diff	0	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
cost-diff	128	(.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (neg.f32 (PI.f32)) x))
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 tau x) (PI.f32)))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
cost-diff	0	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
cost-diff	0	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
cost-diff	0	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
cost-diff	192	(/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x)) tau)

Rules

3 564×	`lower-/.f64`
3 552×	`lower-/.f32`
3 482×	`lower-*.f64`
3 454×	`lower-*.f32`
1 514×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	351
0	77	337
1	157	337
2	392	337
3	1559	335
4	4692	335
5	7107	335
0	8089	335

Stop Event

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

Calls

Call 1

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

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

localize115.0ms (0.9%)

Memory

19.3MiB live, 303.1MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.36328125	(*.f32 (sqrt.f32 (PI.f32)) tau)
accuracy	0.37890625	(*.f32 (sqrt.f32 (PI.f32)) x)
accuracy	0.3802337890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42939379884221013	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (*.f32 (sqrt.f32 (PI.f32)) tau)))
accuracy	0.359375	(*.f32 (neg.f32 (PI.f32)) x)
accuracy	0.359375	(*.f32 (PI.f32) x)
accuracy	0.36328125	(.f32 (.f32 (neg.f32 x) tau) (PI.f32))
accuracy	0.4199600586106521	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.36328125	(.f32 (.f32 tau x) (PI.f32))
accuracy	0.3802337890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42939379884221013	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32)))
accuracy	11.047765384780414	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
accuracy	0.34375	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
accuracy	0.359375	(*.f32 (PI.f32) x)
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3802337890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))

Samples

81.0ms

256×

valid

Compiler

Compiled 351 to 37 computations (89.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 32.0ms (53% of total)

ival-div: 12.0ms (19.9% of total)

ival-sin: 7.0ms (11.6% of total)

ival-sinu: 4.0ms (6.6% of total)

ival-sqrt: 2.0ms (3.3% of total)

ival-neg: 2.0ms (3.3% of total)

ival-pi: 1.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series88.0ms (0.7%)

Memory

-20.3MiB live, 59.8MiB allocated

Counts

23 → 468

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
37.0ms	tau	@	-inf	((/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (* (/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (sin (* (PI) x)) (* (PI) x) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* (* tau x) (PI)) (* (* (neg x) tau) (PI)) (* (neg (PI)) x) (* (sqrt (PI)) x) (* (sqrt (PI)) tau))
4.0ms	x	@	-inf	((/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (* (/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (sin (* (PI) x)) (* (PI) x) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* (* tau x) (PI)) (* (* (neg x) tau) (PI)) (* (neg (PI)) x) (* (sqrt (PI)) x) (* (sqrt (PI)) tau))
4.0ms	x	@	inf	((/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (* (/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (sin (* (PI) x)) (* (PI) x) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* (* tau x) (PI)) (* (* (neg x) tau) (PI)) (* (neg (PI)) x) (* (sqrt (PI)) x) (* (sqrt (PI)) tau))
3.0ms	tau	@	inf	((/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (* (/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (sin (* (PI) x)) (* (PI) x) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* (* tau x) (PI)) (* (* (neg x) tau) (PI)) (* (neg (PI)) x) (* (sqrt (PI)) x) (* (sqrt (PI)) tau))
3.0ms	x	@	0	((/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (* (/ (/ (sin (* tau (* (PI) x))) (* (PI) x)) tau) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (* (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* tau x) (PI))) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (sin (* (PI) x)) (* (PI) x) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)) (* (* tau x) (PI)) (* (* (neg x) tau) (PI)) (* (neg (PI)) x) (* (sqrt (PI)) x) (* (sqrt (PI)) tau))

simplify288.0ms (2.2%)

Memory

7.9MiB live, 238.9MiB allocated

Algorithm

1×	egg-herbie

Rules

19 182×	`lower-fma.f64`
19 182×	`lower-fma.f32`
7 330×	`lower-*.f64`
7 330×	`lower-*.f32`
5 072×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	301	6650
1	1009	6520
2	4016	6398
3	7975	6398
0	8177	6192

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 466

Calls

Call 1

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

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

rewrite427.0ms (3.3%)

Memory

0.8MiB live, 323.0MiB allocated

Rules

5 152×	`lower-/.f64`
5 140×	`lower-/.f32`
5 036×	`lower-*.f64`
5 008×	`lower-*.f32`
998×	`associate-*l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	248
0	77	234
1	245	234
2	1467	220
0	8566	220

Stop Event

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

Counts

23 → 2 483

Calls

Call 1

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

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

eval581.0ms (4.5%)

Memory: 20.8MiB live, 680.9MiB allocated
Compiler: Compiled 88 758 to 4 088 computations (95.4% saved)

prune160.0ms (1.2%)

Memory

26.1MiB live, 500.4MiB allocated

Pruning

44 alts after pruning (41 fresh and 3 done)

	Pruned	Kept	Total
New	3 582	27	3 609
Fresh	18	14	32
Picked	2	3	5
Done	0	0	0
Total	3 602	44	3 646

Accuracy

99.8%

Counts

3 646 → 44

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.3%	(/.f32 (.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (.f32 tau (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) x)
	97.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (PI.f32)) (neg.f32 x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (*.f32 (neg.f32 tau) (sqrt.f32 (PI.f32))))
	96.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (PI.f32)) x)) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (sqrt.f32 (PI.f32)) tau) (.f32 x (PI.f32))))
	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (.f32 x (PI.f32)))
	96.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (cbrt.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x))))
▶	97.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
	98.0%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (.f32 (*.f32 x (PI.f32)) tau))
	95.9%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))))) (.f32 (neg.f32 (PI.f32)) x)))
	97.3%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (.f32 (neg.f32 (PI.f32)) x) tau) x) (/.f32 (neg.f32 (PI.f32)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))))
	97.0%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (.f32 (.f32 tau (.f32 (PI.f32) (PI.f32))) (/.f32 (.f32 x x) (sin.f32 (.f32 (.f32 (PI.f32) x) tau))))))
	66.2%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (*.f32 (PI.f32) x)))
	72.4%	(/.f32 #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
	97.2%	(/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (PI.f32)) (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (neg.f32 x)))))
✓	97.9%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (/.f32 #s(literal 1 binary32) (PI.f32))))
	72.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32)))
	95.3%	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x tau)))) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.0%	(.f32 (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x tau)))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) tau) x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (.f32 (cbrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))) (*.f32 x (PI.f32))))
▶	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
	72.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.5%	(.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))))
	95.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))) (.f32 x (PI.f32))))
	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (sqrt.f32 (PI.f32)) x)))) (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))))
	72.6%	(.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)))
✓	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	72.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x tau)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (*.f32 x (PI.f32)))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) tau)))
	97.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 x (PI.f32)) tau)))
▶	98.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (/.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x))) (PI.f32)))
	98.0%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))
	65.5%	#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	96.6%	#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 x x))))
▶	63.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
✓	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 880 to 1 120 computations (40.4% saved)

simplify211.0ms (1.6%)

Memory

-24.9MiB live, 260.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
cost-diff	800	(.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))
cost-diff	800	(.f32 (.f32 (sqrt.f32 (PI.f32)) x) (*.f32 (sqrt.f32 (PI.f32)) tau))
cost-diff	0	(sin.f32 (*.f32 (PI.f32) x))
cost-diff	0	(/.f32 (sin.f32 (*.f32 (PI.f32) x)) x)
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))
cost-diff	0	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
cost-diff	0	(*.f32 tau x)
cost-diff	0	(.f32 (.f32 tau x) (PI.f32))
cost-diff	0	(sin.f32 (.f32 (.f32 tau x) (PI.f32)))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
cost-diff	0	(fma.f32 tau tau #s(literal 1 binary32))
cost-diff	0	(.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)))
cost-diff	0	(fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
cost-diff	0	(*.f32 x tau)
cost-diff	0	(.f32 (.f32 x tau) (PI.f32))
cost-diff	0	(sin.f32 (.f32 (.f32 x tau) (PI.f32)))
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Rules

28 252×	`lower-fma.f64`
28 248×	`lower-fma.f32`
5 550×	`lower-*.f64`
5 514×	`lower-*.f32`
3 456×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	397
0	94	373
1	191	373
2	469	373
3	1530	373
4	3430	373
5	3982	373
6	4155	373
7	4209	373
8	4209	373
9	5367	373
10	6151	373
0	8011	373

Stop Event

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

Calls

Call 1

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

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

localize134.0ms (1%)

Memory

31.9MiB live, 309.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.37890625	(.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))
accuracy	0.37890625	(*.f32 (sqrt.f32 (PI.f32)) x)
accuracy	0.3802337890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32))))
accuracy	0.42939379884221013	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (*.f32 (sqrt.f32 (PI.f32)) tau)))
accuracy	0.33922793102896015	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.359375	(*.f32 (PI.f32) x)
accuracy	0.3756637695368841	(.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))
accuracy	0.41767504884221013	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.36328125	(.f32 (.f32 tau x) (PI.f32))
accuracy	0.3802337890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42939379884221013	(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	6.423820946797184	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
accuracy	17.838401727069886	(fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32))
accuracy	26.503001012179983	(fma.f32 tau tau #s(literal 1 binary32))
accuracy	0.36328125	(.f32 (.f32 x tau) (PI.f32))
accuracy	0.36328125	(.f32 (.f32 tau x) (PI.f32))
accuracy	0.3802337890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42939379884221013	(/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32)))

Samples

97.0ms

256×

valid

Compiler

Compiled 387 to 47 computations (87.9% saved)

Precisions

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

ival-mult: 35.0ms (44.6% of total)

ival-div: 13.0ms (16.6% of total)

ival-sinu: 13.0ms (16.6% of total)

ival-sin: 7.0ms (8.9% of total)

const: 6.0ms (7.6% of total)

ival-add: 2.0ms (2.5% of total)

ival-sqrt: 2.0ms (2.5% of total)

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

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

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

exact: 0.0ms (0% of total)

series89.0ms (0.7%)

Memory

-30.7MiB live, 171.6MiB allocated

Counts

31 → 600

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
11.0ms	x	@	-inf	((* (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x tau) (PI))) (* (* x tau) (PI)) (* x tau) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (* (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (/ (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) x) (sin (* (PI) x)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (* (sqrt (PI)) x) (sqrt (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI))))) (sin (* (* x (PI)) tau)) (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (* x (PI)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (sin (* tau (* (PI) x))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) (* (sqrt (PI)) x))
10.0ms	x	@	inf	((* (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x tau) (PI))) (* (* x tau) (PI)) (* x tau) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (* (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (/ (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) x) (sin (* (PI) x)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (* (sqrt (PI)) x) (sqrt (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI))))) (sin (* (* x (PI)) tau)) (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (* x (PI)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (sin (* tau (* (PI) x))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) (* (sqrt (PI)) x))
4.0ms	tau	@	-inf	((* (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x tau) (PI))) (* (* x tau) (PI)) (* x tau) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (* (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (/ (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) x) (sin (* (PI) x)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (* (sqrt (PI)) x) (sqrt (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI))))) (sin (* (* x (PI)) tau)) (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (* x (PI)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (sin (* tau (* (PI) x))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) (* (sqrt (PI)) x))
4.0ms	x	@	0	((* (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x tau) (PI))) (* (* x tau) (PI)) (* x tau) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (* (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (/ (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) x) (sin (* (PI) x)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (* (sqrt (PI)) x) (sqrt (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI))))) (sin (* (* x (PI)) tau)) (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (* x (PI)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (sin (* tau (* (PI) x))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) (* (sqrt (PI)) x))
4.0ms	tau	@	inf	((* (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* x tau) (PI))) (* (* x tau) (PI)) (* x tau) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (* (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (/ (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (/ (sin (* (PI) x)) x) (sin (* (PI) x)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau)) (* (* (sqrt (PI)) x) (sqrt (PI))) (* (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI))))) (sin (* (* x (PI)) tau)) (/ (sin (* (* x tau) (PI))) (* (* tau x) (PI))) (/ (sin (* x (PI))) (* x (PI))) (* (PI) (PI)) (/ (sin (* (* tau x) (PI))) (* (* x (PI)) tau)) (* x (PI)) (* (* tau (* (PI) x)) (PI)) (* (PI) x) (sin (* tau (* (PI) x))) (/ (sin (* (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) (* (sqrt (PI)) x))

simplify213.0ms (1.7%)

Memory

35.8MiB live, 383.8MiB allocated

Algorithm

1×	egg-herbie

Rules

19 064×	`lower-fma.f64`
19 064×	`lower-fma.f32`
6 450×	`lower-*.f64`
6 450×	`lower-*.f32`
5 458×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	314	7990
1	1039	7716
2	3948	7558
3	7658	7558
0	8166	7268

Stop Event

1×	iter limit
1×	node limit

Counts

600 → 600

Calls

Call 1

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

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

rewrite242.0ms (1.9%)

Memory

1.2MiB live, 560.1MiB allocated

Rules

4 656×	`lower-*.f64`
4 620×	`lower-*.f32`
4 474×	`lower-/.f64`
4 466×	`lower-/.f32`
3 258×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	317
0	94	305
1	301	293
2	1786	281
0	8449	279

Stop Event

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

Counts

31 → 2 247

Calls

Call 1

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

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

eval324.0ms (2.5%)

Memory: 27.5MiB live, 835.6MiB allocated
Compiler: Compiled 83 338 to 4 218 computations (94.9% saved)

prune211.0ms (1.6%)

Memory

-8.8MiB live, 554.1MiB allocated

Pruning

70 alts after pruning (64 fresh and 6 done)

	Pruned	Kept	Total
New	3 287	40	3 327
Fresh	12	24	36
Picked	2	3	5
Done	0	3	3
Total	3 301	70	3 371

Accuracy

99.8%

Counts

3 371 → 70

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.3%	(/.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) tau)) x)
	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) tau) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) (.f32 (PI.f32) x))
	96.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (PI.f32)) x)) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (sqrt.f32 (PI.f32)) tau) (.f32 x (PI.f32))))
	96.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (cbrt.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x))))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 (.f32 (PI.f32) x) tau))))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	72.4%	(/.f32 (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
▶	97.3%	(/.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	98.0%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))) (.f32 (*.f32 x (PI.f32)) tau))
	72.5%	(/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) x) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.3%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (.f32 (neg.f32 (PI.f32)) x) tau) x) (/.f32 (neg.f32 (PI.f32)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))))
	97.0%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (.f32 (.f32 tau (.f32 (PI.f32) (PI.f32))) (/.f32 (.f32 x x) (sin.f32 (.f32 (.f32 (PI.f32) x) tau))))))
	66.2%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (*.f32 (PI.f32) x)))
▶	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	66.0%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	72.4%	(/.f32 #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
	97.2%	(/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (PI.f32)) (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (neg.f32 x)))))
✓	97.9%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (/.f32 #s(literal 1 binary32) (PI.f32))))
	72.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32)))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32))) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 (.f32 (.f32 (PI.f32) x) tau) (PI.f32))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) x))
	97.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (*.f32 (PI.f32) x) tau)))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) tau) x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))) (*.f32 x (PI.f32))))
✓	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
	72.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) #s(approx (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) #s(literal 1 binary32)))
	97.5%	(.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))))
	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (sqrt.f32 (PI.f32)) x)))) (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))))
	72.6%	(.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)))
✓	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	72.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x tau)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (*.f32 x (PI.f32)))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) tau)))
	95.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))) (.f32 x (PI.f32))))
✓	98.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	72.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
✓	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	72.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.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) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (/.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x))) (PI.f32)))
▶	98.0%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))
	66.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) #s(literal 1 binary32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
	65.5%	#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	96.6%	#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 x x))))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (*.f32 x x) #s(literal 1 binary32)))
	6.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (*.f32 x x) #s(literal 1 binary32)))
▶	9.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
	65.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
	65.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32)))
	37.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
▶	65.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
	4.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
	4.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (.f32 x x) tau))) (.f32 (PI.f32) (PI.f32)))))
✓	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 2 725 to 1 730 computations (36.5% saved)

simplify116.0ms (0.9%)

Memory

-8.7MiB live, 190.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f32 #s(literal 1 binary32) x)
cost-diff	0	(.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))
cost-diff	0	(/.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
cost-diff	160	(.f32 (/.f32 #s(literal 1 binary32) x) (sin.f32 (.f32 (PI.f32) x)))
cost-diff	0	(fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
cost-diff	64	(neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)))
cost-diff	224	(*.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32))))
cost-diff	0	(.f32 (.f32 tau (PI.f32)) (PI.f32))
cost-diff	0	(.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)
cost-diff	0	#s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x))
cost-diff	0	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
cost-diff	0	(.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32))
cost-diff	0	(fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))
cost-diff	0	#s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (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 (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
cost-diff	0	(PI.f32)
cost-diff	0	(*.f32 x (PI.f32))
cost-diff	0	(.f32 (.f32 x (PI.f32)) tau)
cost-diff	352	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))

Rules

6 150×	`lower-*.f64`
6 110×	`lower-*.f32`
5 722×	`lower-fma.f64`
5 716×	`lower-fma.f32`
1 926×	`lower-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	494
0	116	494
1	233	478
2	652	473
3	2899	473
4	5166	473
0	8223	465

Stop Event

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

Calls

Call 1

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

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

localize146.0ms (1.1%)

Memory

6.9MiB live, 281.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.359375	(*.f32 (PI.f32) x)
accuracy	0.3756637695368841	(.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))
accuracy	0.3991012695368841	(.f32 (/.f32 #s(literal 1 binary32) x) (sin.f32 (.f32 (PI.f32) x)))
accuracy	0.41767504884221013	(/.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	6.423820946797184	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
accuracy	17.38884733373282	(fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32))
accuracy	29.859834450668746	(fma.f32 (neg.f32 tau) tau #s(literal 1 binary32))
accuracy	0.359375	(*.f32 (PI.f32) x)
accuracy	0.3756637695368841	(.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))
accuracy	0.41767504884221013	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
accuracy	10.753255851888907	#s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x))
accuracy	0.3671875	(.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32))
accuracy	6.423820946797184	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
accuracy	11.082258232876304	#s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32)))
accuracy	17.420286352640986	(fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))
accuracy	0.33922793102896015	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.359375	(*.f32 x (PI.f32))
accuracy	0.3802337890737681	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.4498825195368841	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))

Samples

107.0ms

256×

valid

Compiler

Compiled 421 to 56 computations (86.7% saved)

Precisions

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

ival-mult: 40.0ms (45.7% of total)

ival-div: 15.0ms (17.1% of total)

ival-sin: 8.0ms (9.1% of total)

ival-add: 7.0ms (8% of total)

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

const: 4.0ms (4.6% of total)

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

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

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

ival-pi: 1.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series49.0ms (0.4%)

Memory

4.3MiB live, 79.8MiB allocated

Counts

26 → 444

Calls

Call 1

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

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

Calls

6 calls:

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

simplify245.0ms (1.9%)

Memory

23.6MiB live, 296.7MiB allocated

Algorithm

1×	egg-herbie

Rules

16 164×	`lower-fma.f64`
16 164×	`lower-fma.f32`
6 712×	`lower-*.f64`
6 712×	`lower-*.f32`
5 266×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	300	6888
1	968	6530
2	3587	6262
3	7388	6262
0	8372	6025

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

Calls

Call 1

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

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

rewrite190.0ms (1.5%)

Memory

-4.3MiB live, 264.7MiB allocated

Rules

4 468×	`lower-/.f64`
4 456×	`lower-/.f32`
4 276×	`lower-*.f64`
4 236×	`lower-*.f32`
4 024×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	362
0	116	352
1	370	333
2	2385	313
0	8442	300

Stop Event

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

Counts

26 → 1 290

Calls

Call 1

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

Outputs
(.f32 (pow.f32 (.f32 tau x) #s(literal -1 binary32)) (pow.f32 (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) x))
(.f32 (pow.f32 (.f32 (.f32 tau (.f32 (PI.f32) x)) x) #s(literal -1 binary32)) (pow.f32 (/.f32 (PI.f32) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 tau (/.f32 (sin.f32 (.f32 (PI.f32) x)) x)) #s(literal -1 binary32)) (pow.f32 (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)))
(.f32 (pow.f32 (/.f32 tau (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)) (pow.f32 (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x)) #s(literal -1 binary32)))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (cbrt.f32 (PI.f32))))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) tau) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) x) (PI.f32))))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (*.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) x))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (*.f32 (PI.f32) x))) x) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 (.f32 (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))) (/.f32 #s(literal 1 binary32) tau))
(.f32 (.f32 #s(literal -1 binary32) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 #s(literal -1 binary32) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x))) (/.f32 #s(literal -1 binary32) x))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) tau))
(.f32 (.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) (/.f32 #s(literal -1 binary32) (.f32 tau (.f32 (PI.f32) x))))
(.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 x) (PI.f32))))
(.f32 (.f32 #s(literal -1 binary32) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (neg.f32 x) (PI.f32)) tau) (.f32 (PI.f32) x))))
(.f32 (.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)) (/.f32 #s(literal -1 binary32) (.f32 tau (*.f32 (PI.f32) x))))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 (.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal 1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (PI.f32)))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 x) (PI.f32))))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) x)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) #s(literal 1 binary32)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) tau))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 #s(literal -1 binary32) (.f32 tau (.f32 (PI.f32) x))))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) #s(literal 1 binary32)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (/.f32 #s(literal 1 binary32) x))
(.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x))) (/.f32 #s(literal 1 binary32) x))
(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))
(.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) x) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32))) (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))) x))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (PI.f32) x)) (/.f32 #s(literal 1 binary32) tau))
(.f32 (/.f32 #s(literal 1 binary32) tau) (pow.f32 (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))) #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) tau) (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (PI.f32) x)))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) tau) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))
(.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 tau (PI.f32))) (/.f32 #s(literal 1 binary32) x))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) tau) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (PI.f32) x) (PI.f32))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) x) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))) (PI.f32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) x) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (PI.f32))) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) x))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (.f32 (.f32 (PI.f32) x) (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) tau) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 tau (PI.f32))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x))
(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (.f32 tau (PI.f32))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) x) tau) (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (*.f32 (PI.f32) x) (PI.f32))))
(.f32 (neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x))))) (/.f32 #s(literal 1 binary32) (neg.f32 (PI.f32))))
(.f32 (neg.f32 (.f32 (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (*.f32 (PI.f32) x))) (PI.f32)))
(.f32 (neg.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 x) (PI.f32))))
(.f32 (neg.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 #s(literal -1 binary32) (.f32 tau (.f32 (PI.f32) x))))
(.f32 (neg.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 #s(literal 1 binary32) (neg.f32 (.f32 tau (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))))))
(.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) x) (.f32 (.f32 (neg.f32 x) (PI.f32)) tau))))
(.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (.f32 tau (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)))))
(.f32 (.f32 (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))))
(.f32 (.f32 #s(literal 1 binary32) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 #s(literal 1 binary32) (.f32 tau (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)))))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (/.f32 #s(literal -1 binary32) (.f32 tau (.f32 (PI.f32) x))))
(.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x)) (/.f32 #s(literal 1 binary32) (*.f32 tau (PI.f32))))
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(/.f32 (+.f32 #s(literal 1 binary32) (pow.f32 (.f32 (neg.f32 (.f32 (neg.f32 tau) tau)) #s(literal 1 binary32)) #s(literal 3 binary32))) (+.f32 #s(literal 1 binary32) (-.f32 (.f32 (.f32 (neg.f32 (.f32 (neg.f32 tau) tau)) #s(literal 1 binary32)) (.f32 (neg.f32 (.f32 (neg.f32 tau) tau)) #s(literal 1 binary32))) (.f32 #s(literal 1 binary32) (.f32 (neg.f32 (.f32 (neg.f32 tau) tau)) #s(literal 1 binary32))))))
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(/.f32 (neg.f32 (neg.f32 (+.f32 (pow.f32 tau #s(literal 6 binary32)) #s(literal 1 binary32)))) (neg.f32 (neg.f32 (+.f32 (fma.f32 tau tau #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32))))))
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(/.f32 (neg.f32 (+.f32 (pow.f32 tau #s(literal 6 binary32)) #s(literal 1 binary32))) (neg.f32 (+.f32 (fma.f32 tau tau #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32)))))
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(/.f32 (neg.f32 (neg.f32 (fma.f32 tau tau #s(literal 1 binary32)))) #s(literal 1 binary32))
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(/.f32 (-.f32 (pow.f32 tau #s(literal 12 binary32)) #s(literal 1 binary32)) (*.f32 (fma.f32 tau tau #s(literal -1 binary32)) (+.f32 (+.f32 (pow.f32 tau #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32)))))
(/.f32 (+.f32 (pow.f32 tau #s(literal 6 binary32)) #s(literal 1 binary32)) (*.f32 #s(literal 1 binary32) (+.f32 (fma.f32 tau tau #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32)))))
(/.f32 (+.f32 (pow.f32 tau #s(literal 6 binary32)) #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 tau #s(literal 4 binary32)) (*.f32 tau tau))))
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(/.f32 (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (neg.f32 (*.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32)))))
(/.f32 (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32))))
(/.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (*.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32))))
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(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 #s(literal 1 binary32) (+.f32 (fma.f32 tau tau #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32)))) (+.f32 (pow.f32 tau #s(literal 6 binary32)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (-.f32 (pow.f32 tau #s(literal 4 binary32)) (*.f32 tau tau))) (+.f32 (pow.f32 tau #s(literal 6 binary32)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 tau tau #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (pow.f32 tau #s(literal 4 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 (fma.f32 tau tau #s(literal -1 binary32)) (+.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (-.f32 (pow.f32 tau #s(literal 8 binary32)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (*.f32 (fma.f32 tau tau #s(literal -1 binary32)) (+.f32 (+.f32 (pow.f32 tau #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32)))) (-.f32 (pow.f32 tau #s(literal 12 binary32)) #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal 1 binary32))))
(-.f32 (/.f32 (/.f32 (pow.f32 tau #s(literal 4 binary32)) (fma.f32 tau tau #s(literal -1 binary32))) #s(literal 1 binary32)) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) #s(literal 1 binary32)))
(-.f32 (/.f32 (-.f32 #s(literal 0 binary32) (pow.f32 tau #s(literal 4 binary32))) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32))))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (neg.f32 (fma.f32 tau tau #s(literal 1 binary32))))
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(-.f32 (/.f32 (/.f32 (pow.f32 tau #s(literal 12 binary32)) (+.f32 (+.f32 (pow.f32 tau #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32)))) (.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32)))) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (pow.f32 tau #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32)))) (.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32)))))
(-.f32 (/.f32 (pow.f32 tau #s(literal 4 binary32)) (.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32)))))
(-.f32 (/.f32 (/.f32 (pow.f32 tau #s(literal 8 binary32)) (+.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (fma.f32 tau tau #s(literal -1 binary32))) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (fma.f32 tau tau #s(literal -1 binary32))))
(-.f32 (/.f32 (/.f32 (pow.f32 tau #s(literal 12 binary32)) (+.f32 (+.f32 (pow.f32 tau #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32)))) (fma.f32 tau tau #s(literal -1 binary32))) (/.f32 (/.f32 #s(literal 1 binary32) (+.f32 (+.f32 (pow.f32 tau #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32)))) (fma.f32 tau tau #s(literal -1 binary32))))
(-.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (+.f32 (pow.f32 tau #s(literal 4 binary32)) (.f32 tau tau)))) (/.f32 (pow.f32 tau #s(literal 6 binary32)) (+.f32 #s(literal 1 binary32) (+.f32 (pow.f32 tau #s(literal 4 binary32)) (.f32 tau tau)))))
(-.f32 (/.f32 (pow.f32 tau #s(literal 8 binary32)) (.f32 (fma.f32 tau tau #s(literal -1 binary32)) (+.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 (fma.f32 tau tau #s(literal -1 binary32)) (+.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)))))
(-.f32 (/.f32 (pow.f32 tau #s(literal 12 binary32)) (.f32 (fma.f32 tau tau #s(literal -1 binary32)) (+.f32 (+.f32 (pow.f32 tau #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32))))) (/.f32 #s(literal 1 binary32) (.f32 (fma.f32 tau tau #s(literal -1 binary32)) (+.f32 (+.f32 (pow.f32 tau #s(literal 8 binary32)) #s(literal 1 binary32)) (pow.f32 tau #s(literal 4 binary32))))))
(-.f32 (/.f32 (pow.f32 tau #s(literal 4 binary32)) (fma.f32 tau tau #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal -1 binary32))))
(-.f32 #s(literal 0 binary32) (/.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1 binary32)))
(-.f32 (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal 1 binary32))) (/.f32 (pow.f32 tau #s(literal 4 binary32)) (fma.f32 tau tau #s(literal 1 binary32))))
(-.f32 #s(literal 1 binary32) (/.f32 (*.f32 tau tau) #s(literal 1 binary32)))
(-.f32 #s(literal 1 binary32) (*.f32 (neg.f32 tau) tau))
(-.f32 #s(literal 1 binary32) (*.f32 tau tau))
(fma.f32 #s(literal -1 binary32) (*.f32 tau tau) #s(literal 1 binary32))
(fma.f32 (*.f32 (neg.f32 tau) tau) #s(literal 1 binary32) #s(literal 1 binary32))
(fma.f32 (neg.f32 tau) (*.f32 tau #s(literal 1 binary32)) #s(literal 1 binary32))
(fma.f32 (neg.f32 tau) (neg.f32 tau) #s(literal 1 binary32))
(fma.f32 (neg.f32 tau) tau #s(literal 1 binary32))
(fma.f32 (*.f32 tau tau) #s(literal 1 binary32) #s(literal 1 binary32))
(fma.f32 tau (*.f32 (neg.f32 tau) #s(literal 1 binary32)) #s(literal 1 binary32))
(fma.f32 tau (*.f32 tau #s(literal 1 binary32)) #s(literal 1 binary32))
(fma.f32 tau (neg.f32 tau) #s(literal 1 binary32))
(fma.f32 tau tau #s(literal 1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 (neg.f32 tau) tau) #s(literal 1 binary32))
(fma.f32 #s(literal 1 binary32) (*.f32 tau tau) #s(literal 1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal -1 binary32))
(pow.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal 1 binary32))
(+.f32 (*.f32 (neg.f32 tau) tau) #s(literal 1 binary32))
(+.f32 (*.f32 tau tau) #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (.f32 (neg.f32 (.f32 (neg.f32 tau) tau)) #s(literal 1 binary32)))
(+.f32 #s(literal 1 binary32) (neg.f32 (*.f32 (neg.f32 tau) tau)))
(+.f32 #s(literal 1 binary32) (*.f32 (neg.f32 tau) tau))
(+.f32 #s(literal 1 binary32) (*.f32 tau tau))
(exp.f32 (neg.f32 (.f32 (log1p.f32 (.f32 tau tau)) #s(literal -1 binary32))))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 5 binary32)) #s(literal 1 binary32)) (cbrt.f32 (PI.f32)))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 4 binary32)) #s(literal 1 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))
(*.f32 (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) (sqrt.f32 (PI.f32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 5 binary32)) (cbrt.f32 (PI.f32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 4 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)))
(*.f32 (sqrt.f32 (PI.f32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 3/2 binary32)) #s(literal 1 binary32)))
(*.f32 (sqrt.f32 (PI.f32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32)))
(.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (pow.f32 (.f32 (cbrt.f32 (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
(.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) (PI.f32)))
(*.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 4 binary32)))
(.f32 (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
(*.f32 (PI.f32) (PI.f32))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32)))
(cbrt.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)))
(sqrt.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)))
(pow.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal 1/3 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal 4 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 3 binary32)) #s(literal 2/3 binary32))
(pow.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal 3 binary32))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal 6 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
(pow.f32 (PI.f32) #s(literal 2 binary32))
(exp.f32 (.f32 (.f32 (log.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal 1 binary32)))
(exp.f32 (.f32 (log.f32 (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)))
(exp.f32 (log.f32 (*.f32 (PI.f32) (PI.f32))))
(exp.f32 (*.f32 (log.f32 (PI.f32)) #s(literal 2 binary32)))

eval284.0ms (2.2%)

Memory: 14.4MiB live, 474.2MiB allocated
Compiler: Compiled 64 200 to 6 200 computations (90.3% saved)

prune172.0ms (1.3%)

Memory

38.6MiB live, 385.3MiB allocated

Pruning

106 alts after pruning (100 fresh and 6 done)

	Pruned	Kept	Total
New	2 507	56	2 563
Fresh	15	44	59
Picked	4	1	5
Done	1	5	6
Total	2 527	106	2 633

Accuracy

99.8%

Counts

2 633 → 106

Alt Table

Click to see full alt table

Status	Accuracy	Program
	65.2%	(/.f32 (/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
	65.3%	(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (PI.f32))
	65.3%	(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32)) (.f32 tau (*.f32 (PI.f32) x)))
	65.2%	(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (.f32 (*.f32 (PI.f32) x) (PI.f32)))
	96.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sqrt.f32 (PI.f32)) x)) (sin.f32 (.f32 x (PI.f32)))) (.f32 (.f32 (sqrt.f32 (PI.f32)) tau) (.f32 x (PI.f32))))
	96.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (cbrt.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x))))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))) (PI.f32))
	98.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (*.f32 (PI.f32) x)))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (sin.f32 (.f32 (.f32 (PI.f32) x) tau))))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	72.4%	(/.f32 (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	97.7%	(/.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (.f32 (PI.f32) x))
	96.4%	(/.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (sin.f32 (.f32 (.f32 (PI.f32) (log.f32 (E.f32))) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	96.2%	(/.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 tau (*.f32 (PI.f32) x)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32))))
	96.7%	(/.f32 (.f32 (.f32 (/.f32 #s(literal 1 binary32) x) (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x)))
	96.8%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x))) x)
	97.8%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (.f32 (.f32 (PI.f32) x) (.f32 (.f32 (neg.f32 x) (PI.f32)) tau)))
	97.0%	(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (neg.f32 x) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)))
	72.5%	(/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) x) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.3%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (.f32 (neg.f32 (PI.f32)) x) tau) x) (/.f32 (neg.f32 (PI.f32)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))))
	97.0%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (.f32 (.f32 tau (.f32 (PI.f32) (PI.f32))) (/.f32 (.f32 x x) (sin.f32 (.f32 (.f32 (PI.f32) x) tau))))))
	66.2%	(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (*.f32 (PI.f32) x)))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) (log.f32 (E.f32)))) (PI.f32)) x)) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	65.2%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 tau (*.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
	65.4%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32))))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32))))
	65.2%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))) (PI.f32)))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))) (PI.f32)))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (PI.f32)))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x)))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) #s(approx ( (* tau (* (PI) x)) (PI)) (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) tau) x)))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	65.2%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	65.3%	(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	72.4%	(/.f32 #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
	65.2%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) tau)))
	65.2%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32))))
	97.2%	(/.f32 #s(literal 1 binary32) (/.f32 (PI.f32) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x))))))
	97.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (/.f32 #s(literal 1 binary32) (PI.f32))))
	72.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32)))
	65.2%	(.f32 (/.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
	65.2%	(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (PI.f32)) #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32))) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 (.f32 (.f32 (PI.f32) x) tau) (PI.f32))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) x))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (.f32 (cbrt.f32 (PI.f32)) tau) x))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))) (*.f32 x (PI.f32))))
✓	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
	72.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) #s(approx (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) #s(literal 1 binary32)))
	96.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/4 binary32)) (.f32 (sqrt.f32 (PI.f32)) x)))) (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 #s(literal 1 binary32) (/.f32 x (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)))))
	72.6%	(.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)))
✓	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	72.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (*.f32 x (PI.f32)))))
	95.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x))) (.f32 x (PI.f32))))
✓	98.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	72.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
✓	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	72.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.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) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (/.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x))) (PI.f32)))
	65.3%	(.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) x) (PI.f32))))
	97.4%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32)))))
	72.6%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32))))
	97.4%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))))
	65.3%	(.f32 (neg.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x)))))
	66.2%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) #s(literal 1 binary32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
	65.5%	#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	96.6%	#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 x x))))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (*.f32 x x) #s(literal 1 binary32)))
	6.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 x x) #s(literal 1 binary32)))
	65.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
	6.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
	8.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (fma.f32 tau tau #s(literal 1 binary32))) (.f32 #s(literal -1 binary32) (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
✓	8.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	8.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (/.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	9.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (neg.f32 tau) tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	9.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 tau tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	7.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal -1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (neg.f32 (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	63.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx ( (neg (- (pow tau 4) 1)) (/ 1 (+ (* (neg tau) tau) 1))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	58.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
	54.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
	65.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	48.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32)))
	37.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
	48.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
	65.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) (*.f32 #s(literal -1/6 binary32) x)) x) (PI.f32) #s(literal 1 binary32))))
	48.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 #s(literal -1/6 binary32) x)) (PI.f32) #s(literal 1 binary32))))
	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (*.f32 x x)) (PI.f32) #s(literal 1 binary32))))
	45.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (*.f32 (PI.f32) x))) (PI.f32) #s(literal 1 binary32))))
	66.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))))
	4.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
	4.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* -1/6 x) x) (PI)) (PI)) 1) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x))))
✓	65.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 5 395 to 1 996 computations (63% saved)

regimes561.0ms (4.3%)

Memory

-96.1MiB live, 790.7MiB allocated

Counts

161 → 1

Calls

Call 1

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

Calls

4 calls:

278.0ms	(*.f32 x (PI.f32))
107.0ms	x
84.0ms	(.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))))
81.0ms	tau

Results

Accuracy	Segments	Branch
98.1%	1	`x`
98.1%	1	`tau`
98.1%	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))))`
98.1%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes252.0ms (1.9%)

Memory

-3.8MiB live, 509.8MiB 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 (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* -1/6 x) x) (PI)) (PI)) 1) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (*.f32 (PI.f32) x))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (*.f32 x x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 #s(literal -1/6 binary32) x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) (*.f32 #s(literal -1/6 binary32) x)) x) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx ( (neg (- (pow tau 4) 1)) (/ 1 (+ (* (neg tau) tau) 1))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (.f32 x x) tau))) (.f32 (PI.f32) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (neg.f32 (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal -1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) #s(approx ( (* tau (* (PI) x)) (PI)) (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) tau) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (.f32 (*.f32 (PI.f32) x) (PI.f32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32)) (.f32 tau (*.f32 (PI.f32) x)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (PI.f32))
(.f32 (neg.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x)))))
(.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) x) (PI.f32))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (PI.f32)) #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) tau)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 tau (*.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))) (PI.f32)))
(/.f32 (/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (/.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (*.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (*.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) x) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) (log.f32 (E.f32)))) (PI.f32)) x)) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) #s(literal 1 binary32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 tau tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (neg.f32 tau) tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (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 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) #s(approx (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) #s(literal 1 binary32)))
(/.f32 #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (/.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (fma.f32 tau tau #s(literal 1 binary32))) (.f32 #s(literal -1 binary32) (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (neg.f32 x) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (.f32 (.f32 (PI.f32) x) (.f32 (.f32 (neg.f32 x) (PI.f32)) tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau x))))
#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 x x))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (/.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x))) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 x (PI.f32)) tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 x (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 (PI.f32) tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (*.f32 x (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

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

Calls

4 calls:

66.0ms	tau
64.0ms	(*.f32 x (PI.f32))
62.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
53.0ms	x

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes263.0ms (2%)

Memory

8.6MiB live, 449.9MiB allocated

Counts

92 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* -1/6 x) x) (PI)) (PI)) 1) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (*.f32 (PI.f32) x))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (*.f32 x x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 #s(literal -1/6 binary32) x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) (*.f32 #s(literal -1/6 binary32) x)) x) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx ( (neg (- (pow tau 4) 1)) (/ 1 (+ (* (neg tau) tau) 1))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (.f32 x x) tau))) (.f32 (PI.f32) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
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#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
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#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal -1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
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#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
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(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
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(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (.f32 (*.f32 (PI.f32) x) (PI.f32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32)) (.f32 tau (*.f32 (PI.f32) x)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (PI.f32))
(.f32 (neg.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x)))))
(.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) x) (PI.f32))))
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(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) tau)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 tau (*.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))) (PI.f32)))
(/.f32 (/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (/.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (*.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
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(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) x) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) (log.f32 (E.f32)))) (PI.f32)) x)) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) #s(literal 1 binary32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 tau tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (neg.f32 tau) tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
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(/.f32 #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (/.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
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#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (neg.f32 x) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)))
(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (.f32 (.f32 (PI.f32) x) (.f32 (.f32 (neg.f32 x) (PI.f32)) tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau x))))
#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (.f32 tau (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 x x))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) x)) (/.f32 (sin.f32 (.f32 tau (*.f32 (PI.f32) x))) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

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

Calls

4 calls:

122.0ms	(*.f32 x (PI.f32))
47.0ms	x
46.0ms	tau
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
97.8%	1	`x`
97.8%	1	`(*.f32 x (PI.f32))`
97.8%	1	`tau`
97.8%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes226.0ms (1.7%)

Memory

-0.6MiB live, 413.7MiB allocated

Counts

85 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* -1/6 x) x) (PI)) (PI)) 1) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (*.f32 (PI.f32) x))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (*.f32 x x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 #s(literal -1/6 binary32) x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) (*.f32 #s(literal -1/6 binary32) x)) x) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx ( (neg (- (pow tau 4) 1)) (/ 1 (+ (* (neg tau) tau) 1))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (.f32 x x) tau))) (.f32 (PI.f32) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (neg.f32 (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal -1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) #s(approx ( (* tau (* (PI) x)) (PI)) (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) tau) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (.f32 (*.f32 (PI.f32) x) (PI.f32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32)) (.f32 tau (*.f32 (PI.f32) x)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (PI.f32))
(.f32 (neg.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x)))))
(.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) x) (PI.f32))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (PI.f32)) #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) tau)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 tau (*.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))) (PI.f32)))
(/.f32 (/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (/.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (*.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (*.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
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(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) x) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) (log.f32 (E.f32)))) (PI.f32)) x)) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) #s(literal 1 binary32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 tau tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (neg.f32 tau) tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (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 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) #s(approx (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) #s(literal 1 binary32)))
(/.f32 #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (/.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (fma.f32 tau tau #s(literal 1 binary32))) (.f32 #s(literal -1 binary32) (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (neg.f32 x) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)))

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

Calls

4 calls:

82.0ms	tau
53.0ms	(.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))))
44.0ms	(*.f32 x (PI.f32))
43.0ms	x

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes240.0ms (1.9%)

Memory

-11.2MiB live, 423.9MiB allocated

Counts

84 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* -1/6 x) x) (PI)) (PI)) 1) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (*.f32 (PI.f32) x))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (*.f32 x x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 #s(literal -1/6 binary32) x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) (*.f32 #s(literal -1/6 binary32) x)) x) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx ( (neg (- (pow tau 4) 1)) (/ 1 (+ (* (neg tau) tau) 1))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (.f32 x x) tau))) (.f32 (PI.f32) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (neg.f32 (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal -1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) #s(approx ( (* tau (* (PI) x)) (PI)) (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) tau) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (.f32 (*.f32 (PI.f32) x) (PI.f32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32)) (.f32 tau (*.f32 (PI.f32) x)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (PI.f32))
(.f32 (neg.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x)))))
(.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) x) (PI.f32))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (PI.f32)) #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) tau)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 tau (*.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))) (PI.f32)))
(/.f32 (/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (/.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (*.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (*.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 (.f32 #s(approx (/ (sin ( (PI) x)) x) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) tau) #s(approx (/ (sin (* x (PI))) (* x (PI))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) (log.f32 (E.f32)))) (PI.f32)) x)) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* (sqrt (PI)) x) (* (sqrt (PI)) tau))) #s(literal 1 binary32)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (*.f32 (sqrt.f32 (PI.f32)) x) (sqrt.f32 (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 tau tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 (.f32 (/.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (.f32 (neg.f32 tau) tau) #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (neg.f32 tau) tau #s(literal 1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (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 (sqrt.f32 (PI.f32)) x) (.f32 (sqrt.f32 (PI.f32)) tau))) #s(approx (/ (sin (* x (PI))) (* (* (sqrt (PI)) x) (sqrt (PI)))) #s(literal 1 binary32)))
(/.f32 #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x)) (.f32 (/.f32 (.f32 (.f32 (neg.f32 x) tau) (PI.f32)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (neg.f32 (PI.f32)) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (neg.f32 (-.f32 (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 0 binary32) (/.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (neg.f32 (fma.f32 tau tau #s(literal 1 binary32))) (.f32 #s(literal -1 binary32) (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32))))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal -1 binary32) (pow.f32 tau #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))

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

Calls

4 calls:

72.0ms	x
64.0ms	(.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))))
57.0ms	tau
43.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
72.6%	1	`x`
72.6%	1	`(*.f32 x (PI.f32))`
72.6%	1	`tau`
72.6%	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 26 to 18 computations (30.8% saved)

regimes195.0ms (1.5%)

Memory

25.2MiB live, 341.6MiB allocated

Counts

69 → 1

Calls

Call 1

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

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

Calls

4 calls:

66.0ms	(*.f32 x (PI.f32))
61.0ms	x
35.0ms	tau
30.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
72.6%	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))))`
72.6%	1	`x`
72.6%	1	`(*.f32 x (PI.f32))`
72.6%	1	`tau`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes234.0ms (1.8%)

Memory

5.5MiB live, 315.6MiB allocated

Counts

66 → 1

Calls

Call 1

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

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

Calls

4 calls:

94.0ms	x
73.0ms	(*.f32 x (PI.f32))
33.0ms	(.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	tau

Results

Accuracy	Segments	Branch
72.6%	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))))`
72.6%	1	`x`
72.6%	1	`(*.f32 x (PI.f32))`
72.6%	1	`tau`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes143.0ms (1.1%)

Memory

-13.7MiB live, 301.2MiB 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 (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* -1/6 x) x) (PI)) (PI)) 1) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (*.f32 (PI.f32) x))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (*.f32 x x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 #s(literal -1/6 binary32) x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) (*.f32 #s(literal -1/6 binary32) x)) x) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx ( (neg (- (pow tau 4) 1)) (/ 1 (+ (* (neg tau) tau) 1))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (.f32 x x) tau))) (.f32 (PI.f32) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (neg.f32 (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal -1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) #s(approx ( (* tau (* (PI) x)) (PI)) (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) tau) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (.f32 (*.f32 (PI.f32) x) (PI.f32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32)) (.f32 tau (*.f32 (PI.f32) x)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (PI.f32))
(.f32 (neg.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x)))))
(.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) x) (PI.f32))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (PI.f32)) #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) tau)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 tau (*.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))) (PI.f32)))
(/.f32 (/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (/.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (*.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (*.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))

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

Calls

4 calls:

38.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
37.0ms	tau
34.0ms	(*.f32 x (PI.f32))
32.0ms	x

Results

Accuracy	Segments	Branch
72.3%	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))))`
72.3%	1	`x`
72.3%	1	`(*.f32 x (PI.f32))`
72.3%	1	`tau`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes148.0ms (1.1%)

Memory

40.8MiB live, 312.5MiB 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 (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* (* (* -1/6 x) x) (PI)) (PI)) 1) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (*.f32 (PI.f32) x))) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (*.f32 x x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) x) (*.f32 #s(literal -1/6 binary32) x)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (PI.f32) (*.f32 #s(literal -1/6 binary32) x)) x) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 #s(literal -1/6 binary32) x) x) (PI.f32)) (PI.f32) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32)) x) x #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx ( (neg (- (pow tau 4) 1)) (/ 1 (+ (* (neg tau) tau) 1))) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(approx (+ ( tau tau) 1) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 (.f32 x x) tau))) (.f32 (PI.f32) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 x (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (PI.f32) (.f32 (.f32 #s(literal -1/6 binary32) (PI.f32)) (fma.f32 tau tau #s(literal 1 binary32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (/ (sin (* (PI) x)) (* (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (neg.f32 (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 #s(literal -1/6 binary32) x)) x #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (+.f32 #s(literal 1 binary32) (.f32 tau tau)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal -1 binary32) (fma.f32 tau tau #s(literal -1 binary32))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 (.f32 #s(literal -1/6 binary32) (fma.f32 tau tau #s(literal 1 binary32))) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 tau tau #s(literal -1 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32)))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) #s(approx ( (* tau (* (PI) x)) (PI)) (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) tau) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (.f32 (.f32 (PI.f32) (PI.f32)) x)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 x tau) (.f32 (PI.f32) (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (PI.f32) x) (.f32 tau (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) tau)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (.f32 (*.f32 (PI.f32) x) (PI.f32)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32)) (.f32 tau (*.f32 (PI.f32) x)))
(/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (PI.f32))
(.f32 (neg.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x))) (/.f32 #s(literal 1 binary32) (.f32 (neg.f32 (PI.f32)) (.f32 tau (.f32 (PI.f32) x)))))
(.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) tau) (/.f32 #s(literal 1 binary32) (.f32 (*.f32 (PI.f32) x) (PI.f32))))
(.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) x))) (PI.f32)) #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) (PI.f32))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (PI.f32) x) (PI.f32)) (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (*.f32 tau (PI.f32)) (PI.f32)) x)) tau)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (*.f32 x (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (PI.f32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 (.f32 tau (*.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (.f32 (PI.f32) x)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 #s(literal -1/6 binary32) (PI.f32))) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau))) (*.f32 x x) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (*.f32 tau (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) x) (PI.f32)))) (PI.f32)))
(/.f32 (/.f32 (/.f32 #s(approx (* (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (/.f32 (/.f32 #s(approx ( (/ (sin (* (PI) x)) x) (sin (* tau (* (PI) x)))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 tau (*.f32 (PI.f32) x))) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (+.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
(/.f32 (sin.f32 (.f32 (PI.f32) x)) #s(approx ( (/ (* (* (neg x) tau) (PI)) (sin (* tau (* (PI) x)))) (* (neg (PI)) x)) (*.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 (-.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (-.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (*.f32 x x) #s(literal 1 binary32)))

Outputs

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

Calls

4 calls:

54.0ms	tau
32.0ms	(*.f32 x (PI.f32))
31.0ms	x
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))))

Results

Accuracy	Segments	Branch
66.6%	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))))`
66.6%	1	`x`
66.6%	1	`(*.f32 x (PI.f32))`
66.6%	1	`tau`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes161.0ms (1.2%)

Memory

-25.7MiB live, 293.5MiB allocated

Accuracy

Total -19.9b remaining (-180.3%)

Threshold costs -19.9b (-180.3%)

Counts

57 → 1

Calls

Call 1

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

46.0ms	(*.f32 x (PI.f32))
32.0ms	x
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))))
26.0ms	tau

Results

Accuracy	Segments	Branch
65.5%	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))))`
65.5%	1	`tau`
65.5%	1	`x`
65.5%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify56.0ms (0.4%)

Memory

-0.0MiB live, 77.2MiB allocated

Algorithm

1×	egg-herbie

Rules

386×	`distribute-lft-neg-in-binary32-*.f32-neg.f32`
196×	`neg-mul-1-binary32-*.f32-neg.f32`
194×	`neg-sub0-binary32--.f32-neg.f32`
160×	`unsub-neg-binary32--.f32-neg.f32-+.f32`
150×	`cancel-sign-sub-binary32-+.f32-neg.f32-*.f32--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	254
1	115	254
2	143	254
3	186	250
4	258	250
5	378	250
6	504	250
7	651	250
8	793	250
9	932	250
10	1042	250
11	1101	250
12	1122	250
13	1127	250
14	1128	250

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

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

soundness1.5s (11.3%)

Memory

26.4MiB live, 1 061.0MiB allocated

Rules

19 182×	`lower-fma.f64`
19 182×	`lower-fma.f32`
19 064×	`lower-fma.f64`
19 064×	`lower-fma.f32`
16 966×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	69	362
0	116	352
1	370	333
2	2385	313
0	8442	300
0	196	1582
1	620	1562
2	2407	1538
3	4137	1538
4	4871	1538
5	5550	1538
6	5940	1538
7	5971	1538
8	5971	1538
0	8816	1486
0	301	6650
1	1009	6520
2	4016	6398
3	7975	6398
0	8177	6192
0	43	248
0	77	234
1	245	234
2	1467	220
0	8566	220
0	300	6888
1	968	6530
2	3587	6262
3	7388	6262
0	8372	6025
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53
0	314	7990
1	1039	7716
2	3948	7558
3	7658	7558
0	8166	7268

Stop Event

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

Compiler

Compiled 988 to 341 computations (65.5% saved)

preprocess186.0ms (1.4%)

Memory

7.4MiB live, 118.3MiB allocated

Remove

(abs x)

(abs tau)

Compiler

Compiled 1 200 to 504 computations (58% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze52.0ms (0.4%)

sample2.6s (20.2%)

explain461.0ms (3.6%)

preprocess79.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify52.0ms (0.4%)

localize52.0ms (0.4%)

series74.0ms (0.6%)

simplify382.0ms (3%)

rewrite260.0ms (2%)

eval227.0ms (1.8%)

prune163.0ms (1.3%)

simplify93.0ms (0.7%)

localize115.0ms (0.9%)

series88.0ms (0.7%)

simplify288.0ms (2.2%)

rewrite427.0ms (3.3%)

eval581.0ms (4.5%)

prune160.0ms (1.2%)

simplify211.0ms (1.6%)

localize134.0ms (1%)

series89.0ms (0.7%)

simplify213.0ms (1.7%)

rewrite242.0ms (1.9%)

eval324.0ms (2.5%)

prune211.0ms (1.6%)

simplify116.0ms (0.9%)

localize146.0ms (1.1%)

series49.0ms (0.4%)

simplify245.0ms (1.9%)

rewrite190.0ms (1.5%)

eval284.0ms (2.2%)

prune172.0ms (1.3%)

regimes561.0ms (4.3%)

regimes252.0ms (1.9%)

regimes263.0ms (2%)

regimes226.0ms (1.7%)

regimes240.0ms (1.9%)

regimes195.0ms (1.5%)

regimes234.0ms (1.8%)

regimes143.0ms (1.1%)

regimes148.0ms (1.1%)

regimes161.0ms (1.2%)

simplify56.0ms (0.4%)

soundness1.5s (11.3%)

preprocess186.0ms (1.4%)

end0.0ms (0%)

Profiling