Metrics for Lanczos kernel

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze30.0ms (0.3%)

Memory

10.7MiB live, 83.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 37 to 21 computations (43.2% saved)

sample1.6s (16.5%)

Memory

7.2MiB live, 2 113.1MiB allocated

Samples

1.3s

8 256×

valid

Precisions

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

const: 209.0ms (20% of total)

ival-sinu: 181.0ms (17.3% of total)

ival-mult: 169.0ms (16.2% of total)

ival-<=: 149.0ms (14.3% of total)

ival-sin: 135.0ms (12.9% of total)

ival-div: 127.0ms (12.2% of total)

ival-pi: 36.0ms (3.4% of total)

ival-and: 24.0ms (2.3% of total)

exact: 9.0ms (0.9% of total)

ival-assert: 4.0ms (0.4% of total)

Bogosity

explain121.0ms (1.2%)

Memory

-4.9MiB live, 198.6MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sin.f32`	`(sin.f32 (*.f32 x (PI.f32)))`	cancellation	1	0

Confusion

	Predicted +	Predicted -
+	1	2
-	0	253

Precision

1.0

Recall

0.3333333333333333

Confusion?

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

Precision?

1.0

Recall?

0.3333333333333333

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

49.0ms

512×

valid

Compiler

Compiled 149 to 34 computations (77.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 10.0ms (29.1% of total)

ival-sinu: 8.0ms (23.3% of total)

ival-sin: 8.0ms (23.3% of total)

ival-div: 6.0ms (17.5% of total)

ival-pi: 2.0ms (5.8% of total)

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

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

preprocess69.0ms (0.7%)

Memory

23.7MiB live, 62.9MiB allocated

Algorithm

1×	egg-herbie

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

prune0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.9%	(.f32 (/.f32 (sin.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)

simplify21.0ms (0.2%)

Memory

-22.1MiB live, 17.3MiB 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))))

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))

localize33.0ms (0.3%)

Memory

9.6MiB live, 48.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.30859375	(*.f32 x (PI.f32))
accuracy	0.3248188718519597	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.3737488281475362	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.42224506837909415	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

Samples

24.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 5.0ms (29.4% of total)

ival-sinu: 4.0ms (23.5% of total)

ival-sin: 4.0ms (23.5% of total)

ival-div: 3.0ms (17.6% of total)

ival-pi: 1.0ms (5.9% of total)

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

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

series35.0ms (0.3%)

Memory

12.1MiB live, 52.5MiB allocated

Counts

6 → 120

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	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)))
7.0ms	x	@	-inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
5.0ms	tau	@	-inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
4.0ms	tau	@	inf	((* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (* x (PI)) tau) (/ (sin (* x (PI))) (* x (PI))) (* x (PI)))
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)))

simplify224.0ms (2.3%)

Memory

5.2MiB live, 237.4MiB allocated

Algorithm

1×	egg-herbie

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

rewrite135.0ms (1.4%)

Memory

-3.0MiB live, 239.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

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

Counts

6 → 670

Calls

Call 1

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

Outputs
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eval91.0ms (0.9%)

Memory: 3.1MiB live, 233.3MiB allocated
Compiler: Compiled 24 307 to 2 341 computations (90.4% saved)

prune112.0ms (1.1%)

Memory

-13.4MiB live, 255.5MiB allocated

Pruning

44 alts after pruning (43 fresh and 1 done)

	Pruned	Kept	Total
New	970	43	1 013
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	970	44	1 014

Accuracy

99.8%

Counts

1 014 → 44

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.2%	(/.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (PI.f32)) (.f32 tau x))
	97.3%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) tau) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32)))
	96.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (.f32 (/.f32 (.f32 tau (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (*.f32 (PI.f32) x)))) (cbrt.f32 (PI.f32))))
	97.8%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))))
	97.9%	(/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (/.f32 (.f32 tau (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (PI.f32))))
	96.2%	(/.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))))
	96.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (.f32 (cbrt.f32 (PI.f32)) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))))
	97.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 tau (.f32 (PI.f32) x))) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (*.f32 (PI.f32) x))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) (neg.f32 tau)))
	97.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) tau)) (.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))
▶	98.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (PI.f32)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x))) (.f32 tau x))
▶	97.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.5%	(/.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)))
	96.9%	(/.f32 (.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) x)) (.f32 (PI.f32) (*.f32 tau (PI.f32))))
	97.3%	(/.f32 (.f32 (.f32 (sin.f32 (.f32 (PI.f32) x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (.f32 (.f32 tau (.f32 (PI.f32) x)) 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)))
	97.4%	(.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)))))
	97.5%	(.f32 (/.f32 (.f32 (/.f32 #s(literal 1 binary32) tau) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.2%	(.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)) x) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) x))
	95.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (cbrt.f32 (PI.f32)))) (.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 (.f32 (sqrt.f32 (PI.f32)) x) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (*.f32 x (PI.f32))))
✓	97.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (cbrt.f32 (PI.f32)) x))))
	97.8%	(.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))))
	68.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (PI.f32)) x)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.7%	(.f32 (/.f32 (sin.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 (.f32 (sqrt.f32 (PI.f32)) tau) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.5%	(.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)))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (/.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) x)) tau) (/.f32 (PI.f32) (sin.f32 (*.f32 (PI.f32) x)))))
▶	97.5%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (PI.f32) (sin.f32 (.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 #s(literal 1 binary32) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32))))
	97.3%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) x)) (neg.f32 tau))))
	60.8%	#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)))
	61.7%	#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))))
▶	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 913 to 1 118 computations (41.6% saved)

simplify129.0ms (1.3%)

Memory

-0.0MiB live, 77.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	317
0	62	315
1	134	315
2	353	315
3	1196	315
4	2457	315
5	2677	315
6	2694	315
7	2694	315
8	3376	315
9	4034	315
10	4323	315
11	4323	315
12	4448	315
13	5447	315
14	5455	315
15	5455	315
16	5455	315
0	5455	315

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize98.0ms (1%)

Memory

-14.8MiB live, 181.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.3248188718519597	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.37109375	(/.f32 (PI.f32) (sin.f32 (*.f32 (PI.f32) x)))
accuracy	0.4091987793053261	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (PI.f32) (sin.f32 (.f32 (PI.f32) x)))))
accuracy	0.42224506837909415	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.30859375	(*.f32 x (PI.f32))
accuracy	0.3248188718519597	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.37890625	(/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))
accuracy	0.42224506837909415	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.3248188718519597	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.33041000976844204	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x)))
accuracy	0.34898378907376804	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
accuracy	0.44826127930532605	(.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32))
accuracy	12.531046195681988	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
accuracy	0.3248188718519597	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.33203125	(/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
accuracy	0.33984375	(/.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)))
accuracy	0.34994125976844204	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (*.f32 (PI.f32) x)))

Samples

71.0ms

256×

valid

Compiler

Compiled 317 to 31 computations (90.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-div: 25.0ms (45.8% of total)

ival-mult: 16.0ms (29.3% of total)

ival-sin: 8.0ms (14.7% of total)

ival-sinu: 4.0ms (7.3% of total)

ival-pi: 1.0ms (1.8% of total)

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

exact: 0.0ms (0% of total)

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

series45.0ms (0.5%)

Memory

9.1MiB live, 88.5MiB allocated

Counts

20 → 420

Calls

Call 1

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

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

6 calls:

Time	Variable		Point	Expression
7.0ms	tau	@	-inf	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (/ (sin (* (PI) x)) (PI)) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (/ (sin (* (PI) x)) (PI)) x)) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ 1 x) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x))))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x)))) (/ 1 x) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (* tau (* (PI) x)) (PI)) (/ (sin (* (PI) x)) (PI)) (* x (PI)) (/ (PI) (sin (* (PI) x))))
6.0ms	x	@	-inf	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (/ (sin (* (PI) x)) (PI)) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (/ (sin (* (PI) x)) (PI)) x)) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ 1 x) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x))))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x)))) (/ 1 x) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (* tau (* (PI) x)) (PI)) (/ (sin (* (PI) x)) (PI)) (* x (PI)) (/ (PI) (sin (* (PI) x))))
4.0ms	tau	@	inf	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (/ (sin (* (PI) x)) (PI)) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (/ (sin (* (PI) x)) (PI)) x)) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ 1 x) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x))))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x)))) (/ 1 x) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (* tau (* (PI) x)) (PI)) (/ (sin (* (PI) x)) (PI)) (* x (PI)) (/ (PI) (sin (* (PI) x))))
4.0ms	x	@	inf	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (/ (sin (* (PI) x)) (PI)) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (/ (sin (* (PI) x)) (PI)) x)) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ 1 x) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x))))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x)))) (/ 1 x) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (* tau (* (PI) x)) (PI)) (/ (sin (* (PI) x)) (PI)) (* x (PI)) (/ (PI) (sin (* (PI) x))))
4.0ms	x	@	0	((/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* tau (* (PI) x))) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/ (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (* (* tau (* (PI) x)) (PI))) (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (/ (sin (* tau (* (PI) x))) x) (/ (/ (sin (* (PI) x)) (PI)) x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (/ (sin (* (PI) x)) (PI)) x)) (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau)) (* (/ 1 x) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x))))) (/ (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x)))) (/ 1 x) (/ (sin (* tau (* (PI) x))) (* tau (* (PI) x))) (* (* tau (* (PI) x)) (PI)) (/ (sin (* (PI) x)) (PI)) (* x (PI)) (/ (PI) (sin (* (PI) x))))

simplify238.0ms (2.4%)

Memory

7.8MiB live, 319.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	441	7470
1	1493	7269
2	5843	7052
0	8029	6800

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 416

Calls

Call 1

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

rewrite155.0ms (1.6%)

Memory

-10.9MiB live, 224.4MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	243
0	62	241
1	247	241
2	1664	231
3	6712	231
0	8318	231

Stop Event

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

Counts

20 → 1 791

Calls

Call 1

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

Outputs
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eval291.0ms (2.9%)

Memory: 48.7MiB live, 351.3MiB allocated
Compiler: Compiled 55 563 to 2 789 computations (95% saved)

prune140.0ms (1.4%)

Memory

-8.4MiB live, 304.9MiB allocated

Pruning

49 alts after pruning (45 fresh and 4 done)

	Pruned	Kept	Total
New	2 285	30	2 315
Fresh	23	15	38
Picked	1	4	5
Done	1	0	1
Total	2 310	49	2 359

Accuracy

99.8%

Counts

2 359 → 49

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (.f32 (.f32 (PI.f32) tau) (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))))
	97.7%	(/.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)))
	96.2%	(/.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))))
	96.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (.f32 (cbrt.f32 (PI.f32)) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) (neg.f32 tau)))
	97.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (PI.f32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (.f32 (neg.f32 tau) (PI.f32)) (*.f32 x x)))
✓	98.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
	96.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) x) tau))
	96.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (*.f32 (PI.f32) tau) (PI.f32)) x))
▶	97.4%	(/.f32 (.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
	61.6%	(/.f32 (.f32 (/.f32 #s(approx (sin ( tau (* (PI) x))) (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	61.5%	(/.f32 (.f32 #s(approx (/ (sin ( tau (* (PI) x))) x) (.f32 tau (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
	97.2%	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (.f32 (PI.f32) tau) (/.f32 (.f32 x (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))) x))
	97.8%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (/.f32 (.f32 (.f32 x (PI.f32)) tau) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (*.f32 x (PI.f32))))
	97.8%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (*.f32 x (PI.f32)) tau)))
	61.7%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))
	60.7%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	97.1%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (.f32 x (PI.f32)) tau) x) (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	97.3%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32))) (sin.f32 (*.f32 x (PI.f32))))
	96.7%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (.f32 (.f32 (PI.f32) (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) tau))
▶	97.8%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
	97.4%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32)) (.f32 (.f32 (.f32 x (PI.f32)) tau) x)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) x))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) x))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.2%	(.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)) x) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
✓	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) x))
	95.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x) (cbrt.f32 (PI.f32)))) (.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 (.f32 (sqrt.f32 (PI.f32)) x) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (*.f32 x (PI.f32))))
	96.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (cbrt.f32 (PI.f32)) x))))
	30.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( (PI) x)) (PI)) x) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
	68.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( (PI) x)) (PI)) x) #s(literal 1 binary32)))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau (PI.f32)) x)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.7%	(.f32 (/.f32 (sin.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 (.f32 (sqrt.f32 (PI.f32)) tau) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	97.0%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (*.f32 (PI.f32) x)))))
✓	97.5%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) (/.f32 (PI.f32) (sin.f32 (.f32 (PI.f32) x)))))
	68.2%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) #s(approx (/ (PI) (sin ( (PI) x))) (/.f32 #s(literal 1 binary32) x))))
	96.9%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) tau) (sin.f32 (.f32 x (PI.f32)))) (.f32 (*.f32 (PI.f32) (PI.f32)) x)))
	61.5%	(.f32 (/.f32 #s(literal 1 binary32) x) #s(approx (/ (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x)))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
	97.5%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32))))
	97.3%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) x)) (neg.f32 tau))))
	96.9%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (PI.f32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (neg.f32 tau) (PI.f32)) (.f32 x x))))
	61.6%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) x))
	61.7%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
▶	96.9%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
▶	60.8%	#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)))
✓	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 2 009 to 1 223 computations (39.1% saved)

simplify117.0ms (1.2%)

Memory

11.6MiB live, 122.8MiB 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	160	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (*.f32 (PI.f32) x)))))
cost-diff	192	(/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (*.f32 (PI.f32) tau)) x)
cost-diff	192	(/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (.f32 (PI.f32) x))))
cost-diff	0	(sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x))
cost-diff	0	(/.f32 (neg.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x))) (*.f32 (PI.f32) x))
cost-diff	0	(/.f32 (.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
cost-diff	128	(neg.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x)))
cost-diff	0	(.f32 tau (.f32 (PI.f32) x))
cost-diff	0	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)))
cost-diff	0	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (/.f32 (sin.f32 (*.f32 (PI.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 (PI.f32))
cost-diff	0	(sin.f32 (*.f32 x (PI.f32)))
cost-diff	0	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
cost-diff	0	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	461
0	106	455
1	225	455
2	582	455
3	2174	451
4	3421	451
5	7303	451
0	8131	451

Stop Event

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

Calls

Call 1

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

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

localize234.0ms (2.4%)

Memory

-28.1MiB live, 219.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.33984375	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (*.f32 (PI.f32) tau))
accuracy	0.359375	(*.f32 (PI.f32) tau)
accuracy	0.37109375	(/.f32 (PI.f32) (sin.f32 (*.f32 (PI.f32) x)))
accuracy	0.4091987793053261	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (*.f32 (PI.f32) x)))))
accuracy	0.33203125	(/.f32 (neg.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x))) (*.f32 (PI.f32) x))
accuracy	0.33984375	(/.f32 (.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (*.f32 (PI.f32) x)))
accuracy	0.34994125976844204	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x))) (.f32 (PI.f32) x)) (sin.f32 (*.f32 (PI.f32) x)))
accuracy	0.359375	(*.f32 (neg.f32 tau) (PI.f32))
accuracy	0.32421875	(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
accuracy	0.3248188718519597	(sin.f32 (.f32 tau (.f32 (PI.f32) x)))
accuracy	0.37890625	(/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))
accuracy	0.39681625976844204	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	7.9729143347231215	#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	19.36614306273412	(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	27.205774392122226	(fma.f32 tau tau #s(literal 1 binary32))
accuracy	0.3248188718519597	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.32650375976844204	(/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.3737488281475362	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.4716987793053261	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))

Samples

191.0ms

256×

valid

Compiler

Compiled 429 to 50 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 172.0ms

ival-sinu: 62.0ms (36.1% of total)

ival-mult: 54.0ms (31.4% of total)

ival-div: 31.0ms (18% of total)

ival-sin: 13.0ms (7.6% of total)

ival-neg: 5.0ms (2.9% of total)

const: 4.0ms (2.3% of total)

ival-add: 2.0ms (1.2% of total)

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

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

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

exact: 0.0ms (0% of total)

series79.0ms (0.8%)

Memory

28.4MiB live, 137.4MiB allocated

Counts

30 → 576

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	tau	@	0	((/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* x (PI)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (* (* x x) tau) (PI))) (/ (sin (* (PI) x)) (PI))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (neg (sin (* (* (neg tau) (PI)) x))) (/ (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (* (neg tau) (PI)) x)) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x)))) (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (* (/ 1 x) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x))))) (/ 1 x) (* (/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau))) (sin (* (* x (PI)) tau)) (* (PI) (PI)) (/ (sin (* (PI) x)) (PI)) (* (* (* x x) tau) (PI)) (* (neg tau) (PI)) (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (/ (PI) (sin (* (PI) x))) (* (PI) tau) (/ (sin (* (* x (PI)) tau)) (* (PI) tau)))
10.0ms	tau	@	inf	((/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* x (PI)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (* (* x x) tau) (PI))) (/ (sin (* (PI) x)) (PI))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (neg (sin (* (* (neg tau) (PI)) x))) (/ (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (* (neg tau) (PI)) x)) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x)))) (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (* (/ 1 x) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x))))) (/ 1 x) (* (/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau))) (sin (* (* x (PI)) tau)) (* (PI) (PI)) (/ (sin (* (PI) x)) (PI)) (* (* (* x x) tau) (PI)) (* (neg tau) (PI)) (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (/ (PI) (sin (* (PI) x))) (* (PI) tau) (/ (sin (* (* x (PI)) tau)) (* (PI) tau)))
10.0ms	x	@	inf	((/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* x (PI)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (* (* x x) tau) (PI))) (/ (sin (* (PI) x)) (PI))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (neg (sin (* (* (neg tau) (PI)) x))) (/ (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (* (neg tau) (PI)) x)) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x)))) (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (* (/ 1 x) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x))))) (/ 1 x) (* (/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau))) (sin (* (* x (PI)) tau)) (* (PI) (PI)) (/ (sin (* (PI) x)) (PI)) (* (* (* x x) tau) (PI)) (* (neg tau) (PI)) (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (/ (PI) (sin (* (PI) x))) (* (PI) tau) (/ (sin (* (* x (PI)) tau)) (* (PI) tau)))
7.0ms	x	@	-inf	((/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* x (PI)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (* (* x x) tau) (PI))) (/ (sin (* (PI) x)) (PI))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (neg (sin (* (* (neg tau) (PI)) x))) (/ (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (* (neg tau) (PI)) x)) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x)))) (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (* (/ 1 x) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x))))) (/ 1 x) (* (/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau))) (sin (* (* x (PI)) tau)) (* (PI) (PI)) (/ (sin (* (PI) x)) (PI)) (* (* (* x x) tau) (PI)) (* (neg tau) (PI)) (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (/ (PI) (sin (* (PI) x))) (* (PI) tau) (/ (sin (* (* x (PI)) tau)) (* (PI) tau)))
7.0ms	tau	@	-inf	((/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))) (sin (* x (PI))) (* x (PI)) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (+ (* tau tau) 1) (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (* (/ (sin (* tau (* (PI) x))) (* (* (* x x) tau) (PI))) (/ (sin (* (PI) x)) (PI))) (sin (* tau (* (PI) x))) (* tau (* (PI) x)) (neg (sin (* (* (neg tau) (PI)) x))) (/ (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (* (neg tau) (PI)) x)) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x)))) (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (* (/ 1 x) (/ (/ (/ (sin (* (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x))))) (/ 1 x) (* (/ (/ (sin (* x (PI))) (* x (PI))) (* (* x (PI)) tau)) (sin (* (* x (PI)) tau))) (sin (* (* x (PI)) tau)) (* (PI) (PI)) (/ (sin (* (PI) x)) (PI)) (* (* (* x x) tau) (PI)) (* (neg tau) (PI)) (* (/ (neg (sin (* (* (neg tau) (PI)) x))) (* (PI) x)) (sin (* (PI) x))) (/ (PI) (sin (* (PI) x))) (* (PI) tau) (/ (sin (* (* x (PI)) tau)) (* (PI) tau)))

simplify244.0ms (2.5%)

Memory

13.8MiB live, 281.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	540	9293
1	1907	8991
2	4321	8805
3	7537	8805
0	8604	8505

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 570

Calls

Call 1

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

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

rewrite242.0ms (2.4%)

Memory

9.7MiB live, 293.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	360
0	106	356
1	373	356
2	2579	334
0	8389	332

Stop Event

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

Counts

30 → 3 317

Calls

Call 1

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

Outputs
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eval380.0ms (3.8%)

Memory: 41.5MiB live, 701.0MiB allocated
Compiler: Compiled 99 367 to 5 914 computations (94% saved)

prune243.0ms (2.5%)

Memory

-25.7MiB live, 519.7MiB allocated

Pruning

81 alts after pruning (78 fresh and 3 done)

	Pruned	Kept	Total
New	3 967	56	4 023
Fresh	18	22	40
Picked	4	1	5
Done	2	2	4
Total	3 991	81	4 072

Accuracy

99.8%

Counts

4 072 → 81

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.5%	(/.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 (.f32 tau x) (PI.f32)))) (PI.f32)) (.f32 tau (.f32 (PI.f32) x)))
	97.2%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))) (PI.f32)) (.f32 (.f32 x x) tau))
▶	97.4%	(/.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 tau (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) x))
	97.7%	(/.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)))
	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))) x)
	96.1%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) x)) (neg.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))))) (.f32 (cbrt.f32 (PI.f32)) (.f32 (.f32 (neg.f32 x) tau) (PI.f32))))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)) (sin.f32 (.f32 (.f32 tau x) (PI.f32)))) (.f32 tau (*.f32 (PI.f32) x)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) (neg.f32 tau)))
	97.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (PI.f32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (.f32 (neg.f32 tau) (PI.f32)) (*.f32 x x)))
	96.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) x) tau))
	96.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (*.f32 (PI.f32) tau) (PI.f32)) x))
	96.9%	(/.f32 (.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (.f32 (.f32 (neg.f32 tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
	97.8%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x) (.f32 (PI.f32) x)))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (PI.f32)))
	97.9%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32))))
▶	98.0%	(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (*.f32 tau x) (PI.f32))))
	97.8%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (*.f32 x (PI.f32)) tau)))
	61.7%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))
	60.7%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	96.8%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (neg.f32 (PI.f32))) (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))))
	97.1%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (.f32 x (PI.f32)) tau) x) (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	97.5%	(.f32 (/.f32 (/.f32 (sin.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	95.8%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (cbrt.f32 (PI.f32)))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	97.3%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32))) (sin.f32 (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x)) tau)))
	61.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (.f32 (PI.f32) x))))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) x))
	96.2%	(.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)) x) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
✓	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) x))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (*.f32 x (PI.f32))))
	96.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (cbrt.f32 (PI.f32)) x))))
	68.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( (PI) x)) (PI)) x) #s(literal 1 binary32)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.7%	(.f32 (/.f32 (sin.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 (.f32 (sqrt.f32 (PI.f32)) tau) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	97.2%	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	68.2%	(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)) (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x)) tau)) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (.f32 (PI.f32) x)))))
✓	97.0%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (*.f32 (PI.f32) x)))))
	68.0%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) #s(approx (/ (PI) (sin (* (PI) x))) (/.f32 #s(literal 1 binary32) x))))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) (.f32 (/.f32 (.f32 tau (PI.f32)) (sin.f32 (.f32 (.f32 tau x) (PI.f32)))) x)))
	68.2%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) #s(approx (/ (PI) (sin ( (PI) x))) (/.f32 #s(literal 1 binary32) x))))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x)) (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (*.f32 (neg.f32 tau) (PI.f32)) x) (PI.f32)))))
	97.4%	(.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 (PI.f32) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau x) (PI.f32))))))
	61.5%	(.f32 (/.f32 #s(literal 1 binary32) x) #s(approx (/ (/ (/ (sin ( (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x)))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
	97.6%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 (.f32 tau x) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (.f32 tau x) (PI.f32)))))
	96.9%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (PI.f32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (neg.f32 tau) (PI.f32)) (.f32 x x))))
	97.5%	(.f32 (.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x)) (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x) (*.f32 (PI.f32) x))))
	97.0%	(.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (*.f32 x x) tau) (PI.f32)) (PI.f32))))
	97.2%	(.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (PI.f32))))
	97.8%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (PI.f32) x)) (.f32 (*.f32 tau x) (PI.f32))))
	26.9%	(.f32 #s(approx (/ (/ (sin ( x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/.f32 (fma.f32 (/.f32 (.f32 (.f32 x x) (PI.f32)) tau) #s(literal -1/6 binary32) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
	96.8%	(.f32 #s(approx (/ (/ (sin ( x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x x)) (.f32 tau (.f32 (PI.f32) (PI.f32))))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	61.6%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) x))
	61.7%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
	31.0%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #s(approx (/ (sin (* (PI) x)) (PI)) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) x))))
	96.8%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (*.f32 (PI.f32) (PI.f32)) tau))))
	61.4%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 #s(approx (sin ( tau (* (PI) x))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))))
▶	8.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
	8.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 #s(literal 1 binary32) (/.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 -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (.f32 x x) #s(literal 1 binary32)))
	60.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (.f32 x x) #s(literal 1 binary32)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (.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)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau (.f32 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)))
	60.8%	#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 (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) #s(literal -1/6 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 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (sqrt.f32 (PI.f32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	60.8%	#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)))
	4.1%	#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 (exp.f32 (.f32 (log.f32 (PI.f32)) #s(literal 2 binary32))) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal 1 binary32) (.f32 tau tau) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	60.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (+.f32 (.f32 tau tau) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	60.7%	#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)))
	60.8%	#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)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 x x)) #s(literal 1 binary32)))
	60.8%	#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)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
	60.7%	#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)))
	60.8%	#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)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
	60.7%	#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 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
	7.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(literal 1 binary32) (.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)))
	34.3%	#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)))
▶	58.0%	#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 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (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 (PI.f32) (PI.f32)) (.f32 x x)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))))
	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 tau)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x x)))))
✓	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 3 234 to 2 132 computations (34.1% saved)

simplify175.0ms (1.8%)

Memory

-4.2MiB live, 107.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	409
0	89	407
1	189	382
2	566	380
3	2787	380
4	4673	380
5	7774	380
0	8318	377

Stop Event

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

Calls

Call 1

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

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

localize174.0ms (1.7%)

Memory

26.8MiB live, 222.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.33984375	(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (*.f32 tau (PI.f32)))
accuracy	0.359375	(*.f32 tau (PI.f32))
accuracy	0.3600387695368841	(/.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 tau (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) x))
accuracy	0.375	(.f32 (.f32 tau x) (PI.f32))
accuracy	0.3248188718519597	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.37337875976844204	(/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (*.f32 (neg.f32 x) (PI.f32))))
accuracy	0.375	(.f32 (.f32 tau x) (PI.f32))
accuracy	0.4716987793053261	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
accuracy	0.47169877930532605	(pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))
accuracy	7.9729143347231215	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
accuracy	20.755393608369786	(fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32))
accuracy	26.598636330307926	(fma.f32 tau tau #s(literal 1 binary32))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	7.9729143347231215	#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 x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
accuracy	12.560526370869002	#s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)))
accuracy	19.056837624477577	(fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
accuracy	0.30859375	(*.f32 (PI.f32) x)
accuracy	0.3248188718519597	(sin.f32 (.f32 (.f32 tau x) (PI.f32)))
accuracy	0.375	(.f32 (.f32 tau x) (PI.f32))
accuracy	0.3912887695368841	(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (*.f32 tau x) (PI.f32))))

Samples

120.0ms

256×

valid

Compiler

Compiled 363 to 47 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 101.0ms

ival-mult: 59.0ms (58.2% of total)

ival-div: 13.0ms (12.8% of total)

ival-sinu: 9.0ms (8.9% of total)

ival-add: 7.0ms (6.9% of total)

ival-sin: 4.0ms (3.9% of total)

const: 4.0ms (3.9% of total)

ival-pow2: 3.0ms (3% of total)

ival-neg: 2.0ms (2% of total)

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

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

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

exact: 0.0ms (0% of total)

series48.0ms (0.5%)

Memory

14.0MiB live, 51.8MiB allocated

Counts

24 → 432

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((/ (sin (* (* tau x) (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) (* (* tau x) (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* -1/6 (* x x)) (* x x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2))) 1) (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2)) (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (* (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (sin (* (* x (PI)) tau))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (PI) x) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* (PI) (PI)) (pow (* (PI) x) 2) (sin (* (* x (PI)) tau)) (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (* tau (PI)))
4.0ms	tau	@	-inf	((/ (sin (* (* tau x) (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) (* (* tau x) (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* -1/6 (* x x)) (* x x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2))) 1) (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2)) (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (* (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (sin (* (* x (PI)) tau))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (PI) x) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* (PI) (PI)) (pow (* (PI) x) 2) (sin (* (* x (PI)) tau)) (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (* tau (PI)))
4.0ms	x	@	-inf	((/ (sin (* (* tau x) (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) (* (* tau x) (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* -1/6 (* x x)) (* x x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2))) 1) (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2)) (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (* (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (sin (* (* x (PI)) tau))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (PI) x) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* (PI) (PI)) (pow (* (PI) x) 2) (sin (* (* x (PI)) tau)) (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (* tau (PI)))
3.0ms	tau	@	inf	((/ (sin (* (* tau x) (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) (* (* tau x) (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* -1/6 (* x x)) (* x x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2))) 1) (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2)) (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (* (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (sin (* (* x (PI)) tau))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (PI) x) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* (PI) (PI)) (pow (* (PI) x) 2) (sin (* (* x (PI)) tau)) (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (* tau (PI)))
3.0ms	tau	@	0	((/ (sin (* (* tau x) (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) (* (* tau x) (PI)))) (sin (* (* tau x) (PI))) (* (* tau x) (PI)) (* tau x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (* -1/6 (* x x)) (* x x) (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+ (* (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2))) 1) (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2)) (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (* (/ (neg (sin (* (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (sin (* (* x (PI)) tau))) (neg (sin (* (PI) x))) (sin (* (PI) x)) (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (PI) x) (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (* (PI) (PI)) (pow (* (PI) x) 2) (sin (* (* x (PI)) tau)) (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (* tau (PI)))

simplify527.0ms (5.3%)

Memory

-213.9MiB live, 253.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	279	6375
1	890	6035
2	3245	5915
3	5862	5911
0	8159	5654

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 430

Calls

Call 1

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

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

rewrite179.0ms (1.8%)

Memory

57.0MiB live, 306.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	287
0	89	285
1	320	264
2	2096	262
0	8376	259

Stop Event

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

Counts

24 → 1 264

Calls

Call 1

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

Outputs
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eval404.0ms (4.1%)

Memory: -12.6MiB live, 460.7MiB allocated
Compiler: Compiled 52 936 to 3 610 computations (93.2% saved)

prune160.0ms (1.6%)

Memory

21.4MiB live, 340.8MiB allocated

Pruning

98 alts after pruning (94 fresh and 4 done)

	Pruned	Kept	Total
New	2 233	36	2 269
Fresh	15	58	73
Picked	4	1	5
Done	0	3	3
Total	2 252	98	2 350

Accuracy

99.8%

Counts

2 350 → 98

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.5%	(/.f32 (/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 (.f32 tau x) (PI.f32)))) (PI.f32)) (.f32 tau (.f32 (PI.f32) x)))
	97.2%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))) (PI.f32)) (.f32 (.f32 x x) tau))
	97.4%	(/.f32 (/.f32 (.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (.f32 (PI.f32) x))) (.f32 x tau)) (.f32 (*.f32 (neg.f32 x) (PI.f32)) (PI.f32)))
	95.9%	(/.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 tau (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (*.f32 (cbrt.f32 (PI.f32)) x)))) x))
	96.9%	(/.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 tau (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) x)) (sqrt.f32 (.f32 (PI.f32) x))))) x))
	68.0%	(/.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 tau (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin ( (PI) x)) (*.f32 (PI.f32) x))) x))
	97.2%	(/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) x) x)) (/.f32 (.f32 (PI.f32) tau) (sin.f32 (.f32 (PI.f32) (.f32 x tau)))))
	97.7%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))) x)
	98.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (*.f32 x tau)))
	97.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (neg.f32 x)) (sin.f32 (.f32 tau (.f32 (PI.f32) x)))) (.f32 (.f32 (PI.f32) (*.f32 (PI.f32) x)) (neg.f32 tau)))
	97.0%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (PI.f32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (.f32 (neg.f32 tau) (PI.f32)) (*.f32 x x)))
	96.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (*.f32 (PI.f32) (PI.f32)) x) tau))
	96.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (*.f32 (PI.f32) tau) (PI.f32)) x))
	96.9%	(/.f32 (.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (.f32 (.f32 (neg.f32 tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) x))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x)))
	97.8%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x) (.f32 (PI.f32) x)))
	97.1%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (PI.f32)))
	95.8%	(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32)) (.f32 (cbrt.f32 (PI.f32)) x)))) (.f32 (.f32 tau x) (PI.f32))))
	68.2%	(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x))) (.f32 (*.f32 tau x) (PI.f32))))
	97.8%	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (/.f32 (.f32 x (PI.f32)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (.f32 (*.f32 x (PI.f32)) tau)))
	61.7%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))
	60.7%	(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 tau (PI.f32)) (PI.f32)) x)) (.f32 (.f32 tau (.f32 (PI.f32) x)) (PI.f32)))
	61.5%	(/.f32 #s(approx (sin (* (* tau x) (PI))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (*.f32 tau x) (PI.f32))))
	96.8%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (neg.f32 (PI.f32))) (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (neg.f32 (sin.f32 (.f32 (PI.f32) x))))))
	97.1%	(/.f32 #s(literal 1 binary32) (/.f32 (.f32 (.f32 (.f32 x (PI.f32)) tau) x) (.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (PI.f32)) (sin.f32 (*.f32 x (PI.f32))))))
	97.5%	(.f32 (/.f32 (/.f32 (sin.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	97.3%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) x) (.f32 (.f32 (.f32 x (PI.f32)) tau) (PI.f32))) (sin.f32 (*.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x)) tau)))
	61.6%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (.f32 (PI.f32) x))))
	97.5%	(.f32 (/.f32 (sin.f32 (.f32 (/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) x)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) x))
	96.2%	(.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)) x) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
✓	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32)) x))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (.f32 (.f32 (sqrt.f32 (PI.f32)) x) (cbrt.f32 (PI.f32))) (pow.f32 (PI.f32) #s(literal 1/6 binary32)))) (*.f32 x (PI.f32))))
	96.4%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (pow.f32 (cbrt.f32 (PI.f32)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (cbrt.f32 (PI.f32)) x))))
	68.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( (PI) x)) (PI)) x) #s(literal 1 binary32)))
	96.7%	(.f32 (/.f32 (sin.f32 (.f32 (sqrt.f32 (PI.f32)) (.f32 (.f32 (sqrt.f32 (PI.f32)) tau) x))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.1%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (*.f32 (PI.f32) x) x)))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) (PI.f32)))
	96.8%	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (sqrt.f32 (.f32 (PI.f32) x)) (sqrt.f32 (.f32 (PI.f32) x))))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	97.6%	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) tau) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
✓	97.2%	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	97.7%	(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	67.9%	(.f32 (/.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
	68.2%	(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)) (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	97.6%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) x)) (sin.f32 (.f32 (PI.f32) x))))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (/.f32 (PI.f32) (/.f32 #s(literal 1 binary32) x)) tau)) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (.f32 (PI.f32) x)))))
✓	97.0%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) (/.f32 (PI.f32) (sin.f32 (*.f32 (PI.f32) x)))))
	68.0%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) #s(approx (/ (PI) (sin (* (PI) x))) (/.f32 #s(literal 1 binary32) x))))
	68.2%	(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) #s(approx (/ (PI) (sin ( (PI) x))) (/.f32 #s(literal 1 binary32) x))))
	97.1%	(.f32 (/.f32 #s(literal 1 binary32) x) (.f32 (.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x)) (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (*.f32 (neg.f32 tau) (PI.f32)) x) (PI.f32)))))
	61.5%	(.f32 (/.f32 #s(literal 1 binary32) x) #s(approx (/ (/ (/ (sin ( (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x)))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
	97.6%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) x) (sin.f32 (.f32 (.f32 tau x) (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (.f32 tau x) (PI.f32)))))
	96.9%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (neg.f32 (PI.f32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (neg.f32 tau) (PI.f32)) (.f32 x x))))
	96.8%	(.f32 (.f32 (/.f32 #s(literal -1 binary32) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (pow.f32 (/.f32 (neg.f32 (PI.f32)) (sin.f32 (.f32 (PI.f32) x))) #s(literal -1 binary32))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	97.5%	(.f32 (.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x)) (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x) (*.f32 (PI.f32) x))))
	97.0%	(.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (*.f32 x x) tau) (PI.f32)) (PI.f32))))
	97.2%	(.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (PI.f32))))
	25.1%	(.f32 #s(approx (/ (/ (sin ( x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/.f32 (fma.f32 (/.f32 (.f32 (.f32 x x) (PI.f32)) tau) #s(literal -1/6 binary32) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
	96.8%	(.f32 #s(approx (/ (/ (sin ( x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x x)) (.f32 tau (.f32 (PI.f32) (PI.f32))))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
	61.6%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) x))
	26.1%	(.f32 #s(approx (/ (neg (sin ( (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (/.f32 (fma.f32 (/.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) tau) (PI.f32) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
	60.8%	#s(approx (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
	61.7%	#s(approx (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
	31.3%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #s(approx (/ (sin (* (PI) x)) (PI)) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) x))))
	96.8%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (*.f32 (PI.f32) (PI.f32)) tau))))
	61.4%	#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 #s(approx (sin ( tau (* (PI) x))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))))
	7.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 (.f32 tau tau) #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (.f32 (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x) #s(literal 1 binary32)))
	7.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x)) #s(literal 1 binary32)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 x x) (PI.f32)) (PI.f32))) #s(literal 1 binary32)))
	8.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (/.f32 #s(literal 1 binary32) (/.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 -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (.f32 x x) #s(literal 1 binary32)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (.f32 x x) #s(literal 1 binary32)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 (.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)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau (.f32 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)))
	60.8%	#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 (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	60.8%	#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)))
	3.8%	#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 (exp.f32 (.f32 (log.f32 (PI.f32)) #s(literal 2 binary32))) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
	7.5%	#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)) #s(literal -1/6 binary32)) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) #s(literal 1 binary32)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal 1 binary32) (.f32 tau tau) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	60.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (+.f32 (.f32 tau tau) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
	60.7%	#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)))
	60.8%	#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)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 x x)) #s(literal 1 binary32)))
	60.8%	#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)) #s(literal -1/6 binary32)) (.f32 (PI.f32) (PI.f32))) (.f32 x x) #s(literal 1 binary32)))
	60.8%	#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)))
	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
	60.7%	#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 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) (*.f32 x x) #s(literal 1 binary32)))
	7.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(literal 1 binary32) (.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)))
	7.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(literal -1/6 binary32) (.f32 (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) (fma.f32 tau tau #s(literal 1 binary32))) #s(literal 1 binary32)))
	38.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
	4.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2))) 1) (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
	60.7%	#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 #s(literal -1/6 binary32) (PI.f32)) (PI.f32)) (*.f32 x x) #s(literal 1 binary32))))
	60.7%	#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 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	11.9%	#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 x)) (*.f32 (sqrt.f32 (PI.f32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal 1 binary32))))
	6.8%	#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 (fma.f32 (pow.f32 (.f32 (PI.f32) x) #s(literal 4 binary32)) #s(literal 1/36 binary32) #s(literal -1 binary32)) (fma.f32 (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) #s(literal -1/6 binary32) #s(literal -1 binary32)))))
	61.6%	#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 (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	4.4%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 (.f32 x x) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)))))
✓	60.8%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 5 334 to 1 940 computations (63.6% saved)

regimes256.0ms (2.6%)

Memory

-14.2MiB live, 298.2MiB allocated

Counts

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

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

Calls

4 calls:

65.0ms	(*.f32 x (PI.f32))
58.0ms	tau
54.0ms	(.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))))
54.0ms	x

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes164.0ms (1.6%)

Memory

-5.3MiB live, 238.9MiB allocated

Counts

102 → 1

Calls

Call 1

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

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

Calls

4 calls:

50.0ms	(.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))))
38.0ms	tau
37.0ms	(*.f32 x (PI.f32))
35.0ms	x

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes136.0ms (1.4%)

Memory

-2.7MiB live, 234.6MiB allocated

Counts

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

42.0ms	(*.f32 x (PI.f32))
29.0ms	tau
29.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
28.0ms	x

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes124.0ms (1.2%)

Memory

17.0MiB live, 178.9MiB allocated

Counts

87 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) #s(approx (+ (* (* -1/6 (* x x)) (* (PI) (PI))) 1) (.f32 (.f32 (.f32 (.f32 x x) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 #s(literal -1/6 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 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.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 #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 tau)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 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) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x x)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2))) 1) (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.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 (.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 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 x x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (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 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 x x) (PI.f32)) (PI.f32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x) #s(literal 1 binary32)))
#s(approx (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
#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 (.f32 tau tau) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal 1 binary32) (.f32 tau tau) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#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 (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau (.f32 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 (fma.f32 (.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)))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 tau (PI.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 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #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 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (.f32 (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) (sqrt.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) (+.f32 (.f32 (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(literal -1/6 binary32) (.f32 (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 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (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)))) (+.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(literal 1 binary32) (.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 (fma.f32 (.f32 tau tau) #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (sqrt.f32 (PI.f32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) x))
(.f32 (/.f32 #s(literal 1 binary32) x) #s(approx (/ (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x)))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) x) #s(approx (/ (/ (/ (sin ( (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x)))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #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 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( (PI) x)) (PI)) x) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( tau (* (PI) x))) x) (.f32 tau (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#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 (sqrt.f32 (PI.f32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 #s(approx (sin ( tau (* (PI) x))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( (PI) x)) (PI)) x) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (sin (* (* tau x) (PI))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (*.f32 tau x) (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x))) (.f32 (*.f32 tau x) (PI.f32))))
(/.f32 (.f32 (/.f32 #s(approx (sin ( tau (* (PI) x))) (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.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 #s(literal 1 binary32) (/.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 -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (.f32 x x) #s(literal 1 binary32)))
(/.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 tau (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin ( (PI) x)) (*.f32 (PI.f32) x))) x))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #s(approx (/ (sin (* (PI) x)) (PI)) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) x))))
(.f32 #s(approx (/ (neg (sin ( (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (/.f32 (fma.f32 (/.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) tau) (PI.f32) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
(.f32 #s(approx (/ (/ (sin ( x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/.f32 (fma.f32 (/.f32 (.f32 (.f32 x x) (PI.f32)) tau) #s(literal -1/6 binary32) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) #s(approx (/ (PI) (sin ( (PI) x))) (/.f32 #s(literal 1 binary32) x))))
(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) #s(approx (/ (PI) (sin (* (PI) x))) (/.f32 #s(literal 1 binary32) 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 (exp.f32 (.f32 (log.f32 (PI.f32)) #s(literal 2 binary32))) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (/.f32 (fma.f32 (pow.f32 (.f32 (PI.f32) x) #s(literal 4 binary32)) #s(literal 1/36 binary32) #s(literal -1 binary32)) (fma.f32 (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) #s(literal -1/6 binary32) #s(literal -1 binary32)))))
(.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (PI.f32)))
(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
(.f32 (/.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (PI.f32) x) tau) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
(/.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (neg.f32 tau) (PI.f32)) x) (.f32 (PI.f32) x)))
(.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (*.f32 x x) tau) (PI.f32)) (PI.f32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 (PI.f32) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (*.f32 tau x))))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 x x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (*.f32 (PI.f32) (PI.f32)) tau))))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
(.f32 #s(approx (/ (/ (sin ( x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 x x)) (.f32 tau (.f32 (PI.f32) (PI.f32))))) (sin.f32 (.f32 (.f32 x (PI.f32)) tau)))
(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (PI.f32) x)) (.f32 (*.f32 tau x) (PI.f32))))
(.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 (PI.f32) x)) (.f32 (.f32 (PI.f32) (.f32 x tau)) x)) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) tau)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (*.f32 (PI.f32) 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 (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 (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 tau x) (PI.f32))) (neg.f32 (sin.f32 (.f32 (PI.f32) x)))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32))))

Calls

4 calls:

40.0ms	x
29.0ms	(*.f32 x (PI.f32))
27.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
23.0ms	tau

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes98.0ms (1%)

Memory

2.9MiB live, 154.6MiB allocated

Counts

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

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

Calls

4 calls:

25.0ms	(*.f32 x (PI.f32))
23.0ms	x
23.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
23.0ms	tau

Results

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

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes85.0ms (0.9%)

Memory

13.4MiB live, 138.9MiB 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 x x) (PI.f32)) #s(literal -1/6 binary32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 (.f32 #s(literal -1/6 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 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.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 #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 tau)) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 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) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x x)) (fma.f32 #s(literal -1/6 binary32) (*.f32 tau tau) #s(literal -1/6 binary32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (+ (* tau tau) 1) (* -1/6 (pow (* (PI) x) 2))) 1) (.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (*.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(approx (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 tau tau)) (.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 (.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 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) (.f32 #s(literal -1/6 binary32) (.f32 x x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (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 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 x x) (PI.f32)) (PI.f32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) x) x)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 #s(literal -1/6 binary32) x)) x) #s(literal 1 binary32)))
#s(approx (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (fma.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) (PI.f32)) (PI.f32)) #s(literal 1 binary32)))
#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 (.f32 tau tau) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 #s(literal 1 binary32) (.f32 tau tau) #s(literal 1 binary32)) (.f32 (.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#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 (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) #s(literal -1/6 binary32))) (*.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 (fma.f32 tau (.f32 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 (fma.f32 (.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)))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) x) (sin (* (PI) x))) (.f32 (.f32 (.f32 tau (PI.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 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 tau tau)) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32))) #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 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 (.f32 (.f32 (.f32 (*.f32 x x) #s(literal -1/6 binary32)) (PI.f32)) (sqrt.f32 (PI.f32))) (sqrt.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) (+.f32 (.f32 (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (/ (/ (sin (* (* tau x) (PI))) (* tau (PI))) (* (/ (* (PI) x) (sin (* (PI) x))) x)) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(literal -1/6 binary32) (.f32 (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 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (fma.f32 tau tau #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (+.f32 (.f32 (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (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)))) (+.f32 (.f32 (.f32 (fma.f32 tau tau #s(literal 1 binary32)) #s(literal -1/6 binary32)) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 #s(literal 1 binary32) (.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 (fma.f32 (.f32 tau tau) #s(literal 1 binary32) #s(literal 1 binary32)) (.f32 #s(literal -1/6 binary32) (pow.f32 (*.f32 (PI.f32) x) #s(literal 2 binary32))) #s(literal 1 binary32)))
(/.f32 #s(approx (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (.f32 tau (sin.f32 (.f32 (PI.f32) x)))) (.f32 tau (.f32 (PI.f32) x)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (*.f32 (sqrt.f32 (PI.f32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) (/.f32 (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32)) x))
(.f32 (/.f32 #s(literal 1 binary32) x) #s(approx (/ (/ (sin ( tau (* (PI) x))) (* tau (* (PI) x))) (/ (PI) (sin (* (PI) x)))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
(.f32 (/.f32 #s(literal 1 binary32) x) #s(approx (/ (/ (/ (sin ( (* x (PI)) tau)) (* (PI) tau)) x) (/ (PI) (sin (* (PI) x)))) (/.f32 (sin.f32 (*.f32 (PI.f32) x)) (PI.f32))))
(.f32 (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) #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 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( (PI) x)) (PI)) x) #s(literal 1 binary32)))
(/.f32 (.f32 #s(approx (/ (sin ( tau (* (PI) x))) x) (.f32 tau (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 tau (*.f32 (PI.f32) x)) (PI.f32)))
#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 (sqrt.f32 (PI.f32)) (pow.f32 (PI.f32) #s(literal 3/2 binary32))) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (neg.f32 #s(approx (sin ( (PI) x)) (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 tau x) (PI.f32)) (.f32 (neg.f32 x) (PI.f32)))) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 #s(approx (sin ( tau (* (PI) x))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (/ (sin ( (PI) x)) (PI)) x) (fma.f32 (.f32 (.f32 #s(literal -1/6 binary32) x) x) (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (.f32 (PI.f32) x))))
(/.f32 #s(approx (sin (* (* tau x) (PI))) (.f32 tau (.f32 (PI.f32) x))) (.f32 (/.f32 (.f32 (PI.f32) x) (sin.f32 (.f32 (PI.f32) x))) (.f32 (*.f32 tau x) (PI.f32))))
(/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin (* (PI) x)) (.f32 (PI.f32) x))) (.f32 (*.f32 tau x) (PI.f32))))
(/.f32 (.f32 (/.f32 #s(approx (sin ( tau (* (PI) x))) (.f32 tau (.f32 (PI.f32) x))) x) (sin.f32 (.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 #s(literal 1 binary32) (/.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 -1/6 binary32) (.f32 (PI.f32) (PI.f32)))))) (.f32 x x) #s(literal 1 binary32)))
(/.f32 (/.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (.f32 tau (PI.f32))) (.f32 (/.f32 (.f32 (PI.f32) x) #s(approx (sin ( (PI) x)) (*.f32 (PI.f32) x))) x))
#s(approx (/ (* (/ (sin (* tau (* (PI) x))) (* (PI) x)) (sin (* (PI) x))) (* tau (* (PI) x))) (.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 x x) tau) (PI.f32))) #s(approx (/ (sin (* (PI) x)) (PI)) (.f32 (fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x x)) (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32)) x))))
(.f32 #s(approx (/ (neg (sin ( (PI) x))) (* (* (* tau x) (PI)) (* (neg x) (PI)))) (/.f32 (fma.f32 (/.f32 (.f32 (.f32 x x) #s(literal -1/6 binary32)) tau) (PI.f32) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
(.f32 #s(approx (/ (/ (sin ( x (PI))) (* x (PI))) (* (* x (PI)) tau)) (/.f32 (fma.f32 (/.f32 (.f32 (.f32 x x) (PI.f32)) tau) #s(literal -1/6 binary32) (/.f32 #s(literal 1 binary32) (.f32 tau (PI.f32)))) x)) (sin.f32 (.f32 (*.f32 x (PI.f32)) tau)))
(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (sin.f32 (.f32 tau (.f32 (PI.f32) x))) (.f32 tau (.f32 (PI.f32) x))) #s(approx (/ (PI) (sin ( (PI) x))) (/.f32 #s(literal 1 binary32) x))))
(.f32 (/.f32 #s(literal 1 binary32) x) (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (PI.f32) tau)) x) #s(approx (/ (PI) (sin (* (PI) x))) (/.f32 #s(literal 1 binary32) 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 (exp.f32 (.f32 (log.f32 (PI.f32)) #s(literal 2 binary32))) #s(literal -1/6 binary32))) (.f32 x x) #s(literal 1 binary32)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(approx (+ (* (* (+ (* tau tau) 1) (* (* (PI) (PI)) -1/6)) (* x x)) 1) (/.f32 (fma.f32 (pow.f32 (.f32 (PI.f32) x) #s(literal 4 binary32)) #s(literal 1/36 binary32) #s(literal -1 binary32)) (fma.f32 (pow.f32 (.f32 (PI.f32) x) #s(literal 2 binary32)) #s(literal -1/6 binary32) #s(literal -1 binary32)))))
(.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (PI.f32))))
(/.f32 (.f32 (sin.f32 (.f32 (.f32 tau x) (PI.f32))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (.f32 (.f32 x x) tau) (PI.f32)) (PI.f32)))

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

Calls

4 calls:

24.0ms	(*.f32 x (PI.f32))
20.0ms	(.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))))
19.0ms	tau
19.0ms	x

Results

Accuracy	Segments	Branch
97.2%	1	`x`
97.2%	1	`tau`
97.2%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
97.2%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes134.0ms (1.3%)

Memory

-15.9MiB live, 144.1MiB allocated

Counts

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

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

Calls

4 calls:

47.0ms	(.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))))
43.0ms	(*.f32 x (PI.f32))
21.0ms	tau
20.0ms	x

Results

Accuracy	Segments	Branch
68.2%	1	`x`
68.2%	1	`tau`
68.2%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
68.2%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes60.0ms (0.6%)

Memory

-17.8MiB live, 105.4MiB allocated

Counts

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

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

Calls

4 calls:

16.0ms	x
15.0ms	tau
13.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
13.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
61.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
61.7%	1	`x`
61.7%	1	`(*.f32 x (PI.f32))`
61.7%	1	`tau`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes90.0ms (0.9%)

Memory

11.3MiB live, 87.9MiB allocated

Counts

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

Outputs
#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)))

Calls

4 calls:

43.0ms	(*.f32 x (PI.f32))
22.0ms	(.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))))
11.0ms	x
11.0ms	tau

Results

Accuracy	Segments	Branch
61.7%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
61.7%	1	`x`
61.7%	1	`(*.f32 x (PI.f32))`
61.7%	1	`tau`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes40.0ms (0.4%)

Memory

24.7MiB live, 63.8MiB allocated

Counts

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

Calls

4 calls:

12.0ms	x
9.0ms	(*.f32 x (PI.f32))
9.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
8.0ms	tau

Results

Accuracy	Segments	Branch
61.6%	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))))`
61.6%	1	`tau`
61.6%	1	`x`
61.6%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes73.0ms (0.7%)

Memory

-9.2MiB live, 65.6MiB allocated

Accuracy

Total -18.4b remaining (-146.8%)

Threshold costs -18.4b (-146.8%)

Counts

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

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

Calls

4 calls:

36.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
19.0ms	tau
8.0ms	(*.f32 x (PI.f32))
8.0ms	x

Results

Accuracy	Segments	Branch
60.8%	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))))`
60.8%	1	`x`
60.8%	1	`(*.f32 x (PI.f32))`
60.8%	1	`tau`

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify60.0ms (0.6%)

Memory

-18.3MiB live, 64.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	78	283
1	116	283
2	145	279
3	189	279
4	262	279
5	386	279
6	545	279
7	741	279
8	917	279
9	1063	279
10	1162	279
11	1200	279
12	1206	279

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.7s (16.8%)

Memory

8.9MiB live, 1 183.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	287
0	89	285
1	320	264
2	2096	262
0	8376	259
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	441	7470
1	1493	7269
2	5843	7052
0	8029	6800
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53
0	540	9293
1	1907	8991
2	4321	8805
3	7537	8805
0	8604	8505
0	59	360
0	106	356
1	373	356
2	2579	334
0	8389	332
0	36	243
0	62	241
1	247	241
2	1664	231
3	6712	231
0	8318	231

Stop Event

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

Compiler

Compiled 699 to 293 computations (58.1% saved)

preprocess123.0ms (1.2%)

Memory

-19.9MiB live, 173.3MiB allocated

Remove

(abs x)

(abs tau)

Compiler

Compiled 1 234 to 552 computations (55.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze30.0ms (0.3%)

sample1.6s (16.5%)

explain121.0ms (1.2%)

preprocess69.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify21.0ms (0.2%)

localize33.0ms (0.3%)

series35.0ms (0.3%)

simplify224.0ms (2.3%)

rewrite135.0ms (1.4%)

eval91.0ms (0.9%)

prune112.0ms (1.1%)

simplify129.0ms (1.3%)

localize98.0ms (1%)

series45.0ms (0.5%)

simplify238.0ms (2.4%)

rewrite155.0ms (1.6%)

eval291.0ms (2.9%)

prune140.0ms (1.4%)

simplify117.0ms (1.2%)

localize234.0ms (2.4%)

series79.0ms (0.8%)

simplify244.0ms (2.5%)

rewrite242.0ms (2.4%)

eval380.0ms (3.8%)

prune243.0ms (2.5%)

simplify175.0ms (1.8%)

localize174.0ms (1.7%)

series48.0ms (0.5%)

simplify527.0ms (5.3%)

rewrite179.0ms (1.8%)

eval404.0ms (4.1%)

prune160.0ms (1.6%)

regimes256.0ms (2.6%)

regimes164.0ms (1.6%)

regimes136.0ms (1.4%)

regimes124.0ms (1.2%)

regimes98.0ms (1%)

regimes85.0ms (0.9%)

regimes134.0ms (1.3%)

regimes60.0ms (0.6%)

regimes90.0ms (0.9%)

regimes40.0ms (0.4%)

regimes73.0ms (0.7%)

simplify60.0ms (0.6%)

soundness1.7s (16.8%)

preprocess123.0ms (1.2%)

end0.0ms (0%)

Profiling