Metrics for Lanczos kernel

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze21.0ms (0.2%)

Memory

-5.1MiB live, 32.8MiB 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 (12.1%)

Memory

38.8MiB live, 2 439.6MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 978.0ms

ival-sin: 252.0ms (25.8% of total)

ival-mult: 230.0ms (23.5% of total)

ival-<=: 152.0ms (15.5% of total)

const: 129.0ms (13.2% of total)

ival-div: 113.0ms (11.6% of total)

ival-pi: 71.0ms (7.3% of total)

ival-and: 20.0ms (2% of total)

exact: 8.0ms (0.8% of total)

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

Bogosity

explain128.0ms (0.9%)

Memory

9.0MiB live, 214.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
2	-	1	(0.9093244671821594 4.4066667556762695)	`(sin.f32 (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`(PI.f32)`
0	-	0	-	`(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))`
0	-	0	-	`(.f32 (.f32 x (PI.f32)) tau)`
0	-	0	-	`(*.f32 x (PI.f32))`
0	-	0	-	`(sin.f32 (*.f32 x (PI.f32)))`
0	-	0	-	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
0	-	0	-	`tau`
0	-	0	-	`(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	1	3
-	0	252

Precision

1.0

Recall

0.25

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	1	2
-	0	0	252

Precision?

1.0

Recall?

0.5

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

55.0ms

512×

valid

Compiler

Compiled 151 to 34 computations (77.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-sin: 21.0ms (51.3% of total)

ival-mult: 11.0ms (26.9% of total)

ival-div: 6.0ms (14.6% of total)

ival-pi: 2.0ms (4.9% of total)

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

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

preprocess78.0ms (0.6%)

Memory

-8.0MiB live, 65.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Symmetry

(abs tau)

(abs x)

Compiler

Compiled 23 to 10 computations (56.5% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Compiler

Compiled 23 to 10 computations (56.5% saved)

simplify53.0ms (0.4%)

Memory

0.2MiB live, 38.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize38.0ms (0.3%)

Memory

26.4MiB live, 68.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.32421875	(*.f32 x (PI.f32))
accuracy	0.3551750488422102	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32)))
accuracy	0.3942206621900837	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.40367128907376804	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))

Samples

29.0ms

256×

valid

Compiler

Compiled 64 to 12 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 9.0ms (41.6% of total)

ival-sin: 9.0ms (41.6% of total)

ival-div: 3.0ms (13.9% of total)

ival-pi: 1.0ms (4.6% of total)

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

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

series30.0ms (0.2%)

Memory

-11.9MiB live, 61.9MiB allocated

Counts

6 → 120

Calls

Call 1

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

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

Calls

30 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(/ (sin (* x (PI))) (* x (PI)))
3.0ms	tau	@	inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
3.0ms	x	@	inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
2.0ms	x	@	0	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))
2.0ms	x	@	-inf	(* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI))))

simplify395.0ms (2.9%)

Memory

15.3MiB live, 499.3MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

rewrite311.0ms (2.3%)

Memory

-27.0MiB live, 394.9MiB allocated

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

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

Counts

6 → 670

Calls

Call 1

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

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

eval98.0ms (0.7%)

Memory: -0.9MiB live, 256.8MiB allocated
Compiler: Compiled 24 386 to 2 296 computations (90.6% saved)

prune298.0ms (2.2%)

Memory

-14.2MiB live, 399.3MiB allocated

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	982	31	1 013
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	982	32	1 014

Accuracy

99.7%

Counts

1 014 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.3%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (PI.f32)))) (*.f32 (PI.f32) tau))
	67.4%	(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
▶	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (neg.f32 (*.f32 x (PI.f32))))
	97.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))) (PI.f32))
	97.6%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
	97.5%	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))))
	97.8%	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 (neg.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
	97.1%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) tau))
▶	97.2%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
	97.2%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x tau)) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))) (PI.f32)))
	96.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.8%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (PI.f32)))
	97.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (.f32 x (sqrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
✓	98.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	97.7%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))))
	85.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	94.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	70.8%	(.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)))
	97.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
▶	97.3%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) (PI.f32)))
	97.5%	(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (*.f32 x (PI.f32)))))
	97.3%	(.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau)))))))
	78.6%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	84.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	77.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	63.9%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
▶	96.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
▶	63.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 1 537 to 826 computations (46.3% saved)

simplify270.0ms (2%)

Memory

18.4MiB live, 401.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))
cost-diff	0	(/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (PI.f32))))
cost-diff	352	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
cost-diff	0	(.f32 (PI.f32) (.f32 x tau))
cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau)
cost-diff	192	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
cost-diff	0	(.f32 x (.f32 tau (PI.f32)))
cost-diff	0	(sin.f32 (.f32 x (.f32 tau (PI.f32))))
cost-diff	0	(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
cost-diff	0	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
cost-diff	0	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32)))))
cost-diff	320	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (neg.f32 (*.f32 x (PI.f32))))

Rules

20 240×	`lower-fma.f64`
20 240×	`lower-fma.f32`
4 262×	`lower-*.f64`
4 226×	`lower-*.f32`
2 178×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	44	402
0	77	406
1	165	406
2	511	398
3	2576	398
4	5916	398
0	8334	398

Stop Event

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

Calls

Call 1

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

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

localize233.0ms (1.7%)

Memory

31.3MiB live, 312.0MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.34375	(.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32))))
accuracy	0.38671875	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.3942206621900837	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.4655075195368841	(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
accuracy	0.3942206621900837	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.401386279305326	(.f32 (PI.f32) (.f32 x (PI.f32)))
accuracy	0.4013862793053261	(/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 x (PI.f32)))))
accuracy	0.4342575195368841	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
accuracy	0.3942206621900837	(sin.f32 (.f32 x (.f32 tau (PI.f32))))
accuracy	0.40072250976844204	(.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))
accuracy	0.4030075195368841	(.f32 (.f32 (*.f32 x x) tau) (PI.f32))
accuracy	0.4450187988422101	(.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32)))))
accuracy	11.772098616487067	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
accuracy	0.38671875	(.f32 (PI.f32) (.f32 x tau))
accuracy	0.3873825195368841	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (neg.f32 (*.f32 x (PI.f32))))
accuracy	0.3942206621900837	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.40367128907376804	(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau)))

Samples

160.0ms

256×

valid

Compiler

Compiled 380 to 41 computations (89.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

ival-mult: 59.0ms (41.1% of total)

ival-sin: 51.0ms (35.5% of total)

ival-pi: 19.0ms (13.2% of total)

ival-div: 12.0ms (8.4% of total)

ival-neg: 2.0ms (1.4% of total)

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

exact: 0.0ms (0% of total)

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

series41.0ms (0.3%)

Memory

-26.9MiB live, 88.9MiB allocated

Counts

19 → 432

Calls

Call 1

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

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

Calls

108 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI)))))
3.0ms	x	@	inf	(/ (sin (* x (PI))) (* x (* (PI) (* x (PI)))))
1.0ms	x	@	0	(* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI)))))
1.0ms	tau	@	inf	(* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI)))))
1.0ms	x	@	-inf	(* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI)))))

simplify399.0ms (2.9%)

Memory

21.9MiB live, 581.3MiB allocated

Algorithm

1×	egg-herbie

Rules

19 832×	`lower-fma.f64`
19 832×	`lower-fma.f32`
8 442×	`lower-*.f64`
8 442×	`lower-*.f32`
5 094×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	430	7620
1	1455	7413
2	5811	7173
0	8655	6940

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 432

Calls

Call 1

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

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

rewrite269.0ms (2%)

Memory

-24.4MiB live, 577.3MiB allocated

Rules

4 388×	`lower-/.f64`
4 374×	`lower-/.f32`
4 172×	`lower-*.f64`
4 136×	`lower-*.f32`
1 842×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	275
0	77	271
1	257	253
2	1780	253
0	8396	253

Stop Event

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

Counts

19 → 2 118

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 tau (neg.f32 (PI.f32))))))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (*.f32 (PI.f32) x))))) #s(literal -1 binary32)))
(+.f32 #s(literal 0 binary32) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
(pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1 binary32))
(-.f32 #s(literal 0 binary32) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 tau (neg.f32 (PI.f32))))))))
(-.f32 (/.f32 #s(literal 0 binary32) (/.f32 tau (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 tau (neg.f32 (PI.f32))))))))
(-.f32 (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
(-.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))))
(-.f32 (/.f32 #s(literal 0 binary32) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 tau (neg.f32 (PI.f32))))))))
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(.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) (PI.f32)))) (/.f32 (sin.f32 (.f32 (PI.f32) x)) x))
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(neg.f32 (.f32 (PI.f32) (.f32 x (neg.f32 (PI.f32)))))
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(.f32 (.f32 (*.f32 (PI.f32) x) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
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eval310.0ms (2.3%)

Memory: 41.1MiB live, 476.1MiB allocated
Compiler: Compiled 68 193 to 2 886 computations (95.8% saved)

prune679.0ms (5%)

Memory

-7.5MiB live, 715.5MiB allocated

Pruning

42 alts after pruning (40 fresh and 2 done)

	Pruned	Kept	Total
New	2 740	29	2 769
Fresh	15	11	26
Picked	4	1	5
Done	0	1	1
Total	2 759	42	2 801

Accuracy

99.7%

Counts

2 801 → 42

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.4%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	67.4%	(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (neg.f32 (*.f32 x (PI.f32))))
	97.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))) (PI.f32))
	97.6%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
▶	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
	97.3%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	76.9%	(/.f32 #s(approx (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (.f32 (neg.f32 x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (PI.f32)))) (neg.f32 (*.f32 x (PI.f32))))
	73.7%	(-.f32 (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	67.3%	(.f32 (/.f32 (/.f32 (-.f32 (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32)) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32))) (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)))) (fma.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)))) (.f32 x (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
	67.4%	(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x x)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
	97.2%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
✓	98.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
▶	85.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	94.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
	70.8%	(.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)))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	97.4%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 x (PI.f32))))
	91.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	70.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	63.0%	(.f32 (/.f32 #s(approx ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (.f32 x (.f32 x (.f32 tau (.f32 (PI.f32) (PI.f32)))))) (.f32 x (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
	67.4%	(.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))))
	92.2%	(.f32 (.f32 (pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1/2 binary32)) (pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1/2 binary32))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
▶	97.2%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	96.9%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau)))
	97.1%	(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 tau (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (PI.f32) (.f32 x (.f32 x (neg.f32 (PI.f32))))))))
	76.9%	(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
▶	63.2%	(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (.f32 tau (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
	78.6%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
	77.6%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
	84.2%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	63.9%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	77.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	96.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	96.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	97.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (PI.f32)) x))))
	97.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
	97.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) x) (.f32 x (.f32 (PI.f32) tau))))))
	97.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) (.f32 x x))))))
✓	63.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 2 209 to 1 199 computations (45.7% saved)

simplify200.0ms (1.5%)

Memory

4.1MiB live, 278.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))
cost-diff	0	(cos.f32 (*.f32 (PI.f32) (fma.f32 x tau (neg.f32 x))))
cost-diff	0	(-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))))
cost-diff	0	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
cost-diff	0	(PI.f32)
cost-diff	0	(*.f32 (PI.f32) x)
cost-diff	0	(sin.f32 (*.f32 (PI.f32) x))
cost-diff	0	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
cost-diff	0	(.f32 (.f32 x (PI.f32)) tau)
cost-diff	0	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
cost-diff	0	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
cost-diff	0	(PI.f32)
cost-diff	0	(*.f32 tau (PI.f32))
cost-diff	0	#s(approx (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (*.f32 tau (PI.f32)))
cost-diff	160	(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (.f32 tau (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
cost-diff	0	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
cost-diff	0	(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))
cost-diff	0	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))
cost-diff	192	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))

Rules

6 286×	`lower-fma.f64`
6 280×	`lower-fma.f32`
3 572×	`lower-*.f64`
3 536×	`lower-*.f32`
3 096×	`lower-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	438
0	90	438
1	197	436
2	488	436
3	1544	436
4	3165	436
5	5064	436
6	7571	436
0	8147	436

Stop Event

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

Calls

Call 1

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

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

localize306.0ms (2.3%)

Memory

-21.7MiB live, 307.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.38089755861065216	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
accuracy	0.40072250976844204	(.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))
accuracy	0.40462875976844204	(*.f32 (PI.f32) (fma.f32 x tau x))
accuracy	10.011401135667931	(-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))))
accuracy	0.3359375	(*.f32 (PI.f32) tau)
accuracy	0.39422066219008367	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
accuracy	0.40072250976844204	(.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))
accuracy	0.42806625976844204	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
accuracy	0.40234375	(.f32 (.f32 x x) #s(literal -1/6 binary32))
accuracy	0.40367128907376804	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	4.471855620944269	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
accuracy	0.3359375	(*.f32 (PI.f32) tau)
accuracy	0.3359375	(*.f32 tau (PI.f32))
accuracy	0.4655075195368841	(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (.f32 tau (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
accuracy	11.493415356098014	#s(approx (/ (* (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (*.f32 tau (PI.f32)))
accuracy	0.3359375	(*.f32 (PI.f32) tau)
accuracy	0.3873825195368841	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
accuracy	0.39422066219008367	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
accuracy	0.40367128907376804	(/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau)))

Samples

195.0ms

256×

valid

Compiler

Compiled 421 to 51 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 127.0ms

ival-mult: 84.0ms (66.2% of total)

ival-sin: 15.0ms (11.8% of total)

ival-div: 11.0ms (8.7% of total)

ival-cos: 6.0ms (4.7% of total)

const: 4.0ms (3.2% of total)

ival-add: 3.0ms (2.4% of total)

ival-pi: 1.0ms (0.8% of total)

ival-sub: 1.0ms (0.8% of total)

ival-neg: 1.0ms (0.8% of total)

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

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

exact: 0.0ms (0% of total)

series65.0ms (0.5%)

Memory

8.3MiB live, 84.6MiB allocated

Counts

25 → 480

Calls

Call 1

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

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (* -1/6 (pow (PI) 2))))) (taylor 0 x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (* 1/36 (* (pow tau 2) (pow (PI) 4)))))))))) (taylor 0 x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ (* -1/6 (* (pow tau 2) (pow (PI) 2))) (+ (* -1/6 (pow (PI) 2)) (* (pow x 2) (+ (* 1/120 (* (pow tau 4) (pow (PI) 4))) (+ (* 1/120 (pow (PI) 4)) (+ (* 1/36 (* (pow tau 2) (pow (PI) 4))) (* (pow x 2) (+ (* -1/720 (* (pow tau 2) (pow (PI) 6))) (+ (* -1/720 (* (pow tau 4) (pow (PI) 6))) (+ (* -1/5040 (* (pow tau 6) (pow (PI) 6))) (* -1/5040 (pow (PI) 6)))))))))))))) (taylor 0 x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor inf x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (* (sin (* tau (* x (PI)))) (sin (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2)))) (taylor -inf x) (#s(alt (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) (patch (/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) x)) #<representation binary32>) () ())) ())
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#s(alt (* 1/2 (/ (- (cos (* (PI) (+ (* -1 x) (* tau x)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor -inf x) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor 0 tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (+ (* 1/2 (* tau (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))) (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2))))) tau) (taylor 0 tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (* tau (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))) (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI)))))))) tau) (taylor 0 tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (+ (* 1/2 (/ (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (* (pow x 2) (pow (PI) 2)))) (* tau (+ (* 1/2 (- (/ (sin (* x (PI))) (* x (PI))) (/ (sin (* -1 (* x (PI)))) (* x (PI))))) (* tau (+ (* 1/2 (* tau (- (* -1/6 (* x (* (PI) (sin (* x (PI)))))) (* -1/6 (* x (* (PI) (sin (* -1 (* x (PI)))))))))) (* 1/2 (- (* -1/2 (cos (* -1 (* x (PI))))) (* -1/2 (cos (* x (PI))))))))))) tau) (taylor 0 tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* 1/2 (/ (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor inf tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* 1/2 (/ (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor inf tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* 1/2 (/ (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor inf tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* 1/2 (/ (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor inf tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* 1/2 (/ (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor -inf tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* 1/2 (/ (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor -inf tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* 1/2 (/ (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor -inf tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* 1/2 (/ (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (* tau (* (pow x 2) (pow (PI) 2))))) (taylor -inf tau) (#s(alt (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) (patch (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2))))) (taylor 0 x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2))))) (taylor 0 x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (+ (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* (pow x 2) (- (* -1/720 (* (pow (PI) 6) (pow (- tau 1) 6))) (* -1/720 (* (pow (PI) 6) (pow (+ 1 tau) 6)))))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2))))) (taylor 0 x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- (+ (* -1/2 (* (pow (PI) 2) (pow (- tau 1) 2))) (* (pow x 2) (- (+ (* 1/24 (* (pow (PI) 4) (pow (- tau 1) 4))) (* (pow x 2) (- (+ (* -1/720 (* (pow (PI) 6) (pow (- tau 1) 6))) (* (pow x 2) (- (* 1/40320 (* (pow (PI) 8) (pow (- tau 1) 8))) (* 1/40320 (* (pow (PI) 8) (pow (+ 1 tau) 8)))))) (* -1/720 (* (pow (PI) 6) (pow (+ 1 tau) 6)))))) (* 1/24 (* (pow (PI) 4) (pow (+ 1 tau) 4)))))) (* -1/2 (* (pow (PI) 2) (pow (+ 1 tau) 2))))) (taylor 0 x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (taylor inf x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (taylor inf x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (taylor inf x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (taylor inf x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (cos (* (PI) (+ (* -1 x) (* tau x)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (taylor -inf x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (cos (* (PI) (+ (* -1 x) (* tau x)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (taylor -inf x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (cos (* (PI) (+ (* -1 x) (* tau x)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (taylor -inf x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (cos (* (PI) (+ (* -1 x) (* tau x)))) (cos (* (PI) (- (* tau x) (* -1 x))))) (taylor -inf x) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (cos (* -1 (* x (PI)))) (cos (* x (PI)))) (taylor 0 tau) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (+ (cos (* -1 (* x (PI)))) (* tau (- (* x (* (PI) (sin (* x (PI))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI)))) (taylor 0 tau) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (+ (cos (* -1 (* x (PI)))) (* tau (- (+ (* tau (- (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* x (PI)))))))) (* x (* (PI) (sin (* x (PI)))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI)))) (taylor 0 tau) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
#s(alt (- (+ (cos (* -1 (* x (PI)))) (* tau (- (+ (* tau (- (+ (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* -1 (* x (PI))))))) (* tau (- (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* x (PI)))))) (* -1/6 (* (pow x 3) (* (pow (PI) 3) (sin (* -1 (* x (PI)))))))))) (* -1/2 (* (pow x 2) (* (pow (PI) 2) (cos (* x (PI)))))))) (* x (* (PI) (sin (* x (PI)))))) (* x (* (PI) (sin (* -1 (* x (PI))))))))) (cos (* x (PI)))) (taylor 0 tau) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
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#s(alt (- (cos (* (PI) (- (* tau x) x))) (cos (* (PI) (+ x (* tau x))))) (taylor inf tau) (#s(alt (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (patch (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) #<representation binary32>) () ())) ())
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#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor inf x) (#s(alt #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ (sin (* x (PI))) (* x (PI))) (taylor -inf x) (#s(alt #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (patch #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor 0 x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor 0 x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor 0 x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor 0 x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f32 (.f32 x x) #s(literal -1/6 binary32)) (patch (.f32 (.f32 x x) #s(literal -1/6 binary32)) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor 0 x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor 0 x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor 0 x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor 0 x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor inf x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* tau (* (pow x 2) (pow (PI) 2))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) (patch (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #<representation binary32>) () ())) ())
#s(alt (* x (* (PI) (+ 1 tau))) (taylor 0 x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* x (* (PI) (+ 1 tau))) (taylor 0 x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* x (* (PI) (+ 1 tau))) (taylor 0 x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* x (* (PI) (+ 1 tau))) (taylor 0 x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* x (* (PI) (+ 1 tau))) (taylor inf x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* x (* (PI) (+ 1 tau))) (taylor inf x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* x (* (PI) (+ 1 tau))) (taylor inf x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* x (* (PI) (+ 1 tau))) (taylor inf x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (* (PI) (- (* -1 tau) 1)))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (* (PI) (- (* -1 tau) 1)))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (* (PI) (- (* -1 tau) 1)))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (* (PI) (- (* -1 tau) 1)))) (taylor -inf x) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* x (PI)) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (+ (* tau (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (+ (* tau (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (+ (* tau (* x (PI))) (* x (PI))) (taylor 0 tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* x (PI)) (/ (* x (PI)) tau))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* x (PI)) (/ (* x (PI)) tau))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* tau (+ (* x (PI)) (/ (* x (PI)) tau))) (taylor inf tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* tau (* x (PI))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* tau (+ (* -1 (* x (PI))) (* -1 (/ (* x (PI)) tau))))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* tau (+ (* -1 (* x (PI))) (* -1 (/ (* x (PI)) tau))))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* tau (+ (* -1 (* x (PI))) (* -1 (/ (* x (PI)) tau))))) (taylor -inf tau) (#s(alt (.f32 (PI.f32) (fma.f32 x tau x)) (patch (.f32 (PI.f32) (fma.f32 x tau x)) #<representation binary32>) () ())) ())

Calls

120 calls:

Time	Variable		Point	Expression
21.0ms	x	@	0	(/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2))
1.0ms	tau	@	-inf	(/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2))
1.0ms	x	@	-inf	(/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2))
1.0ms	tau	@	inf	(/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2))
1.0ms	x	@	inf	(/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2))

simplify503.0ms (3.7%)

Memory

-12.8MiB live, 512.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 510×	`lower-fma.f64`
12 510×	`lower-fma.f32`
8 024×	`lower-*.f64`
8 024×	`lower-*.f32`
3 742×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	587	8170
1	1939	7879
2	5886	7595
0	8673	7327

Stop Event

1×	iter limit
1×	node limit

Counts

480 → 480

Calls

Call 1

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

rewrite935.0ms (6.9%)

Memory

31.0MiB live, 576.0MiB allocated

Rules

4 648×	`lower-/.f64`
4 638×	`lower-/.f32`
4 324×	`lower-*.f64`
4 288×	`lower-*.f32`
4 068×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	295
0	90	286
1	339	276
2	2226	276
0	8867	274

Stop Event

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

Counts

25 → 1 245

Calls

Call 1

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

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

eval282.0ms (2.1%)

Memory: 7.7MiB live, 632.9MiB allocated
Compiler: Compiled 83 896 to 5 194 computations (93.8% saved)

prune786.0ms (5.8%)

Memory

-31.4MiB live, 1 312.6MiB allocated

Pruning

84 alts after pruning (80 fresh and 4 done)

	Pruned	Kept	Total
New	2 646	58	2 704
Fresh	13	22	35
Picked	2	3	5
Done	1	1	2
Total	2 662	84	2 746

Accuracy

99.8%

Counts

2 746 → 84

Alt Table

Click to see full alt table

Status	Accuracy	Program
	67.4%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (PI.f32)) (.f32 (.f32 x (.f32 (PI.f32) tau)) (*.f32 x #s(literal 2 binary32))))
	85.4%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (.f32 (PI.f32) tau)) x)
	85.0%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (.f32 x tau)) (PI.f32))
	85.0%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (PI.f32)) (.f32 x tau))
	85.2%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) tau) (.f32 x (PI.f32)))
	66.0%	(/.f32 (-.f32 (fma.f32 (cos.f32 (.f32 x (.f32 (PI.f32) tau))) (cos.f32 (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	65.0%	(/.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (.f32 (.f32 x (.f32 (PI.f32) tau)) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 x (.f32 (PI.f32) tau)) #s(literal 2 binary32)))) (.f32 (PI.f32) x))
	63.4%	(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (PI.f32)) (/.f32 (.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) tau))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))))) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) #s(literal 1 binary32))) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) (/.f32 (.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) tau))) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x))))))
	63.2%	(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (PI.f32)) #s(literal 2 binary32)) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) #s(literal 2 binary32)))
	66.4%	(/.f32 (-.f32 (.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) #s(literal 2 binary32)) (.f32 (.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) tau))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) tau))) #s(literal 2 binary32)))
	67.3%	(/.f32 (-.f32 (cos.f32 (fma.f32 (.f32 (.f32 x tau) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)) (.f32 (PI.f32) (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	67.3%	(/.f32 (-.f32 (cos.f32 (fma.f32 (.f32 x tau) (PI.f32) (.f32 (PI.f32) (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	67.5%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) (PI.f32)) (*.f32 x tau)) #s(literal 2 binary32)))
	67.1%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32)) (pow.f32 (cbrt.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32))) tau)))) #s(literal 2 binary32)))
	67.6%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	49.1%	(/.f32 (-.f32 #s(approx (cos (* (PI) (+ (* x tau) (neg x)))) (fma.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 #s(literal -1/2 binary32) (.f32 x x)) #s(literal 1 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	32.0%	(/.f32 (-.f32 #s(approx (cos (* (PI) (+ (* x tau) (neg x)))) #s(literal 1 binary32)) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	97.3%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (neg.f32 (*.f32 x (PI.f32))))
	97.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))) (PI.f32))
	97.6%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
✓	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
	85.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( (PI) x)) (.f32 x (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (PI.f32))))) (.f32 (PI.f32) x))
	70.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( (PI) x)) (.f32 x (PI.f32)))) (.f32 (PI.f32) x))
	85.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) tau)
▶	97.3%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	85.6%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (.f32 x (*.f32 (PI.f32) tau)))
	85.2%	(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (.f32 tau (*.f32 (PI.f32) (neg.f32 x))))
	85.4%	(/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
	62.9%	(/.f32 #s(approx (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) tau)) (-.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) tau)))))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	76.9%	(/.f32 #s(approx (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) (sin (* (PI) x))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (PI.f32)))) (*.f32 (PI.f32) x))
	63.9%	(/.f32 #s(approx (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) (sin (* (PI) x))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) x))
	85.1%	(.f32 (/.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x) tau) (PI.f32)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau) (.f32 x (PI.f32))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	97.2%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (PI.f32) tau) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
▶	85.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
	85.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
	70.8%	(.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)))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x tau) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	91.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
▶	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	70.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) tau))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x tau)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (PI.f32)))
	85.1%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (.f32 x tau)))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (.f32 (PI.f32) tau)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	77.8%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	63.9%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	78.1%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.2%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) tau) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.4%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	92.2%	(.f32 (.f32 (pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1/2 binary32)) (pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1/2 binary32))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
	85.2%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.5%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.3%	(.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 x (*.f32 (PI.f32) tau))))
	85.1%	(.f32 (.f32 (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	97.1%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (.f32 (.f32 x (PI.f32)) (PI.f32)) (.f32 x tau))))
	97.0%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))) tau)))
✓	97.2%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	96.9%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau)))
▶	97.7%	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))))
	85.4%	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (.f32 x (*.f32 (PI.f32) tau))))
	85.3%	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))))
	76.9%	(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
✓	63.2%	(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (.f32 tau (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
	78.4%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	64.0%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	84.9%	(.f32 #s(approx (sin ( (PI) x)) (.f32 x (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (PI.f32)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau))))))
	70.5%	(.f32 #s(approx (sin ( (PI) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau))))))
▶	6.3%	#s(approx (/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2)) #s(literal 0 binary32))
	77.6%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
	84.2%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	77.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	96.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	96.7%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	97.3%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (PI.f32)) x))))
	97.0%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 x (.f32 x tau))))))
	97.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) (.f32 x x))))))
✓	63.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 4 634 to 2 538 computations (45.2% saved)

simplify240.0ms (1.8%)

Memory

21.5MiB live, 215.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

5 368×	`lower-fma.f64`
5 364×	`lower-fma.f32`
3 738×	`lower-/.f64`
3 726×	`lower-/.f32`
3 582×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	395
0	105	394
1	208	394
2	461	394
3	1555	394
4	3309	394
5	5574	394
0	8118	393

Stop Event

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

Calls

Call 1

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

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

localize263.0ms (1.9%)

Memory

-20.5MiB live, 216.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.34375	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))
accuracy	0.38089755861065216	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
accuracy	0.39422066219008367	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
accuracy	0.40072250976844204	(.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))
accuracy	0.3942206621900837	(sin.f32 (.f32 (PI.f32) (.f32 x tau)))
accuracy	0.4342575195368841	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
accuracy	0.46392603869603133	(fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32)))
accuracy	4.354882924199204	#s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))
accuracy	0.3942206621900837	(sin.f32 (.f32 (.f32 x (PI.f32)) tau))
accuracy	0.40367128907376804	(/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau))
accuracy	1.0	(*.f32 (PI.f32) (PI.f32))
accuracy	4.471855620944269	#s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32)))
accuracy	29.981931575696134	#s(approx (/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2)) #s(literal 0 binary32))
accuracy	0.33041000976844204	(.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))
accuracy	0.3359375	(*.f32 (PI.f32) tau)
accuracy	0.39422066219008367	(sin.f32 (.f32 x (.f32 (PI.f32) tau)))
accuracy	0.4450187988422101	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))))

Samples

178.0ms

256×

valid

Compiler

Compiled 350 to 56 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

ival-mult: 73.0ms (50.8% of total)

ival-div: 38.0ms (26.5% of total)

ival-sin: 15.0ms (10.4% of total)

ival-cos: 6.0ms (4.2% of total)

ival-add: 4.0ms (2.8% of total)

const: 4.0ms (2.8% of total)

ival-pi: 1.0ms (0.7% of total)

ival-sub: 1.0ms (0.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.1%)

Memory

26.5MiB live, 26.5MiB allocated

Counts

21 → 432

Calls

Call 1

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

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

Calls

108 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+ (* -1/6 (* x (* x (PI)))) (/ 1 (PI)))
0.0ms	x	@	inf	(+ (* -1/6 (* x (* x (PI)))) (/ 1 (PI)))
0.0ms	x	@	0	(* (sin (* x (* (PI) tau))) (/ (sin (* x (PI))) (* (* x (* (PI) tau)) (* x (PI)))))
0.0ms	x	@	-inf	(+ (* -1/6 (* x (* x (PI)))) (/ 1 (PI)))
0.0ms	tau	@	-inf	(* (sin (* x (* (PI) tau))) (/ (sin (* x (PI))) (* (* x (* (PI) tau)) (* x (PI)))))

simplify480.0ms (3.5%)

Memory

-11.7MiB live, 299.6MiB allocated

Algorithm

1×	egg-herbie

Rules

11 094×	`lower-fma.f64`
11 094×	`lower-fma.f32`
8 504×	`lower-*.f64`
8 504×	`lower-*.f32`
2 410×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	428	6852
1	1403	6682
2	5295	6450
0	8264	6238

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 432

Calls

Call 1

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

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

rewrite268.0ms (2%)

Memory

16.0MiB live, 450.3MiB allocated

Rules

4 648×	`lower-/.f64`
4 636×	`lower-/.f32`
4 598×	`lower-*.f64`
4 562×	`lower-*.f32`
4 396×	`lower-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	282
0	105	281
1	368	259
2	2372	259
0	9179	259

Stop Event

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

Counts

21 → 669

Calls

Call 1

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

Outputs
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (neg.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))
(neg.f32 (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 tau (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32))))) #s(literal -2 binary32))))
(neg.f32 (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (neg.f32 (PI.f32))))) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))))
(neg.f32 (/.f32 (neg.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (*.f32 x (PI.f32)))) #s(literal 2 binary32)))))
(exp.f32 (.f32 (log.f32 (/.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (*.f32 x (PI.f32)))))) #s(literal -1 binary32)))
(+.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (neg.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))))))
(pow.f32 (/.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))) #s(literal -1 binary32))
(pow.f32 (/.f32 (.f32 x (.f32 tau (.f32 x (PI.f32)))) (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (/.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 #s(literal 2 binary32) (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) #s(literal -1 binary32))
(fma.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))) (neg.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32)))))))))
(-.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))
(-.f32 (/.f32 #s(literal 0 binary32) (.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) #s(literal -2 binary32))) (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) #s(literal -2 binary32))))
(-.f32 (/.f32 #s(literal 0 binary32) (neg.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (neg.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))
(-.f32 (/.f32 (/.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 3 binary32)) (fma.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x))))))))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32)))) (/.f32 (/.f32 (pow.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) #s(literal 3 binary32)) (fma.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x))))))))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32)))))
(-.f32 (/.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x))))))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32)))) (/.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32)))))
(-.f32 (/.f32 (pow.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 3 binary32)) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (fma.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))))))))) (/.f32 (pow.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) #s(literal 3 binary32)) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (fma.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))))))))))
(-.f32 (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x))))))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))))) (/.f32 (+.f32 #s(literal 1/2 binary32) (.f32 #s(literal 1/2 binary32) (cos.f32 (.f32 #s(literal 2 binary32) (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (+.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))))))
(-.f32 (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32)))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))))) (/.f32 (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))))))
(-.f32 (/.f32 (pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) #s(literal 3 binary32)) (+.f32 (pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) #s(literal 2 binary32)) (+.f32 (pow.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) #s(literal 2 binary32)) (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))))) (/.f32 (pow.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) #s(literal 3 binary32)) (+.f32 (pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) #s(literal 2 binary32)) (+.f32 (pow.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) #s(literal 2 binary32)) (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))))))
(-.f32 (/.f32 (pow.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) #s(literal 2 binary32)) (fma.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))) (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))) (/.f32 (pow.f32 (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) #s(literal 2 binary32)) (fma.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))) (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))))
(/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (sin.f32 (*.f32 x (PI.f32)))))
(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (*.f32 x (PI.f32)))) #s(literal 2 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))))
(/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 tau (.f32 x (PI.f32)))) (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 (sin.f32 (*.f32 x (PI.f32))) (PI.f32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 2 binary32) (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))
(/.f32 #s(literal 1 binary32) (neg.f32 (neg.f32 (/.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32))))))))
(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (sin.f32 (.f32 x (PI.f32)))))))
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(exp.f32 (.f32 (.f32 (log.f32 (PI.f32)) #s(literal 2 binary32)) #s(literal 1 binary32)))
(pow.f32 (PI.f32) #s(literal 2 binary32))
(pow.f32 (*.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
(pow.f32 (cbrt.f32 (PI.f32)) #s(literal 6 binary32))
(pow.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) #s(literal 3 binary32))
(pow.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) #s(literal 2/3 binary32))
(pow.f32 (sqrt.f32 (PI.f32)) #s(literal 4 binary32))
(pow.f32 (neg.f32 (PI.f32)) #s(literal 2 binary32))
(pow.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1/3 binary32))
(sqrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 (PI.f32) (PI.f32))))
(cbrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 (PI.f32) (PI.f32)) (*.f32 (PI.f32) (PI.f32)))))
(*.f32 (PI.f32) (PI.f32))
(.f32 (.f32 (PI.f32) (PI.f32)) #s(literal 1 binary32))
(.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32)))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (cbrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (PI.f32)))))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (pow.f32 (PI.f32) #s(literal 4/3 binary32)))
(*.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (pow.f32 (pow.f32 (PI.f32) #s(literal 4/3 binary32)) #s(literal 1 binary32)))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (PI.f32) (sqrt.f32 (PI.f32))))
(.f32 (sqrt.f32 (PI.f32)) (pow.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)))
(*.f32 (neg.f32 (PI.f32)) (neg.f32 (PI.f32)))
(.f32 (cbrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (PI.f32)))) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))
(.f32 (pow.f32 (.f32 (PI.f32) (sqrt.f32 (PI.f32))) #s(literal 1 binary32)) (sqrt.f32 (PI.f32)))
(.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32)) (pow.f32 (PI.f32) #s(literal 2/3 binary32)))
(.f32 (pow.f32 (.f32 (PI.f32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) #s(literal 1 binary32)) (cbrt.f32 (PI.f32)))
#s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))
(+.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))))
(+.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(pow.f32 (/.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))) (PI.f32))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x (.f32 x x)) #s(literal -1/216 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) #s(literal -1 binary32))
(pow.f32 (/.f32 (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (PI.f32)))))) #s(literal -1 binary32))
(fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 x (.f32 (.f32 x (PI.f32)) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (PI.f32) (.f32 x (.f32 x #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (.f32 x (PI.f32)) (.f32 x #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (.f32 x #s(literal -1/6 binary32)) (.f32 x (PI.f32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (.f32 x (.f32 x #s(literal -1/6 binary32))) (PI.f32) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))))
(fma.f32 #s(literal 1 binary32) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (.f32 x (.f32 x (PI.f32))) #s(literal -1/6 binary32) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) #s(literal 1 binary32) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))))
(fma.f32 #s(literal -1 binary32) (/.f32 #s(literal -1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))))
(fma.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (*.f32 x #s(literal -1/6 binary32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 x (*.f32 x #s(literal -1/6 binary32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (.f32 x x) (.f32 (PI.f32) #s(literal -1/6 binary32)) (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))))
(fma.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (PI.f32))) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))))
(fma.f32 (.f32 (PI.f32) (.f32 x #s(literal -1/6 binary32))) x (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) x (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (.f32 (.f32 x #s(literal -1/6 binary32)) (PI.f32)) x (/.f32 #s(literal 1 binary32) (PI.f32)))
(fma.f32 (/.f32 #s(literal 1 binary32) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (pow.f32 (PI.f32) #s(literal -1/3 binary32)) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))))
(-.f32 (/.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32))))) (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))) (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))))
(-.f32 (/.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))))) (/.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32))))) (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))) (PI.f32))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x (.f32 x x)) #s(literal -1/216 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (PI.f32)))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))) (PI.f32))) (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x (.f32 x x)) #s(literal -1/216 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) (PI.f32))))))))
(/.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x (.f32 x x)) #s(literal -1/216 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))) (PI.f32))))
(/.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x (.f32 x x)) #s(literal -1/216 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (-.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32))))) (/.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (PI.f32)))))
(/.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))))) (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))))
(/.f32 (neg.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x (.f32 x x)) #s(literal -1/216 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (neg.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))) (PI.f32)))))
(/.f32 (neg.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x (.f32 x x)) #s(literal -1/216 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))))) (neg.f32 (+.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (-.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32))))) (/.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (PI.f32))))))
(/.f32 (neg.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32)))))) (neg.f32 (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))))
(/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))))) (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))))
(/.f32 (-.f32 (.f32 (.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32))))) (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))) (.f32 (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))))) (.f32 (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))) (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x (.f32 x x)) #s(literal -1/216 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))))) (neg.f32 (neg.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))))) (PI.f32))))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))))))) (neg.f32 (neg.f32 (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32))))))
(/.f32 (neg.f32 (-.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32))))))) (neg.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))))))
(.f32 (fma.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 (.f32 x (.f32 x x)) (.f32 (.f32 x (.f32 x x)) #s(literal -1/216 binary32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) (PI.f32)) (.f32 x (.f32 #s(literal -1/6 binary32) (*.f32 x (PI.f32))))) (PI.f32)))))
(.f32 (fma.f32 #s(literal 1/36 binary32) (.f32 (.f32 x (.f32 x (PI.f32))) (.f32 x (.f32 x (PI.f32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) (PI.f32))))) (/.f32 #s(literal 1 binary32) (-.f32 (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (PI.f32)))))
(.f32 x (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))))
(.f32 (PI.f32) (.f32 x (.f32 tau (.f32 x (PI.f32)))))
(.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))
(.f32 (.f32 (PI.f32) tau) (.f32 x (.f32 x (PI.f32))))
(.f32 (.f32 tau (.f32 x (PI.f32))) (.f32 x (PI.f32)))
(.f32 (.f32 x (PI.f32)) (.f32 tau (.f32 x (PI.f32))))
(.f32 (.f32 x tau) (.f32 x (.f32 (PI.f32) (PI.f32))))
(.f32 #s(literal 1 binary32) (.f32 tau (.f32 x (.f32 x (*.f32 (PI.f32) (PI.f32))))))
(.f32 (.f32 x (.f32 (PI.f32) (PI.f32))) (.f32 x tau))
(.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) tau)
(.f32 (.f32 x (.f32 x (PI.f32))) (.f32 (PI.f32) tau))
(.f32 (.f32 x (.f32 tau (.f32 x (PI.f32)))) (PI.f32))
(.f32 (pow.f32 (PI.f32) #s(literal 2/3 binary32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (.f32 tau (*.f32 x (PI.f32))))))
(.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (.f32 x (.f32 tau (*.f32 x (PI.f32))))))
(.f32 (.f32 x x) (.f32 (.f32 (PI.f32) tau) (PI.f32)))
(.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) x)
(.f32 (.f32 (.f32 x (.f32 tau (*.f32 x (PI.f32)))) #s(literal 1 binary32)) (PI.f32))
(.f32 (.f32 (.f32 x (.f32 tau (*.f32 x (PI.f32)))) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)))
(.f32 (.f32 (.f32 x (.f32 tau (*.f32 x (PI.f32)))) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))

eval149.0ms (1.1%)

Memory: 14.4MiB live, 249.5MiB allocated
Compiler: Compiled 40 898 to 1 972 computations (95.2% saved)

prune477.0ms (3.5%)

Memory

14.2MiB live, 996.9MiB allocated

Pruning

99 alts after pruning (92 fresh and 7 done)

	Pruned	Kept	Total
New	1 297	33	1 330
Fresh	16	59	75
Picked	2	3	5
Done	0	4	4
Total	1 315	99	1 414

Accuracy

99.8%

Counts

1 414 → 99

Alt Table

Click to see full alt table

Status	Accuracy	Program
	67.4%	(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (PI.f32)) (.f32 (.f32 x (.f32 (PI.f32) tau)) (*.f32 x #s(literal 2 binary32))))
	85.4%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (.f32 (PI.f32) tau)) x)
	85.0%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (.f32 x tau)) (PI.f32))
	85.0%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (PI.f32)) (.f32 x tau))
	97.0%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32))) (.f32 x x)) (.f32 (PI.f32) tau))
	85.4%	(/.f32 (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x #s(literal -1/6 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)))) tau) (.f32 x (PI.f32)))
	65.0%	(/.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (.f32 (.f32 x (.f32 (PI.f32) tau)) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 x (.f32 (PI.f32) tau)) #s(literal 2 binary32)))) (.f32 (PI.f32) x))
	64.2%	(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))) (.f32 x (.f32 (.f32 tau (.f32 x (PI.f32))) #s(literal 2 binary32)))) (.f32 #s(literal 2 binary32) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (PI.f32)))) (.f32 #s(literal 2 binary32) (.f32 x (.f32 (.f32 tau (*.f32 x (PI.f32))) #s(literal 2 binary32)))))
	63.7%	(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 2 binary32)) (/.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))))) (.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))))))
	63.2%	(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (PI.f32)) #s(literal 2 binary32)) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) #s(literal 2 binary32)))
	64.9%	(/.f32 (-.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (.f32 x (.f32 (.f32 tau (.f32 x (PI.f32))) #s(literal 2 binary32)))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (PI.f32)))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (.f32 x (.f32 (.f32 tau (*.f32 x (PI.f32))) #s(literal 2 binary32)))))
	63.7%	(/.f32 (-.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 2 binary32)) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (*.f32 x (PI.f32)))) #s(literal 2 binary32))) #s(literal 2 binary32)))
	65.1%	(/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 x (.f32 (.f32 tau (.f32 x (PI.f32))) #s(literal 2 binary32)))) (.f32 (/.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x))))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (PI.f32)))) (.f32 (/.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x))))) (.f32 x (.f32 (.f32 tau (.f32 x (PI.f32))) #s(literal 2 binary32)))))
	67.3%	(/.f32 (-.f32 (cos.f32 (fma.f32 (.f32 (.f32 x tau) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)) (.f32 (PI.f32) (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	67.3%	(/.f32 (-.f32 (cos.f32 (fma.f32 (.f32 x tau) (PI.f32) (.f32 (PI.f32) (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	67.5%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) (PI.f32)) (*.f32 x tau)) #s(literal 2 binary32)))
	67.6%	(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	49.1%	(/.f32 (-.f32 #s(approx (cos (* (PI) (+ (* x tau) (neg x)))) (fma.f32 (.f32 (+.f32 tau #s(literal -1 binary32)) (.f32 (+.f32 tau #s(literal -1 binary32)) (.f32 (PI.f32) (PI.f32)))) (.f32 #s(literal -1/2 binary32) (.f32 x x)) #s(literal 1 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	32.0%	(/.f32 (-.f32 #s(approx (cos (* (PI) (+ (* x tau) (neg x)))) #s(literal 1 binary32)) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
	97.5%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))) (PI.f32))
	97.6%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
✓	97.9%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
	85.4%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( (PI) x)) (.f32 x (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (PI.f32))))) (.f32 (PI.f32) x))
	70.8%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) #s(approx (sin ( (PI) x)) (.f32 x (PI.f32)))) (.f32 (PI.f32) x))
	85.2%	(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (PI.f32))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) tau)
	97.0%	(/.f32 (.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (sin.f32 (.f32 (PI.f32) x))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	97.3%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) x))
	85.6%	(/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (.f32 x (*.f32 (PI.f32) tau)))
	85.1%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) tau)
	85.6%	(/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x #s(literal -1/6 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)))) (.f32 tau (*.f32 x (PI.f32))))
	85.2%	(/.f32 (.f32 (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))) (.f32 tau (*.f32 (PI.f32) (neg.f32 x))))
	85.4%	(/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (*.f32 (PI.f32) tau)))))
	76.9%	(/.f32 #s(approx (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) (sin (* (PI) x))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (PI.f32)))) (*.f32 (PI.f32) x))
	63.9%	(/.f32 #s(approx (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) (sin (* (PI) x))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) x))
	62.9%	(/.f32 #s(approx (* (sin (* x (* (PI) tau))) (sin (* (PI) x))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	84.8%	(/.f32 #s(literal 1 binary32) (/.f32 tau (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))))
	74.8%	(-.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))
	85.2%	(.f32 (/.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau) (.f32 x (PI.f32))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	97.2%	(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (.f32 x tau) (sqrt.f32 (PI.f32))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 (PI.f32) tau) x)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.3%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 (PI.f32) tau) x)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.6%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))
	70.8%	(.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)))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x tau) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
	85.1%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	96.9%	(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
	91.2%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 (.f32 x x) (.f32 (PI.f32) (fma.f32 (.f32 (.f32 x x) #s(literal 1/120 binary32)) (*.f32 (PI.f32) (PI.f32)) #s(literal -1/6 binary32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
✓	85.0%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	70.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* x (* x (PI)))) (/ 1 (PI))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	70.5%	(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))))
	85.0%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x tau)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (PI.f32)))
	85.1%	(.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (PI.f32)) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (.f32 x tau)))
	97.3%	(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau))))) (sin.f32 (.f32 (PI.f32) (.f32 x tau))))
	85.2%	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (.f32 (PI.f32) tau)) (/.f32 #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 x #s(literal -1/6 binary32)) (.f32 x (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) x))
	85.1%	(.f32 (/.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) x) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x #s(literal -1/6 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (.f32 (PI.f32) tau)))
	77.8%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
	77.8%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	63.9%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	78.1%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	78.0%	(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
	77.8%	(.f32 (/.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	63.9%	(.f32 (/.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) tau) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	77.8%	(.f32 (/.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32))))) tau) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	85.2%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 (PI.f32) tau) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.4%	(.f32 (/.f32 #s(literal 1 binary32) (/.f32 (.f32 x (.f32 (PI.f32) tau)) (sin.f32 (.f32 x (.f32 (PI.f32) tau))))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	92.2%	(.f32 (.f32 (pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1/2 binary32)) (pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1/2 binary32))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
	85.2%	(.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) x) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.5%	(.f32 (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	85.0%	(.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 x (.f32 #s(literal -1/6 binary32) (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x))) (/.f32 #s(literal 1 binary32) tau))
	85.3%	(.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 x #s(literal -1/6 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32)))) (/.f32 #s(literal 1 binary32) (.f32 tau (*.f32 x (PI.f32)))))
	85.1%	(.f32 (.f32 (neg.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (/.f32 #s(literal 1 binary32) (.f32 tau (.f32 (PI.f32) (neg.f32 x))))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	97.2%	(.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))))
	97.1%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (.f32 (.f32 x (PI.f32)) (PI.f32)) (.f32 x tau))))
	97.0%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (PI.f32)))) tau)))
✓	97.2%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
	96.9%	(.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau)))
	97.2%	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) x)))
✓	97.7%	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))))
	85.3%	(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 (PI.f32) tau))) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32)))))
	85.4%	(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x #s(literal -1/6 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (.f32 tau (*.f32 x (PI.f32)))))
	76.9%	(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
✓	63.2%	(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (.f32 tau (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
	78.4%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
	78.4%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	64.0%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
	64.0%	(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
	77.8%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) tau) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	63.9%	(.f32 #s(approx (/ (sin ( (PI) (* x tau))) tau) (.f32 x (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
	84.9%	(.f32 #s(approx (sin ( (PI) x)) (.f32 x (fma.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (PI.f32)))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau))))))
	70.5%	(.f32 #s(approx (sin ( (PI) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau))))))
✓	6.3%	#s(approx (/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2)) #s(literal 0 binary32))
	77.6%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
	84.2%	#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 4 binary32)) (fma.f32 #s(literal 1/120 binary32) (.f32 (.f32 tau tau) (.f32 tau tau)) (fma.f32 (.f32 tau tau) #s(literal 1/36 binary32) #s(literal 1/120 binary32)))) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)))) #s(literal 1 binary32)))
	77.6%	#s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* (PI) x))) (* (PI) (* x (* x (* (PI) tau))))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 (PI.f32) (.f32 tau tau) (PI.f32))))) #s(literal 1 binary32)))
	77.6%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
	96.5%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 (.f32 (PI.f32) x) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (.f32 x x) tau) (PI.f32))))))
	97.1%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (.f32 (sin.f32 (.f32 x (.f32 tau (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 (PI.f32) (.f32 (.f32 (PI.f32) tau) (.f32 x x))))))
✓	63.2%	#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))

Compiler

Compiled 6 952 to 2 107 computations (69.7% saved)

regimes438.0ms (3.2%)

Memory

-273.9MiB live, 394.0MiB allocated

Counts

152 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) #s(literal 1 binary32))
#s(approx (/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (.f32 tau (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* (PI) x))) (* (PI) (* x (* x (* (PI) tau))))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 (PI.f32) (.f32 tau tau) (PI.f32))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) tau) (.f32 x (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
(/.f32 #s(approx (* (sin (* x (* (PI) tau))) (sin (* (PI) x))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(/.f32 #s(approx (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) (sin (* (PI) x))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (PI.f32)))) (*.f32 (PI.f32) x))
(.f32 (/.f32 #s(approx ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (.f32 x (.f32 x (.f32 tau (.f32 (PI.f32) (PI.f32)))))) (.f32 x (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
(/.f32 #s(approx (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (.f32 (neg.f32 x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (PI.f32)))) (neg.f32 (*.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) tau) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) tau) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
(/.f32 #s(approx (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) tau)) (-.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) tau)))))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32))))) tau) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
(.f32 (/.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (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 (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) (sin (* (PI) x))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) x))
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(.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (/.f32 (sin.f32 (.f32 (PI.f32) (*.f32 x tau))) (PI.f32)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) (*.f32 x (PI.f32))))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (*.f32 (PI.f32) x))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) x) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) (.f32 (PI.f32) (*.f32 x tau))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (.f32 (PI.f32) (.f32 x tau)))) (sin.f32 (*.f32 x (PI.f32)))) (PI.f32))
(/.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (PI.f32)))) (*.f32 (PI.f32) tau))
(/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (/.f32 (neg.f32 (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))) (neg.f32 (.f32 (PI.f32) (*.f32 x tau)))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (PI.f32) (.f32 x tau))) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (neg.f32 (*.f32 x (PI.f32))))
(/.f32 (.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 (.f32 (PI.f32) tau) x)) (neg.f32 (sin.f32 (.f32 x (PI.f32))))) (neg.f32 (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 (PI.f32) x)) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (.f32 (/.f32 #s(literal 1 binary32) (.f32 x (PI.f32))) (sin.f32 (.f32 x (PI.f32)))))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x))) (PI.f32)) (/.f32 #s(literal 1 binary32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (/.f32 (sin.f32 (.f32 x (PI.f32))) x) (PI.f32)))
(.f32 (/.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (.f32 x (PI.f32))) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) tau))
(/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 x (.f32 (PI.f32) (.f32 (PI.f32) (.f32 x tau)))) #s(literal 2 binary32)))
(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32))))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (.f32 (.f32 x (PI.f32)) (PI.f32)) (*.f32 x tau)) #s(literal 2 binary32)))
(/.f32 (/.f32 (.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (PI.f32))) (.f32 x x)) (.f32 (PI.f32) tau))
(.f32 (neg.f32 (sin.f32 (.f32 (PI.f32) x))) (/.f32 #s(literal 1 binary32) (.f32 (/.f32 tau (sin.f32 (.f32 x (.f32 (PI.f32) tau)))) (.f32 (PI.f32) (.f32 x (.f32 x (neg.f32 (PI.f32))))))))
(.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (/.f32 #s(literal 1 binary32) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32))))
(.f32 (/.f32 (.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) (sin.f32 (.f32 x (PI.f32)))) (.f32 x tau)) (/.f32 (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32))) (PI.f32)))
(/.f32 (-.f32 (cos.f32 (fma.f32 (.f32 x tau) (PI.f32) (.f32 (PI.f32) (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(/.f32 (/.f32 (-.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (PI.f32)) (.f32 (.f32 x (.f32 (PI.f32) tau)) (*.f32 x #s(literal 2 binary32))))
(.f32 (/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x x)) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 tau (.f32 x (sqrt.f32 (PI.f32)))) (sqrt.f32 (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 (-.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (.f32 (.f32 x (.f32 (PI.f32) tau)) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 x (.f32 (PI.f32) tau)) #s(literal 2 binary32)))) (.f32 (PI.f32) x))
(-.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (/.f32 #s(literal 1/2 binary32) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))))
(-.f32 (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))) (/.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau))))))
(/.f32 (-.f32 (.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) #s(literal 2 binary32)) (.f32 (.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) tau))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) tau))) #s(literal 2 binary32)))
(/.f32 (-.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 2 binary32)) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (*.f32 x (PI.f32)))) #s(literal 2 binary32))) #s(literal 2 binary32)))
(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (PI.f32)) #s(literal 2 binary32)) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x (PI.f32)))))) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) #s(literal 2 binary32)))
(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))))) (.f32 x (.f32 (.f32 tau (.f32 x (PI.f32))) #s(literal 2 binary32)))) (.f32 #s(literal 2 binary32) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (PI.f32)))) (.f32 #s(literal 2 binary32) (.f32 x (.f32 (.f32 tau (*.f32 x (PI.f32))) #s(literal 2 binary32)))))
(/.f32 (-.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (.f32 x (.f32 (.f32 tau (.f32 x (PI.f32))) #s(literal 2 binary32)))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (PI.f32)))) (.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (.f32 x (.f32 (.f32 tau (*.f32 x (PI.f32))) #s(literal 2 binary32)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (.f32 (pow.f32 (PI.f32) #s(literal 6 binary32)) #s(literal -1/5040 binary32)) (.f32 #s(literal 1/120 binary32) (pow.f32 (PI.f32) #s(literal 4 binary32)))) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))))
(/.f32 (-.f32 (cos.f32 (fma.f32 (.f32 (.f32 x tau) (pow.f32 (PI.f32) #s(literal 2/3 binary32))) (cbrt.f32 (PI.f32)) (.f32 (PI.f32) (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (pow.f32 (PI.f32) #s(literal 1/6 binary32)) (.f32 x (sqrt.f32 (PI.f32)))))) (*.f32 x (PI.f32))))
(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 x (-.f32 (.f32 (PI.f32) tau) (PI.f32)))) (PI.f32)) (/.f32 (.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) tau))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))))) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) #s(literal 1 binary32))) (.f32 (.f32 (.f32 x (.f32 (PI.f32) tau)) (.f32 x #s(literal 2 binary32))) (/.f32 (.f32 (.f32 #s(literal 2 binary32) (.f32 x (PI.f32))) (.f32 x (.f32 (PI.f32) tau))) (cos.f32 (*.f32 (PI.f32) (fma.f32 x tau x))))))
(/.f32 (-.f32 (.f32 (/.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 2 binary32)) (/.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))))) (.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (.f32 (.f32 tau (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))) (/.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))))))
(/.f32 (-.f32 (.f32 #s(literal 1 binary32) (.f32 x (.f32 (.f32 tau (.f32 x (PI.f32))) #s(literal 2 binary32)))) (.f32 (/.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x))))) (/.f32 (cos.f32 (.f32 x (fma.f32 (PI.f32) tau (PI.f32)))) (PI.f32)))) (.f32 (/.f32 (.f32 x (.f32 (.f32 (PI.f32) (.f32 tau (.f32 x (PI.f32)))) #s(literal 2 binary32))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x))))) (.f32 x (.f32 (.f32 tau (.f32 x (PI.f32))) #s(literal 2 binary32)))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 (cbrt.f32 (PI.f32)) (.f32 (cbrt.f32 (PI.f32)) (.f32 x (cbrt.f32 (PI.f32))))) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(/.f32 (-.f32 (fma.f32 (cos.f32 (.f32 x (.f32 (PI.f32) tau))) (cos.f32 (.f32 x (PI.f32))) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 x (PI.f32))))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(/.f32 (-.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (.f32 (pow.f32 (cbrt.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32)) (pow.f32 (cbrt.f32 (sqrt.f32 (PI.f32))) #s(literal 3 binary32))) tau)))) #s(literal 2 binary32)))
(.f32 (.f32 (pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1/2 binary32)) (pow.f32 (/.f32 (.f32 (PI.f32) (.f32 x x)) (.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (sin.f32 (.f32 (PI.f32) x)))) #s(literal -1/2 binary32))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
(.f32 (/.f32 (/.f32 (-.f32 (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32)) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32))) (.f32 (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)))) (fma.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau (neg.f32 x)))) #s(literal 1/2 binary32) (.f32 (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x))) #s(literal 1/2 binary32)))) (.f32 x (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))

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:

300.0ms	x
47.0ms	(*.f32 x (PI.f32))
45.0ms	tau
39.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes122.0ms (0.9%)

Memory

-14.6MiB live, 185.9MiB allocated

Counts

107 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes101.0ms (0.7%)

Memory

11.3MiB live, 173.8MiB allocated

Counts

85 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

26.0ms	x
25.0ms	tau
24.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
23.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
97.1%	1	`x`
97.1%	1	`tau`
97.1%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
97.1%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes96.0ms (0.7%)

Memory

4.4MiB live, 159.2MiB allocated

Counts

83 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

24.0ms	x
24.0ms	(*.f32 x (PI.f32))
22.0ms	tau
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))))

Results

Accuracy	Segments	Branch
91.2%	1	`x`
91.2%	1	`(*.f32 x (PI.f32))`
91.2%	1	`tau`
91.2%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes152.0ms (1.1%)

Memory

12.7MiB live, 123.4MiB allocated

Counts

81 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

78.0ms	x
26.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
23.0ms	tau
20.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
85.6%	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))))`
85.6%	1	`x`
85.6%	1	`(*.f32 x (PI.f32))`
85.6%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes52.0ms (0.4%)

Memory

-10.6MiB live, 112.3MiB 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 (/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2)) #s(literal 0 binary32))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) #s(literal 1 binary32)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (.f32 tau (PI.f32))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
#s(approx (* (/ (sin (* (* x (PI)) tau)) (* (* x (PI)) tau)) (/ (sin (* x (PI))) (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (PI.f32)) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) #s(literal 1 binary32)))
#s(approx (/ (* (sin (* x (* (PI) tau))) (sin (* (PI) x))) (* (PI) (* x (* x (* (PI) tau))))) (fma.f32 x (.f32 x (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (fma.f32 (PI.f32) (.f32 tau tau) (PI.f32))))) #s(literal 1 binary32)))
#s(approx (/ (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (fma.f32 (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32)))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32)) #s(literal 1 binary32)))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) tau) (.f32 x (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
(/.f32 #s(approx (* (sin (* x (* (PI) tau))) (sin (* (PI) x))) (.f32 (.f32 x x) (.f32 tau (.f32 (PI.f32) (PI.f32))))) (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32)))) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 (.f32 tau tau) (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (PI.f32)))) #s(literal 1 binary32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (.f32 tau (PI.f32)))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(/.f32 #s(approx (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) (sin (* (PI) x))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (PI.f32)))) (*.f32 (PI.f32) x))
(.f32 (/.f32 #s(approx ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (.f32 x (.f32 x (.f32 tau (.f32 (PI.f32) (PI.f32)))))) (.f32 x (.f32 x (PI.f32)))) (/.f32 #s(literal 1 binary32) (*.f32 (PI.f32) tau)))
(/.f32 #s(approx (* (/ (sin (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (.f32 (neg.f32 x) (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (fma.f32 #s(literal -1/6 binary32) (.f32 tau tau) #s(literal -1/6 binary32))) (PI.f32)))) (neg.f32 (*.f32 x (PI.f32))))
(.f32 (/.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (.f32 tau (PI.f32)))) tau) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
(.f32 #s(approx (/ ( (sin (* (PI) (* x tau))) (sin (* x (PI)))) (* x (* x (PI)))) (fma.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/6 binary32) (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32)))) (fma.f32 tau (.f32 tau tau) tau)) (.f32 tau (PI.f32)))) (/.f32 #s(literal 1 binary32) (.f32 (PI.f32) tau)))
(.f32 #s(approx (/ (sin ( (PI) (* x tau))) tau) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32)))) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
(/.f32 #s(approx (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (.f32 (.f32 x x) (.f32 (.f32 #s(literal -1/2 binary32) (.f32 (PI.f32) (PI.f32))) (.f32 (+.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) tau)) (-.f32 (+.f32 tau #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) tau)))))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin (* x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 tau (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 x (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 x (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (fma.f32 #s(literal -1/6 binary32) (.f32 (.f32 tau tau) (.f32 tau (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) (PI.f32))))))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (* x (PI)) tau)) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
(.f32 (/.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 tau (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau tau))) (PI.f32))))) tau) #s(approx (/ (sin (* x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
(.f32 (/.f32 #s(approx (sin ( (PI) (* x tau))) (.f32 x (fma.f32 (.f32 x x) (.f32 (.f32 (PI.f32) (.f32 (PI.f32) (PI.f32))) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau tau)))) (.f32 tau (PI.f32))))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 (fma.f32 #s(literal -1/6 binary32) (.f32 x (.f32 x (PI.f32))) (/.f32 #s(literal 1 binary32) (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 (* (PI) (* x tau))) (* (PI) (* x tau))) (neg (sin (* x (PI))))) (neg (* x (PI)))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (.f32 x (PI.f32))))
(/.f32 #s(approx (* (/ (sin (* x (* (PI) tau))) (* x (* (PI) tau))) (sin (* (PI) x))) (sin.f32 (.f32 x (PI.f32)))) (.f32 (PI.f32) x))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) #s(literal 1 binary32)))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(literal 1 binary32) (*.f32 x (PI.f32)))))
(.f32 (/.f32 (sin.f32 (.f32 (PI.f32) (.f32 x tau))) tau) #s(approx (/ (sin ( x (PI))) (* x (* (PI) (* x (PI))))) (/.f32 #s(approx (+ (* -1/6 (* x (* x (PI)))) (/ 1 (PI))) (/.f32 #s(literal 1 binary32) (PI.f32))) x)))
(/.f32 (-.f32 #s(approx (cos (* (PI) (+ (* x tau) (neg x)))) #s(literal 1 binary32)) (cos.f32 (.f32 (PI.f32) (fma.f32 x tau x)))) (.f32 (.f32 (PI.f32) (.f32 x (.f32 x (.f32 (PI.f32) tau)))) #s(literal 2 binary32)))
(.f32 #s(approx (sin ( (PI) x)) (.f32 x (PI.f32))) (/.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (.f32 (PI.f32) (.f32 x (.f32 x (*.f32 (PI.f32) tau))))))
(.f32 #s(approx (/ (sin ( (* x (PI)) tau)) (* (* x (PI)) tau)) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (.f32 tau (.f32 tau (.f32 (PI.f32) (PI.f32))))) #s(literal 1 binary32))) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
(.f32 (sin.f32 (.f32 tau (.f32 x (PI.f32)))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x #s(literal -1/6 binary32)) (.f32 x (.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))) (.f32 tau (*.f32 x (PI.f32)))))
(.f32 (sin.f32 (.f32 x (.f32 (PI.f32) tau))) (/.f32 #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))) (.f32 x (*.f32 (PI.f32) tau))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x tau) (PI.f32))) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x tau) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x #s(literal -1/6 binary32)) x) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x tau) (PI.f32))) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 (PI.f32) (PI.f32)) (.f32 (*.f32 x x) #s(literal -1/6 binary32)) #s(literal 1 binary32))))
(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) #s(approx (/ (sin ( x (PI))) (* x (PI))) (fma.f32 (.f32 x x) (.f32 #s(literal -1/6 binary32) (*.f32 (PI.f32) (PI.f32))) #s(literal 1 binary32))))

Outputs

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

Calls

4 calls:

14.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
12.0ms	(*.f32 x (PI.f32))
12.0ms	x
11.0ms	tau

Results

Accuracy	Segments	Branch
85.6%	1	`x`
85.6%	1	`tau`
85.6%	1	`(*.f32 x (PI.f32))`
85.6%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes50.0ms (0.4%)

Memory

-1.1MiB live, 77.2MiB allocated

Counts

40 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

14.0ms	x
13.0ms	(*.f32 x (PI.f32))
11.0ms	tau
11.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
85.4%	1	`x`
85.4%	1	`tau`
85.4%	1	`(*.f32 x (PI.f32))`
85.4%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes56.0ms (0.4%)

Memory

21.8MiB live, 59.7MiB allocated

Counts

36 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

25.0ms	(*.f32 x (PI.f32))
10.0ms	tau
10.0ms	x
10.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))

Results

Accuracy	Segments	Branch
85.4%	1	`tau`
85.4%	1	`x`
85.4%	1	`(*.f32 x (PI.f32))`
85.4%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes61.0ms (0.5%)

Memory

-4.6MiB live, 71.3MiB allocated

Counts

35 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

30.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
11.0ms	tau
10.0ms	(*.f32 x (PI.f32))
9.0ms	x

Results

Accuracy	Segments	Branch
78.6%	1	`x`
78.6%	1	`tau`
78.6%	1	`(*.f32 x (PI.f32))`
78.6%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes48.0ms (0.4%)

Memory

-5.7MiB live, 75.2MiB allocated

Counts

34 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

17.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
11.0ms	x
10.0ms	tau
9.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
78.4%	1	`x`
78.4%	1	`(*.f32 x (PI.f32))`
78.4%	1	`tau`
78.4%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes18.0ms (0.1%)

Memory

-2.7MiB live, 34.5MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

6.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
4.0ms	(*.f32 x (PI.f32))
4.0ms	x
4.0ms	tau

Results

Accuracy	Segments	Branch
77.6%	1	`tau`
77.6%	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))))`
77.6%	1	`x`
77.6%	1	`(*.f32 x (PI.f32))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes16.0ms (0.1%)

Memory

-7.0MiB live, 29.5MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

6.0ms	x
3.0ms	tau
3.0ms	(.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))))
3.0ms	(*.f32 x (PI.f32))

Results

Accuracy	Segments	Branch
77.6%	1	`x`
77.6%	1	`(*.f32 x (PI.f32))`
77.6%	1	`tau`
77.6%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes10.0ms (0.1%)

Memory

25.0MiB live, 24.9MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
64.0%	1	`x`
64.0%	1	`(*.f32 x (PI.f32))`
64.0%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
64.0%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes13.0ms (0.1%)

Memory

-23.8MiB live, 18.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

#s(approx (/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2)) #s(literal 0 binary32))

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

Outputs

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

Calls

4 calls:

7.0ms	x
2.0ms	(*.f32 x (PI.f32))
2.0ms	(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))
2.0ms	tau

Results

Accuracy	Segments	Branch
64.0%	1	`(.f32 (/.f32 (sin.f32 (.f32 (.f32 x (PI.f32)) tau)) (.f32 (.f32 x (PI.f32)) tau)) (/.f32 (sin.f32 (.f32 x (PI.f32))) (*.f32 x (PI.f32))))`
64.0%	1	`x`
64.0%	1	`(*.f32 x (PI.f32))`
64.0%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

regimes6.0ms (0%)

Memory

13.9MiB live, 13.9MiB allocated

Accuracy

Total -18.3b remaining (-155.1%)

Threshold costs -18.3b (-155.1%)

Counts

2 → 1

Calls

Call 1

Inputs

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

#s(approx (/ (- (cos (* (PI) (+ (* x tau) (neg x)))) (cos (* (PI) (+ (* x tau) x)))) (* (* (PI) (* x (* x (* (PI) tau)))) 2)) #s(literal 0 binary32))

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
63.2%	1	`x`
63.2%	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))))`
63.2%	1	`(*.f32 x (PI.f32))`
63.2%	1	`tau`

Compiler

Compiled 34 to 18 computations (47.1% saved)

simplify8.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	528
1	143	528

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.9s (14.2%)

Memory

30.4MiB live, 1 291.3MiB allocated

Rules

19 832×	`lower-fma.f64`
19 832×	`lower-fma.f32`
16 966×	`lower-fma.f64`
16 966×	`lower-fma.f32`
12 510×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	587	8170
1	1939	7879
2	5886	7595
0	8673	7327
0	196	1582
1	620	1562
2	2413	1538
3	4145	1538
4	4880	1538
5	5560	1538
6	5950	1538
7	5981	1538
8	5981	1538
0	8826	1486
0	10	55
0	18	55
1	63	55
2	483	53
3	6485	53
0	8114	53
0	428	6852
1	1403	6682
2	5295	6450
0	8264	6238
0	430	7620
1	1455	7413
2	5811	7173
0	8655	6940
0	44	275
0	77	271
1	257	253
2	1780	253
0	8396	253
0	63	282
0	105	281
1	368	259
2	2372	259
0	9179	259
0	52	295
0	90	286
1	339	276
2	2226	276
0	8867	274

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

Compiler

Compiled 790 to 341 computations (56.8% saved)

preprocess111.0ms (0.8%)

Memory

46.6MiB live, 190.0MiB allocated

Remove

(abs x)

(abs tau)

Compiler

Compiled 1 672 to 592 computations (64.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze21.0ms (0.2%)

sample1.6s (12.1%)

explain128.0ms (0.9%)

preprocess78.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify53.0ms (0.4%)

localize38.0ms (0.3%)

series30.0ms (0.2%)

simplify395.0ms (2.9%)

rewrite311.0ms (2.3%)

eval98.0ms (0.7%)

prune298.0ms (2.2%)

simplify270.0ms (2%)

localize233.0ms (1.7%)

series41.0ms (0.3%)

simplify399.0ms (2.9%)

rewrite269.0ms (2%)

eval310.0ms (2.3%)

prune679.0ms (5%)

simplify200.0ms (1.5%)

localize306.0ms (2.3%)

series65.0ms (0.5%)

simplify503.0ms (3.7%)

rewrite935.0ms (6.9%)

eval282.0ms (2.1%)

prune786.0ms (5.8%)

simplify240.0ms (1.8%)

localize263.0ms (1.9%)

series19.0ms (0.1%)

simplify480.0ms (3.5%)

rewrite268.0ms (2%)

eval149.0ms (1.1%)

prune477.0ms (3.5%)

regimes438.0ms (3.2%)

regimes122.0ms (0.9%)

regimes101.0ms (0.7%)

regimes96.0ms (0.7%)

regimes152.0ms (1.1%)

regimes52.0ms (0.4%)

regimes50.0ms (0.4%)

regimes56.0ms (0.4%)

regimes61.0ms (0.5%)

regimes48.0ms (0.4%)

regimes18.0ms (0.1%)

regimes16.0ms (0.1%)

regimes10.0ms (0.1%)

regimes13.0ms (0.1%)

regimes6.0ms (0%)

simplify8.0ms (0.1%)

soundness1.9s (14.2%)

preprocess111.0ms (0.8%)

end0.0ms (0%)

Profiling